**Mesomechanics and Thermodynamics of Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones**

## L.E. Panin

262 Thermodynamics – Fundamentals and Its Application in Science

Applied Sciences 2010:29C (2) 77-95.

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[33] Adebayo G.B, Adekola F.A, Olatunji G.A, Bello I.A. Some Thermodynamic Parameters of Two Indigenous Mineral Dyes Applied on Wool Material Bulletin of Pure and

[34] Derbyshire A.N., Peters R.H. An Explanation of Dyeing Mechanisms in Terms of Non-

[35] Zollinger H. The Dye and the Substrate: The Role of Hydrophobic Bonding in Dyeing

[36] Iyer S.R.S., Ghanekar A.S., Singh G.S. The Chemistry of Synthetic Dyes Vol. VII Ed. by

[37] Ferrini B., Kimura Y., Zollinger H. A Contribution to the Dyeing Mechanism of Acid

[38] Asquith R.S., Kwok W.F., Otterburn M.S. An Assessment of Some Thermodynamic Treatments of Wool Dyeing Systems Textile Research Journal 1980;50 333-336. [39] Kumar A., Choudhury R. Textile Preparation and Dyeing Science Publishers ISBN 1-

[40] Samanta A.K., Agarwal P., Datta S., Physico-chemical Studies on Dyeing of Jute and Cotton Fabrics Using Jackfruit Wood Extract: Part II Dyeing Kinetics and

Thermodynamic Studies Indian Journal of Fiber&Textile Research 2008;33 66-72.

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/51515

## **1. Introduction**

Biological membranes are liquid heterocrystals with low shear stability. The main structureforming bonds in biological membranes are covalent and hydrogen bonds, and hydrophobic and weak electrostatic interactions. These bonds are responsible for high membrane elasticity – a property of particularly importance to erythrocytes, which have to pass through blood capillaries of diameter equal to the erythrocyte one. Any structural changes that increase the erythrocyte membrane viscosity hamper the motion of erythrocytes through capillaries and may result in diffuse hypoxia. In this context, of great interest is the effect of stress hormones (cortisol, adrenaline, noradrenaline) on the behavior of erythrocyte membranes.

The nonspecific binding of stress hormones with erythrocyte membranes was studied earlier in [1]. It was shown that excess of these hormones in blood are capable for nonspecific binding with blood cells, primarily with erythrocytes, producing changes in rheological properties of the blood. It was found that CO, OH, and NH active groups incorporated in the structure of hormones can form hydrogen bonds with similar groups of proteins and phospholipids of erythrocyte membranes. Hydrophobic rings of hormones can participate in hydrophobic interactions with residues of phospholipid fatty acids, as a result of which complex domains arise in the membrane structure, the membrane microviscosity increases, and the motion of erythrocytes through capillaries becomes difficult. This effect is particularly dangerous to heart because it can leads to coronary syndrome Х [2, 3]. Physicians still fail to understand the nature of this phenomenon, which shows up as

© 2012 Panin, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

exertional angina and ischemic ST segment depression on electrocardiograms with a normally functioning left ventricle.

Mesomechanics and Thermodynamics of

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 265

10 min in air at 24 C and humidity of 40%. After evaporation of excessive surface moisture, the smear was observed under a «Solver Bio» atomic force microscope (NT-MDT, Russia) at 24 C using a semi-contact mode. An analogous procedure of obtaining red blood cells for the AFM examination was employed earlier by other authors [7]. In each experiment first a control specimen without hormones, and then the experimental one have been tested. Silicon cantilevers NSG11 (NT-MDT, Russia) with a resonant frequency between 120 and 180 kHz and spring constant ~ 6 N/m were used (all of these probe parameters were offered by manufacturer). Images of the surface relief of erythrocyte membrane after absorption of

hormones were obtained with the scan size 11 µm2 and 1.31.3 µm2.

**Figure 1.** Chemical structure of steroid hormones.

Anabolic steroid hormones have been used for many decades, finding their most extensive use in sports medicine. Nowadays, it is impossible to train as an international class athlete without anabolic hormones. A coach's aspiration for high sporting results prompts that coach to use an ever increasing amount of anabolic steroids. Lacking a profound knowledge of sports medicine, such a coach cannot imagine all of the negative effects of anabolics on the body of an athlete. Moreover, sports medicine itself has no comprehensive information on the subject. As a consequence, the number of sudden and unexpected deaths of atheletes during the competitions has drastically increased in recent years [4].

Physicochemical analysis of the behavior of erythrocyte membranes as liquid heterocrystals makes it possible to disclose a link between structural changes in erythrocyte membranes and erythrocyte function. Of particular interest is activity of the Na+, K+-ATPhase that supports the transmembrane potential of cells and precludes their aggregation. It was previously supposed that the regulatory action of different ligands can be based on certain conformational changes of the Na+, K+-АТPhase [5]; however, the mechanism by which steroid hormones affect the activity of the Na+, K+-АТPase is poorly known.

In this work, the mechanism of testosterone, androsterone, dehydroepiandrosterone (DHEA), dehydroepiandrosterone sulfate (DHEAS) and cortisol interaction with structural components of erythrocyte membranes (mesomechanics and termodinamics of nanostructural transition) changes in their microviscosity and functional characteristics during the interaction have been studied. The results obtained could also shed light on the causes of cardiovascular catastrophes, which are often observed in sportsmen taking anabolic steroid hormones for a long time [6].

## **2. Materials and methods**

The action of five hormones: testosterone, androsterone, dehydroepiandrosterone (DHEA), dehydroepiandrosterone sulfate (DHEAS) and cortisol (Amersham) is analyzed in the work (Fig. 1).

For this purpose, the following methods were used.

## **2.1. Atomic force microscopy (AFM) of erythrocytes**

Erythrocytes were obtained from fresh blood after decapitation of Wistar rats under light nembutal narcosis. Blood was diluted twofold by isotonic phosphate buffer (рН 7.35) containing 0.043 M of КН2РО4 and 0.136 M of Na2НРО4. After precipitation of cells by centrifuging at 330 g for 10 min, supernatant liquor was decanted, and the washing procedure was repeated twice more.

All the procedures were performed at 4 C [1]. The resulting erythrocyte suspension of 20 mcl volume was deposited onto a glass slide as a thin smear. The smear was predried for 10 min in air at 24 C and humidity of 40%. After evaporation of excessive surface moisture, the smear was observed under a «Solver Bio» atomic force microscope (NT-MDT, Russia) at 24 C using a semi-contact mode. An analogous procedure of obtaining red blood cells for the AFM examination was employed earlier by other authors [7]. In each experiment first a control specimen without hormones, and then the experimental one have been tested. Silicon cantilevers NSG11 (NT-MDT, Russia) with a resonant frequency between 120 and 180 kHz and spring constant ~ 6 N/m were used (all of these probe parameters were offered by manufacturer). Images of the surface relief of erythrocyte membrane after absorption of hormones were obtained with the scan size 11 µm2 and 1.31.3 µm2.

**Figure 1.** Chemical structure of steroid hormones.

264 Thermodynamics – Fundamentals and Its Application in Science

anabolic steroid hormones for a long time [6].

For this purpose, the following methods were used.

**2.1. Atomic force microscopy (AFM) of erythrocytes** 

**2. Materials and methods** 

procedure was repeated twice more.

(Fig. 1).

normally functioning left ventricle.

exertional angina and ischemic ST segment depression on electrocardiograms with a

Anabolic steroid hormones have been used for many decades, finding their most extensive use in sports medicine. Nowadays, it is impossible to train as an international class athlete without anabolic hormones. A coach's aspiration for high sporting results prompts that coach to use an ever increasing amount of anabolic steroids. Lacking a profound knowledge of sports medicine, such a coach cannot imagine all of the negative effects of anabolics on the body of an athlete. Moreover, sports medicine itself has no comprehensive information on the subject. As a consequence, the number of sudden and unexpected deaths of atheletes

Physicochemical analysis of the behavior of erythrocyte membranes as liquid heterocrystals makes it possible to disclose a link between structural changes in erythrocyte membranes and erythrocyte function. Of particular interest is activity of the Na+, K+-ATPhase that supports the transmembrane potential of cells and precludes their aggregation. It was previously supposed that the regulatory action of different ligands can be based on certain conformational changes of the Na+, K+-АТPhase [5]; however, the mechanism by which

In this work, the mechanism of testosterone, androsterone, dehydroepiandrosterone (DHEA), dehydroepiandrosterone sulfate (DHEAS) and cortisol interaction with structural components of erythrocyte membranes (mesomechanics and termodinamics of nanostructural transition) changes in their microviscosity and functional characteristics during the interaction have been studied. The results obtained could also shed light on the causes of cardiovascular catastrophes, which are often observed in sportsmen taking

The action of five hormones: testosterone, androsterone, dehydroepiandrosterone (DHEA), dehydroepiandrosterone sulfate (DHEAS) and cortisol (Amersham) is analyzed in the work

Erythrocytes were obtained from fresh blood after decapitation of Wistar rats under light nembutal narcosis. Blood was diluted twofold by isotonic phosphate buffer (рН 7.35) containing 0.043 M of КН2РО4 and 0.136 M of Na2НРО4. After precipitation of cells by centrifuging at 330 g for 10 min, supernatant liquor was decanted, and the washing

All the procedures were performed at 4 C [1]. The resulting erythrocyte suspension of 20 mcl volume was deposited onto a glass slide as a thin smear. The smear was predried for

during the competitions has drastically increased in recent years [4].

steroid hormones affect the activity of the Na+, K+-АТPase is poorly known.

## **2.2. IR spectroscopy of erythrocyte shadows**

Erythrocyte shadows were obtained after their hemolysis in hypotonic phosphate buffer (рН 7.35) containing 2.75 mM of KH2РО4 and 8.5 mM of Na2НРО4. Shadows were precipitated by centrifuging at 5500 g, supernatant liquor was decanted. The washing procedure was repeated four more times [8]. All operations and further storage of shadows were performed at 4 C.

Mesomechanics and Thermodynamics of

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 267

, *<sup>n</sup> B nS S B* (1)

(3)

(2)

system. Spectral width of the slits was 1.5/10. The tryptophan absorption spectrum was recorded in the range of 220 nm ≤ ≤ 300 nm at the emission wavelength = 332 nm. Testosterone, androsterone, dehydroepiandrosterone (DHEA) and dehydroepiandrosterone sulfate (DHEAS) were dissolved in a mixture of dimethyl sulfoxide (DMS) and ethanol (1 : 1, V/V). Concentration of the hormone in the initial mother liquor was 10–3 M. If necessary, the solution was diluted with hypotonic phosphate buffer to obtain a desired

A solution of hormones with the concentration 10–6 M was prepared in hypotonic phosphate buffer. The time of hormone incubation with shadows was one hour. Absorption and emission spectra were taken, the average value of emission and absorption intensity was measured. For each hormone (testosterone, androsterone, dehydroepiandrosterone (DHEA) and dehydroepiandrosterone sulfate (DHEAS)), the binding constant Kb was calculated by the method [10] as well as the stoichiometric concentration of a bound hormone Bmax and a change in free energy of the system *G* . The interaction of hormone and erythrocyte

where *B* is a membrane protein, *S* is the hormone, and *n* is the number of moles of hormone

, *<sup>n</sup>*

*S B*

*S B* 

where *<sup>n</sup> S B* is the concentration of bound protein, *B* is the concentration of free protein, and *S* is the concentration of free hormone. It is supposed that hormone, upon binding to protein, completely quenches its fluorescence. Thus, the fluorescence intensity *F* will be proportional to the concentration of free protein. Let's write *C* for total concentration of

max

where *F* is the intensity of tryptophan fluorescence at = 332 nm (the excitation wavelength λ = 228 nm), max *F* is the intensity of tryptophan fluorescence in the absence of hormone (when the entire protein is free), *β* is the proportionality factor, and *AS* is the stoichiometric concentration of hormone. When concentration of hormone exceeds *AS* , the fluorescence quenching does not increase. Dividing the first equation of set (2) by the second

*F C F Cx* 

,

max max

(4)

, where *F F*

*x QC Q <sup>F</sup>*

per a mole of proteins. The binding constant *Kb* was calculated by the formula

*c*

*K*

protein in the cuvette, and *x* for concentration of the bound protein. Then,

concentration.

one gives

membrane is described by the equation

A film for taking the IR spectra of erythrocyte shadows was prepared in a cuvette with fluorite backing via slow evaporation of water under weak vacuum at a pressure of ca. 0.1 atm (ca. 0.5·104 Pa) and temperature 4±1 C [8]. Drying lasted 180 min. A suspension of erythrocyte shadows in a 0.001 M phosphate buffer with pH 7.35 and volume 60 mcl was introduced into a cuvette. This was supplemented with 30 mcl of the same buffer and 1.0 mcl of the hormone solution with concentration 10–6 M. Stirring and incubation lasted 10 min at 16-17 C. The cuvette was placed horizontally on a special table of a vacuum unit.

When the film was prepared, the cuvette was transferred into an optical chamber and blown with dry air for 30 min, then the scanning unit was switched on. IR spectra were taken on a Specord-M80 spectrometer (Germany, Leipzig), sequentially experiment and control against the fluorite backing, or experiment and control to obtain a difference spectrum. Integration, determination of the spectrum band frequency, and mathematical processing were performed with special programs enclosed to the spectrometer. Erythrocyte suspensions were examined upon addition of cortisol using UV (Evolution 300, Thermo Scientific, USA). Merk or Sigma reagents were used in the work.

## **2.3. Fluorescence analysis of erythrocyte shadows**

Fluorescence measurements were performed with a Shimadzu spectrofluorophotometer RF-5301(PC)SCE. 4 ml of hypotonic phosphate buffer containing 2.75 mM of КН2РО4 and 8.5 mM of Na2HPО4 (рН 7.35), and erythrocyte shadows were poured into a quartz cuvette of size 1 1 4 cm3. The concentration of shadow proteins was determined by the Warburg– Christian method from changes in the optical density of suspension [9]. On the average, it varied in the range of 0.100-0.250 mg/ml.

A cuvette with the shadow suspension was placed into a spectrofluorimeter thermostat for 1 hour. Getting a stationary temperature regime in the cuvette was controlled by an electronic thermometer. In all the experiments, temperature in the cuvette was 36 C. After establishing a stationary temperature in the cuvette, intensity of the intrinsic fluorescence of tryptophan residues in protein membranes was measured. The tryptophan emission spectrum was taken in the range of 300 nm ≤ ≤ 400 nm at the excitation wavelength 281 nm, with the maximum of emission intensity observed at 332 nm. The average value of maximum emission intensity was obtained graphically after its continuous measuring for 4 minutes. Intensity of tryptophan fluorescence fluctuated within 1%. The possible reasons include variation of temperature in the cuvette with suspension, instrumental error in determination of fluorescence intensity, and photochemical reactions occurring in the system. Spectral width of the slits was 1.5/10. The tryptophan absorption spectrum was recorded in the range of 220 nm ≤ ≤ 300 nm at the emission wavelength = 332 nm. Testosterone, androsterone, dehydroepiandrosterone (DHEA) and dehydroepiandrosterone sulfate (DHEAS) were dissolved in a mixture of dimethyl sulfoxide (DMS) and ethanol (1 : 1, V/V). Concentration of the hormone in the initial mother liquor was 10–3 M. If necessary, the solution was diluted with hypotonic phosphate buffer to obtain a desired concentration.

266 Thermodynamics – Fundamentals and Its Application in Science

**2.2. IR spectroscopy of erythrocyte shadows** 

Merk or Sigma reagents were used in the work.

varied in the range of 0.100-0.250 mg/ml.

**2.3. Fluorescence analysis of erythrocyte shadows** 

were performed at 4 C.

Erythrocyte shadows were obtained after their hemolysis in hypotonic phosphate buffer (рН 7.35) containing 2.75 mM of KH2РО4 and 8.5 mM of Na2НРО4. Shadows were precipitated by centrifuging at 5500 g, supernatant liquor was decanted. The washing procedure was repeated four more times [8]. All operations and further storage of shadows

A film for taking the IR spectra of erythrocyte shadows was prepared in a cuvette with fluorite backing via slow evaporation of water under weak vacuum at a pressure of ca. 0.1 atm (ca. 0.5·104 Pa) and temperature 4±1 C [8]. Drying lasted 180 min. A suspension of erythrocyte shadows in a 0.001 M phosphate buffer with pH 7.35 and volume 60 mcl was introduced into a cuvette. This was supplemented with 30 mcl of the same buffer and 1.0 mcl of the hormone solution with concentration 10–6 M. Stirring and incubation lasted 10 min at 16-17 C. The cuvette was placed horizontally on a special table of a vacuum unit.

When the film was prepared, the cuvette was transferred into an optical chamber and blown with dry air for 30 min, then the scanning unit was switched on. IR spectra were taken on a Specord-M80 spectrometer (Germany, Leipzig), sequentially experiment and control against the fluorite backing, or experiment and control to obtain a difference spectrum. Integration, determination of the spectrum band frequency, and mathematical processing were performed with special programs enclosed to the spectrometer. Erythrocyte suspensions were examined upon addition of cortisol using UV (Evolution 300, Thermo Scientific, USA).

Fluorescence measurements were performed with a Shimadzu spectrofluorophotometer RF-5301(PC)SCE. 4 ml of hypotonic phosphate buffer containing 2.75 mM of КН2РО4 and 8.5 mM of Na2HPО4 (рН 7.35), and erythrocyte shadows were poured into a quartz cuvette of size 1 1 4 cm3. The concentration of shadow proteins was determined by the Warburg– Christian method from changes in the optical density of suspension [9]. On the average, it

A cuvette with the shadow suspension was placed into a spectrofluorimeter thermostat for 1 hour. Getting a stationary temperature regime in the cuvette was controlled by an electronic thermometer. In all the experiments, temperature in the cuvette was 36 C. After establishing a stationary temperature in the cuvette, intensity of the intrinsic fluorescence of tryptophan residues in protein membranes was measured. The tryptophan emission spectrum was taken in the range of 300 nm ≤ ≤ 400 nm at the excitation wavelength 281 nm, with the maximum of emission intensity observed at 332 nm. The average value of maximum emission intensity was obtained graphically after its continuous measuring for 4 minutes. Intensity of tryptophan fluorescence fluctuated within 1%. The possible reasons include variation of temperature in the cuvette with suspension, instrumental error in determination of fluorescence intensity, and photochemical reactions occurring in the A solution of hormones with the concentration 10–6 M was prepared in hypotonic phosphate buffer. The time of hormone incubation with shadows was one hour. Absorption and emission spectra were taken, the average value of emission and absorption intensity was measured. For each hormone (testosterone, androsterone, dehydroepiandrosterone (DHEA) and dehydroepiandrosterone sulfate (DHEAS)), the binding constant Kb was calculated by the method [10] as well as the stoichiometric concentration of a bound hormone Bmax and a change in free energy of the system *G* . The interaction of hormone and erythrocyte membrane is described by the equation

$$B + nS = S\_n B\_\prime \tag{1}$$

where *B* is a membrane protein, *S* is the hormone, and *n* is the number of moles of hormone per a mole of proteins. The binding constant *Kb* was calculated by the formula

$$K\_c = \frac{\left\lceil \begin{smallmatrix} S\_n B \\ \hline \end{smallmatrix} \right\rceil}{\left\lceil \begin{smallmatrix} S \\ \hline \end{smallmatrix} \right\rceil \cdot \left\lceil \begin{smallmatrix} B \\ \hline \end{smallmatrix} \right\rceil},\tag{2}$$

where *<sup>n</sup> S B* is the concentration of bound protein, *B* is the concentration of free protein, and *S* is the concentration of free hormone. It is supposed that hormone, upon binding to protein, completely quenches its fluorescence. Thus, the fluorescence intensity *F* will be proportional to the concentration of free protein. Let's write *C* for total concentration of protein in the cuvette, and *x* for concentration of the bound protein. Then,

$$\begin{aligned} F\_{\text{max}} &= \beta \mathbf{C} \\ F &= \beta \left( \mathbf{C} - \mathbf{x} \right) \end{aligned} \tag{3}$$

where *F* is the intensity of tryptophan fluorescence at = 332 nm (the excitation wavelength λ = 228 nm), max *F* is the intensity of tryptophan fluorescence in the absence of hormone (when the entire protein is free), *β* is the proportionality factor, and *AS* is the stoichiometric concentration of hormone. When concentration of hormone exceeds *AS* , the fluorescence quenching does not increase. Dividing the first equation of set (2) by the second one gives

$$\text{tax} = \text{Q} \cdot \text{C} \text{ } \text{ where } \text{Q} = \frac{F\_{\text{max}} - F}{F\_{\text{max}}} \tag{4}$$

 *S A nx A nQC* , where *A* is the total concentration of hormone; *AS <sup>n</sup> <sup>C</sup>* ; *B CxC Q* (1 ) . Substitution of (2) and (3) into expression for binding constant (1) gives

$$K\_c = \frac{\mathcal{Q}}{(1 - \mathcal{Q})(A - n\mathcal{Q}\mathcal{C})} \tag{5}$$

Mesomechanics and Thermodynamics of

 ( )/ 0 *A* , where

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 269

Membrane microviscosity for translational diffusion of pyrene probe was calculated as a ratio of fluorescence intensity of the pyrene dimer to fluorescence intensity of the pyrene monomer. Microviscosity of erythrocyte membranes was measured also on a Shimadzu RF-5301(PC)SCE spectrofluorimeter. The experimental specimen was prepared as follows: 4 ml of hypotonic phosphate buffer containing 2.75 mM of KH2РО4 and 8.5 mM of Na2НРО4 (рН 7.35), a fluorescent pyrene probe, erythrocyte shadows and a specified amount of hormone were placed in a quartz cuvette of size 1 1 4 cm3. Before use, all the components were stored at 4 C. The concentration of shadow protein in the cuvette was 0.100-0.250 mg/ml; that of pyrene, 7.76·10–6 M. Pyrene was diluted in ethanol, its initial concentration being 1.5·10–3 M. The cuvette was placed into the spectrofluorimeter thermostat for 10 min, then the fluorescence measurements were performed at 36 C. Before placing the specimen into the spectrofluorimeter thermostat, it was shaken vigorously for 1 min. For fluorescence measurements of shadows upon their loading with a different amount of hormones, each time a new specimen was prepared by the same procedure. Such a procedure is necessary because pyrene favors fast degradation of

To measure microviscosity of a lipid bilayer near proteins (the region of protein-lipid interaction), we used the excitation wavelength = 281 nm and spectral slit width 1.5/5. Microviscosity of a lipid bilayer far from proteins (the region of lipid-lipid interaction) was measured with the excitation wavelength = 337 nm and spectral slit width 1.5/3. At that, the maxima of emission intensity were observed at = 374 nm and = 393 nm (the vibronic emission peaks of excited pyrene monomers), and = 468 nm (the emission maximum of

added to the shadow suspension. For the region of lipid-lipid interaction, relative

468 393 468 393

0 ( ) (0) *A F FA F A F*

where 468 *F A*( ) is the fluorescence intensity of pyrene at wavelength = 468 nm in a specimen at the hormone concentration *A* in suspension; 468 *F* (0) is the fluorescence intensity of pyrene at wavelength = 468 nm in a specimen with no hormone in suspension. 393 *F A*( ) and 393 *F* (0) are the fluorescence intensities of pyrene at wavelength = 393 nm at the hormone concentration *A* in suspension and without hormone in suspension, respectively.

For the region of protein-lipid interaction, relative microviscosity was calculated by the

(0) are microviscosities of membranes, respectively, with and without hormone

(0) ( )

(9)

The relative microviscosity of membranes was determined as a ratio

 

**2.4. Measurement of erythrocyte membrane microviscosity** 

erythrocyte membranes.

excited pyrene dimer).

microviscosity was calculated by the formula

The excitation wavelength is 337 nm.

( ) *A* and

formula

In our case, molar mass of membrane proteins is unknown, so the concentration of proteins in cuvette *C* is determined in mg/ml, and concentration of hormones *A* in mol/l. The constant *n* is expressed in moles of molecules of hormone per milligram of protein (M/mg) and is a ratio of the maximum concentration of bound hormone to the concentration of membrane proteins. This can be written as

$$B\_{MAX} = \frac{A\_S}{C} \left[ \begin{array}{c} \text{mole} \\ \text{mg protein} \end{array} \right] \tag{6}$$

Changes in Gibbs free energy *G* of the system upon transition of hormone from aqueous medium to erythrocyte membrane are calculated by the formula

$$
\Delta G = -RT \cdot \ln(K\_c) \left[ \bigvee\_{mole} \right] \tag{7}
$$

where 8.314 *<sup>J</sup> <sup>R</sup> K mole* , and *T* is the absolute thermodynamic temperature.

The measurement errors appeared due to inaccuracy in volumetric dosing of the shadow suspension specimens and their titration against hormones. Specimens were dosed using pipette dispensers DPAOF-1000 and DPAOF-50, their relative error at (20±2)C being 1% and 2%, respectively. 4 ml of the buffer was taken once with a DPAOF-1000 pipette, and suspension of erythrocytes and hormones was dosed twice using a DPAOF-50 pipette. The fluorescence intensity of erythrocyte shadows *F* is directly proportional to the concentrations of proteins *C* and hormones *A* in the specimen. Relative error *EF* in measuring the *F* value can be estimated by the formula

$$E\_F = \sqrt{\left(1\%\right)^2 + \left(2\%\right)^2 + \left(2\%\right)^2} = \Im \%. \tag{8}$$

Relative measurement errors for Kb and *MAX B* can be obtained in the same way. They are equal to 10%.

In calculation, the values of fluorescence intensity *F* were corrected for dilution of suspension after the introduction of solution with hormone, for quenching of tryptophan emission by the solvent (a mixture of DMS and ethanol), for proper fluorescence of hormones, and evaporation of water from the cuvette.

## **2.4. Measurement of erythrocyte membrane microviscosity**

268 Thermodynamics – Fundamentals and Its Application in Science

membrane proteins. This can be written as

Changes in Gibbs free energy

where 8.314 *<sup>J</sup> <sup>R</sup>*

equal to 10%.

gives

*S A nx A nQC* , where *A* is the total concentration of hormone; *AS <sup>n</sup>*

*B CxC Q* (1 ) . Substitution of (2) and (3) into expression for binding constant (1)

(1 )( ) *<sup>c</sup>*

In our case, molar mass of membrane proteins is unknown, so the concentration of proteins in cuvette *C* is determined in mg/ml, and concentration of hormones *A* in mol/l. The constant *n* is expressed in moles of molecules of hormone per milligram of protein (M/mg) and is a ratio of the maximum concentration of bound hormone to the concentration of

> *C mg protein*

> > ln( ) , *<sup>c</sup>*

*<sup>J</sup> G RT K mole*

The measurement errors appeared due to inaccuracy in volumetric dosing of the shadow suspension specimens and their titration against hormones. Specimens were dosed using pipette dispensers DPAOF-1000 and DPAOF-50, their relative error at (20±2)C being 1% and 2%, respectively. 4 ml of the buffer was taken once with a DPAOF-1000 pipette, and suspension of erythrocytes and hormones was dosed twice using a DPAOF-50 pipette. The fluorescence intensity of erythrocyte shadows *F* is directly proportional to the concentrations of proteins *C* and hormones *A* in the specimen. Relative error *EF* in

Relative measurement errors for Kb and *MAX B* can be obtained in the same way. They are

In calculation, the values of fluorescence intensity *F* were corrected for dilution of suspension after the introduction of solution with hormone, for quenching of tryptophan emission by the solvent (a mixture of DMS and ethanol), for proper fluorescence of

*K mole* , and *T* is the absolute thermodynamic temperature.

*Q A nQC* (5)

*G* of the system upon transition of hormone from aqueous

(7)

<sup>222</sup> 1% 2% 2% 3%. *<sup>F</sup> <sup>E</sup>* (8)

(6)

*<sup>Q</sup> <sup>K</sup>*

*S*

*<sup>A</sup> <sup>B</sup> mole*

*MAX*

medium to erythrocyte membrane are calculated by the formula

measuring the *F* value can be estimated by the formula

hormones, and evaporation of water from the cuvette.

*<sup>C</sup>* ;

Membrane microviscosity for translational diffusion of pyrene probe was calculated as a ratio of fluorescence intensity of the pyrene dimer to fluorescence intensity of the pyrene monomer. Microviscosity of erythrocyte membranes was measured also on a Shimadzu RF-5301(PC)SCE spectrofluorimeter. The experimental specimen was prepared as follows: 4 ml of hypotonic phosphate buffer containing 2.75 mM of KH2РО4 and 8.5 mM of Na2НРО4 (рН 7.35), a fluorescent pyrene probe, erythrocyte shadows and a specified amount of hormone were placed in a quartz cuvette of size 1 1 4 cm3. Before use, all the components were stored at 4 C. The concentration of shadow protein in the cuvette was 0.100-0.250 mg/ml; that of pyrene, 7.76·10–6 M. Pyrene was diluted in ethanol, its initial concentration being 1.5·10–3 M. The cuvette was placed into the spectrofluorimeter thermostat for 10 min, then the fluorescence measurements were performed at 36 C. Before placing the specimen into the spectrofluorimeter thermostat, it was shaken vigorously for 1 min. For fluorescence measurements of shadows upon their loading with a different amount of hormones, each time a new specimen was prepared by the same procedure. Such a procedure is necessary because pyrene favors fast degradation of erythrocyte membranes.

To measure microviscosity of a lipid bilayer near proteins (the region of protein-lipid interaction), we used the excitation wavelength = 281 nm and spectral slit width 1.5/5. Microviscosity of a lipid bilayer far from proteins (the region of lipid-lipid interaction) was measured with the excitation wavelength = 337 nm and spectral slit width 1.5/3. At that, the maxima of emission intensity were observed at = 374 nm and = 393 nm (the vibronic emission peaks of excited pyrene monomers), and = 468 nm (the emission maximum of excited pyrene dimer).

The relative microviscosity of membranes was determined as a ratio ( )/ 0 *A* , where ( ) *A* and (0) are microviscosities of membranes, respectively, with and without hormone added to the shadow suspension. For the region of lipid-lipid interaction, relative microviscosity was calculated by the formula

$$\frac{\eta\left(A\right)}{\eta\left(0\right)} = \frac{F\_{468}\left(0\right)}{F\_{468}\left(A\right)} \cdot \frac{F\_{393}\left(A\right)}{F\_{393}\left(0\right)}\tag{9}$$

where 468 *F A*( ) is the fluorescence intensity of pyrene at wavelength = 468 nm in a specimen at the hormone concentration *A* in suspension; 468 *F* (0) is the fluorescence intensity of pyrene at wavelength = 468 nm in a specimen with no hormone in suspension. 393 *F A*( ) and 393 *F* (0) are the fluorescence intensities of pyrene at wavelength = 393 nm at the hormone concentration *A* in suspension and without hormone in suspension, respectively. The excitation wavelength is 337 nm.

For the region of protein-lipid interaction, relative microviscosity was calculated by the formula

$$\frac{\eta\left(A\right)}{\eta\left(0\right)} = \frac{F\_{468}\left(0\right) - I\_{468}}{F\_{468}\left(A\right) - I\_{468}} \cdot \frac{F\_{393}\left(A\right) - I\_{393}}{F\_{393}\left(0\right) - I\_{393}}\tag{10}$$

Mesomechanics and Thermodynamics of

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 271

and DHEAS did not affect deep layers of the membranes, so the effect was much less pronounced. IR spectroscopy allowed us to reveal the nature of these structural

**Figure 2.** Control surface of rat erythrocyte. The erythrocyte suspension was supplemented with DMS and ethanol (0.25% of the mixture volume): (a) scan size 1 1 µm2; (b) center section of the surface.

transformations.

where 393 *I* and 468 *I* are the fluorescence intensities of tryptophan at wavelength = 393 nm and = 468 nm, respectively. The excitation wavelength is = 281 nm. A relative measurement error for relative microviscosity was equal to 6%.

## **2.5. Change of the Na+, K+-АТPase activity**

Erythrocytes were extracted from fresh blood of rats. Erythrocyte suspensions with hormones of differing concentration were analyzed to activity of the Na+, K+-АТPhase. The experimental procedures used in these investigations are described in [5].

## **3. Results**

## **3.1. Atomic force microscopy**

Under atomic force microscope, erythrocytes of healthy animals looked as large biconcave discs ca. 6 µm in diameter, which agrees with the results obtained by other authors [7]. At a higher magnification, their surface showed a slight nonuniformity caused most likely by the presence of membrane proteins. When the erythrocyte suspension was supplemented with DMS and ethanol (0.25% of the mixture volume), the surface nonuniformity increased, probably due to denaturating effect of solvent on the surface structural proteins (Fig. 2). Domains with the length 200-250 nm and height 2 nm are seen. The pattern changed upon addition of testosterone to erythrocyte suspension with the final concentration 10-7 M (Fig. 3). The interaction of testosterone with erythrocyte membranes leads to their restructuring. The surface is tuberous, there are domains of size 400 х 400 nm and height 20-25 nm, with smaller domains on the surface of large ones: size 50 х 50 µm2 and height 10 nm. Between them, there are regions of loosened substance that form hollows. In this case, there are pronounced distortions in the primary structure of erythrocyte membranes.

Other structural changes of erythrocyte membranes were obtained in our study upon interaction with androsterone (Fig. 4) with the final concentration 10–6 M. The surface is flat, there are domains of size 100 х 100 nm and height 6-8 nm. In comparison with control specimens, domains decreased in area, but increased in height.

The surface of rat erythrocyte after adsorption of DHEA is depicted in Fig. 5. Concentration of the hormone is 10–7 M. The surface is tuberous, there are domains of size 220 х 220 nm and height 20 -25 nm. However, they are not separated into subdomains, as in the case of testosterone.

Of the four hormones, DHEAS has the weakest effect on the membrane morphology. The surface of rat erythrocyte after adsorption of DHEAS is shown in Fig. 6. Concentration of the hormone is 10–7 M. The surface is flat, there are domains of size 100 х 100 nm and height 3 - 4 nm. Changes are insignificant in comparison with control. It can be suggested that DHEA and DHEAS did not affect deep layers of the membranes, so the effect was much less pronounced. IR spectroscopy allowed us to reveal the nature of these structural transformations.

270 Thermodynamics – Fundamentals and Its Application in Science

**2.5. Change of the Na+, K+-АТPase activity** 

**3. Results** 

testosterone.

**3.1. Atomic force microscopy** 

 

measurement error for relative microviscosity was equal to 6%.

experimental procedures used in these investigations are described in [5].

pronounced distortions in the primary structure of erythrocyte membranes.

specimens, domains decreased in area, but increased in height.

468 468 393 393 468 468 393 393

(10)

(0) ( )

0 ( ) (0) *A F I F AI F AI F I*

where 393 *I* and 468 *I* are the fluorescence intensities of tryptophan at wavelength = 393 nm and = 468 nm, respectively. The excitation wavelength is = 281 nm. A relative

Erythrocytes were extracted from fresh blood of rats. Erythrocyte suspensions with hormones of differing concentration were analyzed to activity of the Na+, K+-АТPhase. The

Under atomic force microscope, erythrocytes of healthy animals looked as large biconcave discs ca. 6 µm in diameter, which agrees with the results obtained by other authors [7]. At a higher magnification, their surface showed a slight nonuniformity caused most likely by the presence of membrane proteins. When the erythrocyte suspension was supplemented with DMS and ethanol (0.25% of the mixture volume), the surface nonuniformity increased, probably due to denaturating effect of solvent on the surface structural proteins (Fig. 2). Domains with the length 200-250 nm and height 2 nm are seen. The pattern changed upon addition of testosterone to erythrocyte suspension with the final concentration 10-7 M (Fig. 3). The interaction of testosterone with erythrocyte membranes leads to their restructuring. The surface is tuberous, there are domains of size 400 х 400 nm and height 20-25 nm, with smaller domains on the surface of large ones: size 50 х 50 µm2 and height 10 nm. Between them, there are regions of loosened substance that form hollows. In this case, there are

Other structural changes of erythrocyte membranes were obtained in our study upon interaction with androsterone (Fig. 4) with the final concentration 10–6 M. The surface is flat, there are domains of size 100 х 100 nm and height 6-8 nm. In comparison with control

The surface of rat erythrocyte after adsorption of DHEA is depicted in Fig. 5. Concentration of the hormone is 10–7 M. The surface is tuberous, there are domains of size 220 х 220 nm and height 20 -25 nm. However, they are not separated into subdomains, as in the case of

Of the four hormones, DHEAS has the weakest effect on the membrane morphology. The surface of rat erythrocyte after adsorption of DHEAS is shown in Fig. 6. Concentration of the hormone is 10–7 M. The surface is flat, there are domains of size 100 х 100 nm and height 3 - 4 nm. Changes are insignificant in comparison with control. It can be suggested that DHEA

**Figure 2.** Control surface of rat erythrocyte. The erythrocyte suspension was supplemented with DMS and ethanol (0.25% of the mixture volume): (a) scan size 1 1 µm2; (b) center section of the surface.

Mesomechanics and Thermodynamics of

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 273

= 36 cm–1). The bands 2852 and 2932 cm–1 increased in intensity;

= 36 cm–1) is caused by the formation of hydrogen bond

but also -helix at 1650 and 1656 cm–1, and -structure at 1686 and 1520 cm–1. Besides, we recorded NH stretching vibrations in proteins (3308 cm–1), CH stretching vibrations in proteins and phospholipids (2948, 2930 and 2848 cm–1), and a set of bands corresponding to phospholipids, in particular, C=O bond (1748 cm–1), P=O bond (1236 cm–1), СН<sup>2</sup> deformation vibrations (1460 and 1386 cm–1), О4С4-С5О5 bond (1048 cm–1) and C-C bond of deformation vibrations (978 cm–1). It should be noted that С=О band (1736 cm–1) is quite narrow, which gives grounds to suggest that phospholipids in membranes of normal erythrocytes are well ordered at a level of ester bonds of higher carboxylic acids and

Under the action of testosterone, intensity of absorption bands 1544, 1656 and 3292 cm–1 increased by 30% and more (Fig. 8, Table 1). Absorption band of NН bond showed a

the ratio of band intensities 2852/2932 cm–1 changed. The enhancement of integral intensity of the indicated absorption bands indicates an increased ordering of membrane proteins

The fraction of -helices grows due to structural transition tangle →-helix. A 3308→3272 cm–

between keto group (C3=O) in testosterone A-ring and NH bond of peptide group in membrane protein or indole ring in tryptophan. An increased intensity of the 2932 and 2852 cm–1 bands together with a growing intensity ratio 2852/2932 cm–1 confirm the rising orderliness of the entire membrane. Absorption band 1740 cm–1 (С=О bond of the ester group in phospholipids) increased in intensity and shifted to the short-wave region. The enhanced intensity of С=О bond reflects an increased ordering of phospholipids within domains and an increased interdomain ordering. The short-wave shift of this band is caused by the formation of hydrogen bond between OH group at С17 carbon atom in testosterone Dring and С=О bond in phospholipids. Similar to segnetoelectrics a hysteresis phenomenon was observed in erythrocyte membranes [11, 12]. The spectrin-actin-ankyrin meshwork, which is connected both with membrane proteins and phospholipids, also contributes to the ordering of phospholipids. The 1088→ → 1098 and 1236 1248 cm–1 shifts of absorption bands to the short-wave region result from dehydration of phospholipids due to increase in their orderliness, since the hydration process shifts these bands to the long-wave region [13] An increased intensity of bands 1098 and 1247 cm–1 (Р-О-С and Р=О bonds of phospholipids, respectively) in comparison with control specimens confirms an enhanced ordering of

Thus, the formation of complex domains in erythrocyte membranes upon their interaction with testosterone is caused by simultaneous interaction of СО and OH groups of the hormone with СО and NН groups both of proteins and phospholipids. In the process, water

is displaced to adjacent regions, which is accompanied by membrane loosening.

glycerol.

*3.2.1. Effect of testosterone* 

3308 → 3272 cm–1 shift (

1 band shift of NH bond (

and, in particular, an increased fraction of -helices.

phospholipids under the action of the hormone.

**Figure 3.** Surface of rat erythrocyte after adsorption of testosterone. Concentration of the hormone is 10-7 M: (a) scan size 1.5 1.5 µm2; (b) center section of the surface.

#### **3.2. IR spectroscopy of erythrocyte shadows**

Analysis of IR spectra of erythrocyte shadows obtained from rats with no hormone loading (Fig. 7) revealed in membrane-bound proteins not only a disordered structure, but also -helix at 1650 and 1656 cm–1, and -structure at 1686 and 1520 cm–1. Besides, we recorded NH stretching vibrations in proteins (3308 cm–1), CH stretching vibrations in proteins and phospholipids (2948, 2930 and 2848 cm–1), and a set of bands corresponding to phospholipids, in particular, C=O bond (1748 cm–1), P=O bond (1236 cm–1), СН<sup>2</sup> deformation vibrations (1460 and 1386 cm–1), О4С4-С5О5 bond (1048 cm–1) and C-C bond of deformation vibrations (978 cm–1). It should be noted that С=О band (1736 cm–1) is quite narrow, which gives grounds to suggest that phospholipids in membranes of normal erythrocytes are well ordered at a level of ester bonds of higher carboxylic acids and glycerol.

## *3.2.1. Effect of testosterone*

272 Thermodynamics – Fundamentals and Its Application in Science

**Figure 3.** Surface of rat erythrocyte after adsorption of testosterone.

**3.2. IR spectroscopy of erythrocyte shadows** 

Concentration of the hormone is 10-7 M: (a) scan size 1.5 1.5 µm2; (b) center section of the surface.

Analysis of IR spectra of erythrocyte shadows obtained from rats with no hormone loading (Fig. 7) revealed in membrane-bound proteins not only a disordered structure, Under the action of testosterone, intensity of absorption bands 1544, 1656 and 3292 cm–1 increased by 30% and more (Fig. 8, Table 1). Absorption band of NН bond showed a 3308 → 3272 cm–1 shift ( = 36 cm–1). The bands 2852 and 2932 cm–1 increased in intensity; the ratio of band intensities 2852/2932 cm–1 changed. The enhancement of integral intensity of the indicated absorption bands indicates an increased ordering of membrane proteins and, in particular, an increased fraction of -helices.

The fraction of -helices grows due to structural transition tangle →-helix. A 3308→3272 cm– 1 band shift of NH bond ( = 36 cm–1) is caused by the formation of hydrogen bond between keto group (C3=O) in testosterone A-ring and NH bond of peptide group in membrane protein or indole ring in tryptophan. An increased intensity of the 2932 and 2852 cm–1 bands together with a growing intensity ratio 2852/2932 cm–1 confirm the rising orderliness of the entire membrane. Absorption band 1740 cm–1 (С=О bond of the ester group in phospholipids) increased in intensity and shifted to the short-wave region. The enhanced intensity of С=О bond reflects an increased ordering of phospholipids within domains and an increased interdomain ordering. The short-wave shift of this band is caused by the formation of hydrogen bond between OH group at С17 carbon atom in testosterone Dring and С=О bond in phospholipids. Similar to segnetoelectrics a hysteresis phenomenon was observed in erythrocyte membranes [11, 12]. The spectrin-actin-ankyrin meshwork, which is connected both with membrane proteins and phospholipids, also contributes to the ordering of phospholipids. The 1088→ → 1098 and 1236 1248 cm–1 shifts of absorption bands to the short-wave region result from dehydration of phospholipids due to increase in their orderliness, since the hydration process shifts these bands to the long-wave region [13] An increased intensity of bands 1098 and 1247 cm–1 (Р-О-С and Р=О bonds of phospholipids, respectively) in comparison with control specimens confirms an enhanced ordering of phospholipids under the action of the hormone.

Thus, the formation of complex domains in erythrocyte membranes upon their interaction with testosterone is caused by simultaneous interaction of СО and OH groups of the hormone with СО and NН groups both of proteins and phospholipids. In the process, water is displaced to adjacent regions, which is accompanied by membrane loosening.

Mesomechanics and Thermodynamics of

= 2 cm–1) (Table 1). Integral

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 275

intensity of absorption bands of СО (1654 cm–1) and NН groups (3280 cm–1) increased by 30% and more. There appeared a band at 1635 cm–1 corresponding to the -structure. An increase in intensity of stretching vibrations of CH bonds at 2848 and 2930 cm–1 was observed. The frequency shift of NH bond is related with the formation of hydrogen bond with С17=О group of the hormone D-ring. Androsterone has a more flexible structure as compared to cholesterol: its А, В and С-rings can take a more favorable conformation during the interaction with membrane proteins. Only D-ring has a flat structure, due to the presence of carbon С17 with sр2 hybridization. Hydrophobic interaction with the membrane surface should also be taken into account. High conformational mobility of the molecule creates more advantageous steric conditions for hydrophobic interaction both with tryptophan, which fluorescence quenching was observed in our study, and hydrophobic regions on the membrane surface. This increases the constant of their binding to hormone and leads to more pronounced structural changes in the membranes. An increase in intensity of СО-peptide bond is related with the growing fraction of -helices due to transition tangle →-helix. An increase in intensity of absorption band 1620-1635 cm–1 is caused by structural transition tangle →-structure. Of interest is a hypothesis stating that the indicated transitions may take place in contractile proteins, since their removal from the

Incubation of DHEA with erythrocyte shadows showed that the frequency of stretching vibrations of NН peptide bond shifted by 20 cm–1 to the long-wave region (3308 → 3288 cm–1), whereas halfwidth of amide A decreased. An increase in the integral intensity of absorption

A 1236→1247.6 cm–1 band shift points to dehydration of phosphate groups in phospholipids. Shifting of the frequency of С=О bond in phospholipids (1748 1732 cm → –1) was observed; intensity of this band also increased. The 2930→ → 2925.8 and 2848 2851 cm–1 shifts (СН stretching vibrations) took place, intensity of the bands increased. The intensity ratio

Incubation of DHEAS with erythrocyte shadows resulted in the band shift 3308→3286 cm–1 (NН peptide bond) by 22 cm–1 (Table 1). Bands at 1548, 1656 and 3298 cm–1 increased in intensity with respect to control specimen; however, this was more pronounced upon addition of DHEA as compared to DHEAS. Absorption bands 1632 and 1684 cm–1 attributed to -structure were observed. The band shift was recorded: 2930→ → 2928 and 2848 2852 cm–1, which was accompanied by a change in the 2852/2928 cm–1 ratio. The band at 1236 cm–1 (Р=О bond) showed a strong splitting and had 3-4 bands in the region of 1236-1256 cm–1. Bands at

however, it was less pronounced than in the case of DHEA addition. The DHEAS hormone

bond) were observed. A 1748-1738 cm–1 shift was detected;

region by 38 cm–1 as well as shifting of NН bond of amide II (

membrane results in a decrease or disappearance of transitions [12-13].

bands at 1546, 1654.9 and 3288 cm–1 was observed (Table 1).

*3.2.4. Effect of dehydroepiandrosterone sulfate* 

*3.2.3. Effect of dehydroepiandrosterone* 

2852/2924 cm–1 changed.

1084 and 1100 cm–1 (P-O-

**Figure 4.** Surface of rat erythrocyte after adsorption of androsterone. Concentration of the hormone is 10-6 M: (a) scan size 1.5 1.5 µm2; (b) center section of the surface.

#### *3.2.2. Effect of androsterone*

Incubation of rat erythrocyte shadows with androsterone (CC = 2.76 x 10–8 M) results in shifting the frequency of NH bonds (stretching vibrations of amide A) to the long-wave region by 38 cm–1 as well as shifting of NН bond of amide II ( = 2 cm–1) (Table 1). Integral intensity of absorption bands of СО (1654 cm–1) and NН groups (3280 cm–1) increased by 30% and more. There appeared a band at 1635 cm–1 corresponding to the -structure. An increase in intensity of stretching vibrations of CH bonds at 2848 and 2930 cm–1 was observed. The frequency shift of NH bond is related with the formation of hydrogen bond with С17=О group of the hormone D-ring. Androsterone has a more flexible structure as compared to cholesterol: its А, В and С-rings can take a more favorable conformation during the interaction with membrane proteins. Only D-ring has a flat structure, due to the presence of carbon С17 with sр2 hybridization. Hydrophobic interaction with the membrane surface should also be taken into account. High conformational mobility of the molecule creates more advantageous steric conditions for hydrophobic interaction both with tryptophan, which fluorescence quenching was observed in our study, and hydrophobic regions on the membrane surface. This increases the constant of their binding to hormone and leads to more pronounced structural changes in the membranes. An increase in intensity of СО-peptide bond is related with the growing fraction of -helices due to transition tangle →-helix. An increase in intensity of absorption band 1620-1635 cm–1 is caused by structural transition tangle →-structure. Of interest is a hypothesis stating that the indicated transitions may take place in contractile proteins, since their removal from the membrane results in a decrease or disappearance of transitions [12-13].

## *3.2.3. Effect of dehydroepiandrosterone*

274 Thermodynamics – Fundamentals and Its Application in Science

**Figure 4.** Surface of rat erythrocyte after adsorption of androsterone.

*3.2.2. Effect of androsterone* 

Concentration of the hormone is 10-6 M: (a) scan size 1.5 1.5 µm2; (b) center section of the surface.

Incubation of rat erythrocyte shadows with androsterone (CC = 2.76 x 10–8 M) results in shifting the frequency of NH bonds (stretching vibrations of amide A) to the long-wave Incubation of DHEA with erythrocyte shadows showed that the frequency of stretching vibrations of NН peptide bond shifted by 20 cm–1 to the long-wave region (3308 → 3288 cm–1), whereas halfwidth of amide A decreased. An increase in the integral intensity of absorption bands at 1546, 1654.9 and 3288 cm–1 was observed (Table 1).

A 1236→1247.6 cm–1 band shift points to dehydration of phosphate groups in phospholipids. Shifting of the frequency of С=О bond in phospholipids (1748 1732 cm → –1) was observed; intensity of this band also increased. The 2930→ → 2925.8 and 2848 2851 cm–1 shifts (СН stretching vibrations) took place, intensity of the bands increased. The intensity ratio 2852/2924 cm–1 changed.

## *3.2.4. Effect of dehydroepiandrosterone sulfate*

Incubation of DHEAS with erythrocyte shadows resulted in the band shift 3308→3286 cm–1 (NН peptide bond) by 22 cm–1 (Table 1). Bands at 1548, 1656 and 3298 cm–1 increased in intensity with respect to control specimen; however, this was more pronounced upon addition of DHEA as compared to DHEAS. Absorption bands 1632 and 1684 cm–1 attributed to -structure were observed. The band shift was recorded: 2930→ → 2928 and 2848 2852 cm–1, which was accompanied by a change in the 2852/2928 cm–1 ratio. The band at 1236 cm–1 (Р=О bond) showed a strong splitting and had 3-4 bands in the region of 1236-1256 cm–1. Bands at 1084 and 1100 cm–1 (P-O bond) were observed. A 1748-1738 cm–1 shift was detected; however, it was less pronounced than in the case of DHEA addition. The DHEAS hormone has a stronger binding with hydrophilic heads of phospholipids as compared to DHEA, and a weaker binding with membrane proteins. This suggests that DHEAS molecules cannot penetrate deep into the membrane due to their higher hydrophilicity with respect to DHEA.

Mesomechanics and Thermodynamics of

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 277

**Figure 6.** Surface of rat erythrocyte after adsorption of DHEAS.

Concentration of the hormone is 10-7 M; (a) scan size 1 1 µm2; (b) center section of the surface.

Overall, it can be concluded that the interaction of DHEA and DHEAS with erythrocyte membranes is accompanied by the formation of hydrogen bonds between keto group (С17=О) and NН group of proteins as well as between ОН group at С3 in the A-ring of the hormones and C=O group in biomembrane phospholipids. The formation of indicated

**Figure 5.** Surface of rat erythrocyte after adsorption of DHEA. Concentration of the hormone is 10-7 M; (a) scan size 1 1 µm2; (b) center section of the surface.

**Figure 5.** Surface of rat erythrocyte after adsorption of DHEA.

Concentration of the hormone is 10-7 M; (a) scan size 1 1 µm2; (b) center section of the surface.

has a stronger binding with hydrophilic heads of phospholipids as compared to DHEA, and a weaker binding with membrane proteins. This suggests that DHEAS molecules cannot penetrate deep into the membrane due to their higher hydrophilicity with respect to DHEA.

**Figure 6.** Surface of rat erythrocyte after adsorption of DHEAS. Concentration of the hormone is 10-7 M; (a) scan size 1 1 µm2; (b) center section of the surface.

Overall, it can be concluded that the interaction of DHEA and DHEAS with erythrocyte membranes is accompanied by the formation of hydrogen bonds between keto group (С17=О) and NН group of proteins as well as between ОН group at С3 in the A-ring of the hormones and C=O group in biomembrane phospholipids. The formation of indicated hydrogen bonds leads to ordering of membrane proteins (transition tangle →-helix) and phospholipids. Hydrophobic interactions of hormone with the surface of erythrocyte membranes also contribute to their structural rearrangement; however, they are much less pronounced for DHEAS as compared to DHEA. The reason is that substitution of ОН group by SO3 strongly diminishes the energy of hydrogen bond, since in ОН group the unshared pair of electrons is located on the oxygen atom, whereas in SO3 group it is delocalized over the entire -conjugated bond.

Mesomechanics and Thermodynamics of

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 279

androsterone. Fluorescence quenching was even less pronounced with DHEA (Fig. 11). In this case, the maximum quenching occurred at a concentration of 2.4·10–6 M. And finally, the lowest fluorescence quenching was observed for DHEAS (Fig. 12). The maximum quenching took place at a concentration of 5.3·10–6 M, which is 2.2 times higher as compared to DHEA.

**Figure 7.** IR spectra of rat erythrocyte membranes (control) (Cphosph.buff. = 0.01 M, pH 7.35, relative

humidity 0%): (a) ν = 900-1800 cm-1, (b) ν = 2600-3700 cm-1.

## **4. Fluorescence analysis**

In the study, absorption intensity (D) and emission intensity (F) of tryptophan were estimated at different wavelengths. Corrections were made for dilution of erythrocyte shadow suspension after the introduction of a hormone solution, for tryptophan emission quenching by a solvent (DMS : ethanol), intrinsic fluorescence of hormones, and evaporation of water from a cuvette. To obtain a correction for solvent, the erythrocyte shadow suspension was titrated with solvent.

It was shown that solvent decreases the intensity of tryptophan absorption at λ = 227.8 nm by 33% and results in its long-wave shift to λ = 230.2 nm. Absorption intensity at λ = 281 nm changed only by 1.3% without a long-wave shifting. A maximum of emission intensity differed from control specimen also at λ = 332 nm. It did not shift upon addition of solvent, but its intensity decreased by 1.3%.

Upon addition of testosterone with the final concentration 3·10–6 M to erythrocyte shadows, the absorption intensity at 227 nm diminished by 19 a.u. or by 2.8%; this was accompanied by an upward shift of λ to 230.4 nm. As the hormone concentration increased to 6.05·10–6 M, the absorption intensity at 227 nm decreased by 25 a.u., or 5.0%, which was accompanied by shifting the absorption maximum to 232 nm. In the region of 280 nm, addition of hormone caused only minor changes in fluorescence. Considerable changes in the spectrum were obtained upon addition of androsterone to the shadows. Even at a concentration of 6.92 · 10– 8 M, which is two orders of magnitude lower compared to the case of testosterone, the absorption intensity at 227 nm decreased by 90 a.u., or 122%. It means that this hormone penetrates deeper into erythrocyte membranes than testosterone and enhances the tangle → -helix transition in proteins, thus increasing their ordering. When erythrocyte shadows were supplemented with DHEA or DHEAS, the hypochromic effect was weak or entirely absent. A decrease in absorption intensity and a long-wave shift observed in our study can be attributed to the effect of solvent.

Analysis of the tryptophan fluorescence quenching spectra testifies that all four hormones interact with membrane-bound proteins, although a degree of this interaction differs (Figs. 9-12). The most pronounced quenching was observed in the case of androsterone (Fig. 9). The maximum fluorescence quenching was observed at a concentration of 2.2·10–8 M. Testosterone showed a lower fluorescence quenching (Fig. 10). The maximum quenching was observed at a concentration of 1.2·10–7 M, which is 5.5 times higher as compared to androsterone. Fluorescence quenching was even less pronounced with DHEA (Fig. 11). In this case, the maximum quenching occurred at a concentration of 2.4·10–6 M. And finally, the lowest fluorescence quenching was observed for DHEAS (Fig. 12). The maximum quenching took place at a concentration of 5.3·10–6 M, which is 2.2 times higher as compared to DHEA.

278 Thermodynamics – Fundamentals and Its Application in Science

the entire -conjugated bond.

**4. Fluorescence analysis** 

suspension was titrated with solvent.

but its intensity decreased by 1.3%.

be attributed to the effect of solvent.

hydrogen bonds leads to ordering of membrane proteins (transition tangle →-helix) and phospholipids. Hydrophobic interactions of hormone with the surface of erythrocyte membranes also contribute to their structural rearrangement; however, they are much less pronounced for DHEAS as compared to DHEA. The reason is that substitution of ОН group by SO3 strongly diminishes the energy of hydrogen bond, since in ОН group the unshared pair of electrons is located on the oxygen atom, whereas in SO3 group it is delocalized over

In the study, absorption intensity (D) and emission intensity (F) of tryptophan were estimated at different wavelengths. Corrections were made for dilution of erythrocyte shadow suspension after the introduction of a hormone solution, for tryptophan emission quenching by a solvent (DMS : ethanol), intrinsic fluorescence of hormones, and evaporation of water from a cuvette. To obtain a correction for solvent, the erythrocyte shadow

It was shown that solvent decreases the intensity of tryptophan absorption at λ = 227.8 nm by 33% and results in its long-wave shift to λ = 230.2 nm. Absorption intensity at λ = 281 nm changed only by 1.3% without a long-wave shifting. A maximum of emission intensity differed from control specimen also at λ = 332 nm. It did not shift upon addition of solvent,

Upon addition of testosterone with the final concentration 3·10–6 M to erythrocyte shadows, the absorption intensity at 227 nm diminished by 19 a.u. or by 2.8%; this was accompanied by an upward shift of λ to 230.4 nm. As the hormone concentration increased to 6.05·10–6 M, the absorption intensity at 227 nm decreased by 25 a.u., or 5.0%, which was accompanied by shifting the absorption maximum to 232 nm. In the region of 280 nm, addition of hormone caused only minor changes in fluorescence. Considerable changes in the spectrum were obtained upon addition of androsterone to the shadows. Even at a concentration of 6.92 · 10– 8 M, which is two orders of magnitude lower compared to the case of testosterone, the absorption intensity at 227 nm decreased by 90 a.u., or 122%. It means that this hormone penetrates deeper into erythrocyte membranes than testosterone and enhances the tangle → -helix transition in proteins, thus increasing their ordering. When erythrocyte shadows were supplemented with DHEA or DHEAS, the hypochromic effect was weak or entirely absent. A decrease in absorption intensity and a long-wave shift observed in our study can

Analysis of the tryptophan fluorescence quenching spectra testifies that all four hormones interact with membrane-bound proteins, although a degree of this interaction differs (Figs. 9-12). The most pronounced quenching was observed in the case of androsterone (Fig. 9). The maximum fluorescence quenching was observed at a concentration of 2.2·10–8 M. Testosterone showed a lower fluorescence quenching (Fig. 10). The maximum quenching was observed at a concentration of 1.2·10–7 M, which is 5.5 times higher as compared to

**Figure 7.** IR spectra of rat erythrocyte membranes (control) (Cphosph.buff. = 0.01 M, pH 7.35, relative humidity 0%): (a) ν = 900-1800 cm-1, (b) ν = 2600-3700 cm-1.

Mesomechanics and Thermodynamics of

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 281

According to the results obtained, testosterone and androsterone penetrate deeper into erythrocyte membrane and have a stronger effect on the structure of membrane-bound proteins toward their increased ordering. DHEA and DHEAS have some effect on erythrocyte membranes; these hormones adsorb on the membrane surface, but do not penetrate deep into hydrophobic layer of the membranes. These hormones have a weaker

This conclusion is confirmed by the calculated values of hormone binding constant (Кb), total amount of bound hormone (Вmax), and changes in free energy (∆G) upon hormone transition from free state to the membrane-bound one (Table 2). The highest values of К<sup>b</sup> were obtained in our study for testosterone and androsterone, Кb for androsterone being higher by a factor of 4. Amount of the bound hormone (Вmax) obeyed an inverse relationship: it was 2.4 times higher in the case of testosterone as compared to androsterone. Changes in free energy upon interaction of hormones with erythrocyte membranes were most

1260

1739.4 1247

1240

1236

1654.9 3288.0 1732 1247.6 1088 1070.7 2956.3

**Table 1.** IR spectroscopy. Frequency parameters of rat erythrocyte shadows after their interaction with

1738 1248.0 1084 1070

νC=O νP=O νP-O-C νO5С4-

3308 1748 1236 1080 1056 2948

1098 1088

1098 1088 С5O4

1065 1076

1052.7

νCH stretch.

2930 2848

2928 2848

2956.4 2924 2850

2925.8 2851.8

2952.0 2926.4 2852.0

2958

AСО

1.2150 10

2.2433 10

2.1266 10

1.2598 10

binding with proteins via hydrogen bonds.

Compound νCO νNH

1655.4 1686

> 1656 1635 1620

> 1657 1684 1632

1656.0 1680 1632.0 stretch.

3270 329 2

3272 3298 3309

3286 3300 3312

pronounced

Shadows (control)

Shadows + androsterone (A = 2.76 х 10–8 М)

Shadows + testosterone (A = 2.7 х 10–

Shadows + DHEA (A = 2.64 х 10–8 М)

Shadows + DHEAS (А = 1.63 х 10–8 М)

hormones

<sup>8</sup> М)

**Figure 8.** IR spectra of rat erythrocyte membranes incubated with testosterone (CC = 2.7 10-8 M, Cphosph.buff. = 0.001 M, pH 7.35, relative humidity 0%): (a) ν = 900-1800 cm-1, (b) ν = 2600-3700 cm-1.

According to the results obtained, testosterone and androsterone penetrate deeper into erythrocyte membrane and have a stronger effect on the structure of membrane-bound proteins toward their increased ordering. DHEA and DHEAS have some effect on erythrocyte membranes; these hormones adsorb on the membrane surface, but do not penetrate deep into hydrophobic layer of the membranes. These hormones have a weaker binding with proteins via hydrogen bonds.

280 Thermodynamics – Fundamentals and Its Application in Science

**Figure 8.** IR spectra of rat erythrocyte membranes incubated with testosterone (CC = 2.7 10-8 M, Cphosph.buff. = 0.001 M, pH 7.35, relative humidity 0%): (a) ν = 900-1800 cm-1, (b) ν = 2600-3700 cm-1.

This conclusion is confirmed by the calculated values of hormone binding constant (Кb), total amount of bound hormone (Вmax), and changes in free energy (∆G) upon hormone transition from free state to the membrane-bound one (Table 2). The highest values of К<sup>b</sup> were obtained in our study for testosterone and androsterone, Кb for androsterone being higher by a factor of 4. Amount of the bound hormone (Вmax) obeyed an inverse relationship: it was 2.4 times higher in the case of testosterone as compared to androsterone. Changes in free energy upon interaction of hormones with erythrocyte membranes were most pronounced


**Table 1.** IR spectroscopy. Frequency parameters of rat erythrocyte shadows after their interaction with hormones

Mesomechanics and Thermodynamics of

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 283

All values for DHEA and DHEAS strongly differed from those listed above. Binding constants were nearly two orders of magnitude lower. Amount of the bound hormone (Вmax) was much greater, indicating a low specificity of interaction with the membranes. Changes

Thus, a comparison of two pairs of hormones demonstrated their considerable difference from each other. The higher is Кb, the greater is the binding specificity and the lower is the amount of bound hormone (Вmax). Large negative values of ∆G for testosterone and androsterone testify that their interaction with erythrocyte membranes increases their ordering (negentropy). DHEA and DHEAS are characterized by a low specificity of binding

**Figure 12.** Q = (Fmax - F)/Fmax versus the concentration A of dehydroepiandrosterone sulfate hormone

It shows up even when hormones are compared with each other. In DHEA, substitution of ОН group by SО3Н in the 3rd position of A-ring decreases Кb by a factor of 3.8 and increases Вmax by a factor of 2.2. A decrease in ∆G is also pronounced. The reason is that the presence of ОН group and additionally of two keto groups and an S atom enhances the interaction of DHEAS with hydrophilic СО and NН groups of the surface proteins. DHEA and DHEAS cannot bind to the proteins residing in hydrophobic layer of the membrane. These two hormones do not change the conformational state of spectrin-actin-ankyrin meshwork and have only a slight effect on the morphology of membrane surface. DHEAS, being most hydrophilic among the four hormones, has the weakest effect. As hormone hydrophilicity increases, the amount of membrane-bound hormone rises and Кb decreases. During the interaction of testosterone and androsterone with erythrocyte membranes, both hydrogen bonds and hydrophobic interactions may strongly contribute to the growth of Кb. This is explained by a deeper penetration of hormones into hydrophobic layer of erythrocyte membrane, which increases the specificity of their interaction. The accompanying structural transitions in membrane proteins, tangle →β-structure →-helix, increase ordering of these proteins and substantially raise the ∆G value. Results obtained in the study agree well with

introduced into a cuvette. Concentration of membrane protein C = 0.139 mg/mL.

changes in microviscosity of erythrocyte membranes.

in free energy (∆G) were low for both hormones (Table 2).

to membranes.

**Figure 9.** Q = (Fmax - F)/Fmax versus the concentration A of androsterone hormone introduced into a cuvette. Concentration of membrane protein C = 0.203 mg/mL.

**Figure 10.** Q = (Fmax- F)/Fmax versus the concentration A of testosterone hormone introduced into a cuvette. Concentration of membrane protein C = 0.101 mg/mL.

**Figure 11.** Q = (Fmax \_ F)/Fmax versus the concentration A of dehydroepiandrosterone hormone introduced into a cuvette. Concentration of membrane protein C = 0.139 mg/mL.

All values for DHEA and DHEAS strongly differed from those listed above. Binding constants were nearly two orders of magnitude lower. Amount of the bound hormone (Вmax) was much greater, indicating a low specificity of interaction with the membranes. Changes in free energy (∆G) were low for both hormones (Table 2).

282 Thermodynamics – Fundamentals and Its Application in Science

cuvette. Concentration of membrane protein C = 0.203 mg/mL.

cuvette. Concentration of membrane protein C = 0.101 mg/mL.

**Figure 9.** Q = (Fmax - F)/Fmax versus the concentration A of androsterone hormone introduced into a

**Figure 10.** Q = (Fmax- F)/Fmax versus the concentration A of testosterone hormone introduced into a

**Figure 11.** Q = (Fmax \_ F)/Fmax versus the concentration A of dehydroepiandrosterone hormone

introduced into a cuvette. Concentration of membrane protein C = 0.139 mg/mL.

Thus, a comparison of two pairs of hormones demonstrated their considerable difference from each other. The higher is Кb, the greater is the binding specificity and the lower is the amount of bound hormone (Вmax). Large negative values of ∆G for testosterone and androsterone testify that their interaction with erythrocyte membranes increases their ordering (negentropy). DHEA and DHEAS are characterized by a low specificity of binding to membranes.

**Figure 12.** Q = (Fmax - F)/Fmax versus the concentration A of dehydroepiandrosterone sulfate hormone introduced into a cuvette. Concentration of membrane protein C = 0.139 mg/mL.

It shows up even when hormones are compared with each other. In DHEA, substitution of ОН group by SО3Н in the 3rd position of A-ring decreases Кb by a factor of 3.8 and increases Вmax by a factor of 2.2. A decrease in ∆G is also pronounced. The reason is that the presence of ОН group and additionally of two keto groups and an S atom enhances the interaction of DHEAS with hydrophilic СО and NН groups of the surface proteins. DHEA and DHEAS cannot bind to the proteins residing in hydrophobic layer of the membrane. These two hormones do not change the conformational state of spectrin-actin-ankyrin meshwork and have only a slight effect on the morphology of membrane surface. DHEAS, being most hydrophilic among the four hormones, has the weakest effect. As hormone hydrophilicity increases, the amount of membrane-bound hormone rises and Кb decreases. During the interaction of testosterone and androsterone with erythrocyte membranes, both hydrogen bonds and hydrophobic interactions may strongly contribute to the growth of Кb. This is explained by a deeper penetration of hormones into hydrophobic layer of erythrocyte membrane, which increases the specificity of their interaction. The accompanying structural transitions in membrane proteins, tangle →β-structure →-helix, increase ordering of these proteins and substantially raise the ∆G value. Results obtained in the study agree well with changes in microviscosity of erythrocyte membranes.


Mesomechanics and Thermodynamics of

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 285

reached their minima also at the same concentrations. Microviscosity in the region of protein-lipid interactions increased earlier, at lower concentrations of hormone, and was more pronounced than in the region of lipid-lipid interactions. Structural changes were

**Figure 13.** Changes in the relative microviscosity of membranes η(A)/η(0) of erythrocyte shadows at the concentration A of androsterone hormone. Concentration of shadows C = 0.133 mg protein/mL. Line 1 shows changes of the region of lipid-lipid interaction; line 2 – the region of protein-lipid interaction.

**Figure 14.** Changes in the relative microviscosity of membranes η(A)/η(0) of erythrocyte shadows at the concentration A of testosterone hormone. Concentration of shadows C = 0.117 mg protein/mL. 1 - the

The mechanism of changes in membrane microviscosity under the action of a more hydrophilic hormone DHEAS is quite different. Microviscosity goes to a constant value at a higher concentration of DHEAS in suspension as compared to that of DHEA (5·10–6 M versus 1.5·10–6 M for DHEA). First changes of microviscosity appeared in the region of lipid-

region of lipid-lipid interaction; 2 – the region of protein-lipid interaction.

initiated in proteins and involved lipids due to cooperativity.

**Table 2.** Parameters of steroid binding to erythrocyte membrane based on tryptophan fluorescence quenching of membrane proteins

## **5. Changes in microviscosity**

In erythrocyte membrane, a fluorescent pyrene probe is distributed in the lipid phase and can be a source of information on the state of its deeper layers. The rate of its migration and the ability to form excimers upon interaction with each other are estimated. This is the way to determine changes in microviscosity of the membranes.

In our study, an increase in microviscosity was most pronounced at the addition of androsterone to erythrocyte membranes. Microviscosity started to grow at a hormone concentration of 10–8 M, the growth proceeding up to 2.5·10–8 M with subsequent saturation (Fig. 13). The S-shaped curve points to high cooperativity in changing the conformational state of the membrane. A microviscosity increment attained 50% with respect to the initial state. In the region of protein-lipid interactions it appeared earlier and reached a higher value as compared to the region of lipid-lipid interactions. The absorption intensity (D) and emission intensity (F) of tryptophan in membrane proteins started to decrease at the same concentrations and attained a maximum also at the same concentrations (Fig. 9). Thus, our results revealed a cooperative nature of changes in erythrocyte membranes under the action of androsterone.

Addition of testosterone produced similar changes in membrane microviscosity. In the region of protein-lipid interactions, microviscosity increased at lower concentrations of hormone and attained higher values as compared to the region of lipid-lipid interactions (Fig. 14). In both cases, the revealed structural changes were initiated in proteins and carried over to lipids by virtue of cooperativity.

The effect of DHEA and especially DHEAS on erythrocyte membranes is much less pronounced as compared to testosterone (Figs. 15, 16). DHEA and DHEAS increased microviscosity by 10% with respect to initial values. In these experiments, the concentration of DHEAS reached 8·10–6 M. For DHEA, the growth started at a hormone concentration of 5·10–7 M and attained its maximum at 1.5·10–6 M (Fig. 15). Alteration of viscosity was described by S-curve and correlated with a decrease in fluorescence and absorption of tryptophan (Fig. 11). The latter processes started at the same hormone concentrations and reached their minima also at the same concentrations. Microviscosity in the region of protein-lipid interactions increased earlier, at lower concentrations of hormone, and was more pronounced than in the region of lipid-lipid interactions. Structural changes were initiated in proteins and involved lipids due to cooperativity.

284 Thermodynamics – Fundamentals and Its Application in Science

(М–1)

to determine changes in microviscosity of the membranes.

testosterone (2.24±0.22)x106 (1.09±0.11)x10–9 -37.6 androsterone (3.2±0.32)x106 (4.46±0.45)x10–10 -38.5 DHEA (5.99±0.60)x104 (1.80±0.18)x10–8 -28.3 DHEAS (1.56±0.16)x104 (4.03±0.40)x10–8 -24.8 **Table 2.** Parameters of steroid binding to erythrocyte membrane based on tryptophan fluorescence

In erythrocyte membrane, a fluorescent pyrene probe is distributed in the lipid phase and can be a source of information on the state of its deeper layers. The rate of its migration and the ability to form excimers upon interaction with each other are estimated. This is the way

In our study, an increase in microviscosity was most pronounced at the addition of androsterone to erythrocyte membranes. Microviscosity started to grow at a hormone concentration of 10–8 M, the growth proceeding up to 2.5·10–8 M with subsequent saturation (Fig. 13). The S-shaped curve points to high cooperativity in changing the conformational state of the membrane. A microviscosity increment attained 50% with respect to the initial state. In the region of protein-lipid interactions it appeared earlier and reached a higher value as compared to the region of lipid-lipid interactions. The absorption intensity (D) and emission intensity (F) of tryptophan in membrane proteins started to decrease at the same concentrations and attained a maximum also at the same concentrations (Fig. 9). Thus, our results revealed a cooperative nature of changes in erythrocyte membranes under the action

Addition of testosterone produced similar changes in membrane microviscosity. In the region of protein-lipid interactions, microviscosity increased at lower concentrations of hormone and attained higher values as compared to the region of lipid-lipid interactions (Fig. 14). In both cases, the revealed structural changes were initiated in proteins and carried

The effect of DHEA and especially DHEAS on erythrocyte membranes is much less pronounced as compared to testosterone (Figs. 15, 16). DHEA and DHEAS increased microviscosity by 10% with respect to initial values. In these experiments, the concentration of DHEAS reached 8·10–6 M. For DHEA, the growth started at a hormone concentration of 5·10–7 M and attained its maximum at 1.5·10–6 M (Fig. 15). Alteration of viscosity was described by S-curve and correlated with a decrease in fluorescence and absorption of tryptophan (Fig. 11). The latter processes started at the same hormone concentrations and

Amount of bound hormone Bmax (mol/mg protein)

Changes in free energy G (kJ/mol)

Steroid hormone Binding constant К<sup>b</sup>

quenching of membrane proteins

of androsterone.

over to lipids by virtue of cooperativity.

**5. Changes in microviscosity** 

**Figure 13.** Changes in the relative microviscosity of membranes η(A)/η(0) of erythrocyte shadows at the concentration A of androsterone hormone. Concentration of shadows C = 0.133 mg protein/mL. Line 1 shows changes of the region of lipid-lipid interaction; line 2 – the region of protein-lipid interaction.

**Figure 14.** Changes in the relative microviscosity of membranes η(A)/η(0) of erythrocyte shadows at the concentration A of testosterone hormone. Concentration of shadows C = 0.117 mg protein/mL. 1 - the region of lipid-lipid interaction; 2 – the region of protein-lipid interaction.

The mechanism of changes in membrane microviscosity under the action of a more hydrophilic hormone DHEAS is quite different. Microviscosity goes to a constant value at a higher concentration of DHEAS in suspension as compared to that of DHEA (5·10–6 M versus 1.5·10–6 M for DHEA). First changes of microviscosity appeared in the region of lipid-

lipid interactions (Fig. 16), which was followed by an increase of microviscosity in the region of protein-lipid interactions. DHEAS interacted with polar heads of phospholipids, then structural changes carried over to proteins due to cooperativity. Hydrophilic molecules of DHEAS cannot penetrate deep into hydrophobic layer of the membranes. There are only minor structural changes in the spectrin-actin-ankyrin meshwork and weak changes in membrane microviscosity.

Mesomechanics and Thermodynamics of

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 287

**6. Change of the membrane microviscosity, and Na+, K+-ATPase activity** 

were analyzed. For this purpose cortisol and adrenalin were used.

as that with adrenaline.

respectively.

respective concentrations of 3 · 10–8 and 5 · 10–8 M.

Erythrocyte suspensions from fresh blood of rats with hormones of differing concentration

Under the action of hormones, the microviscosity of erythrocyte membranes increases following a saturation curve (Fig. 17). This increase depends on the hormone type and differs greatly for protein-lipid and lipid-lipid interactions. As can be seen from Fig. 17, protein-lipid interaction makes a decisive contribution to the increase in membrane microviscosity under the action of hormones. It is due to this contribution that the system of compaction domains is formed in the membrane, resulting in an increase in erythrocyte rigidity. The effect depends strongly on the hormone type. Adrenaline, which penetrates the entire erythrocyte bulk, rapidly increases the erythrocyte microviscosity, and the latter comes to saturation even at small hormone concentrations of 17·10-9 M. Cortisol acts on an erythrocyte surface layer alone; hence, the microviscosity reaches saturation only at a cortisol concentration of 60· 10-9 M, and the increase in viscosity with cortisol is half as much

The most important result concerns the influence of hormones on the activity of the Na+, K+- АТPase (Fig. 18). For both hormones analyzed, increasing the hormone concentration causes the quantity first to increase, reach its maximum, and then to decrease. The maximum of activity corresponds to the hormone concentration at which the microviscosity reaches saturation. A good correlation is found between the stages of variation in activity and in

Adrenaline, which is responsible for the rapid increase in erythrocyte microviscosity, is responsible as well for the rapid increase in the Na+, K+-АТPase activity and for its subsequent fast decline following the maximum (Fig. 18a). Increasing the cortisol concentration (Fig. 18b) causes a slow increase in microviscosity and Na+, K+-АТPase activity (γ), and then a slow decrease in γ whose value does remain high at a very high hormone concentration. At a 20· 10-9 hormone concentration, the activity γ is 0.05 and 0.03 mol/h·mg protein for adrenaline and cortisol, respectively. At the stage of decline in γ at 60· 10-9 hormone concentration, γ ~ 0.02 and 0.035 mol/h·mg protein for adrenaline and cortisol,

The maximum activity γ in the series of adrenaline and cortisol is observed at their

Important information on the nature of structural changes produced in erythrocytes by the analyzed hormones was obtained with infrared spectroscopy [14]. The increase in the absorption band intensity of CO- (1655.2 cm–1) and NH-bonds (1548 and 3290 cm–1) by about 20 % with cortisol points to enhanced ordering of membrane proteins due to the tangle helix structural transition [15]. The shift 3308 3280 in stretching vibrations of the peptide NH-bond and the increase in its intensity owes to the formation of a hydrogen bond between cortisol and NH-bond of proteins. The increase in the absorption band intensity of

microviscosity with an increase in the concentration of different types of hormones.

**Figure 15.** Changes in the relative microviscosity of membranes η(A)/η(0) of erythrocyte shadows at the concentration A of hormone DHEA. Concentration of shadows C = 0.113 mg protein/mL. 1 - the region of lipid-lipid interaction; 2 – the region of protein-lipid interaction.

**Figure 16.** Changes in the relative microviscosity of membranes η(A)/η(0) of erythrocyte shadows at the concentration A of DHEAS hormone. Concentration of shadows C = 0.290 mg protein/mL. 1 - the region of lipid-lipid interaction; 2 – the region of protein-lipid interaction

## **6. Change of the membrane microviscosity, and Na+, K+-ATPase activity**

286 Thermodynamics – Fundamentals and Its Application in Science

membrane microviscosity.

lipid interactions (Fig. 16), which was followed by an increase of microviscosity in the region of protein-lipid interactions. DHEAS interacted with polar heads of phospholipids, then structural changes carried over to proteins due to cooperativity. Hydrophilic molecules of DHEAS cannot penetrate deep into hydrophobic layer of the membranes. There are only minor structural changes in the spectrin-actin-ankyrin meshwork and weak changes in

**Figure 15.** Changes in the relative microviscosity of membranes η(A)/η(0) of erythrocyte shadows at the concentration A of hormone DHEA. Concentration of shadows C = 0.113 mg protein/mL. 1 - the region

**Figure 16.** Changes in the relative microviscosity of membranes η(A)/η(0) of erythrocyte shadows at the concentration A of DHEAS hormone. Concentration of shadows C = 0.290 mg protein/mL. 1 - the region

of lipid-lipid interaction; 2 – the region of protein-lipid interaction.

of lipid-lipid interaction; 2 – the region of protein-lipid interaction

Erythrocyte suspensions from fresh blood of rats with hormones of differing concentration were analyzed. For this purpose cortisol and adrenalin were used.

Under the action of hormones, the microviscosity of erythrocyte membranes increases following a saturation curve (Fig. 17). This increase depends on the hormone type and differs greatly for protein-lipid and lipid-lipid interactions. As can be seen from Fig. 17, protein-lipid interaction makes a decisive contribution to the increase in membrane microviscosity under the action of hormones. It is due to this contribution that the system of compaction domains is formed in the membrane, resulting in an increase in erythrocyte rigidity. The effect depends strongly on the hormone type. Adrenaline, which penetrates the entire erythrocyte bulk, rapidly increases the erythrocyte microviscosity, and the latter comes to saturation even at small hormone concentrations of 17·10-9 M. Cortisol acts on an erythrocyte surface layer alone; hence, the microviscosity reaches saturation only at a cortisol concentration of 60· 10-9 M, and the increase in viscosity with cortisol is half as much as that with adrenaline.

The most important result concerns the influence of hormones on the activity of the Na+, K+- АТPase (Fig. 18). For both hormones analyzed, increasing the hormone concentration causes the quantity first to increase, reach its maximum, and then to decrease. The maximum of activity corresponds to the hormone concentration at which the microviscosity reaches saturation. A good correlation is found between the stages of variation in activity and in microviscosity with an increase in the concentration of different types of hormones.

Adrenaline, which is responsible for the rapid increase in erythrocyte microviscosity, is responsible as well for the rapid increase in the Na+, K+-АТPase activity and for its subsequent fast decline following the maximum (Fig. 18a). Increasing the cortisol concentration (Fig. 18b) causes a slow increase in microviscosity and Na+, K+-АТPase activity (γ), and then a slow decrease in γ whose value does remain high at a very high hormone concentration. At a 20· 10-9 hormone concentration, the activity γ is 0.05 and 0.03 mol/h·mg protein for adrenaline and cortisol, respectively. At the stage of decline in γ at 60· 10-9 hormone concentration, γ ~ 0.02 and 0.035 mol/h·mg protein for adrenaline and cortisol, respectively.

The maximum activity γ in the series of adrenaline and cortisol is observed at their respective concentrations of 3 · 10–8 and 5 · 10–8 M.

Important information on the nature of structural changes produced in erythrocytes by the analyzed hormones was obtained with infrared spectroscopy [14]. The increase in the absorption band intensity of CO- (1655.2 cm–1) and NH-bonds (1548 and 3290 cm–1) by about 20 % with cortisol points to enhanced ordering of membrane proteins due to the tangle helix structural transition [15]. The shift 3308 3280 in stretching vibrations of the peptide NH-bond and the increase in its intensity owes to the formation of a hydrogen bond between cortisol and NH-bond of proteins. The increase in the absorption band intensity of the С=О-bond of phospholipids and its shift 1748 1740 points to enhancement of ordering of higher carboxylic acids and to a decrease in phospholipid entropy.

Mesomechanics and Thermodynamics of

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 289

**Figure 18.** Changes in the activity of Na+, K+-ATPase of erythrocyte membranes as a function of a

hormone concentration in suspension: a – adrenaline; b – cortisol.

**Figure 17.** Changes in the relative microviscosity of membranes (L) of erythrocyte shadows at the concentration A for adrenaline (a) and cortisol (b) hormones added to the shadows suspension. Concentration of shadows C = 0.128 mg protein/ml. Concentration of pyrene in the suspension is 7.7·10-6 M, temperature of the specimens 309.1±0.1 K (36C), pH of the suspension 7.35. The measured value of L(A) exhibit an error of 6%. 1 - the region of lipid-lipid interaction; 2 – the region of protein-lipid interaction

of higher carboxylic acids and to a decrease in phospholipid entropy.

the С=О-bond of phospholipids and its shift 1748 1740 points to enhancement of ordering

**Figure 17.** Changes in the relative microviscosity of membranes (L) of erythrocyte shadows at the concentration A for adrenaline (a) and cortisol (b) hormones added to the shadows suspension. Concentration of shadows C = 0.128 mg protein/ml. Concentration of pyrene in the suspension is 7.7·10-6 M, temperature of the specimens 309.1±0.1 K (36C), pH of the suspension 7.35. The measured value of L(A) exhibit an error of 6%. 1 - the region of lipid-lipid interaction; 2 – the region of protein-lipid

interaction

**Figure 18.** Changes in the activity of Na+, K+-ATPase of erythrocyte membranes as a function of a hormone concentration in suspension: a – adrenaline; b – cortisol.

The concurrent hormone interaction with protein and phospholipids enhances the proteinlipid interactions resulting in a complex domain structure in erythrocytes. The frequency shift of the Р=О-bond toward the short-wave range and the increase in its intensity is associated with dehydration of membranes due to its hormone-induced compressive deformation. It is the loss of bound water that increases the frequency of the P = O-bond [16]. The displacement of water dipoles from protein-lipid domains to adjacent regions leads to the development of mesobands of localized deformation and discontinuities in them.

Mesomechanics and Thermodynamics of

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 291

**Figure 19.** Changes in the optical density of absorption band 418 nm at the addition of cortisol to

An increase in the optical density in the regions of 600-700 and 310 nm, which points to increasing diffusion of light has been also observed. In these regions, optical density changed by ~5.5%, which considerably exceeds the measurement error (0.5%) (Fig. 19). It should be noted that absorption band at 418 nm may shift spontaneously by ± 2-3 nm in different runs, generally to the short-wave region. Shifting of this band occurs either due to fluctuations in the structure of hemoglobin itself [18] or by the action of fluctuations in the

The analysis of IR spectra of rat erythrocyte ghosts not loaded with hormone (control, Fig. 7) revealed not only a disordered structure, but also the presence of -helix 1650-1656 cm–1 and βstructure (1686 and 1520 cm–1) in the proteins of rat erythrocyte ghosts [1]. NН stretching vibrations of proteins (3308 cm–1), CH stretching vibrations of hydrocarbon chains in proteins and phospholipids (2948, 2930 and 2848 cm–1) as well as some bands typical of phospholipids, in particular, C=O bond (1748 cm–1), Р=О bond (1236 cm–1), СН2 deformation vibrations (1460 and 1386 cm–1) of hydrocarbon chains, О4-С4-С5-О5 bond (1048 cm–1) of monosaccharides in glycolipids and glycoproteins, and С-С deformation vibrations (978 cm–1) have been recorded. Note that the С=О band (1736 cm–1) is quite narrow; hence it follows that phospholipids are

Analysis of the IR spectra of rat erythrocyte ghosts upon incubation with cortisol at its concentration of 4.4 . 10–8 M revealed a ca. 20% increase in intensity of the absorption bands

well ordered at the level of ester bonds in higher carboxylic acids and glycerol.

human erythrocyte suspensions (C = 10-8 – 6 · 10-8 M).

structure of membrane and cell as a whole [19, 20].

The obtained experimental results suggest that an important role in the action of hormones on erythrocytes belongs to two factors:


The first factor causes an increase in energy quanta hν (phonone) required for structural transitions in mass transfer through erythrocyte membranes. This factor increases the activity of the Na+, K+-АТPase at the first stage of growth of hormone concentrations.

The second factor retards microscale structural transitions. Once the microviscosity ceases to increase (the formation of the domain structure is completed), the contribution of the first factor no longer grows, the contribution of the second factor continues to escalate, and the activity of the Na+, K+-АТPase decreases.

## **7. Effect of cortisol**

Here we try to go beyond the influence of cortisol on the red cell membrane, and consider the action of the hormone on erythrocyte as a multi-layered liquid crystal system.

The mechanism of erythrocyte deformation and structural transformation of membranes and hemoglobin by the action of cortisol is still scantily investigated. The interaction of hemoglobin with contraction proteins and band 3 protein of erythrocytes is reported by Discher, D.E., Mohandas, N. & Evans, E.A [17]. These works imply that the disturbance and deformation of erythrocyte membrane caused by cortisol or other external factors can be transferred to hemoglobin by means of band 3 integral protein or contraction proteins. According to modern ideas, contraction proteins reside as at the inner as outside of membrane. Within this concept, a reverse response is also possible, i.e., the disturbance can be transferred from hemoglobin to the cell membrane.

The addition of cortisol to erythrocyte suspension with the hormone concentration of 10–8 to 610–8 M produced a set of UV spectral curves. A maximum of absorption band at 418 nm was shown to decrease with increasing the hormone concentration. A decrease in the optical density was 22% as compared to erythrocyte suspension without hormone (control) (Fig. 19). The resulting set of curves was used to plot the dependences of optical density for band 418 nm on the concentration of hormones.

on erythrocytes belongs to two factors:

activity of the Na+, K+-АТPase decreases.

be transferred from hemoglobin to the cell membrane.

band 418 nm on the concentration of hormones.

(macroscale);

(microscale).

**7. Effect of cortisol** 

The concurrent hormone interaction with protein and phospholipids enhances the proteinlipid interactions resulting in a complex domain structure in erythrocytes. The frequency shift of the Р=О-bond toward the short-wave range and the increase in its intensity is associated with dehydration of membranes due to its hormone-induced compressive deformation. It is the loss of bound water that increases the frequency of the P = O-bond [16]. The displacement of water dipoles from protein-lipid domains to adjacent regions leads to the development of mesobands of localized deformation and discontinuities in them.

The obtained experimental results suggest that an important role in the action of hormones



The first factor causes an increase in energy quanta hν (phonone) required for structural transitions in mass transfer through erythrocyte membranes. This factor increases the

The second factor retards microscale structural transitions. Once the microviscosity ceases to increase (the formation of the domain structure is completed), the contribution of the first factor no longer grows, the contribution of the second factor continues to escalate, and the

Here we try to go beyond the influence of cortisol on the red cell membrane, and consider

The mechanism of erythrocyte deformation and structural transformation of membranes and hemoglobin by the action of cortisol is still scantily investigated. The interaction of hemoglobin with contraction proteins and band 3 protein of erythrocytes is reported by Discher, D.E., Mohandas, N. & Evans, E.A [17]. These works imply that the disturbance and deformation of erythrocyte membrane caused by cortisol or other external factors can be transferred to hemoglobin by means of band 3 integral protein or contraction proteins. According to modern ideas, contraction proteins reside as at the inner as outside of membrane. Within this concept, a reverse response is also possible, i.e., the disturbance can

The addition of cortisol to erythrocyte suspension with the hormone concentration of 10–8 to 610–8 M produced a set of UV spectral curves. A maximum of absorption band at 418 nm was shown to decrease with increasing the hormone concentration. A decrease in the optical density was 22% as compared to erythrocyte suspension without hormone (control) (Fig. 19). The resulting set of curves was used to plot the dependences of optical density for

the action of the hormone on erythrocyte as a multi-layered liquid crystal system.

activity of the Na+, K+-АТPase at the first stage of growth of hormone concentrations.

**Figure 19.** Changes in the optical density of absorption band 418 nm at the addition of cortisol to human erythrocyte suspensions (C = 10-8 – 6 · 10-8 M).

An increase in the optical density in the regions of 600-700 and 310 nm, which points to increasing diffusion of light has been also observed. In these regions, optical density changed by ~5.5%, which considerably exceeds the measurement error (0.5%) (Fig. 19). It should be noted that absorption band at 418 nm may shift spontaneously by ± 2-3 nm in different runs, generally to the short-wave region. Shifting of this band occurs either due to fluctuations in the structure of hemoglobin itself [18] or by the action of fluctuations in the structure of membrane and cell as a whole [19, 20].

The analysis of IR spectra of rat erythrocyte ghosts not loaded with hormone (control, Fig. 7) revealed not only a disordered structure, but also the presence of -helix 1650-1656 cm–1 and βstructure (1686 and 1520 cm–1) in the proteins of rat erythrocyte ghosts [1]. NН stretching vibrations of proteins (3308 cm–1), CH stretching vibrations of hydrocarbon chains in proteins and phospholipids (2948, 2930 and 2848 cm–1) as well as some bands typical of phospholipids, in particular, C=O bond (1748 cm–1), Р=О bond (1236 cm–1), СН2 deformation vibrations (1460 and 1386 cm–1) of hydrocarbon chains, О4-С4-С5-О5 bond (1048 cm–1) of monosaccharides in glycolipids and glycoproteins, and С-С deformation vibrations (978 cm–1) have been recorded. Note that the С=О band (1736 cm–1) is quite narrow; hence it follows that phospholipids are well ordered at the level of ester bonds in higher carboxylic acids and glycerol.

Analysis of the IR spectra of rat erythrocyte ghosts upon incubation with cortisol at its concentration of 4.4 . 10–8 M revealed a ca. 20% increase in intensity of the absorption bands

of CO (1655.2 cm–1) and NH bonds (1548 and 3290 cm–1), the effect building up with an increase in the hormone concentration (Table 3, Fig. 20). A growing intensity of the band 1655.2 cm–1 testifies an increase in the fraction of -helix [8]. The increasing fraction of helices in membrane proteins is related with the structural transition tangle -helix.

Mesomechanics and Thermodynamics of

2930 2848

2848,9

2925 2852

2935,8 2871,7 3030,2

2937,5 2872,3 3028,4 3052,4

1060,2 2956,6

1,2150E + 01

1,5169E + 01

1,5640E + 01

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 293

structure of membrane proteins (tangle β-structure transition) involving also the contraction proteins. Shifting of some other absorption bands attributed both to proteins

Noteworthy are the shift of absorption band 2870 cm–1 corresponding to stretching vibrations of CH bond in hemoglobin [23], and a more pronounced splitting in the region of stretching and deformation vibrations of phospholipid CH orderliness in and between the domains. A stronger splitting of CH bonds testifies the formation of new lipid-protein clusters as a result of intermolecular interaction, due to compaction of membrane elements caused by structural transformation of the contraction proteins network. In our earlier studies of high density lipoproteins (HDL), when calculating the enthalpy of structural transitions from experimental data, the occurrence of smectic A smectic C transition in HDL phospholipids [8] has been suggested. Such a transitions may occur here, since it has a

Of interest is the appearance of the absorption band 2851.8 cm–1, which is assigned to stretching vibrations of CH bond in phospholipids [8]. This band results from structural

CO NH **val.** C=O P=O P-O-C 05C4-C504 CH val. ACO

3308 1748 1236 1080 1056 2948

1236 1080 1051,2 2924,2

1740 1239 1083,7 - 2962

1245,7 1106,2 2956,8

1100,0 1089,5

and phospholipids was observed too (Fig. 21).

low enthalpy [8, 24].

No. The object of measurement

 Ghosts (control)

2 Ghosts + cortisol (C= 4,4·10-8 M)

3 Ghosts + cortisol (C= 10-7 M)

4 Erythrocytes (control)

5 Erythrocytes + cortisol (C= 10-8 M)

their interaction with hormones

transition in membrane phospholipids.

1655,4 1686

1656,0 1630

1642,7 1627,5

1655,2 3290,4

1649,9 3282,1

3308.0

3272,0

3285,3 3270,2 3247,3

3280 3300 1743 -

1741,1 1707,5

Note. ACO is the integral intensity of absorption band νCO of the peptide bond in semilogarithmic form.

**Table 3.** Frequency characteristics of human erythrocytes and rat erythrocyte ghosts before and after

1239,4 1201,3

A shift of NН bond (stretching vibrations of peptide bond, 3308 → 3280 cm–1, ∆ν = 28 cm–1) was accompanied by a growth of its intensity, which is related with the formation of hydrogen bond between cortisol and NН group. Hydrogen bond is likely to form between keto group of A-ring (C3=О) and NН group of the membrane protein. Meanwhile, keto group (C20=О) of D-ring and OH group at С11 in C-ring could also be involved in the formation of hydrogen bonds. The presence of several hydrophilic groups strongly changes the biological activity of cortisol and other steroid hormones, in distinction to cholesterol. Cholesterol binds to phospholipids mainly due to hydrophobic interaction (Van der Waals forces) with fatty acid residues [19]. Shifting of CH bond stretching vibrations 2848 2852 cm-1 (∆ν = 4 cm-1) and 2930 2925 cm-1 (∆ν = 5 cm-1) were observed. The latter increased in intensity under the action of hormone. Changes in intensity of this band confirm the presence of structural transition, but cannot differentiate the place where the transition occurs — in membrane proteins or in phospholipids, as CH bond is present both in proteins and phospholipids. However, as seen from our experimental data, this band reflects mainly the changes in phospholipid orderliness.

An increase in intensity of the absorption band of phospholipid C=O bond and its shift 1748 1740 cm–1 were observed. This increase of the band intensity indicates a growing orderliness of higher carboxylic acids and a decreasing entropy in phospholipids. Shift of the band is related with the formation of hydrogen bond between hormone, for example OH group at C21, and CO bond of phospholipids. Such interaction of the hormone simultaneously with protein and phospholipids can occur at the interface between protein and phospholipids, i.e., in a near-boundary or annular layer of the band 3 integral protein, glycophorin and other proteins.

P=O bond shifted in frequency by 3 cm–1 to the short-wave region and increased in intensity. Shifting of P=O bond to the short-wave region is attributed to dehydration of membranes during their deformation under the action of hormone. A loss of bound water increases the frequency of P=O bond [1]. Deformation (contraction) occurs due to spectrin-actin and spectrin-ankyrin networks [19], since the extraction of spectrin from membrane relieves the deformation caused by hormones. It should be noted that 30% of membrane proteins is represented by spectrin. Overall, contraction proteins constitute 55-60% of all membrane proteins [21]. Steroids can attack either the spectrin-actin-ankyrin network located both on internal and external surfaces of the membrane or the integral proteins associated with contraction proteins [22].

Our FTIR spectroscopy study of the hormone effect on intact erythrocytes revealed considerable changes of the spectra in absorption regions both of proteins and phospholipids. In particular, cortisol gave rise to absorption band 1636 cm–1 corresponding to β-structure of membrane proteins, which indicates a transformation in the secondary structure of membrane proteins (tangle β-structure transition) involving also the contraction proteins. Shifting of some other absorption bands attributed both to proteins and phospholipids was observed too (Fig. 21).

292 Thermodynamics – Fundamentals and Its Application in Science

reflects mainly the changes in phospholipid orderliness.

glycophorin and other proteins.

contraction proteins [22].

of CO (1655.2 cm–1) and NH bonds (1548 and 3290 cm–1), the effect building up with an increase in the hormone concentration (Table 3, Fig. 20). A growing intensity of the band 1655.2 cm–1 testifies an increase in the fraction of -helix [8]. The increasing fraction of helices in membrane proteins is related with the structural transition tangle -helix.

A shift of NН bond (stretching vibrations of peptide bond, 3308 → 3280 cm–1, ∆ν = 28 cm–1) was accompanied by a growth of its intensity, which is related with the formation of hydrogen bond between cortisol and NН group. Hydrogen bond is likely to form between keto group of A-ring (C3=О) and NН group of the membrane protein. Meanwhile, keto group (C20=О) of D-ring and OH group at С11 in C-ring could also be involved in the formation of hydrogen bonds. The presence of several hydrophilic groups strongly changes the biological activity of cortisol and other steroid hormones, in distinction to cholesterol. Cholesterol binds to phospholipids mainly due to hydrophobic interaction (Van der Waals forces) with fatty acid residues [19]. Shifting of CH bond stretching vibrations 2848 2852 cm-1 (∆ν = 4 cm-1) and 2930 2925 cm-1 (∆ν = 5 cm-1) were observed. The latter increased in intensity under the action of hormone. Changes in intensity of this band confirm the presence of structural transition, but cannot differentiate the place where the transition occurs — in membrane proteins or in phospholipids, as CH bond is present both in proteins and phospholipids. However, as seen from our experimental data, this band

An increase in intensity of the absorption band of phospholipid C=O bond and its shift 1748 1740 cm–1 were observed. This increase of the band intensity indicates a growing orderliness of higher carboxylic acids and a decreasing entropy in phospholipids. Shift of the band is related with the formation of hydrogen bond between hormone, for example OH group at C21, and CO bond of phospholipids. Such interaction of the hormone simultaneously with protein and phospholipids can occur at the interface between protein and phospholipids, i.e., in a near-boundary or annular layer of the band 3 integral protein,

P=O bond shifted in frequency by 3 cm–1 to the short-wave region and increased in intensity. Shifting of P=O bond to the short-wave region is attributed to dehydration of membranes during their deformation under the action of hormone. A loss of bound water increases the frequency of P=O bond [1]. Deformation (contraction) occurs due to spectrin-actin and spectrin-ankyrin networks [19], since the extraction of spectrin from membrane relieves the deformation caused by hormones. It should be noted that 30% of membrane proteins is represented by spectrin. Overall, contraction proteins constitute 55-60% of all membrane proteins [21]. Steroids can attack either the spectrin-actin-ankyrin network located both on internal and external surfaces of the membrane or the integral proteins associated with

Our FTIR spectroscopy study of the hormone effect on intact erythrocytes revealed considerable changes of the spectra in absorption regions both of proteins and phospholipids. In particular, cortisol gave rise to absorption band 1636 cm–1 corresponding to β-structure of membrane proteins, which indicates a transformation in the secondary Noteworthy are the shift of absorption band 2870 cm–1 corresponding to stretching vibrations of CH bond in hemoglobin [23], and a more pronounced splitting in the region of stretching and deformation vibrations of phospholipid CH orderliness in and between the domains. A stronger splitting of CH bonds testifies the formation of new lipid-protein clusters as a result of intermolecular interaction, due to compaction of membrane elements caused by structural transformation of the contraction proteins network. In our earlier studies of high density lipoproteins (HDL), when calculating the enthalpy of structural transitions from experimental data, the occurrence of smectic A smectic C transition in HDL phospholipids [8] has been suggested. Such a transitions may occur here, since it has a low enthalpy [8, 24].

Of interest is the appearance of the absorption band 2851.8 cm–1, which is assigned to stretching vibrations of CH bond in phospholipids [8]. This band results from structural transition in membrane phospholipids.


Note. ACO is the integral intensity of absorption band νCO of the peptide bond in semilogarithmic form.

**Table 3.** Frequency characteristics of human erythrocytes and rat erythrocyte ghosts before and after their interaction with hormones

Mesomechanics and Thermodynamics of

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 295

**Figure 21.** FTIR spectra of human erythrocytes at th addition of cortisol (C = 3 · 10-8 M): a. - ν = 1000 –

Splitting in the region of 1088 (РОС bond) and 3282 cm–1 (NH bond) was observed. Splitting of these bands indicates an increasing orderliness in phospholipids and membrane proteins,

1800 cm-1, b. - ν = 2600 – 3400 cm-1.

**Figure 20.** IR spectraof rat erythrocyte ghosts at the addition of cortisol (C = 4.4· 10-8 M): a. - ν = 1000 – 1800 cm-1, b. - ν = 2600 – 3400 cm-1.

Mesomechanics and Thermodynamics of Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 295

294 Thermodynamics – Fundamentals and Its Application in Science

**Figure 20.** IR spectraof rat erythrocyte ghosts at the addition of cortisol (C = 4.4· 10-8 M): a. - ν = 1000 –

1800 cm-1, b. - ν = 2600 – 3400 cm-1.

**Figure 21.** FTIR spectra of human erythrocytes at th addition of cortisol (C = 3 · 10-8 M): a. - ν = 1000 – 1800 cm-1, b. - ν = 2600 – 3400 cm-1.

Splitting in the region of 1088 (РОС bond) and 3282 cm–1 (NH bond) was observed. Splitting of these bands indicates an increasing orderliness in phospholipids and membrane proteins, respectively. An increase in the fraction of β-structure points to the tangle β-structure transitions; however, in this case more pronounced is the -helix β-structure transition, due to redistribution of intensity between absorption bands at 1650 and 1638 cm–1. The first band corresponds to -helices, the second one to β-structure [19].

Mesomechanics and Thermodynamics of

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 297



lg (1/D) = (*pi ∙* log *pi*)/*k*, and (14)

( log ) / 1 / 10 , then *p pk <sup>D</sup> i i* (15)

(17)

( log ) / ( log ) / <sup>10</sup> or 1 / 10 *p pk p pk <sup>D</sup> i i i i* (16)

However, of prime importance for us is that increasing negentropy is always supported by increasing amount of structural information. This can be expressed by the following

where *pi* is the probability of individual events in the system. Thus, the informational component in this equation determines an increase of negentropy in the system and is

Developing the concept about a correspondence between negentropy and structural

If in the Helmholtz equation for free energy entropy is replaced by *D*, this gives the

log / <sup>10</sup> *<sup>T</sup> F U p pk i i*

Thus, *F* can be considered as a function of the amount of structural information in a system. This equation is essential for understanding the self-organization processes in living systems, so as the cell. An increase in the amount of structural information determines the transition from liquid crystal to crystal. This may incapacitate a cell from its functioning. It has been already shown that the interaction of steroid hormones increases microviscosity of erythrocyte membranes in the regions of lipid-lipid and protein-lipid interactions. At low concentrations of hormones in the incubation medium, the activity of erythrocyte Na+,K+- АТPase even increases, probably due to growing elasticity of the lipid microenvironment of the enzyme, which facilitates structural transitions in the enzyme itself. At high concentrations of hormones (the saturation phase), an increase in microviscosity in the region of lipid-protein interactions makes impossible structural transitions in the enzyme; so, its activity rapidly drops. This determines a dome shape of the enzyme activity curve. Since erythrocyte is a liquid crystal cooperative system, changes occur not only in the activity of Na+,K+-АТPase of erythrocyte membranes, but also in the state of cell

equation:

Hence,

following expression:

related with acquisition of new properties.

information, we can present the following equality:

hemoglobin, its ordering and ability to bind oxygen.

Using the fourth derivative of the absorption band 1600-1700 cm-1 the maintenance of elements of the secondary structure in the erythrocyte membranes has been calculated. The results are given in Table 4. This table shows the considerable increase of β-structure under the action of adrenaline. In this case we observe the structural transition tangle β-structure. However, the increase of -helices and decrease of tangle under the action of cortisol has been seen. So it can be concluded the structural transition tangle -helix took place.

A comparison of IR spectra obtained from ghosts and intact erythrocytes revealed some general regularities: 1) splitting of absorption bands of NH peptide bonds, 2) an increased intensity of absorption bands corresponding to β-structure, 3) splitting of absorption bands corresponding to CH bonds of phospholipids, 4) a frequency shift of some bands (Table 4). However, there is also a distinction related with the appearance of absorption bands at 2870 and 1108 cm–1 corresponding to hemoglobin [23]. These bands are shifting when erythrocytes are subjected to the action of hormones.


**Table 4.** The quantitative definition of the elements of secondary structure in membrane proteins

Thus, these results suggest that the erythrocyte react to the effect of steroid hormones as a complex liquid-crystalline co-operative system in which nanostructured transitions are irreversible and are closely associated with the functional activity of cells.

## **8. Thermodynamics of nanostructural transitions in erythrocyte as a liquid crystal system, a relation with the cell function**

The application of IR and UV spectroscopy showed that the interaction of steroid hormones with erythrocytes increases the ordering of both the membranes and hemoglobin, which means an increase in negentropy.

E. Schrodinger defined it as

$$-S = k \lg \text{ (1/D)},\tag{11}$$

where –*S* is the negative entropy, or negentropy; *k* is the Boltzmann's constant equal to 3.2983 · 10–24 cal/deg; *D* is the quantitative measure of disorderliness of atoms in the system, lg (1/*D*) is the negative logarithm of *D*, and 1/*D* is the measure of orderliness.

However, of prime importance for us is that increasing negentropy is always supported by increasing amount of structural information. This can be expressed by the following equation:

$$\mathbf{S} \cdot \mathbf{S} = \mathbf{k} \lg(\mathbf{1}/\mathbf{D}) + \sum \mathbf{p} \cdot \log \mathbf{p} \,\tag{12}$$

where *pi* is the probability of individual events in the system. Thus, the informational component in this equation determines an increase of negentropy in the system and is related with acquisition of new properties.

Developing the concept about a correspondence between negentropy and structural information, we can present the following equality:

$$\mathbf{i} \cdot \mathbf{S} = k \lg(\mathbf{1}/\mathbf{D}) = \sum p\_i \cdot \log p\_i \tag{13}$$

Hence,

296 Thermodynamics – Fundamentals and Its Application in Science

band corresponds to -helices, the second one to β-structure [19].

be concluded the structural transition tangle -helix took place.

erythrocytes are subjected to the action of hormones.

Conformation Erythrocyte

respectively. An increase in the fraction of β-structure points to the tangle β-structure transitions; however, in this case more pronounced is the -helix β-structure transition, due to redistribution of intensity between absorption bands at 1650 and 1638 cm–1. The first

Using the fourth derivative of the absorption band 1600-1700 cm-1 the maintenance of elements of the secondary structure in the erythrocyte membranes has been calculated. The results are given in Table 4. This table shows the considerable increase of β-structure under the action of adrenaline. In this case we observe the structural transition tangle β-structure. However, the increase of -helices and decrease of tangle under the action of cortisol has been seen. So it can

A comparison of IR spectra obtained from ghosts and intact erythrocytes revealed some general regularities: 1) splitting of absorption bands of NH peptide bonds, 2) an increased intensity of absorption bands corresponding to β-structure, 3) splitting of absorption bands corresponding to CH bonds of phospholipids, 4) a frequency shift of some bands (Table 4). However, there is also a distinction related with the appearance of absorption bands at 2870 and 1108 cm–1 corresponding to hemoglobin [23]. These bands are shifting when

(control)


Thus, these results suggest that the erythrocyte react to the effect of steroid hormones as a complex liquid-crystalline co-operative system in which nanostructured transitions are

The application of IR and UV spectroscopy showed that the interaction of steroid hormones with erythrocytes increases the ordering of both the membranes and hemoglobin, which

–*S* = *k* lg (1/*D*), (11)

where –*S* is the negative entropy, or negentropy; *k* is the Boltzmann's constant equal to 3.2983 · 10–24 cal/deg; *D* is the quantitative measure of disorderliness of atoms in the system,

lg (1/*D*) is the negative logarithm of *D*, and 1/*D* is the measure of orderliness.

**8. Thermodynamics of nanostructural transitions in erythrocyte as a** 

irreversible and are closely associated with the functional activity of cells.

**liquid crystal system, a relation with the cell function** 

means an increase in negentropy.

E. Schrodinger defined it as

Erythrocyte + cortisol Ccortis = 3· 10-8 M

$$\log\left(1/\mathcal{D}\right) = \left(\sum p\_{l} \cdot \log p\right) / k\_{l} \text{ and} \tag{14}$$

$$1/D = 10^{\left(\sum p\_{\dot{j}} \log p\_{\dot{j}}\right)/k} \; , \; \text{then} \tag{15}$$

$$D = 10^{-\left(\sum p\_{\dot{I}} \log p\_{\dot{I}}\right)/k} \quad \text{or} \ 1/10^{\left(\sum p\_{\dot{I}} \log p\_{\dot{I}}\right)/k} \tag{16}$$

If in the Helmholtz equation for free energy entropy is replaced by *D*, this gives the following expression:

$$F = \mathcal{U} - \frac{T}{10^{\sum p\_j \log p\_j / k}}\tag{17}$$

Thus, *F* can be considered as a function of the amount of structural information in a system. This equation is essential for understanding the self-organization processes in living systems, so as the cell. An increase in the amount of structural information determines the transition from liquid crystal to crystal. This may incapacitate a cell from its functioning. It has been already shown that the interaction of steroid hormones increases microviscosity of erythrocyte membranes in the regions of lipid-lipid and protein-lipid interactions. At low concentrations of hormones in the incubation medium, the activity of erythrocyte Na+,K+- АТPase even increases, probably due to growing elasticity of the lipid microenvironment of the enzyme, which facilitates structural transitions in the enzyme itself. At high concentrations of hormones (the saturation phase), an increase in microviscosity in the region of lipid-protein interactions makes impossible structural transitions in the enzyme; so, its activity rapidly drops. This determines a dome shape of the enzyme activity curve. Since erythrocyte is a liquid crystal cooperative system, changes occur not only in the activity of Na+,K+-АТPase of erythrocyte membranes, but also in the state of cell hemoglobin, its ordering and ability to bind oxygen.

It seems interesting to compare changes in liquid crystals with those occurring in solid crystals in the fields of external action.

Destruction of solid and liquid crystals increases the molar volume [24, 25].

A dependence of the Gibbs thermodynamic potential F() on the molar volume taking into account local zones of different scale stress concentrators is described by the equation:

$$\mathbf{F(v) = U - TS + p} \mathbf{v - \Sigma \mu \mathbf{C} \Delta} \tag{18}$$

Mesomechanics and Thermodynamics of

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 299

These quantitative interrelations underlie transition of the system to a new structural level

**Figure 22.** The dependence of the Gibbs thermodynamic potential F (v) from the molar volume v in the

In biological membranes as liquid crystals, destruction is related with structural transitions and is generally accompanied by increasing structural orderliness (the order order transition). Earlier [1], it was shown that the action of steroid hormones on erythrocyte membranes disturbs the mechanisms of self-organization that operate in the cells in normal functional condition. The active CO, NH and OH groups of stress hormones interact with CO and NH groups both of proteins and phospholipids in biological membranes. This leads to the formation of complex protein-lipid clusters, where "compressive" hydrophobic interactions are reinforced. Molecularly bound water is displaced to adjacent regions. Here, hydrostatic forces increase the "tensile" tangential stresses. Mobile nanostructural boundaries are formed, along which the biological membranes are destructed. This results in the formation of numerous pores and mesostrips of plastic deformation. In terms of physical mesomechanics, these transformations resemble those developing in solid crystals in the fields of external action (Fig. 23). However, in biological membranes such selforganization may be related even with increasing order and decreasing entropy, but this is incompatible with conditions that determine cell viability. Structural transitions cover the membrane-bound enzymes, transmembrane carriers and hormone receptors. It is reasonable to say that cell membranes go to a new level of homeostasis (self-organization) which is incompatible with life. The nature of life implies dynamics. The cell dies. Here, one can tell about thermodynamic features related with changes in the structure and function (properties) of solid crystals and biological membranes in the fields of external action.

light of local zones of stress concentrators of different scales [26].

of homeostasis.

where i – chemical potential, Ci – concentration (Fig. 22, [26]) .

At critical values of molar volume i = (1,2…6), the thermodynamic potential F() has local minima. They reflect local nonequilibrium potentials in the zones of different scale hydrostatic tension. Critical values of *υ<sup>i</sup>* correspond to different levels of homeostasis in a deformable solid:

0 is an equilibrium crystal; the initial level of homeostasis;

1 are the zones of stress microconcentrators where dislocation cores are generated; the next level of homeostasis;

2, 3 are the zones of stress meso- and macroconcentrators where local structural-phase transitions with the formation of meso- and macrostripes of local plastic deformation take place; the next levels of homeostasis;

4 corresponds to intersection of curve F() with the abscissa. At a further increase of the local molar volume, changes of the Gibbs thermodynamic potential proceed under the conditions of F() 0, and the system becomes unstable. Various forms of material failure appear; solid crystal starts to behave as a liquid one.

 6 – the existence of two phases is possible: at = 5 – the vacancy phase atom, at 6 – different thermodynamic levels of the crystal lattice in a deformable solid, different levels of its homeostasis.

Thus, plastic deformation of solid and liquid heterocrystals in the fields of external action is a multilevel process of their destruction, with the corresponding levels of crystal lattice selforganization and levels of its homeostasis, i.e., the destruction via different phases of strengthening (self-organization). On solid crystals this decreases the orderliness and amount of structural information. In liquid crystals this increases the orderliness and amount of structural information i.e. liquid crystal → crystal transition.

Dependence of Gibbs thermodynamic potential on the molar volume and changes in the structural information (I), taking into account local zones of stress concentrators is determined by the expression:

$$F(\nu, I) = \mathcal{U} - T / 10^{\left(\sum p\_{\dot{j}} \log p\_{\dot{j}}\right) / k} + p\nu - \Sigma \mu\_{\dot{j}} \mathcal{C}\_{\dot{j}} \tag{19}$$

These quantitative interrelations underlie transition of the system to a new structural level of homeostasis.

298 Thermodynamics – Fundamentals and Its Application in Science

crystals in the fields of external action.

deformable solid:

level of homeostasis;

its homeostasis.

determined by the expression:

place; the next levels of homeostasis;

It seems interesting to compare changes in liquid crystals with those occurring in solid

A dependence of the Gibbs thermodynamic potential F() on the molar volume taking into account local zones of different scale stress concentrators is described by the equation:

F() = U – TS + p - iCi, (18)

At critical values of molar volume i = (1,2…6), the thermodynamic potential F() has local minima. They reflect local nonequilibrium potentials in the zones of different scale hydrostatic tension. Critical values of *υ<sup>i</sup>* correspond to different levels of homeostasis in a

1 are the zones of stress microconcentrators where dislocation cores are generated; the next

2, 3 are the zones of stress meso- and macroconcentrators where local structural-phase transitions with the formation of meso- and macrostripes of local plastic deformation take

4 corresponds to intersection of curve F() with the abscissa. At a further increase of the local molar volume, changes of the Gibbs thermodynamic potential proceed under the conditions of F() 0, and the system becomes unstable. Various forms of material failure

 6 – the existence of two phases is possible: at = 5 – the vacancy phase atom, at 6 – different thermodynamic levels of the crystal lattice in a deformable solid, different levels of

Thus, plastic deformation of solid and liquid heterocrystals in the fields of external action is a multilevel process of their destruction, with the corresponding levels of crystal lattice selforganization and levels of its homeostasis, i.e., the destruction via different phases of strengthening (self-organization). On solid crystals this decreases the orderliness and amount of structural information. In liquid crystals this increases the orderliness and

Dependence of Gibbs thermodynamic potential on the molar volume and changes in the structural information (I), taking into account local zones of stress concentrators is

*i i F I UT p Ci i*

 

(19)

amount of structural information i.e. liquid crystal → crystal transition.

( log ) / ( , ) / 10 *p pk*

Destruction of solid and liquid crystals increases the molar volume [24, 25].

where i – chemical potential, Ci – concentration (Fig. 22, [26]) .

0 is an equilibrium crystal; the initial level of homeostasis;

appear; solid crystal starts to behave as a liquid one.

**Figure 22.** The dependence of the Gibbs thermodynamic potential F (v) from the molar volume v in the light of local zones of stress concentrators of different scales [26].

In biological membranes as liquid crystals, destruction is related with structural transitions and is generally accompanied by increasing structural orderliness (the order order transition). Earlier [1], it was shown that the action of steroid hormones on erythrocyte membranes disturbs the mechanisms of self-organization that operate in the cells in normal functional condition. The active CO, NH and OH groups of stress hormones interact with CO and NH groups both of proteins and phospholipids in biological membranes. This leads to the formation of complex protein-lipid clusters, where "compressive" hydrophobic interactions are reinforced. Molecularly bound water is displaced to adjacent regions. Here, hydrostatic forces increase the "tensile" tangential stresses. Mobile nanostructural boundaries are formed, along which the biological membranes are destructed. This results in the formation of numerous pores and mesostrips of plastic deformation. In terms of physical mesomechanics, these transformations resemble those developing in solid crystals in the fields of external action (Fig. 23). However, in biological membranes such selforganization may be related even with increasing order and decreasing entropy, but this is incompatible with conditions that determine cell viability. Structural transitions cover the membrane-bound enzymes, transmembrane carriers and hormone receptors. It is reasonable to say that cell membranes go to a new level of homeostasis (self-organization) which is incompatible with life. The nature of life implies dynamics. The cell dies. Here, one can tell about thermodynamic features related with changes in the structure and function (properties) of solid crystals and biological membranes in the fields of external action.

Various structural transitions (phase transitions, nanostructural, etc.) strongly contribute to the functional activity of a cell. These are the transitions like smectic A smectic C, smectic cholesteric, and nematic isotropic state; in proteins, the transitions tangle structure and tangle -helix. They all affect the vital characteristics of a cell. I. Prigogine believed that there is "a wonderful analogy between instability of nonequilibrium origin and phase transitions" [27]. This problem is of great interest and deserves special examination.

Mesomechanics and Thermodynamics of

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 301

Biomembranes are of vital importance in the processes of self-organization of cell metabolism. These processes are transport of organic compounds through cell (plasma) membranes with delivery of nutrients to the cell and removal of their decay products (metabolism); diffusion of gases (O2, CO2) through a cell membrane; passive and active ion transport and production of electrochemical potential on the outer and inner surfaces of plasma membranes, and many others. All membranes are liquid crystals. Their behavior in an organism obeys physicochemical laws. The mechanism of their self-organization is the

Multilevel systems mean the "hierarchy of scales of shear stability loss of the internal structure of a loaded material in local regions at the nano-, micro-, meso- and macrolevels" [26]. In liquid crystals, this is associated with lipid-lipid, protein-lipid, and protein-protein interactions, i.e. with cooperative behavior of a liquid crystal as a system. The ordering of these crystals as well as the nature of their components is determined by covalent and hydrogen bonds, weak electrostatic and hydrophobic interactions. Shear stability loss of natural liquid crystals depends on structural phase transitions such as the formation of smectic, cholesteric, nematic and isotropic structures and transitions between them. For membrane-bound proteins, states like α- helix, -structure and chaotic coil are of significance. Structural transitions can be reversible and irreversible. In the latter case, defects are accumulated in liquid crystals, making some functions of the cell membranes unrealizable. The cell dies. These transitions, as a rule, arise on the surfaces of cell membranes and, because of cooperativeness, go deep into their lower levels. They can be also initiated at the inner membrane or particle interfaces and can be related to lipids and proteins. Thus, the case in point is different thermodynamic states of liquid crystals. The low transition enthalpy suggests that the transitions involve low-energy bonds, mainly hydrogen bonds, weak electrostatic and hydrophobic interactions. The external factors capable of changing (disrupting) the interactions are also physicochemical in nature. Among these factors are variations in temperature, pH, electrolyte content, etc. However, they are all of no fundamental character, and the behavior of liquid crystals under external actions fit in the same concept as the behavior of solid crystal does. It is very important for medicine.

As indicated in the report of World Health Organization, cardiovascular pathology, infections and oncological diseases are three main causes of human mortality all over the world [28]. Cardiovascular diseases stand first in this short list. In 2005 they killed 17.5 million people, which constitutes 30% of all deaths in the world. WHO predicts that in 2015 these diseases may take away the lives of 20 millions people. This will be caused mainly by

Especially dangerous is myocardial ischemia, which is related with the formation of atherosclerotic plaques within the coronary arteries and a considerable decrease in the blood flow rate. Such mechanism of tissue hypoxia development is typical of the older age groups. However, this pathology may develop also by a different mechanism. Nowadays acute

same as that of multilevel systems.

infarctions and strokes, i.e. acute tissue hypoxia.

**9. Conclusion** 

Thus, on the curve of thermodynamic Gibbs potential versus molar volume F(υ), solid crystals fall in the region of strongly negative values, whereas liquid crystals are located near zero. Structural transformations taking place in the fields of external action draw together the positions of liquid and solid crystals on the functional curve. Morphologically, the destruction patterns of crystals are quite similar (Fig. 9a and b).

Thermodynamically, cells as hierarchic multilevel liquid crystal systems can function only near a zero value of thermodynamic Gibbs potential, i.e. in the region where reversible nanostructural transitions underlying life processes can occur.

**Figure 23.** a – Atomic force microscopy. The surface of rat erythrocytes after adsorption of cortisol. Concentration of the hormone is 10-6M. Deep meso-bands with bifurcation are seen; b – Formation of micropore chains along localized-deformation shear-bands. Plate of high-pure aluminum 180 nm thick glued on flat specimen of commercial Al. Alternative bending, Т = 293 К; cycle number N = 17.55106 [26]. Biomembranes are of vital importance in the processes of self-organization of cell metabolism. These processes are transport of organic compounds through cell (plasma) membranes with delivery of nutrients to the cell and removal of their decay products (metabolism); diffusion of gases (O2, CO2) through a cell membrane; passive and active ion transport and production of electrochemical potential on the outer and inner surfaces of plasma membranes, and many others. All membranes are liquid crystals. Their behavior in an organism obeys physicochemical laws. The mechanism of their self-organization is the same as that of multilevel systems.

Multilevel systems mean the "hierarchy of scales of shear stability loss of the internal structure of a loaded material in local regions at the nano-, micro-, meso- and macrolevels" [26]. In liquid crystals, this is associated with lipid-lipid, protein-lipid, and protein-protein interactions, i.e. with cooperative behavior of a liquid crystal as a system. The ordering of these crystals as well as the nature of their components is determined by covalent and hydrogen bonds, weak electrostatic and hydrophobic interactions. Shear stability loss of natural liquid crystals depends on structural phase transitions such as the formation of smectic, cholesteric, nematic and isotropic structures and transitions between them. For membrane-bound proteins, states like α- helix, -structure and chaotic coil are of significance. Structural transitions can be reversible and irreversible. In the latter case, defects are accumulated in liquid crystals, making some functions of the cell membranes unrealizable. The cell dies. These transitions, as a rule, arise on the surfaces of cell membranes and, because of cooperativeness, go deep into their lower levels. They can be also initiated at the inner membrane or particle interfaces and can be related to lipids and proteins. Thus, the case in point is different thermodynamic states of liquid crystals. The low transition enthalpy suggests that the transitions involve low-energy bonds, mainly hydrogen bonds, weak electrostatic and hydrophobic interactions. The external factors capable of changing (disrupting) the interactions are also physicochemical in nature. Among these factors are variations in temperature, pH, electrolyte content, etc. However, they are all of no fundamental character, and the behavior of liquid crystals under external actions fit in the same concept as the behavior of solid crystal does. It is very important for medicine.

As indicated in the report of World Health Organization, cardiovascular pathology, infections and oncological diseases are three main causes of human mortality all over the world [28]. Cardiovascular diseases stand first in this short list. In 2005 they killed 17.5 million people, which constitutes 30% of all deaths in the world. WHO predicts that in 2015 these diseases may take away the lives of 20 millions people. This will be caused mainly by infarctions and strokes, i.e. acute tissue hypoxia.

## **9. Conclusion**

300 Thermodynamics – Fundamentals and Its Application in Science

examination.

Various structural transitions (phase transitions, nanostructural, etc.) strongly contribute to the functional activity of a cell. These are the transitions like smectic A smectic C, smectic cholesteric, and nematic isotropic state; in proteins, the transitions tangle structure and tangle -helix. They all affect the vital characteristics of a cell. I. Prigogine believed that there is "a wonderful analogy between instability of nonequilibrium origin and phase transitions" [27]. This problem is of great interest and deserves special

Thus, on the curve of thermodynamic Gibbs potential versus molar volume F(υ), solid crystals fall in the region of strongly negative values, whereas liquid crystals are located near zero. Structural transformations taking place in the fields of external action draw together the positions of liquid and solid crystals on the functional curve. Morphologically,

Thermodynamically, cells as hierarchic multilevel liquid crystal systems can function only near a zero value of thermodynamic Gibbs potential, i.e. in the region where reversible

**Figure 23.** a – Atomic force microscopy. The surface of rat erythrocytes after adsorption of cortisol. Concentration of the hormone is 10-6M. Deep meso-bands with bifurcation are seen; b – Formation of micropore chains along localized-deformation shear-bands. Plate of high-pure aluminum 180 nm thick glued on flat specimen of commercial Al. Alternative bending, Т = 293 К; cycle number N = 17.55106 [26].

the destruction patterns of crystals are quite similar (Fig. 9a and b).

nanostructural transitions underlying life processes can occur.

a

b

Especially dangerous is myocardial ischemia, which is related with the formation of atherosclerotic plaques within the coronary arteries and a considerable decrease in the blood flow rate. Such mechanism of tissue hypoxia development is typical of the older age groups. However, this pathology may develop also by a different mechanism. Nowadays acute

myocardial ischemia and coronary deficiency are often observed in young people. There are many cases of sudden death that occur in young sportsmen during the competitions [29]. Coronary arteries of sportsmen are free of plaques, nevertheless, acute coronary deficiency develops somehow. Stress hormones and steroid anabolics may be a possible reason.

Mesomechanics and Thermodynamics of

Nanostructural Transitions in Biological Membranes Under the Action of Steroid Hormones 303

[1] Panin, L.E.; Mokrushnikov, P.V.; Kunitsyn, V.G. & Zaitsev, B.N. (2010). Interaction mechanism of cortisol and catecholamines with structural components of erythrocyte membranes. *J. Phys. Chem. B.* Vol. 114. No. 29, ( Jul. 29, 2010) pp. 9462-9473. ISSN 1520-

[2] Hurst, T; Olson, T.H.; Olson, L.E. & Appleton, C.P. (2006). Cardiac syndrome X and endothelial dysfunction: new concepts in prognosis and treatment. *Am. J. Med.* Vol. 119.

[3] Rubart, M. & Zipes, D.P. (2005). Mechanisms of sudden cardiac death. *J. Clin. Invest.*

[4] Courson, R. (2007). Preventing sudden death on the athletic field: the emergency action plan. *Curr Sports Med Rep.,* Vol. 6, No. 2, (Apr. 2007) pp. 93-100, ISSN 1537-890X [5] Jorgensen, P.L.; Hakansson, K.O. & Karlish, S.J. (2003) Structure and mechanism of Na+,K+-ATPase. *Annu. Rev. Physiol*. Vol. 65, (May 2002) pp. 817–849. ISSN 0066-4278 [6] Golden, G.A.; Mason, P.E.; Rubin, R.T. & Mason, R.P. (1998) Biophysical membrane interactions of steroid hormones: a potential complementary mechanism of steroid action. *Clin. Neuropharmacol.* Vol. 21. No. 3, (May-Jun. 1998) pp. 181-189. ISSN 0362-5664 [7] Wu, Y.; Hu, Y.; Cai, J.; Ma, S.; Wang, X.; Chen, Y. & Pan, Y. (2009) Time-dependent surface adhesive force and morphology of RBC measured by AFM. *Micron.* Vol. 40. No.

[8] Kunitsyn, V.G.; Panin, L.E. & Polyakov, L.M. (2001). Anomalous change of viscosity and conductivity in blood plasma lipoproteins in the physiological temperature range.

[9] Dawson, R.M.C.; Elliot, D.C.; Elliot, W.H. & Jones, K.M. (1986). *Data for biochemical* 

[10] Attallah, N.A. & Lata, G.F. (1968). Steroid-protein interactions studies by fluorescence quenching. *Biochim. Biophys. Acta,* Vol. 168. Issue 2, pp. 321-333, ISSN 0005-2795 [11] Storozhok, S.A.; Sannikov, A.G. & Zakharov, Yu.M. (1997). *Molecular Structure of Erythrocyte Membranes and Their Mechanical Properties,* Tyumen University, Tyumen. [12] Murray, R.K.; Granner D.K.; Mayes P.A. & Rodwell V.W. (2003). *Harper's Illustrated* 

[13] Ooi, Т.; Itsuka, E.; Onari, S. et al. (1988). *Biopolymers,* Imanisi Y. (Ed.), Mir, ISBN is

[14] Panin L.E., Panin V.E. (2011). Thermodynamics and mesomechanics of nanostructural transitions in biological membranes under stress. *Int. J. Terraspace Science and* 

[15] Miyazawa, T. & Blout, E.R. (1961) The infrared spectra of polypeptide in various conformations: amid I and II bands. *J. Am. Chem. Soc.* Vol. 83, No. 3 (Febr. 1961) pp.

[16] Semenov, M.A.; Gasan A.J.; Bol'bukh T.V.; et. al. (1996). Hydration and structural transitions of DNA from Micrococcus lysodeikticus in films. *Biophysics*, Vol. 41. No. 5,

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*research.* Clarendon Press, ISBN is absent, Oxford, United Kingdom.

*Biochemistry*, 26th ed., The McGraw-Hill Companies, Inc.

*Engineering.* V. 3. Iss. 1. pp. 3-12. ISSN:1943-3514

(Sept. – Oct. 1996) pp. 1007-1016. ISSN 0006-3509.

No. 7, (Jul. 2006) pp. 560-566. ISSN 0002-9343

3, (Apr. 2009) pp. 359-364. ISSN 0968-4328.

absent: Moscow, Russia

712-719. ISSN 0002-7863

Vol. 115. No. 9, (Sep. 2005) pp. 2305-2315. ISSN 0021-9738

**10. References** 

6106

Today the world is changing very rapidly, and not everybody can adjust to these changes. Chronic stress becomes a wide-spread phenomenon [18]. Such reaction may be very pronounced in anxious persons. This is why cardiac syndrome X is often diagnosed now. Its clinical characteristics include angina chest pain with exertion and ischemic type ST segment depression on electrocardiogram, without angiographic signs of coronary artery stenosis and with normal left ventricle function. It means that acute coronary deficiency of obscure etiology occurs not only in sportsmen, but also among people at large [30].

Cortisol is the main stress hormone. It is a cholesterol derivative, and cholesterol is the essential component of all cell membranes. Of special interest is the erythrocyte membrane. Erythrocyte is a specialized cell that transfers oxygen from lungs to tissues by means of hemoglobin (Нb). In capillaries, oxyhemoglobin НbO2 decomposes, and O2 diffuses to the organ and tissue cells. The first obstacle to such diffusion is erythrocyte membrane. Changes in the properties of erythrocyte membrane determine the rate of oxygen diffusion across the membrane. Besides, capillary and erythrocyte may have comparable diameters. Sometimes the erythrocyte diameter happens to be even larger. To go through so small capillary, erythrocyte should have a high plasticity. Structural transformations in erythrocyte membrane under the action of stress hormones may be reflected not only in its plasticity, but also in the mechanism of gas exchange.

In this work, an attempt to elucidate the effect of steroid hormones on the structure of erythrocyte membranes and their physicochemical properties, i.e. the introduction of principles and regularities of physical mesomechanics in biology and medicine provides a deep insight into the mechanism interrelating structure and function of biological membranes, both in the norm and at systemic membrane pathology (upon variation of hormone concentration, temperature, pH, electrochemical potential, etc. has been made.

Thus, from a thermodynamic standpoint, life is the ability of cells to undergo reversible nanostructural transitions near a zero value of thermodynamic Gibbs potential. A loss of this ability leads to cell death and development of pathology.

## **Author details**

L.E. Panin *Scientific Research Institute of Biochemistry SB RAMS, Russia* 

## **Acknowledgement**

The author is grateful to Dr. Sci. (med.) V.G. Kunitsyn and Ph. D. (phys.-math.) P.V. Mokrushnikov for participation in the preparation of experimental material.

## **10. References**

302 Thermodynamics – Fundamentals and Its Application in Science

but also in the mechanism of gas exchange.

**Author details** 

**Acknowledgement** 

L.E. Panin

this ability leads to cell death and development of pathology.

*Scientific Research Institute of Biochemistry SB RAMS, Russia* 

myocardial ischemia and coronary deficiency are often observed in young people. There are many cases of sudden death that occur in young sportsmen during the competitions [29]. Coronary arteries of sportsmen are free of plaques, nevertheless, acute coronary deficiency

Today the world is changing very rapidly, and not everybody can adjust to these changes. Chronic stress becomes a wide-spread phenomenon [18]. Such reaction may be very pronounced in anxious persons. This is why cardiac syndrome X is often diagnosed now. Its clinical characteristics include angina chest pain with exertion and ischemic type ST segment depression on electrocardiogram, without angiographic signs of coronary artery stenosis and with normal left ventricle function. It means that acute coronary deficiency of obscure

Cortisol is the main stress hormone. It is a cholesterol derivative, and cholesterol is the essential component of all cell membranes. Of special interest is the erythrocyte membrane. Erythrocyte is a specialized cell that transfers oxygen from lungs to tissues by means of hemoglobin (Нb). In capillaries, oxyhemoglobin НbO2 decomposes, and O2 diffuses to the organ and tissue cells. The first obstacle to such diffusion is erythrocyte membrane. Changes in the properties of erythrocyte membrane determine the rate of oxygen diffusion across the membrane. Besides, capillary and erythrocyte may have comparable diameters. Sometimes the erythrocyte diameter happens to be even larger. To go through so small capillary, erythrocyte should have a high plasticity. Structural transformations in erythrocyte membrane under the action of stress hormones may be reflected not only in its plasticity,

In this work, an attempt to elucidate the effect of steroid hormones on the structure of erythrocyte membranes and their physicochemical properties, i.e. the introduction of principles and regularities of physical mesomechanics in biology and medicine provides a deep insight into the mechanism interrelating structure and function of biological membranes, both in the norm and at systemic membrane pathology (upon variation of hormone concentration, temperature, pH, electrochemical potential, etc. has been made.

Thus, from a thermodynamic standpoint, life is the ability of cells to undergo reversible nanostructural transitions near a zero value of thermodynamic Gibbs potential. A loss of

The author is grateful to Dr. Sci. (med.) V.G. Kunitsyn and Ph. D. (phys.-math.) P.V.

Mokrushnikov for participation in the preparation of experimental material.

develops somehow. Stress hormones and steroid anabolics may be a possible reason.

etiology occurs not only in sportsmen, but also among people at large [30].

	- [17] Discher, D.E., Mohandas, N. & Evans, E.A. (1994). Molecular maps of red cell deformation: hidden elasticity and in situ connectivity. *Science.* Vol. 266. No. 5187, (Nov. 1994) pp. 1032-1035. ISSN 0036-8075.

**Chapter 12** 

© 2012 Liu and Wang, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**Thermodynamics of Resulting Complexes** 

Cyclodextrins (CDs), a class of macrocyclic oligosaccharides consisting of six, seven, or eight glucose units linked by *α*-1,4-glucose bonds, have been widely used as receptors in molecular recognition in the field of supramolecular chemistry because they are able to form inclusion complexes with hydrophobic guests in aqueous solution owing to their hydrophilic outer surface and their lipophilic cavity [1–3]. Therefore, much effort has been devoted to the design and synthesis of a wide variety of cyclodextrin (CD) derivatives to explore their binding behaviors for model substrates [4]. In order to further explore their inclusion complexation mechanism, most of these studies have been focused on the binding modes and complexation thermodynamics based on CDs and their derivatives in recent years [5]. Among the numerous guests researched, bile salts attracted much more attention because they are one kind of important surfactant-like biological amphipathic compounds possessing a steroid skeleton, which have distinctive detergent properties and play an important role in the metabolism and excretion of cholesterol in mammals [6]. For example: the thermodynamics and structure of inclusion compounds of glyco- and tauro-conjugated bile salts with CDs and their derivatives have been studied by Holm et al. during the last years [7–11]; the interactions of different kinds of bile salts with *β*-CD dimers linked through their secondary faces have been investigated by Reinhoudt and Vargas-Berenguel et al. [12– 14]. It has been demonstrated that the formation of inclusion complexes between CDs and guest molecules is cooperatively governed by several weak forces, such as van der Waals interactions, hydrophobic interactions, hydrogen bonding, electrostatic interactions, and every weak force does its contribution to the complexation. In this chapter, the related investigations concerned on the binding modes, binding abilities, molecular selectivities and their thermodynamic origins of CDs and their derivatives with four typical bile salts (Cholate (CA), Deoxycholate (DCA), Glycocholate (GCA), and Taurocholate (TCA)) (Figure

**Between Cyclodextrins and Bile Salts** 

Additional information is available at the end of the chapter

Yu Liu and Kui Wang

http://dx.doi.org/10.5772/51406

**1. Introduction** 


Yu Liu and Kui Wang

304 Thermodynamics – Fundamentals and Its Application in Science

1994) pp. 1032-1035. ISSN 0036-8075.

ISBN 978-91-85917-06-8.

pp. 6731- 6736. ISSN 0027-8424

Tyumen.

Berto. p. 48-51.

ISSN 0918-2918

206) pp. 5-9. ISSN 0023-2149. Russian.

[17] Discher, D.E., Mohandas, N. & Evans, E.A. (1994). Molecular maps of red cell deformation: hidden elasticity and in situ connectivity. *Science.* Vol. 266. No. 5187, (Nov.

[18] Shnol, S.E. (1979) *Physicochemical factors of biological evolution,* Nauka, Moscow (Rus.)

[19] Kunitsyn, V.G. (2002). *Structural phase transitions in erythrocyte membranes, lipoproteins* 

[20] Park, Y.; Best, C.A.; Badizadegan, K., Dasari, R.R.; Feld, M.S.; Kuriabova, T.; Henle, M.L.; Levine, A.J. & Popescu, G. (2010). Measurement of red blood cell mechanics during morphological changes. *Proc. Natl. Acad. Sci. U S A*. Vol. 107. No. 15, (Apr. 2010)

[21] Bennett, V. (1984) In: *Cell Membranes: Methods and Reviews*, eds. Elson, E., Frazier, W. &

[22] Storozhok, S. A.; Sannikov, A. G. & Zakharov, Yu. M. (1997) *Molecular Structure of Erythrocyte Membranes and Their Mechanical Properties,* Tyumen Gos. University:

[23] Wolkers, W.F.; Crowe, L.M.; Tsvetkova, N.M.; Tablin, F. & Crowe, J.H. (2002). In situ assessment of erythrocyte membrane properties during cold storage. *Mol. Membr. Biol.* 

[24] Panin, L.E. & Kunitsyn, V.G. (2009). Mechanism and thermodynamics of multilevel structural transitions in liquid crystals under external actions. *Physical Mesomechanics,*

[25] Panin, L.E. (2011). Thermodynamics and mesomechanics of nanostructural transitions in biological membranes under the action of male sex hormones. 13-th International conference on mesomechanics. Vicenza, Italy, 6-8 July 2011. Eds. G.Sih, P. Lazzarin, F.

[26] Panin, V.E. & Egorushkin, V.E. (2008). Nonequilibrium thermodynamics of a deformed solid as a multiscale system. Corpuscular-wave dualism of plastic shear. *Physical Mesomechanics*. Vol. 11. No. 3-4, (May - August 2008) pp. 105 – 123. ISSN 1029-9599. [27] Nicolis, G. & Prigogine, I. (1979). *Self-Organization in Non-Equilibrium Systems. From* 

[28] Vermel', A.E. (2006). Cardiac syndrome X. *Klin Med (Mosk).* Vol. 84. No. 6 (Nov.–Dec.

[29] Montagnana, M.; Lippi, G.; Franchini, M.; Banfi, G. & Guidi, G.C. (2008). Sudden cardiac death in young athletes. *Intern Med.* Vol. 47, No. 15, (Aug. 2008) pp. 1373-1378,

[30] Panin, L.E. & Usenko, G.A. (2004). *Anxiety, adaptation and prenosological clinical* 

*Dissipative structures to Order through Fluctuations*, Mir, Moscow, Russia.

*examination*. SB RAMS, Novosibirsk, ISBN 5-93239-050-6 (Rus.)

*and macromolecules.* Thesis, Dr. Sci. (biol.), Novosibirsk. (Rus.)

Glaser, L. Vol. 2, Plenum, New York, pp. 149-195.

Vol. 19. No. 1, (Jan-Mar 2002) pp. 59-65. ISSN 0968-7688

Vol. 12. No. 1-2, (Jan. – Apr. 2009) pp. 78-84. ISSN 1029-9599

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/51406

## **1. Introduction**

Cyclodextrins (CDs), a class of macrocyclic oligosaccharides consisting of six, seven, or eight glucose units linked by *α*-1,4-glucose bonds, have been widely used as receptors in molecular recognition in the field of supramolecular chemistry because they are able to form inclusion complexes with hydrophobic guests in aqueous solution owing to their hydrophilic outer surface and their lipophilic cavity [1–3]. Therefore, much effort has been devoted to the design and synthesis of a wide variety of cyclodextrin (CD) derivatives to explore their binding behaviors for model substrates [4]. In order to further explore their inclusion complexation mechanism, most of these studies have been focused on the binding modes and complexation thermodynamics based on CDs and their derivatives in recent years [5]. Among the numerous guests researched, bile salts attracted much more attention because they are one kind of important surfactant-like biological amphipathic compounds possessing a steroid skeleton, which have distinctive detergent properties and play an important role in the metabolism and excretion of cholesterol in mammals [6]. For example: the thermodynamics and structure of inclusion compounds of glyco- and tauro-conjugated bile salts with CDs and their derivatives have been studied by Holm et al. during the last years [7–11]; the interactions of different kinds of bile salts with *β*-CD dimers linked through their secondary faces have been investigated by Reinhoudt and Vargas-Berenguel et al. [12– 14]. It has been demonstrated that the formation of inclusion complexes between CDs and guest molecules is cooperatively governed by several weak forces, such as van der Waals interactions, hydrophobic interactions, hydrogen bonding, electrostatic interactions, and every weak force does its contribution to the complexation. In this chapter, the related investigations concerned on the binding modes, binding abilities, molecular selectivities and their thermodynamic origins of CDs and their derivatives with four typical bile salts (Cholate (CA), Deoxycholate (DCA), Glycocholate (GCA), and Taurocholate (TCA)) (Figure

© 2012 Liu and Wang, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1) have been summarized, which will be discussed from the aspect of the types of host molecules: (1) natural CD series; (2) modified CD series; (3) bridged CD series. This summary is helpful to improve understanding of the correlation between the structural features and molecular-recognition mechanism from thermodynamic viewpoints, and further guide its biological, medicinal and pharmaceutical applications in the future.

Thermodynamics of Resulting Complexes Between Cyclodextrins and Bile Salts 307

**Figure 2.** Structure of natural *β*-CD

equation:

**2.2. Complexation thermodynamics for bile salts and natural CD series** 

The microcalorimetric titrations can be used to simultaneously determine the enthalpy and equilibrium constant from a single titration curve. Titrations were performed below the critical micelle concentration of bile salts. In each run, a solution of the host (guest) molecules in syringe was sequentially injected into the calorimeter sample cell containing a solution of guests (hosts). Each addition of hosts (guests) into the sample cell gave rise to a heat of reaction, caused by the formation of inclusion complexes between hosts and guests. The heats of reaction decrease after each injection because less and less molecules in cell are available to form inclusion complexes. A control experiment was performed to determine the heat of dilution by injecting a host (guest) solution into a pure solution containing no guest (host) molecules. The dilution enthalpy was subtracted from the apparent enthalpy obtained in each titration run, and the net reaction enthalpy was analyzed by using the "one set of binding sites" model. This model will work for any number of sites *N* if all sites have the same *K*s and *H*°. In this case, the total heat *Q* was fitted via a nonlinear least-squares minimization method to the total host concentration in cell (*M*t) using the following

 *Q* = (*NX*t*HV*o/2){1 + *M*t/(*NX*t) + 1/(*NK*S*X*t) – {[1 + *M*t/(*NX*t) + 1/(*NK*S*X*t)]2 – 4*M*t/(*NX*t)}1/2} (1)

where *N* is the number of binding sites of host, *X*t is the total concentration of guests in cell and *V*o is the cell volume. The value of *Q* above can be calculated (for any designated values of *N*, *K*, and *H*) at the end of the *i*th injection and designated *Q*(*i*). Then the correct

where d*Vi* is the volume of titrant added to the solution. Along with obtaining of *K*s and *H*° in this fitting program, the *N* value in eq 1 can also be obtained, which represents the

The ORIGIN software (Microcal), used for the calculation of the binding constant (*K*s) and standard molar reaction enthalpy (*H*°) from the titration curve, gave the relevant standard derivation on the basis of the scatter of data points in a single titration experiment. The binding

*Q*(*i*) = *Q*(*i*) + d*Vi*/(<ital> *V*o){[*Q*(*i*) + *Q*(*i* – 1)]/2} – *Q*(*i* – 1) (2)

expression for the heat released, *Q*(*i*), from the *i*th injection is

numbers of guests bound to one host molecule.

**Figure 1.** Molecular structures of four typical bile salts

## **2. Natural CD series**

### **2.1. Binding modes for bile salts and natural CD series**

Since two protons located closely in space (the corresponding internuclear distance is smaller than 3–4 Å) can produce NOE (Nuclear Overhauser Effect) cross-peaks between the relevant protons in NOESY (Nuclear Overhauser Effect Spectroscopy) or ROESY (Rotating Frame Overhauser Effect Spectroscopy) spectra, 2D NMR spectroscopy has become an important method for the investigation of the interaction between different kinds of CDs and guest molecules. It is well-known that only H3, H5, and H6 of CDs can give cross-peaks for analyzing host–guest interactions, as H2 and H4 are not facing to the inner cavity and H1 is affected by D2O. For example, the ROESY study on the resulting complex of natural *β*-CD **1** (Figure 2) with CA has been reported by Tato et al. [15,16]. The results successfully indicated that in the 1:1 complex between **1** and CA the steroid body entered forward into the inner cavity of **1** by the side of the secondary hydroxyl groups, with the side chain folded toward the steroid body, i.e., rings D and C are totally and partially included, respectively. Therefore, the binding modes of bile salts with different kinds of CDs have been widely deduced by 2D NMR spectroscopy during the last years.

**Figure 2.** Structure of natural *β*-CD

1) have been summarized, which will be discussed from the aspect of the types of host molecules: (1) natural CD series; (2) modified CD series; (3) bridged CD series. This summary is helpful to improve understanding of the correlation between the structural features and molecular-recognition mechanism from thermodynamic viewpoints, and

further guide its biological, medicinal and pharmaceutical applications in the future.

Glycocholate (GCA) OH CONHCH2COONa Taurocholate (TCA) OH CONHCH2CH2SO3Na

Since two protons located closely in space (the corresponding internuclear distance is smaller than 3–4 Å) can produce NOE (Nuclear Overhauser Effect) cross-peaks between the relevant protons in NOESY (Nuclear Overhauser Effect Spectroscopy) or ROESY (Rotating Frame Overhauser Effect Spectroscopy) spectra, 2D NMR spectroscopy has become an important method for the investigation of the interaction between different kinds of CDs and guest molecules. It is well-known that only H3, H5, and H6 of CDs can give cross-peaks for analyzing host–guest interactions, as H2 and H4 are not facing to the inner cavity and H1 is affected by D2O. For example, the ROESY study on the resulting complex of natural *β*-CD **1** (Figure 2) with CA has been reported by Tato et al. [15,16]. The results successfully indicated that in the 1:1 complex between **1** and CA the steroid body entered forward into the inner cavity of **1** by the side of the secondary hydroxyl groups, with the side chain folded toward the steroid body, i.e., rings D and C are totally and partially included, respectively. Therefore, the binding modes of bile salts with different kinds of CDs have

Guests R1 R2 Cholate (CA) OH COONa Deoxycholate (DCA) H COONa

**2.1. Binding modes for bile salts and natural CD series** 

been widely deduced by 2D NMR spectroscopy during the last years.

**Figure 1.** Molecular structures of four typical bile salts

**2. Natural CD series** 

#### **2.2. Complexation thermodynamics for bile salts and natural CD series**

The microcalorimetric titrations can be used to simultaneously determine the enthalpy and equilibrium constant from a single titration curve. Titrations were performed below the critical micelle concentration of bile salts. In each run, a solution of the host (guest) molecules in syringe was sequentially injected into the calorimeter sample cell containing a solution of guests (hosts). Each addition of hosts (guests) into the sample cell gave rise to a heat of reaction, caused by the formation of inclusion complexes between hosts and guests. The heats of reaction decrease after each injection because less and less molecules in cell are available to form inclusion complexes. A control experiment was performed to determine the heat of dilution by injecting a host (guest) solution into a pure solution containing no guest (host) molecules. The dilution enthalpy was subtracted from the apparent enthalpy obtained in each titration run, and the net reaction enthalpy was analyzed by using the "one set of binding sites" model. This model will work for any number of sites *N* if all sites have the same *K*s and *H*°. In this case, the total heat *Q* was fitted via a nonlinear least-squares minimization method to the total host concentration in cell (*M*t) using the following equation:

$$Q = \left(\text{NX}\iota\text{\&HV}\_{\circ}\text{\&}\right)\left(1 + M\iota\text{\&(NX}\iota\right) + 1/\text{(NX}\iota\text{\&}\text{\&)} - \left\{\left[1 + M\iota\text{\&(NX}\iota\right) + 1/\text{(NX}\iota\text{\&)}\right]^2 - 4M\iota\text{\&(NX}\iota\text{\&)}\right\}^{1/2}\tag{1}$$

where *N* is the number of binding sites of host, *X*t is the total concentration of guests in cell and *V*o is the cell volume. The value of *Q* above can be calculated (for any designated values of *N*, *K*, and *H*) at the end of the *i*th injection and designated *Q*(*i*). Then the correct expression for the heat released, *Q*(*i*), from the *i*th injection is

$$
\Delta Q(i) = Q(i) + \text{d}V / (\text{} \, V\_0) [Q(i) + Q(i-1)] / 2 \rangle - Q(i-1) \tag{2}
$$

where d*Vi* is the volume of titrant added to the solution. Along with obtaining of *K*s and *H*° in this fitting program, the *N* value in eq 1 can also be obtained, which represents the numbers of guests bound to one host molecule.

The ORIGIN software (Microcal), used for the calculation of the binding constant (*K*s) and standard molar reaction enthalpy (*H*°) from the titration curve, gave the relevant standard derivation on the basis of the scatter of data points in a single titration experiment. The binding stoichiometry was also given as a parameter when fitting the binding isotherm. Knowledge of the binding constant (*K*s) and molar reaction enthalpy (*H*°) enabled the calculation of the standard free energy of binding (*G*°) and entropy change (*S*°) according to

$$
\Delta G^{\ominus} = -RT\ln\text{Ks} = \Delta H^{\ominus} - T\Delta S^{\ominus} \tag{3}
$$

Thermodynamics of Resulting Complexes Between Cyclodextrins and Bile Salts 309

The ROESY experiments of modified *β*-CD **3** in the presence of CA or DCA have been performed in D2O by Liu et al. [17]. The results indicate that the D-ring of CA is accommodated shallowly in the cavity and CA enters **3** from the second side of CD with the side chain and D-ring. At the same time, the side chain with the negative carboxylate group of CA moves toward the positive protonated amino group of **3**. For the resulting complex of DCA–**3**, the ROESY spectrum exhibits entirely different NOE cross-peaks and the D-ring of DCA is included within the cavity of CD from the primary side of CD. Meanwhile, the

2D ROESY NMR experiment of **5** and CA has also been performed by Liu et al. in D2O to investigate the binding mode between bile salt and CD [18]. The results show that steroid

In host **8**, the adenine group is deeply inserted into the *β*-CD cavity with an orientation parallel to the C7 axis of *β*-CD while the thymine and uracil groups are shallowly inserted in the *β*-CD cavity with an orientation perpendicular to the C7 axis of *β*-CD [19]. As a result, upon complexation with DCA guest, the deeply included adenine group in host **8** should be expelled from the cavity upon complexation with DCA guest, however, the shallowly included thymine and uracil groups in hosts **9** and **10** are hardly influenced by the inclusion

The binding modes of L/D-Trp-*β-*CD (**11** and **12**) with bile salts have been examined by Liu et al. by 2D ROESY NMR experiments [20]. For L-Trp-*β*-CD (**11**), the results show that in the absence of guest, L-Trp residue is only shallowly included or perching on the rim of the CD cavity. However, in the presence of DCA, the D-ring of DCA is close to the wide end of CD cavity, and the D-ring of DCA and the side chain is co-included in the same cavity from the primary side of **11**. For D-Trp-*β*-CD (**12**), the 2D NMR results indicate that the D-Trp residue attached to *β*-CD is more deeply self-included than the corresponding L-Trp residue in the absence of guest. However, in the presence of DCA, the carboxylate side chain and D-ring of

The binding modes of L/D-Tyr-*β-*CD (**13** and **14**) with bile salts have further been examined by Liu et al. by 2D ROESY NMR experiments [21]. The results show that the L-tyrosine moiety was self-included in the *β*-CD cavity from the narrow opening. The DCA guest entered the *β*-CD cavity from the wide opening with the tail and the D ring and coexisted with the Ltyrosine substituent in the *β*-CD cavity to form a cooperative inclusion manner. For Dtyrosine-modified *β*-CD (**14**), the D-tyrosine substituent was deeply self-included in the *β-*CD cavity and might be located in the center of the *β*-CD cavity. Upon complexation with DCA, the D-tyrosine substituent of **14** would partially move out of the *β-*CD cavity. Compared with

DCA + **13** complex, DCA penetrated into the *β*-CD cavity of **14** more deeply (Figure 4).

body enters the CD cavity from the second side with its tail and D-ring parts.

ethide protons of chiral tether interact with H6 of CD.

*3.1.3. Tryptophan- and Tyrosine-modified β-CDs* 

DCA penetrate into the CD cavity from the secondary side shallowly.

*3.1.2. Nucleobase-modified β-CDs* 

of DCA guest.

where *R* is the gas constant and *T* is the absolute temperature.

The microcalorimetric experiments of natural *β*-CD **1** with bile salts (CA, DCA, GCA, and TCA) showed typical titration curves of 1:1 complex formation [17]. The stoichiometric ratios observed from curve-fitting results of the binding isotherm fell within the range of 0.9–1.1. This clearly indicated that the majority of the inclusion complexes had a 1:1 stoichiometry of bile salts and **1**.

Thermodynamically, the binding behaviors of bile salts by **1** were entirely driven by favorable enthalpy changes accompanied by small unfavorable entropy changes, which are attributed to the predominant contribution of the van der Waals interactions arising from the size/shape fit and geometrical complement between host and guest and to the accompanying decreases in translational and structural freedoms upon complexation.

As can be seen from Table 1, the enthalpy change for the complexation of **1** with DCA is more favorable than that with CA, which directly contributes to the increased complex stability. It is reasonable that DCA possesses a more hydrophobic structure due to the absence of C-7 hydroxyl group as compared with CA, as a result, it is easier to bind into the cavity of **1**, which leads to more favorable hydrophobic and van der Waals interactions and gives larger enthalpy and entropy changes. However, the enhanced favorable entropy gain by the desolvation effect may be canceled by the unfavorable entropy change caused by the structural freezing of the resulting complexes of **1** and DCA. Therefore, the stronger interaction between **1** and DCA only shows the larger negative enthalpy change, directly contributing the relatively larger complex stability constant. Meanwhile, **1** shows a lower binding ability upon complexation with GCA and TCA. Compared with **1** and CA, the complexation of **1** with GCA and TCA exhibit similar enthalpy changes but much more unfavorable entropy changes. The more polar side chains of GCA and TCA may be the reason for it.

## **3. Modified CD series**

## **3.1. Binding modes for bile salts and modified CD series**

## *3.1.1. Aminated β-CDs*

The ROESY study on the resulting complex of **2** (Figure 3) with CA has been reported by Tato et al. [15]. The results exhibited different interactions of the side chain of CA with H5 and H6 of **2** from natural *β*-CD **1**. The facts indicated that the side chain was unfolded, with the negative carboxylate group moving toward the positive protonated amino group, and the side-chain elongation produced a deeper penetration of the steroid body in the inner cavity of **2**.

The ROESY experiments of modified *β*-CD **3** in the presence of CA or DCA have been performed in D2O by Liu et al. [17]. The results indicate that the D-ring of CA is accommodated shallowly in the cavity and CA enters **3** from the second side of CD with the side chain and D-ring. At the same time, the side chain with the negative carboxylate group of CA moves toward the positive protonated amino group of **3**. For the resulting complex of DCA–**3**, the ROESY spectrum exhibits entirely different NOE cross-peaks and the D-ring of DCA is included within the cavity of CD from the primary side of CD. Meanwhile, the ethide protons of chiral tether interact with H6 of CD.

2D ROESY NMR experiment of **5** and CA has also been performed by Liu et al. in D2O to investigate the binding mode between bile salt and CD [18]. The results show that steroid body enters the CD cavity from the second side with its tail and D-ring parts.

## *3.1.2. Nucleobase-modified β-CDs*

308 Thermodynamics – Fundamentals and Its Application in Science

stoichiometry of bile salts and **1**.

stoichiometry was also given as a parameter when fitting the binding isotherm. Knowledge of the binding constant (*K*s) and molar reaction enthalpy (*H*°) enabled the calculation of the

The microcalorimetric experiments of natural *β*-CD **1** with bile salts (CA, DCA, GCA, and TCA) showed typical titration curves of 1:1 complex formation [17]. The stoichiometric ratios observed from curve-fitting results of the binding isotherm fell within the range of 0.9–1.1. This clearly indicated that the majority of the inclusion complexes had a 1:1

Thermodynamically, the binding behaviors of bile salts by **1** were entirely driven by favorable enthalpy changes accompanied by small unfavorable entropy changes, which are attributed to the predominant contribution of the van der Waals interactions arising from the size/shape fit and geometrical complement between host and guest and to the accompanying decreases in translational and structural freedoms upon complexation.

As can be seen from Table 1, the enthalpy change for the complexation of **1** with DCA is more favorable than that with CA, which directly contributes to the increased complex stability. It is reasonable that DCA possesses a more hydrophobic structure due to the absence of C-7 hydroxyl group as compared with CA, as a result, it is easier to bind into the cavity of **1**, which leads to more favorable hydrophobic and van der Waals interactions and gives larger enthalpy and entropy changes. However, the enhanced favorable entropy gain by the desolvation effect may be canceled by the unfavorable entropy change caused by the structural freezing of the resulting complexes of **1** and DCA. Therefore, the stronger interaction between **1** and DCA only shows the larger negative enthalpy change, directly contributing the relatively larger complex stability constant. Meanwhile, **1** shows a lower binding ability upon complexation with GCA and TCA. Compared with **1** and CA, the complexation of **1** with GCA and TCA exhibit similar enthalpy changes but much more unfavorable entropy changes. The more polar

The ROESY study on the resulting complex of **2** (Figure 3) with CA has been reported by Tato et al. [15]. The results exhibited different interactions of the side chain of CA with H5 and H6 of **2** from natural *β*-CD **1**. The facts indicated that the side chain was unfolded, with the negative carboxylate group moving toward the positive protonated amino group, and the side-chain elongation produced a deeper penetration of the steroid body in the inner

Δ*G*° = –*RT* ln*K*S = Δ*H*° – *T*Δ*S*° (3)

standard free energy of binding (*G*°) and entropy change (*S*°) according to

where *R* is the gas constant and *T* is the absolute temperature.

side chains of GCA and TCA may be the reason for it.

**3.1. Binding modes for bile salts and modified CD series** 

**3. Modified CD series** 

*3.1.1. Aminated β-CDs* 

cavity of **2**.

In host **8**, the adenine group is deeply inserted into the *β*-CD cavity with an orientation parallel to the C7 axis of *β*-CD while the thymine and uracil groups are shallowly inserted in the *β*-CD cavity with an orientation perpendicular to the C7 axis of *β*-CD [19]. As a result, upon complexation with DCA guest, the deeply included adenine group in host **8** should be expelled from the cavity upon complexation with DCA guest, however, the shallowly included thymine and uracil groups in hosts **9** and **10** are hardly influenced by the inclusion of DCA guest.

## *3.1.3. Tryptophan- and Tyrosine-modified β-CDs*

The binding modes of L/D-Trp-*β-*CD (**11** and **12**) with bile salts have been examined by Liu et al. by 2D ROESY NMR experiments [20]. For L-Trp-*β*-CD (**11**), the results show that in the absence of guest, L-Trp residue is only shallowly included or perching on the rim of the CD cavity. However, in the presence of DCA, the D-ring of DCA is close to the wide end of CD cavity, and the D-ring of DCA and the side chain is co-included in the same cavity from the primary side of **11**. For D-Trp-*β*-CD (**12**), the 2D NMR results indicate that the D-Trp residue attached to *β*-CD is more deeply self-included than the corresponding L-Trp residue in the absence of guest. However, in the presence of DCA, the carboxylate side chain and D-ring of DCA penetrate into the CD cavity from the secondary side shallowly.

The binding modes of L/D-Tyr-*β-*CD (**13** and **14**) with bile salts have further been examined by Liu et al. by 2D ROESY NMR experiments [21]. The results show that the L-tyrosine moiety was self-included in the *β*-CD cavity from the narrow opening. The DCA guest entered the *β*-CD cavity from the wide opening with the tail and the D ring and coexisted with the Ltyrosine substituent in the *β*-CD cavity to form a cooperative inclusion manner. For Dtyrosine-modified *β*-CD (**14**), the D-tyrosine substituent was deeply self-included in the *β-*CD cavity and might be located in the center of the *β*-CD cavity. Upon complexation with DCA, the D-tyrosine substituent of **14** would partially move out of the *β-*CD cavity. Compared with DCA + **13** complex, DCA penetrated into the *β*-CD cavity of **14** more deeply (Figure 4).

310 Thermodynamics – Fundamentals and Its Application in Science

**Figure 4.** The possible binding modes of **11**–**14** (**11** (c); **12** (d); **13** (a); **14** (b)) with DCA

*3.2.1. Aminated β-CDs* 

**3.2. Complexation thermodynamics for bile salts and modified CD series** 

The microcalorimetric experiments of aminated *β*-CDs with bile salts clearly indicate that the majority of the inclusion complexes had a 1:1 stoichiometry [17]. Thermodynamically, the binding constants of **4** upon inclusion complexation with DCA, GCA, and TCA are less than that with natural *β*-CD **1**. It is reasonable that modified *β*-CD **4** decreased the microenvironment hydrophobicity of natural *β*-CD cavity due to the hydrophilic carboxylic group in the sidearm, and at the same time there is electrostatic repulsion between the anionic carboxylate at the sidearm of **4** and anionic carboxylate or sulfonate of bile salts. Unexpectedly, the resulting complex stability of aminated *β*-CD **4** with CA is higher than that of native *β*-CD **1**, which is mainly attributed to the more favorable enthalpy change. The possible reason may be the enhanced cooperative van der Waals, hydrogen-bonding, and electrostatic interactions exceeding the decreased hydrophobicity of the interior of *β*-CD **4**.

Positively charged monoamino-modified *β*-CD **2** and modified *β*-CD **3** possessing an additional binding site in the chiral arm evidently enhance the molecular binding ability and selectivity towards CA and DCA compared to those for native *β*-CD **1**, which is mainly attributed to the more favorable enthalpy change accompanied with unfavorable entropy change [17]. The more favorable enthalpy change most likely originates from effective electrostatic interactions and the additional binding site of hydroxyl group. In addition, the

**Figure 3.** Structures of mono-modified *β*-CD derivatives

**Figure 4.** The possible binding modes of **11**–**14** (**11** (c); **12** (d); **13** (a); **14** (b)) with DCA

### **3.2. Complexation thermodynamics for bile salts and modified CD series**

#### *3.2.1. Aminated β-CDs*

310 Thermodynamics – Fundamentals and Its Application in Science

**Figure 3.** Structures of mono-modified *β*-CD derivatives

The microcalorimetric experiments of aminated *β*-CDs with bile salts clearly indicate that the majority of the inclusion complexes had a 1:1 stoichiometry [17]. Thermodynamically, the binding constants of **4** upon inclusion complexation with DCA, GCA, and TCA are less than that with natural *β*-CD **1**. It is reasonable that modified *β*-CD **4** decreased the microenvironment hydrophobicity of natural *β*-CD cavity due to the hydrophilic carboxylic group in the sidearm, and at the same time there is electrostatic repulsion between the anionic carboxylate at the sidearm of **4** and anionic carboxylate or sulfonate of bile salts. Unexpectedly, the resulting complex stability of aminated *β*-CD **4** with CA is higher than that of native *β*-CD **1**, which is mainly attributed to the more favorable enthalpy change. The possible reason may be the enhanced cooperative van der Waals, hydrogen-bonding, and electrostatic interactions exceeding the decreased hydrophobicity of the interior of *β*-CD **4**.

Positively charged monoamino-modified *β*-CD **2** and modified *β*-CD **3** possessing an additional binding site in the chiral arm evidently enhance the molecular binding ability and selectivity towards CA and DCA compared to those for native *β*-CD **1**, which is mainly attributed to the more favorable enthalpy change accompanied with unfavorable entropy change [17]. The more favorable enthalpy change most likely originates from effective electrostatic interactions and the additional binding site of hydroxyl group. In addition, the

unfavorable entropy change is likely to originate from the conformation fixation of host and guest and the rigid complex formation upon complexation. *β*-CD derivatives **2** and **3** give a lower binding ability upon complexation with GCA and TCA as compared to the complexation with CA and DCA, which is similar to that for the complexation of *β*-CD **1** and derivative **4**. For the same reason, the more polar side chains at C23 for GCA and TCA remarkably affect their binding thermodynamics.

Thermodynamics of Resulting Complexes Between Cyclodextrins and Bile Salts 313

The ITC experiments of hosts **13** and **14** with bile salts (CA, DCA, GCA, and TCA) also showed the typical titration curves of the 1:1 complex formation [21]. The stoichiometric ratio "*N*" observed from the curve-fitting results was within the range 0.9 to 1.1, which clearly indicated that the majority of the inclusion complexes had a 1:1 binding mode. Thermodynamically, the binding of all CDs with the bile salts was entirely driven by the favorable enthalpy changes accompanied by the unfavorable entropy changes. **14** gave the higher bind ability toward CA and DCA than **1** and **12** due to the introduction of D-tyrosine substituent and the conformational difference between **12** and **14**. In addition, the bind constant of **14** for DCA was slightly bigger than that for CA. Possessing a more hydrophobic structure due to the absence of the C-7 hydroxyl group as compared with CA, DCA was easier to bind to the *β*-CD cavity than CA, which consequently led to the more favorable hydrophobic interactions between hosts and guests. Host **14** exhibited the obviously smaller binding abilities for GCA and TCA guests than **1** and **12**. Thermodynamically, the decreased binding affinities of host **14** toward GCA and TCA arose from the entropy change rather than the enthalpy change due to the weakened hydrophobic interactions and the relatively poor size-fit between host and guest. Compared with **1** and **11**, **13** showed clearly decreased binding abilities toward all four of the bile salts, especially for GCA and TCA. Thermodynamically, the inclusion complexation of **13** with four bile salts exhibited the favorable enthalpy changes and unfavorable entropy changes. The favorable enthalpy gain of **13** was slightly higher than those of **1** and **11**, but the entropy loss of **13** was much more

The interactions of CA, DCA, GCA, and TCA with **15** and **16** have been studied by Ollila et al. by means of isothermal titration calorimetry [23]. The results show that both CA and DCA bound to **15** and **16** with a 1:1 stoichiometry. The binding constant was significantly higher for DCA to **15** and **16** compared to CA. This difference in binding affinity is likely explained by the more hydrophobic nature of DCA due to the absence of the C-7 hydroxyl group, which is present in CA. The binding affinity was somewhat lower for CA binding to **15** compared to **16**, while DCA showed a markedly lower affinity for **15** compared to **16**. GCA and TCA have lower affinities to **15** and **16** compared to CA and DCA. TCA bound with lower affinity to **15** compared to GCA. Both GCA and TCA gave the same 1:1

For **17**, all the hydroxyls are methylated, and the loss of hydrogen bonds for the resulting complexes is inevitable [24]. Therefore, host **17** only shows weak complex stability constants to bile salts, which are much lower than those of **1** and **16**. In addition, the release of higher energy water molecules in the cavity of *β*-CD upon complexation with guests makes the inclusion complexation more favorable, which cannot be obtained in the cases of **17** because almost no water molecule resides in the cavity of **17**. Besides that, **17** should need some conformational adjustment to accommodate bile guests, which is entropy-unfavorable for

than those of **1** and **11** toward corresponding guests.

stoichiometry for binding to **15** and **16** as did CA and DCA.

the inclusion complexation.

*3.2.4. Methyl-β-CD and 2-hydroxypropyl-β-CD* 

A study of 13C chemical shifts as a function of concentration at different pH values has been performed by Tato et al., which shows a different behavior of complexation for CA and DCA with **5** resulting in 1:1 and 1:2 inclusion complexes [22]. However, the complexation phenomena do not depend on the pH of the solution. 13C NMR chemical shifts of the host and guest molecules change on passing from the free to the complexed state. The side chains in **5** at position C-6 have a significant effect on the complexation process with the bile salts. The ROESY experiments confirm the overlap of the CA molecule with **5** resulting a 1:1 inclusion complex, while in the case of DCA molecule, the first molecule of **5** encapsulates the bile salt to a larger extent than the second molecule of **5**, resulting a 1:2 inclusion complex. Hence the most important factors for the formation of a stable inclusion complex are the relative size of **5** and the bile salt molecules, the nonpolar cavity of **5**, the hydrophobicity of the bile salts, and the presence of an electrostatic environment outside the toroidal cavity.

## *3.2.2. Nucleobase-modified β-CDs*

The nucleobase-modified *β*-CDs **8**–**10** exhibit distinguishable binding abilities toward bile salts compared with parent *β*-CD **1** [19]. Host **10** shows increased binding of TCA/GCA. Host **9** exhibits increased binding of GCA while hosts **8**–**10** show less binding of the other bile salts. The inclusion complexation of hosts **8**–**10** is driven by favorable enthalpy changes, accompanied with unfavorable entropy changes. The driven forces are hydrogen-bonding and van der Waals interactions, simultaneously producing marked geometric configuration change. Host **8** displays weaker binding ability for every bile salt than hosts **9** and **10** owing to expelling adenine group from *β*-CD cavity to accommodate bile guests in hosts **8**, which is unfavorable to the host–guest complexation.

## *3.2.3. Tryptophan- and tyrosine-modified β-CDs*

The microcalorimetric titrations of L/D-Trp-modified *β*-CD (**11** and **12**) with a series of bile acids, i.e., CA, DCA, GCA, and TCA, showed typical titration curves, which can be nicely analyzed by assuming the 1:1 complex stoichiometry [20]. Modified *β*-CDs **11** and **12**  exhibited appreciably smaller binding abilities for GCA and TCA guests than those of native *β*-CD **1** since GCA and TCA, possessing a strongly hydrophilic and hydrated sulfonate tail, are not expected to deeply penetrate into the CD cavity by removing the originally included L/D-Trp group out of the hydrophobic cavity. In contrast, DCA and CA, possessing a less hydrophilic/hydrated carboxylate tail, showed comparable or even stronger binding and higher selectivities for host's chirality than TCA and GCA.

The ITC experiments of hosts **13** and **14** with bile salts (CA, DCA, GCA, and TCA) also showed the typical titration curves of the 1:1 complex formation [21]. The stoichiometric ratio "*N*" observed from the curve-fitting results was within the range 0.9 to 1.1, which clearly indicated that the majority of the inclusion complexes had a 1:1 binding mode. Thermodynamically, the binding of all CDs with the bile salts was entirely driven by the favorable enthalpy changes accompanied by the unfavorable entropy changes. **14** gave the higher bind ability toward CA and DCA than **1** and **12** due to the introduction of D-tyrosine substituent and the conformational difference between **12** and **14**. In addition, the bind constant of **14** for DCA was slightly bigger than that for CA. Possessing a more hydrophobic structure due to the absence of the C-7 hydroxyl group as compared with CA, DCA was easier to bind to the *β*-CD cavity than CA, which consequently led to the more favorable hydrophobic interactions between hosts and guests. Host **14** exhibited the obviously smaller binding abilities for GCA and TCA guests than **1** and **12**. Thermodynamically, the decreased binding affinities of host **14** toward GCA and TCA arose from the entropy change rather than the enthalpy change due to the weakened hydrophobic interactions and the relatively poor size-fit between host and guest. Compared with **1** and **11**, **13** showed clearly decreased binding abilities toward all four of the bile salts, especially for GCA and TCA. Thermodynamically, the inclusion complexation of **13** with four bile salts exhibited the favorable enthalpy changes and unfavorable entropy changes. The favorable enthalpy gain of **13** was slightly higher than those of **1** and **11**, but the entropy loss of **13** was much more than those of **1** and **11** toward corresponding guests.

#### *3.2.4. Methyl-β-CD and 2-hydroxypropyl-β-CD*

312 Thermodynamics – Fundamentals and Its Application in Science

remarkably affect their binding thermodynamics.

toroidal cavity.

*3.2.2. Nucleobase-modified β-CDs* 

unfavorable to the host–guest complexation.

*3.2.3. Tryptophan- and tyrosine-modified β-CDs* 

higher selectivities for host's chirality than TCA and GCA.

unfavorable entropy change is likely to originate from the conformation fixation of host and guest and the rigid complex formation upon complexation. *β*-CD derivatives **2** and **3** give a lower binding ability upon complexation with GCA and TCA as compared to the complexation with CA and DCA, which is similar to that for the complexation of *β*-CD **1** and derivative **4**. For the same reason, the more polar side chains at C23 for GCA and TCA

A study of 13C chemical shifts as a function of concentration at different pH values has been performed by Tato et al., which shows a different behavior of complexation for CA and DCA with **5** resulting in 1:1 and 1:2 inclusion complexes [22]. However, the complexation phenomena do not depend on the pH of the solution. 13C NMR chemical shifts of the host and guest molecules change on passing from the free to the complexed state. The side chains in **5** at position C-6 have a significant effect on the complexation process with the bile salts. The ROESY experiments confirm the overlap of the CA molecule with **5** resulting a 1:1 inclusion complex, while in the case of DCA molecule, the first molecule of **5** encapsulates the bile salt to a larger extent than the second molecule of **5**, resulting a 1:2 inclusion complex. Hence the most important factors for the formation of a stable inclusion complex are the relative size of **5** and the bile salt molecules, the nonpolar cavity of **5**, the hydrophobicity of the bile salts, and the presence of an electrostatic environment outside the

The nucleobase-modified *β*-CDs **8**–**10** exhibit distinguishable binding abilities toward bile salts compared with parent *β*-CD **1** [19]. Host **10** shows increased binding of TCA/GCA. Host **9** exhibits increased binding of GCA while hosts **8**–**10** show less binding of the other bile salts. The inclusion complexation of hosts **8**–**10** is driven by favorable enthalpy changes, accompanied with unfavorable entropy changes. The driven forces are hydrogen-bonding and van der Waals interactions, simultaneously producing marked geometric configuration change. Host **8** displays weaker binding ability for every bile salt than hosts **9** and **10** owing to expelling adenine group from *β*-CD cavity to accommodate bile guests in hosts **8**, which is

The microcalorimetric titrations of L/D-Trp-modified *β*-CD (**11** and **12**) with a series of bile acids, i.e., CA, DCA, GCA, and TCA, showed typical titration curves, which can be nicely analyzed by assuming the 1:1 complex stoichiometry [20]. Modified *β*-CDs **11** and **12**  exhibited appreciably smaller binding abilities for GCA and TCA guests than those of native *β*-CD **1** since GCA and TCA, possessing a strongly hydrophilic and hydrated sulfonate tail, are not expected to deeply penetrate into the CD cavity by removing the originally included L/D-Trp group out of the hydrophobic cavity. In contrast, DCA and CA, possessing a less hydrophilic/hydrated carboxylate tail, showed comparable or even stronger binding and The interactions of CA, DCA, GCA, and TCA with **15** and **16** have been studied by Ollila et al. by means of isothermal titration calorimetry [23]. The results show that both CA and DCA bound to **15** and **16** with a 1:1 stoichiometry. The binding constant was significantly higher for DCA to **15** and **16** compared to CA. This difference in binding affinity is likely explained by the more hydrophobic nature of DCA due to the absence of the C-7 hydroxyl group, which is present in CA. The binding affinity was somewhat lower for CA binding to **15** compared to **16**, while DCA showed a markedly lower affinity for **15** compared to **16**. GCA and TCA have lower affinities to **15** and **16** compared to CA and DCA. TCA bound with lower affinity to **15** compared to GCA. Both GCA and TCA gave the same 1:1 stoichiometry for binding to **15** and **16** as did CA and DCA.

For **17**, all the hydroxyls are methylated, and the loss of hydrogen bonds for the resulting complexes is inevitable [24]. Therefore, host **17** only shows weak complex stability constants to bile salts, which are much lower than those of **1** and **16**. In addition, the release of higher energy water molecules in the cavity of *β*-CD upon complexation with guests makes the inclusion complexation more favorable, which cannot be obtained in the cases of **17** because almost no water molecule resides in the cavity of **17**. Besides that, **17** should need some conformational adjustment to accommodate bile guests, which is entropy-unfavorable for the inclusion complexation.

## **3.3. Binding modes for bile salts and chromophore-modified CD series**

## *3.3.1. Anthryl-modified β-CDs*

1H ROESY experiment has been performed by Liu et al. to confirm the binding model of host **19** with CA [25]. The results indicate that CA molecule is included into the hydrophobic cavity from the secondary side of *β*-CD, with the side chain folded towards the steroid skeleton, and the anthracene group is excluded outside the cavity of *β*-CD. CA molecule and the tether of *β*-CD can be co-included into the cavity through the induced-fit interaction between host and guest.

Thermodynamics of Resulting Complexes Between Cyclodextrins and Bile Salts 315

encapsulate more tightly the steroid guests than the other, through the size/shape-matching

Thermodynamically, the inclusion complexation of **18**–**20** with steroid guests is entirely driven by favorable enthalpy contribution with negative or minor positive entropy change [25]. The strong interaction between host and guest leads to the more favorable negative enthalpy change, which is counteracted by the relative more unfavorable negative entropy change. The introduction of anthracene group with different chain length, and additional binding site to CD rim can significantly enhance the binding ability of parent CD toward steroid guests.

The binding behaviors of two *β*-CD derivatives bearing 8-hydroxyquinolino and triazolylquinolino groups (**21** and **22**) with bile salts have been studied in aqueous buffer solution by means of microcalorimetrical titration [26]. The results showed that the host–guest binding behaviors were mainly driven by the favorable enthalpy changes, accompanied by the unfavorable entropy changes, and the hydrogen-bonding interactions and van der Waals

The binding stoichiometry of the permethylated *β*-CD derivatives **23** and **24** with bile salts has been determined by the Job's plot method, which showed that hosts and guests formed 1:1 complexes [24]. Thermodynamically, hosts **23** and **24** show much higher binding ability to bile salts than permethylated *β*-CD **17** when the naphthalene (or quinoline) sidearm is appended on it. The pronounced enhancement of complex stabilities for hosts **23** and **24** can be attributed to the cooperative complex interactions of both the cavity of permethylated *β*-CD and the chromophore sidearms. Furthermore, it should be mentioned that host **24** always forms more stable complexes with bile guests than host **23**, which indicates that the N atom on

the quinoline ring plays a crucial role during the course of recognition of bile guests.

interactions were the main driven forces governing the host–guest binding.

and the induced-fit interactions between the host and guest.

**Figure 5.** The possible binding mode of **22** with DCA

*3.4.2. Quinolinyl- and naphthyl-modified β-CDs* 

## *3.3.2. Quinolinyl- and naphthyl-modified β-CDs*

2D ROESY NMR experiments accompanied with molecular modeling studies have been performed by Liu et al. to investigate the binding modes of DCA with **21** and **22** [26]. The results show that the side chain and D-ring of bile salts were encapsulated in the *β*-CD cavity from the wide opening (Figure 5).

2D ROESY NMR experiment of complex of **23** with CA has also been performed to investigate the binding geometry between permethylated *β*-CDs and bile salts [24]. The results show that CA is deeply included into the cavity of host **23** with its ring A in the region of the narrow side and ring D in the region of the broad side. However, upon complexation with CA guest, the appended naphthalene group in **23** is not entirely expelled out of the cavity of permethylated *β*-CD but is removed from the central cavity to the region of the narrow torus rim. The cooperative inclusion manner of both guest molecule and substituent sidearm into the cavity is mainly benefited from the extended framework of permethylated *β*-CD.

## **3.4. Complexation thermodynamics for bile salts and chromophore-modified CD series**

## *3.4.1. Anthryl-modified β-CDs*

The stoichiometric ratios gotten from curve-fitting results of the binding isotherm fell within the range of 0.9–1.1, indicating that the resulting complexes of bile salts and CDs (**18**–**20**) are 1:1 [25]. As compared with parent *β*-CD **1**, modified *β*-CDs **18**–**20** with different chain length not only enhanced molecular binding ability but also significant molecular selectivity upon inclusion complexation with homologous steroids, except for resulting complex of **20** with TCA. The stability constants for the inclusion complexation of hosts and the each steroid molecule decreased in the following order: DCA > CA > GCA > TCA. The hydroxyl group at the C7 carbon atom of CA, GCA and TCA guests prevented deeper inclusion of the steroids in the *β*-CD cavity than that of DCA guest. On the other hand, the tether length of the host and induced-fit interactions also played crucial roles in the selective molecular binding process of modified *β*-CD **18**–**20** with guests. Host **19** possessing suitable tether length could encapsulate more tightly the steroid guests than the other, through the size/shape-matching and the induced-fit interactions between the host and guest.

Thermodynamically, the inclusion complexation of **18**–**20** with steroid guests is entirely driven by favorable enthalpy contribution with negative or minor positive entropy change [25]. The strong interaction between host and guest leads to the more favorable negative enthalpy change, which is counteracted by the relative more unfavorable negative entropy change. The introduction of anthracene group with different chain length, and additional binding site to CD rim can significantly enhance the binding ability of parent CD toward steroid guests.

**Figure 5.** The possible binding mode of **22** with DCA

314 Thermodynamics – Fundamentals and Its Application in Science

*3.3.2. Quinolinyl- and naphthyl-modified β-CDs* 

cavity from the wide opening (Figure 5).

*3.3.1. Anthryl-modified β-CDs* 

between host and guest.

permethylated *β*-CD.

*3.4.1. Anthryl-modified β-CDs* 

**series** 

**3.3. Binding modes for bile salts and chromophore-modified CD series** 

1H ROESY experiment has been performed by Liu et al. to confirm the binding model of host **19** with CA [25]. The results indicate that CA molecule is included into the hydrophobic cavity from the secondary side of *β*-CD, with the side chain folded towards the steroid skeleton, and the anthracene group is excluded outside the cavity of *β*-CD. CA molecule and the tether of *β*-CD can be co-included into the cavity through the induced-fit interaction

2D ROESY NMR experiments accompanied with molecular modeling studies have been performed by Liu et al. to investigate the binding modes of DCA with **21** and **22** [26]. The results show that the side chain and D-ring of bile salts were encapsulated in the *β*-CD

2D ROESY NMR experiment of complex of **23** with CA has also been performed to investigate the binding geometry between permethylated *β*-CDs and bile salts [24]. The results show that CA is deeply included into the cavity of host **23** with its ring A in the region of the narrow side and ring D in the region of the broad side. However, upon complexation with CA guest, the appended naphthalene group in **23** is not entirely expelled out of the cavity of permethylated *β*-CD but is removed from the central cavity to the region of the narrow torus rim. The cooperative inclusion manner of both guest molecule and substituent sidearm into the cavity is mainly benefited from the extended framework of

**3.4. Complexation thermodynamics for bile salts and chromophore-modified CD** 

The stoichiometric ratios gotten from curve-fitting results of the binding isotherm fell within the range of 0.9–1.1, indicating that the resulting complexes of bile salts and CDs (**18**–**20**) are 1:1 [25]. As compared with parent *β*-CD **1**, modified *β*-CDs **18**–**20** with different chain length not only enhanced molecular binding ability but also significant molecular selectivity upon inclusion complexation with homologous steroids, except for resulting complex of **20** with TCA. The stability constants for the inclusion complexation of hosts and the each steroid molecule decreased in the following order: DCA > CA > GCA > TCA. The hydroxyl group at the C7 carbon atom of CA, GCA and TCA guests prevented deeper inclusion of the steroids in the *β*-CD cavity than that of DCA guest. On the other hand, the tether length of the host and induced-fit interactions also played crucial roles in the selective molecular binding process of modified *β*-CD **18**–**20** with guests. Host **19** possessing suitable tether length could

## *3.4.2. Quinolinyl- and naphthyl-modified β-CDs*

The binding behaviors of two *β*-CD derivatives bearing 8-hydroxyquinolino and triazolylquinolino groups (**21** and **22**) with bile salts have been studied in aqueous buffer solution by means of microcalorimetrical titration [26]. The results showed that the host–guest binding behaviors were mainly driven by the favorable enthalpy changes, accompanied by the unfavorable entropy changes, and the hydrogen-bonding interactions and van der Waals interactions were the main driven forces governing the host–guest binding.

The binding stoichiometry of the permethylated *β*-CD derivatives **23** and **24** with bile salts has been determined by the Job's plot method, which showed that hosts and guests formed 1:1 complexes [24]. Thermodynamically, hosts **23** and **24** show much higher binding ability to bile salts than permethylated *β*-CD **17** when the naphthalene (or quinoline) sidearm is appended on it. The pronounced enhancement of complex stabilities for hosts **23** and **24** can be attributed to the cooperative complex interactions of both the cavity of permethylated *β*-CD and the chromophore sidearms. Furthermore, it should be mentioned that host **24** always forms more stable complexes with bile guests than host **23**, which indicates that the N atom on the quinoline ring plays a crucial role during the course of recognition of bile guests.

316 Thermodynamics – Fundamentals and Its Application in Science


Hosts Guests pH *K*s *H TS* Methods Refs. **11** CA 7.2 (PBS) 2020 –23.2 –4.3 ITC 20

**12** CA 7.2 (PBS) 6680 –37.9 –14.5 ITC 20

**13** CA 7.2 (PBS) 871 –26.7 –9.9 ITC 21

**14** CA 7.2 (PBS) 8689 –41.7 –19.2 ITC 21

**<sup>15</sup>**CA 7.4

**<sup>16</sup>**CA 7.4

DCA 7.4

GCA 7.4

TCA 7.4

DCA 7.4

GCA 7.4

TCA 7.4

DCA 7.2 (PBS) 2310 –32.1 –12.9 ITC 20 GCA 7.2 (PBS) 1110 –23.4 –6.0 ITC 20 TCA 7.2 (PBS) 1060 –23.1 –5.8 ITC 20

DCA 7.2 (PBS) 6770 –46.0 –24.1 ITC 20 GCA 7.2 (PBS) 1760 –24.9 –6.4 ITC 20 TCA 7.2 (PBS) 1470 –24.3 –6.2 ITC 20

DCA 7.2 (PBS) 1087 –33.1 –15.8 ITC 21 GCA 7.2 (PBS) 428 –28.3 –13.3 ITC 21 TCA 7.2 (PBS) 391 –25.7 –10.9 ITC 21

DCA 7.2 (PBS) 9962 –50.5 –27.9 ITC 21 GCA 7.2 (PBS) 1105 –30.5 –13.1 ITC 21 TCA 7.2 (PBS) 809 –26.7 –10.1 ITC 21

(Tris–NaCl) 2510 –7.9 38.6 ITC 23

(Tris–NaCl) 4429 –10.65 34.0 ITC 23

(Tris–NaCl) 1764 –8.2 34.5 ITC 23

(Tris–NaCl) 1399 –8.75 31.0 ITC 23

(Tris–NaCl) 2693 –5.7 46.6 ITC 23

(Tris–NaCl) 6276 –6.8 49.9 ITC 23

(Tris–NaCl) 1958 –7.9 36.6 ITC 23

(Tris–NaCl) 2148 –7.2 39.6 ITC 23

**17** CA 7.2 (PBS) 61 ITC 24

**18** CA 7.2 (PBS) 11760 –42.70 –19.47 ITC 25

DCA 7.2 (PBS) 774 ITC 24 GCA 7.2 (PBS) 228 ITC 24 TCA 7.2 (PBS) 162 ITC 24

DCA 7.2 (PBS) 15030 –42.72 –18.87 ITC 25 GCA 7.2 (PBS) 3870 –25.23 –4.75 ITC 25 TCA 7.2 (PBS) 2647 –20.99 –1.47 ITC 25


Hosts Guests pH *K*s *H TS* Methods Refs. **1** CA 7.2 (PBS) 4068 –22.98 –2.38 ITC 17 DCA 7.2 (PBS) 4844 –25.79 –4.76 ITC 17 GCA 7.2 (PBS) 2394 –22.99 –3.7 ITC 17 TCA 7.2 (PBS) 2293 –23.77 –4.59 ITC 17 **2** CA 7.2 (PBS) 11160 –25.53 –2.43 ITC 17 DCA 7.2 (PBS) 7705 –32.16 –9.98 ITC 17 GCA 7.2 (PBS) 2075 –25.90 –6.97 ITC 17 TCA 7.2 (PBS) 2309 –26.89 –7.69 ITC 17 **3** CA 7.2 (PBS) 16920 –28.11 –3.98 ITC 17 DCA 7.2 (PBS) 9382 –35.78 –13.11 ITC 17 GCA 7.2 (PBS) 3904 –24.74 –4.24 ITC 17 TCA 7.2 (PBS) 2796 –20.37 –0.7 ITC 17 **4** CA 7.2 (PBS) 4832 –24.90 –3.87 ITC 17 DCA 7.2 (PBS) 4034 –38.91 –18.33 ITC 17 GCA 7.2 (PBS) 2221 –19.75 –0.65 ITC 17 TCA 7.2 (PBS) 1322 –32.75 –14.93 ITC 17 **5** CA 7.2 (PBS) 11060 –36.44 –13.36 ITC 18

> DCA 7.2 (PBS) 11350 –41.15 –18.01 ITC 18 GCA 7.2 (PBS) 3050 –25.48 –5.59 ITC 18 TCA 7.2 (PBS) 3061 –18.43 1.47 ITC 18

> DCA 7.2 (PBS) 30300 –38.13 –12.55 ITC 18 GCA 7.2 (PBS) 3098 –25.82 –5.89 ITC 18 TCA 7.2 (PBS) 4659 –14.86 6.08 ITC 18

> DCA 7.2 (PBS) 24785 –27.59 –2.51 ITC 18 GCA 7.2 (PBS) 4722 –21.22 –0.25 ITC 18 TCA 7.2 (PBS) 3022 –24.29 –4.43 ITC 18

> DCA 7.2 (PBS) 2839 –34.8 –14.9 ITC 19 GCA 7.2 (PBS) 1032 –25.7 –8.5 ITC 19 TCA 7.2 (PBS) 1003 –26.6 –9.5 ITC 19

> DCA 7.2 (PBS) 3137 –34.0 –14.0 ITC 19 GCA 7.2 (PBS) 2898 –31.2 –11.4 ITC 19 TCA 7.2 (PBS) 2284 –30.0 –10.8 ITC 19

> DCA 7.2 (PBS) 3813 –33.7 –13.3 ITC 19 GCA 7.2 (PBS) 3140 –29.6 –9.7 ITC 19 TCA 7.2 (PBS) 2402 –28.8 –9.5 ITC 19

**6** CA 7.2 (PBS) 25315 –34.26 –9.13 ITC 18

**7** CA 7.2 (PBS) 25850 –23.53 1.65 ITC 18

**8** CA 7.2 (PBS) 1726 –31.0 –13.3 ITC 19

**9** CA 7.2 (PBS) 2567 –29.3 –9.9 ITC 19

**10** CA 7.2 (PBS) 2605 –28.6 –9.1 ITC 19



Hosts Guests pH *K*s *H TS* Methods Refs. **27** CA 7.0 (PBS) 1650 Fluorescence 38

**28** CA 7.0 (PBS) 588 Fluorescence 38

**29** CA 7.0 (PBS) 60.4 Fluorescence 38

**30** CA aqueous solution – Fluorescence 36

**31** CA aqueous solution – Fluorescence 36

**32** CA aqueous solution – Fluorescence 36

–: The guest-induced variations in the excimer emission are too small for these values to be determined.

**Table 1.** Complex stability constants (*K*s/M1), enthalpy (*H*°/(kJmol1)), and entropy changes

(*TS*°/(kJmol1)) for intermolecular complexation of bile salts with natural *β*-CD and its mono-modified

All the permethylated *β*-CD derivatives (**17**, **23** and **24**) present the weakest binding ability to CA guest because the cavity of permethylated *β*-CD possesses a broader hydrophobic region in comparison with **1**, and then permethylated *β*-CD is more suitable to include bile guests with longer tails (GCA and TCA) than **1** [24]. Moreover, there are similar structures between CA and DCA except for the difference of one hydroxyl in ring B. It is attractive that DCA can be included more tightly by **17**, **23** and **24** than CA. One reasonable explanation is that the absence of one hydroxyl in ring B makes the whole framework of DCA more hydrophobic than CA, and thereby DCA is more suitable to be immersed into the cavity of

ROESY experiments for the complexes of CDs (**25**, **26**, **33**, and **35**) and DCA have been performed to illustrate the binding modes between the CDs and bile salts [27]. The results show that the bridge linker does not interact with DCA and the bile salt molecule is not

PBS: Phosphate Buffer Solution; ITC: Isothermal Titration Calorimetry;

**4.1. Binding modes for bile salts and bridged CD series** 

*4.1.1. Diseleno- and bipyridine-bridged β-CDs* 

Tris: Tris(hydroxymethyl)aminomethane;

derivatives in aqueous solution

permethylated *β*-CDs.

**4. Bridged CD series** 

DCA 7.0 (PBS) 2660 Fluorescence 38

DCA 7.0 (PBS) 1520 Fluorescence 38

DCA 7.0 (PBS) 1030 Fluorescence 38

DCA aqueous solution – Fluorescence 36 GCA aqueous solution – Fluorescence 36

DCA aqueous solution – Fluorescence 36 GCA aqueous solution – Fluorescence 36

DCA aqueous solution – Fluorescence 36 GCA aqueous solution – Fluorescence 36


PBS: Phosphate Buffer Solution; ITC: Isothermal Titration Calorimetry;

Tris: Tris(hydroxymethyl)aminomethane;

318 Thermodynamics – Fundamentals and Its Application in Science

**<sup>23</sup>**CA 7.2

**<sup>24</sup>**CA 7.2

**<sup>25</sup>**CA 7.4

**<sup>26</sup>**CA 7.4

DCA 7.2

GCA 7.2

TCA 7.2

DCA 7.2

GCA 7.2

TCA 7.2

DCA 7.4

DCA 7.4

Hosts Guests pH *K*s *H TS* Methods Refs. **19** CA 7.2 (PBS) 18965 –32.37 –7.95 ITC 25

**20** CA 7.2 (PBS) 11850 –33.23 –9.98 ITC 25

**21** CA 7.2 (PBS) 2216 –25.04 –5.94 ITC 26

**22** CA 7.2 (PBS) 2443 –35.60 –16.25 ITC 26

DCA 7.2 (PBS) 22485 –36.48 –11.46 ITC 25 GCA 7.2 (PBS) 4888 –21.61 –0.56 ITC 25 TCA 7.2 (PBS) 3755 –19.15 0.7 ITC 25

DCA 7.2 (PBS) 13365 –39.57 –16.20 ITC 25 GCA 7.2 (PBS) 4254 –20.07 0.65 ITC 25 TCA 7.2 (PBS) 1833 –26.58 –7.96 ITC 25

DCA 7.2 (PBS) 2007 –51.92 –33.07 ITC 26 GCA 7.2 (PBS) 2434 –31.07 –11.74 ITC 26 TCA 7.2 (PBS) 3478 –23.98 –3.76 ITC 26

DCA 7.2 (PBS) 3177 –33.89 –13.90 ITC 26 GCA 7.2 (PBS) 2811 –34.94 –15.24 ITC 26 TCA 7.2 (PBS) 2809 –30.37 –10.68 ITC 26

(Tris–HCl) 910 Fluorescence 24

(Tris–HCl) 4320 Fluorescence 24

(Tris–HCl) 4340 Fluorescence 24

(Tris–HCl) 3820 Fluorescence 24

(Tris–HCl) 3290 Fluorescence 24

(Tris–HCl) 7460 Fluorescence 24

(Tris–HCl) 10690 Fluorescence 24

(Tris–HCl) 8710 Fluorescence 24

(Tris–NaCl) 7400 –22.3 –0.2 ITC 27

(Tris–NaCl) 6700 –32.1 –10.2 ITC 27

(Tris–NaCl) 1280 –28.3 –10.5 ITC 27

(Tris–NaCl) 2570 –33.3 –13.8 ITC 27

–: The guest-induced variations in the excimer emission are too small for these values to be determined.

**Table 1.** Complex stability constants (*K*s/M1), enthalpy (*H*°/(kJmol1)), and entropy changes (*TS*°/(kJmol1)) for intermolecular complexation of bile salts with natural *β*-CD and its mono-modified derivatives in aqueous solution

All the permethylated *β*-CD derivatives (**17**, **23** and **24**) present the weakest binding ability to CA guest because the cavity of permethylated *β*-CD possesses a broader hydrophobic region in comparison with **1**, and then permethylated *β*-CD is more suitable to include bile guests with longer tails (GCA and TCA) than **1** [24]. Moreover, there are similar structures between CA and DCA except for the difference of one hydroxyl in ring B. It is attractive that DCA can be included more tightly by **17**, **23** and **24** than CA. One reasonable explanation is that the absence of one hydroxyl in ring B makes the whole framework of DCA more hydrophobic than CA, and thereby DCA is more suitable to be immersed into the cavity of permethylated *β*-CDs.

## **4. Bridged CD series**

### **4.1. Binding modes for bile salts and bridged CD series**

### *4.1.1. Diseleno- and bipyridine-bridged β-CDs*

ROESY experiments for the complexes of CDs (**25**, **26**, **33**, and **35**) and DCA have been performed to illustrate the binding modes between the CDs and bile salts [27]. The results show that the bridge linker does not interact with DCA and the bile salt molecule is not

cooperatively bound by the two cavities of one dimer molecule. DCA is not included in the cavity of the dimer from the primary side (narrow open), but penetrates slightly into the cavity from the secondary side (wide open) using the side chain and D-ring moiety. For **33** (Figure 6), the A-ring moiety of DCA is simultaneously shallowly included in one of the cavities of another CD to form a liner structure. For monomer **25**, the D-ring moiety of DCA penetrates deep into the cavity of **25** from the secondary side. However, for monomer **26**, DCA is included in the cavity of **26** from the secondary side by its A-ring moiety, differing from other CDs (by D-ring moiety).

Thermodynamics of Resulting Complexes Between Cyclodextrins and Bile Salts 321

**Figure 6.** Structures of bridged *β*-CDs

To further obtain the information about the binding modes of bile salts with diseleno- and bipyridine-bridged *β*-CDs, 2D ROESY spectra for typical host–guest pairs have also been determined by Liu et al. [28]. For dimer **35** and CA, the results indicate that the carboxylate side chain and D-ring of CA may penetrate into the CD cavity from the secondary side shallowly and two CA molecules are bound separately into two cavities of **35** from the secondary side, which is consistent with the 1:2 binding stoichiometry (Figure 7a). For dimer **39** and DCA, the results are quite different and show a 1:1 cooperative binding mode. The A-ring of DCA penetrates deeply into one CD cavity of **39**, attributing to the less steric hindrance and higher hydrophobicity of the substituent group on the C-7 position of DCA (Figure 7b). Under the same experiment using DCA as guest, host **38** adopts a different binding mode from **39**. The carboxylate side chain of two DCA molecules deeply penetrates into the CD cavity of **38** from the secondary side separately.

## *4.1.2. Oligoethylenediamino-bridged β-CDs*

To obtain the information about the binding modes between bile salts and oligoethylenediamino-bridged *β*-CD dimers (**42**–**44**), 2D ROESY spectra for typical host– guest pairs have been determined by Liu et al. [29]. The results of ROESY experiments indicated that the D ring and side-chain of bile salt guest enter one *β*-CD cavity from the wide opening, and the linker group is partially self-included in the other *β*-CD cavity (Figure 8).

## *4.1.3. Aromatic diamino- and sulfonyldianiline-bridged β-CDs*

From ROESY experiments, Zhao et al. found that the D-ring of CA is wholly included in the CD cavity of **45** from the wide opening, while the side-chain is located near the narrow opening of CD cavity and folded toward the steroid body and the phenyl moiety is not driven out of the CD cavity even after the guest inclusion [30]. Similar binding mode is also observed in other cases of **45**/bile salts complexes.

The binding modes between the aromatic diamino-bridged *β*-CDs **46**–**48** and bile salts have also been investigated by Zhao et al. via 2D ROESY experiments and the results show that the D-ring of CA is wholly included in the CD cavity with the wide opening, while the side chain is located near the narrow opening of the CD cavity and is folded toward the steroid body [31]. The phenyl moiety is not driven out of the CD cavity even after the guest inclusion.

**Figure 6.** Structures of bridged *β*-CDs

320 Thermodynamics – Fundamentals and Its Application in Science

into the CD cavity of **38** from the secondary side separately.

*4.1.3. Aromatic diamino- and sulfonyldianiline-bridged β-CDs* 

observed in other cases of **45**/bile salts complexes.

*4.1.2. Oligoethylenediamino-bridged β-CDs* 

(Figure 8).

from other CDs (by D-ring moiety).

cooperatively bound by the two cavities of one dimer molecule. DCA is not included in the cavity of the dimer from the primary side (narrow open), but penetrates slightly into the cavity from the secondary side (wide open) using the side chain and D-ring moiety. For **33** (Figure 6), the A-ring moiety of DCA is simultaneously shallowly included in one of the cavities of another CD to form a liner structure. For monomer **25**, the D-ring moiety of DCA penetrates deep into the cavity of **25** from the secondary side. However, for monomer **26**, DCA is included in the cavity of **26** from the secondary side by its A-ring moiety, differing

To further obtain the information about the binding modes of bile salts with diseleno- and bipyridine-bridged *β*-CDs, 2D ROESY spectra for typical host–guest pairs have also been determined by Liu et al. [28]. For dimer **35** and CA, the results indicate that the carboxylate side chain and D-ring of CA may penetrate into the CD cavity from the secondary side shallowly and two CA molecules are bound separately into two cavities of **35** from the secondary side, which is consistent with the 1:2 binding stoichiometry (Figure 7a). For dimer **39** and DCA, the results are quite different and show a 1:1 cooperative binding mode. The A-ring of DCA penetrates deeply into one CD cavity of **39**, attributing to the less steric hindrance and higher hydrophobicity of the substituent group on the C-7 position of DCA (Figure 7b). Under the same experiment using DCA as guest, host **38** adopts a different binding mode from **39**. The carboxylate side chain of two DCA molecules deeply penetrates

To obtain the information about the binding modes between bile salts and oligoethylenediamino-bridged *β*-CD dimers (**42**–**44**), 2D ROESY spectra for typical host– guest pairs have been determined by Liu et al. [29]. The results of ROESY experiments indicated that the D ring and side-chain of bile salt guest enter one *β*-CD cavity from the wide opening, and the linker group is partially self-included in the other *β*-CD cavity

From ROESY experiments, Zhao et al. found that the D-ring of CA is wholly included in the CD cavity of **45** from the wide opening, while the side-chain is located near the narrow opening of CD cavity and folded toward the steroid body and the phenyl moiety is not driven out of the CD cavity even after the guest inclusion [30]. Similar binding mode is also

The binding modes between the aromatic diamino-bridged *β*-CDs **46**–**48** and bile salts have also been investigated by Zhao et al. via 2D ROESY experiments and the results show that the D-ring of CA is wholly included in the CD cavity with the wide opening, while the side chain is located near the narrow opening of the CD cavity and is folded toward the steroid body [31].

The phenyl moiety is not driven out of the CD cavity even after the guest inclusion.

To obtain the information about the binding modes between bile salts and sulfonyldianilinebridged *β*-CD **49**, 2D ROESY spectra for typical host–guest pairs have further been determined by Zhao et al. [32]. The correlation signals, along with the 1:1 binding stoichiometry, jointly indicate a host-linker-guest binding mode between **49** and CA. That is, upon complexation with **49**, the carboxylate tail and the D ring of CA penetrate into one CD cavity of **49** from the wide opening deeply, while the phenyl moiety of the CD linker is partially self-included in the other *β*-CD cavity. Similar binding modes are also observed in other cases of **49**/bile salt complexes.

Thermodynamics of Resulting Complexes Between Cyclodextrins and Bile Salts 323

**4.2. Complexation thermodynamics for bile salts and bridged CD series** 

To elucidate the difference in binding behavior between the CD dimer and monomer, two CD dimers (**33** and **35**) and their monomer analogs (**25** and **26**) have been used for titration microcalorimetry with CA and DCA [27]. It is interesting that the results of the thermodynamic measurements show a 1:1 binding stoichiometry for hosts **25**, **26** and **33**, but 1:2 stoichiometry for host **35**. In addition, although the stability constants for the complexation between dimer **33** and the bile salts are much larger than those for monomer **26**, the long-linked dimer **35** unusually displays a lower cavity binding ability than its corresponding monomer **25** upon complexation with both guests CA and DCA. The enhancement of the binding ability of dimer **33** compared to monomer **26** could be ascribed not only to the cooperative binding but also partly to the peculiar self-inclusion conformation of **26** that leads to more unfavorable entropy changes, especially for the **26**– CA pair. For **35**, the two guest molecules are separately and independently included in the two cavities of **35** because the longer linker, especially the ethylenediamino moiety of dimer **35**, makes it possess a relatively large conformational freedom. As the considerable entropy loss cancels the advantage of enthalpy gain, dimer **35** displays relatively weak binding abilities. Both hosts **35** and **25** show similar binding ability for DCA and CA. The reason is that either binding with host **35** or host **25**, the two guest bile salts are included into the cavity of CDs by its D-ring and side-chain moiety, which reduces the influence of the substituent in C7. However, while binding with hosts **33** and **26**, the A-ring moiety participates in the binding process, so the more hydrophobic C7 substituent of DCA makes it bind more strongly with the host CDs, giving the higher binding constants than with CA,

Either for diseleno-bridged *β*-CDs (**34**–**37**) or for bipyridine-bridged *β*-CDs (**38**–**41**), the host– guest stoichiometry changes in the same order, that is, from 1:2 to 1:1 with the increase of spacer length [28]. For diseleno-bridged *β*-CDs, only **36** and **37** adopt the 1:1 binding mode. However, for bipyridine-bridged *β*-CDs, only host **38** adopts the 1:2 binding mode; the others all show the 1:1 cooperative binding mode. The thermodynamic results reveal that, with the longest spacer, **37** gives the largest stability constants in all diseleno-bridged *β*-CDs, while the largest stability constants of bipyridine-bridged *β*-CDs toward each guest molecule is obtained by the dimers **39** and **40** with the moderate spacer lengths, which suggests that only the CD dimers possessing the proper spacer length can give the perfect

For the dimers adopting 1:1 cooperative binding mode, the enthalpy changes are not only the main contribution to the binding process but also the determining factor for the binding abilities [28]. Comparing the diseleno-bridged *β*-CDs with bipyridine-bridged *β*-CDs, all of the bipyridine-bridged *β*-CDs display much stronger binding abilities toward bile salts than corresponding diseleno-bridged *β*-CDs, which indicate that the presence of rigid spacer favors formation of a relatively fixed binding mode and results in the close contact between

*4.2.1. Diseleno- and bipyridine-bridged β-CDs* 

especially for host **26**.

cooperative binding toward guests.

## *4.1.4. Binaphthyl-, biquinoline- and dithio-bridged β-CDs*

The binding modes of binaphthyl-, biquinoline- and dithio-bridged *β*-CDs (**50**–**55**) and bile salts have been investigated by 2D ROESY experiments in aqueous solution [33]. The results show that CA enters the CD cavity of **53** from the second side of CD with the side chain and D-ring. The side chain with the negative carboxylate group of CA moves toward the positive protonated amino group of **53**. The other binaphthyl-, biquinoline- and dithio-bridged *β*-CDs/bile salts complexes show a similar binding mode as the complex **53**/CA, with only a slight degree of difference in the depth of guest insertion.

**Figure 7.** The possible binding modes of **35** with CA (a) and **39** with DCA (b)

**Figure 8.** The possible binding mode of **42**–**44** with CA

#### **4.2. Complexation thermodynamics for bile salts and bridged CD series**

#### *4.2.1. Diseleno- and bipyridine-bridged β-CDs*

322 Thermodynamics – Fundamentals and Its Application in Science

*4.1.4. Binaphthyl-, biquinoline- and dithio-bridged β-CDs* 

slight degree of difference in the depth of guest insertion.

**Figure 7.** The possible binding modes of **35** with CA (a) and **39** with DCA (b)

**Figure 8.** The possible binding mode of **42**–**44** with CA

other cases of **49**/bile salt complexes.

To obtain the information about the binding modes between bile salts and sulfonyldianilinebridged *β*-CD **49**, 2D ROESY spectra for typical host–guest pairs have further been determined by Zhao et al. [32]. The correlation signals, along with the 1:1 binding stoichiometry, jointly indicate a host-linker-guest binding mode between **49** and CA. That is, upon complexation with **49**, the carboxylate tail and the D ring of CA penetrate into one CD cavity of **49** from the wide opening deeply, while the phenyl moiety of the CD linker is partially self-included in the other *β*-CD cavity. Similar binding modes are also observed in

The binding modes of binaphthyl-, biquinoline- and dithio-bridged *β*-CDs (**50**–**55**) and bile salts have been investigated by 2D ROESY experiments in aqueous solution [33]. The results show that CA enters the CD cavity of **53** from the second side of CD with the side chain and D-ring. The side chain with the negative carboxylate group of CA moves toward the positive protonated amino group of **53**. The other binaphthyl-, biquinoline- and dithio-bridged *β*-CDs/bile salts complexes show a similar binding mode as the complex **53**/CA, with only a To elucidate the difference in binding behavior between the CD dimer and monomer, two CD dimers (**33** and **35**) and their monomer analogs (**25** and **26**) have been used for titration microcalorimetry with CA and DCA [27]. It is interesting that the results of the thermodynamic measurements show a 1:1 binding stoichiometry for hosts **25**, **26** and **33**, but 1:2 stoichiometry for host **35**. In addition, although the stability constants for the complexation between dimer **33** and the bile salts are much larger than those for monomer **26**, the long-linked dimer **35** unusually displays a lower cavity binding ability than its corresponding monomer **25** upon complexation with both guests CA and DCA. The enhancement of the binding ability of dimer **33** compared to monomer **26** could be ascribed not only to the cooperative binding but also partly to the peculiar self-inclusion conformation of **26** that leads to more unfavorable entropy changes, especially for the **26**– CA pair. For **35**, the two guest molecules are separately and independently included in the two cavities of **35** because the longer linker, especially the ethylenediamino moiety of dimer **35**, makes it possess a relatively large conformational freedom. As the considerable entropy loss cancels the advantage of enthalpy gain, dimer **35** displays relatively weak binding abilities. Both hosts **35** and **25** show similar binding ability for DCA and CA. The reason is that either binding with host **35** or host **25**, the two guest bile salts are included into the cavity of CDs by its D-ring and side-chain moiety, which reduces the influence of the substituent in C7. However, while binding with hosts **33** and **26**, the A-ring moiety participates in the binding process, so the more hydrophobic C7 substituent of DCA makes it bind more strongly with the host CDs, giving the higher binding constants than with CA, especially for host **26**.

Either for diseleno-bridged *β*-CDs (**34**–**37**) or for bipyridine-bridged *β*-CDs (**38**–**41**), the host– guest stoichiometry changes in the same order, that is, from 1:2 to 1:1 with the increase of spacer length [28]. For diseleno-bridged *β*-CDs, only **36** and **37** adopt the 1:1 binding mode. However, for bipyridine-bridged *β*-CDs, only host **38** adopts the 1:2 binding mode; the others all show the 1:1 cooperative binding mode. The thermodynamic results reveal that, with the longest spacer, **37** gives the largest stability constants in all diseleno-bridged *β*-CDs, while the largest stability constants of bipyridine-bridged *β*-CDs toward each guest molecule is obtained by the dimers **39** and **40** with the moderate spacer lengths, which suggests that only the CD dimers possessing the proper spacer length can give the perfect cooperative binding toward guests.

For the dimers adopting 1:1 cooperative binding mode, the enthalpy changes are not only the main contribution to the binding process but also the determining factor for the binding abilities [28]. Comparing the diseleno-bridged *β*-CDs with bipyridine-bridged *β*-CDs, all of the bipyridine-bridged *β*-CDs display much stronger binding abilities toward bile salts than corresponding diseleno-bridged *β*-CDs, which indicate that the presence of rigid spacer favors formation of a relatively fixed binding mode and results in the close contact between two CD cavities and guest molecule, leading to the stronger binding abilities. On the other hand, due to the presence of the bipyridine fragment**,** the hydrogen bond between the hydroxyl group of the bile salt and the nitrogen atom of bipyridine might also be taken as a plausible explanation for the strong binding abilities of bipyridine-bridged *β*-CDs as compared with diseleno-bridged *β*-CDs. Upon complexation with CA and DCA, all dimer hosts adopting a 1:1 binding mode show higher binding abilities than native *β*-CD **1** due to more favorable enthalpy changes, which perfectly confirms the advantage of cooperative binding of guests by two CD cavities.

Thermodynamics of Resulting Complexes Between Cyclodextrins and Bile Salts 325

complexation with *β*-CD dimers due to the relatively poor hydrophobic interactions

The stoichiometry for the inclusion complexation of **45** with bile salts were determined by the continuous variation method and the results showed a 1:1 inclusion complexation between **45** and bile salts [30]. The stability constants for the inclusion complexation of **45** with bile salts are much higher than those values for the native *β*-CD **1**. These enhanced binding abilities of **45** may be mainly attributed to the cooperative host-linker-guest binding mode between host and guest because the linker group provides some additional binding interactions towards the accommodate guest. Host **45** displays higher binding ability for CA than for DCA due to the hydrogen bond interactions between the 7-hydroxy group of CA and the 2- and 3-hydroxy group of CD. Host **45** shows the weaker binding abilities upon inclusion complexation with GCA and TCA than that of CA and DCA because GCA and TCA are unfavorable to insert into the cavity from the second side of CD cavity with their D

The stoichiometries for inclusion complexation of aromatic diamino-bridged *β*-CDs **46**–**48**  with bile salts were further determined by the continuous variation method and the results show that all the hosts and guests form 1:1 complexes [31]. *β*-CD dimers **46**–**48** also show enhanced binding ability toward bile salts as compared with *β*-CD **1**. The enhanced binding abilities of aromatic diamino-bridged *β*-CDs may be mainly attributed to the cooperative host-linker-guest binding mode between host and guest. In addition to the association of the CD cavity with a guest molecule, the linker group provides some additional binding

Unlike the *β*-CD **1**, the bridged *β*-CDs **46**–**48** show larger binding constants for CA than for DCA [31]. Among them, the host **47** gave the highest stability constant for inclusion complexation with CA. One possible reason for the stronger affinity for CA may involve hydrogen-bond interactions between the 7-hydroxy group of CA and the 2- and 3-hydroxy groups of CD, which subsequently strengthen the host–guest association. Moreover, all the hosts show lower binding ability for complexation with GCA and TCA as compared with complexation with CA and DCA. The highest binding constants towards GCA and TCA are with host **47**. The universally decreased binding ability toward GCA and TCA must be related to structure differences between CA and DCA. Attributing to the more hydrophilic tail, which is attached to the end of the D ring, GCA and TCA are unfavorable for insertion

The binding constants for the complexation of each bile salt by hosts **46**–**48** increases in the following order: **47** *>* **48** *>* **46** [31]. That is, host **47** with a tether of moderate length and rigidity among the *β*-CD dimers studied is the most suitable for inclusion complexation with bile salts. This may be attributable to the strict size fit between these bile salts and the moderate length-tethered *β*-CD dimer **47**, which consequently exhibits strong van der Waals

*4.2.3. Aromatic diamino- and sulfonyldianiline-bridged β-CDs* 

ring attributing to the more hydrophilic tail attached to the end of the D ring.

into the cavity from the second side of the *β*-CD cavity with their D ring.

and hydrophobic interactions between host and guest.

interactions towards the accommodated guest.

between host and guest.

## *4.2.2. Oligoethylenediamino-Bridged β-CDs*

1:1 binding stoichiometry is observed for all the complexes between bile salts and oligoethylenediamino-bridged *β*-CDs (**42**–**44**) [29]. The inclusion complexation of bile salts with **42**–**44** is driven by favorable enthalpy changes, accompanied by slight to moderate entropy loss. Interestingly, the enthalpy changes for the inclusion complexation of **42**–**44**  increased, while the entropic changes decreased, with the elongation of the linker group, giving a binding constant **42** > **43** > **44**. The stronger binding of bile salts by the short-linked *β*-CD dimer is not thermodynamically accomplished by an increase of the originally favorable enthalpy gain, but by a reduction of the unfavorable entropy loss. The shortlinked *β*-CD dimer, with a better size and hydrophobicity match to bile salts, may experience more extensive desolvation upon complexation, and thus exhibits the less unfavorable entropy loss. With the elongation of linker group, the protonated amino group in the linker is located distant from the anionic carboxylate (or sulfonate) tail of bile salt, which consequently weakens the electrostatic interactions between the linker group and bile salt. Moreover, the increase of the number of -NH- fragments in the linker group decrease the hydrophobicity of *β*-CD dimer to some extent, which is also unfavorable to the hydrophobic interactions between host and guest.

The stability constants of the complexes formed by *β*-CD dimers **42**–**44** with bile salts are larger than those of the complexes formed by native *β*-CD **1** [29]. These enhanced binding abilities of *β*-CD dimers may be mainly attributed to the cooperative host-linker-guest binding mode between host and guest. The electrostatic interactions between the protonated amino groups in the linker and the anionic carboxylate (or sulfonate) tail of bile salt may strengthen the inclusion complexations of these *β*-CD dimers with bile salts. Moreover, the hydrogen bond interactions of the hydroxyl groups of *β*-CD and the -NH- fragments of the oligo(ethylenediamino) linker with the carboxylate (or sulfonate) tail of bile salt also contribute to the enhanced binding abilities of *β*-CD dimers **42**–**44**.

Compared with CA, GCA and TCA, DCA possesses a more hydrophobic structure due to the absence of C-7 hydroxyl group, which consequently leads to stronger hydrophobic interactions between host and guest. Therefore, DCA gives the highest binding abilities among the bile salts examined upon complexation with most CDs [29]. Possess more polar side-chains, GCA and TCA show weak binding abilities upon inclusion complexation complexation with *β*-CD dimers due to the relatively poor hydrophobic interactions between host and guest.

#### *4.2.3. Aromatic diamino- and sulfonyldianiline-bridged β-CDs*

324 Thermodynamics – Fundamentals and Its Application in Science

binding of guests by two CD cavities.

*4.2.2. Oligoethylenediamino-Bridged β-CDs* 

hydrophobic interactions between host and guest.

contribute to the enhanced binding abilities of *β*-CD dimers **42**–**44**.

two CD cavities and guest molecule, leading to the stronger binding abilities. On the other hand, due to the presence of the bipyridine fragment**,** the hydrogen bond between the hydroxyl group of the bile salt and the nitrogen atom of bipyridine might also be taken as a plausible explanation for the strong binding abilities of bipyridine-bridged *β*-CDs as compared with diseleno-bridged *β*-CDs. Upon complexation with CA and DCA, all dimer hosts adopting a 1:1 binding mode show higher binding abilities than native *β*-CD **1** due to more favorable enthalpy changes, which perfectly confirms the advantage of cooperative

1:1 binding stoichiometry is observed for all the complexes between bile salts and oligoethylenediamino-bridged *β*-CDs (**42**–**44**) [29]. The inclusion complexation of bile salts with **42**–**44** is driven by favorable enthalpy changes, accompanied by slight to moderate entropy loss. Interestingly, the enthalpy changes for the inclusion complexation of **42**–**44**  increased, while the entropic changes decreased, with the elongation of the linker group, giving a binding constant **42** > **43** > **44**. The stronger binding of bile salts by the short-linked *β*-CD dimer is not thermodynamically accomplished by an increase of the originally favorable enthalpy gain, but by a reduction of the unfavorable entropy loss. The shortlinked *β*-CD dimer, with a better size and hydrophobicity match to bile salts, may experience more extensive desolvation upon complexation, and thus exhibits the less unfavorable entropy loss. With the elongation of linker group, the protonated amino group in the linker is located distant from the anionic carboxylate (or sulfonate) tail of bile salt, which consequently weakens the electrostatic interactions between the linker group and bile salt. Moreover, the increase of the number of -NH- fragments in the linker group decrease the hydrophobicity of *β*-CD dimer to some extent, which is also unfavorable to the

The stability constants of the complexes formed by *β*-CD dimers **42**–**44** with bile salts are larger than those of the complexes formed by native *β*-CD **1** [29]. These enhanced binding abilities of *β*-CD dimers may be mainly attributed to the cooperative host-linker-guest binding mode between host and guest. The electrostatic interactions between the protonated amino groups in the linker and the anionic carboxylate (or sulfonate) tail of bile salt may strengthen the inclusion complexations of these *β*-CD dimers with bile salts. Moreover, the hydrogen bond interactions of the hydroxyl groups of *β*-CD and the -NH- fragments of the oligo(ethylenediamino) linker with the carboxylate (or sulfonate) tail of bile salt also

Compared with CA, GCA and TCA, DCA possesses a more hydrophobic structure due to the absence of C-7 hydroxyl group, which consequently leads to stronger hydrophobic interactions between host and guest. Therefore, DCA gives the highest binding abilities among the bile salts examined upon complexation with most CDs [29]. Possess more polar side-chains, GCA and TCA show weak binding abilities upon inclusion complexation The stoichiometry for the inclusion complexation of **45** with bile salts were determined by the continuous variation method and the results showed a 1:1 inclusion complexation between **45** and bile salts [30]. The stability constants for the inclusion complexation of **45** with bile salts are much higher than those values for the native *β*-CD **1**. These enhanced binding abilities of **45** may be mainly attributed to the cooperative host-linker-guest binding mode between host and guest because the linker group provides some additional binding interactions towards the accommodate guest. Host **45** displays higher binding ability for CA than for DCA due to the hydrogen bond interactions between the 7-hydroxy group of CA and the 2- and 3-hydroxy group of CD. Host **45** shows the weaker binding abilities upon inclusion complexation with GCA and TCA than that of CA and DCA because GCA and TCA are unfavorable to insert into the cavity from the second side of CD cavity with their D ring attributing to the more hydrophilic tail attached to the end of the D ring.

The stoichiometries for inclusion complexation of aromatic diamino-bridged *β*-CDs **46**–**48**  with bile salts were further determined by the continuous variation method and the results show that all the hosts and guests form 1:1 complexes [31]. *β*-CD dimers **46**–**48** also show enhanced binding ability toward bile salts as compared with *β*-CD **1**. The enhanced binding abilities of aromatic diamino-bridged *β*-CDs may be mainly attributed to the cooperative host-linker-guest binding mode between host and guest. In addition to the association of the CD cavity with a guest molecule, the linker group provides some additional binding interactions towards the accommodated guest.

Unlike the *β*-CD **1**, the bridged *β*-CDs **46**–**48** show larger binding constants for CA than for DCA [31]. Among them, the host **47** gave the highest stability constant for inclusion complexation with CA. One possible reason for the stronger affinity for CA may involve hydrogen-bond interactions between the 7-hydroxy group of CA and the 2- and 3-hydroxy groups of CD, which subsequently strengthen the host–guest association. Moreover, all the hosts show lower binding ability for complexation with GCA and TCA as compared with complexation with CA and DCA. The highest binding constants towards GCA and TCA are with host **47**. The universally decreased binding ability toward GCA and TCA must be related to structure differences between CA and DCA. Attributing to the more hydrophilic tail, which is attached to the end of the D ring, GCA and TCA are unfavorable for insertion into the cavity from the second side of the *β*-CD cavity with their D ring.

The binding constants for the complexation of each bile salt by hosts **46**–**48** increases in the following order: **47** *>* **48** *>* **46** [31]. That is, host **47** with a tether of moderate length and rigidity among the *β*-CD dimers studied is the most suitable for inclusion complexation with bile salts. This may be attributable to the strict size fit between these bile salts and the moderate length-tethered *β*-CD dimer **47**, which consequently exhibits strong van der Waals and hydrophobic interactions between host and guest.

The stoichiometry for the inclusion complexation of sulfonyldianiline-bridged *β*-CD **49** with bile salts has also been determined by the "continuous variation" method and the results indicate that all the bile salts can form 1:1 complexes with **49** [32]. Thermodynamically, the binding constants of **49** with bile salts are larger than those of native *β*-CD **1**. The enhanced binding abilities of **49** may be also mainly attributed to the cooperative host-linker-guest binding mode between host and guest. In addition to the association of the CD cavity with a guest molecule, the linker group provides some additional binding interactions towards the accommodate guest. Distinctly, the binding constant is significantly higher for DCA compared to CA by native *β*-CD **1**. However, different from native *β*-CD **1**, sulfonyldianiline-bridged *β*-CD **49** reverses this binding selectivity, showing larger binding constants for CA than DCA. One possible reason for the stronger affinity for CA may involve H-bond interactions between CA and CD, which subsequently strengthen the hostguest association. Moreover, all the hosts show a weaker binding ability upon complexation with GCA and TCA than with CA and DCA. The universal decreased binding ability toward GCA and TCA must relate to the structure differences from CA and DCA. Attributing to the more hydrophilic tail, which is attached to the end of the D ring, GCA and TCA are unfavorable to insert into the cavity from the second side of *β*-CD cavity with their D ring. It is worthy to note that the binding ability of **49** is significantly larger for TCA than for GCA, which leads to a relatively strong molecular selectivity.

Thermodynamics of Resulting Complexes Between Cyclodextrins and Bile Salts 327

**52**, which possibly originates from the conformation fixation of host and guest and the rigid

Mostly, bridged *β*-CDs **50**, **51**, and **53**–**55** give the lower binding ability upon complexation with GCA and TCA as compared with the complexation with CA and DCA, which is similar as the complexation of *β*-CD **1** and bridged *β*-CD **52** [33]. The universal decreased binding ability toward GCA and TCA must relate to the structure differences from CA and DCA. The more polar side chains at C23 for GCA and TCA remarkably affect their binding

2D ROESY NMR and circular dichroism spectroscopy experiments for the complexes of bile salts with bridged and metallobridged CDs with naphthalenecarboxyl linkers have been performed by Liu et al. to investigate the binding modes between host and guests [34]. The result of **57**/DCA complex showed that the guest DCA was included in the *β*-CD cavity with the D-ring and the carboxylic tail located near the narrow opening but the B-ring located near the wide opening and the naphthyl group was excluded from the *β*-CD cavity upon inclusion complexation. Moreover, the result of 2D ROESY NMR showed that the ethylenediamino moiety of the linker group was also partially self-included in the *β*-CD cavity from the narrow opening. Similar results were also found in other ROESY

2D NMR experiments in D2O and molecular modeling studies for the complexes of bridged and metallobridged *β*-CDs with biquinoline linkers and bile salts have been performed by Liu et al. to deduce the binding modes between the bile salts and *β*-CD dimers [35,36]. The results show that a cooperative "host-tether-guest" binding mode is operative in the association of *β*-CD dimers with a guest molecule; upon complexation with *β*-CD dimers, the guest steroid is embedded into one hydrophobic *β*-CD cavity from the primary side, while the tether group is partly self-included in the other cavity. In the metallobridged *β*-CDs, the tether group is entirely excluded from the *β*-CD cavities as a result of metal coordination. This arrangement allows two side groups of the guest molecule to be embedded into the hydrophobic *β*-CD cavities from the primary side of the *β*-CD to form a

1H ROESY experiments have been performed in D2O to investigate the binding modes between bridged and metallobridged *β*-CDs with oxamidobisbenzoyl linkers and bile salts [37]. The results show a "host-linker-guest" binding mode between **66** and CA. That is, upon inclusion complexation with *β*-CD dimer, the carboxylate tail and the D-ring of CA enter

**4.3. Binding modes for bile salts and metallobridged CD series** 

*4.3.1. Metallobridged β-CDs with naphthalenecarboxyl linkers* 

experiments of hosts **57** and **59** with bile salts.

sandwich host–guest inclusion complex.

*4.3.3. Metallobridged β-CDs with oxamidobisbenzoyl linkers* 

*4.3.2. Metallobridged β-CDs with biquinoline linkers* 

complex formation upon complexation.

thermodynamics.

### *4.2.4. Binaphthyl-, biquinoline- and dithio-bridged β-CDs*

The stoichiometric ratios from the binding patterns for the titrations of steroids with binaphthyl-, biquinoline- and dithio-bridged *β*-CDs **50**–**55** fell within the range of 1.8-2.1, which clearly indicates that the majority of the inclusion complexes have a 1:2 stoichiometry of steroids and bridged *β*-CDs [33]. Thermodynamically, bridged *β*-CD **52**, possessing a relatively short and rigid tether without amino groups, still gives an enhanced binding ability upon complexation with steroids, except TCA, when compared its one single unit of cavity with that of native *β*-CD **1**. The enthalpy changes for the inclusion complexation of bridged *β*-CD **52** with DCA and CA are more negative than that of native *β*-CD **1**, resulting in the relatively stronger binding. On the other hand, the enthalpy change for the complexation of **52** with DCA is higher than that with CA, which directly contributes to the increased complex stability. It is reasonable that, possessing the more hydrophobic structure due to the absence of C-7 hydroxyl group as compared with CA, DCA is easier to bind into the *β*-CD cavity than CA, which should lead to the more favorable van der Waals interactions.

All the complexation of aminated bridged *β*-CDs (**50**, **51**, and **53**–**55**) toward DCA and CA give more negative enthalpy changes as compared with that of neutral bridged *β*-CD **52**, validating the contribution of the attractive electrostatic interactions between positively charged protonated amino group of *β*-CD tethers and negatively charged carboxylate group of DCA and CA [33]. Accompanied with the more exothermic reaction enthalpies, the inclusion complexation of DCA and CA by aminated bridged *β*-CDs (**50**, **51**, and **53**–**55**) exhibits more unfavorable entropy changes compared to that for neutral bridged bis(*β*-CD) **52**, which possibly originates from the conformation fixation of host and guest and the rigid complex formation upon complexation.

Mostly, bridged *β*-CDs **50**, **51**, and **53**–**55** give the lower binding ability upon complexation with GCA and TCA as compared with the complexation with CA and DCA, which is similar as the complexation of *β*-CD **1** and bridged *β*-CD **52** [33]. The universal decreased binding ability toward GCA and TCA must relate to the structure differences from CA and DCA. The more polar side chains at C23 for GCA and TCA remarkably affect their binding thermodynamics.

## **4.3. Binding modes for bile salts and metallobridged CD series**

## *4.3.1. Metallobridged β-CDs with naphthalenecarboxyl linkers*

326 Thermodynamics – Fundamentals and Its Application in Science

for GCA, which leads to a relatively strong molecular selectivity.

*4.2.4. Binaphthyl-, biquinoline- and dithio-bridged β-CDs* 

interactions.

The stoichiometry for the inclusion complexation of sulfonyldianiline-bridged *β*-CD **49** with bile salts has also been determined by the "continuous variation" method and the results indicate that all the bile salts can form 1:1 complexes with **49** [32]. Thermodynamically, the binding constants of **49** with bile salts are larger than those of native *β*-CD **1**. The enhanced binding abilities of **49** may be also mainly attributed to the cooperative host-linker-guest binding mode between host and guest. In addition to the association of the CD cavity with a guest molecule, the linker group provides some additional binding interactions towards the accommodate guest. Distinctly, the binding constant is significantly higher for DCA compared to CA by native *β*-CD **1**. However, different from native *β*-CD **1**, sulfonyldianiline-bridged *β*-CD **49** reverses this binding selectivity, showing larger binding constants for CA than DCA. One possible reason for the stronger affinity for CA may involve H-bond interactions between CA and CD, which subsequently strengthen the hostguest association. Moreover, all the hosts show a weaker binding ability upon complexation with GCA and TCA than with CA and DCA. The universal decreased binding ability toward GCA and TCA must relate to the structure differences from CA and DCA. Attributing to the more hydrophilic tail, which is attached to the end of the D ring, GCA and TCA are unfavorable to insert into the cavity from the second side of *β*-CD cavity with their D ring. It is worthy to note that the binding ability of **49** is significantly larger for TCA than

The stoichiometric ratios from the binding patterns for the titrations of steroids with binaphthyl-, biquinoline- and dithio-bridged *β*-CDs **50**–**55** fell within the range of 1.8-2.1, which clearly indicates that the majority of the inclusion complexes have a 1:2 stoichiometry of steroids and bridged *β*-CDs [33]. Thermodynamically, bridged *β*-CD **52**, possessing a relatively short and rigid tether without amino groups, still gives an enhanced binding ability upon complexation with steroids, except TCA, when compared its one single unit of cavity with that of native *β*-CD **1**. The enthalpy changes for the inclusion complexation of bridged *β*-CD **52** with DCA and CA are more negative than that of native *β*-CD **1**, resulting in the relatively stronger binding. On the other hand, the enthalpy change for the complexation of **52** with DCA is higher than that with CA, which directly contributes to the increased complex stability. It is reasonable that, possessing the more hydrophobic structure due to the absence of C-7 hydroxyl group as compared with CA, DCA is easier to bind into the *β*-CD cavity than CA, which should lead to the more favorable van der Waals

All the complexation of aminated bridged *β*-CDs (**50**, **51**, and **53**–**55**) toward DCA and CA give more negative enthalpy changes as compared with that of neutral bridged *β*-CD **52**, validating the contribution of the attractive electrostatic interactions between positively charged protonated amino group of *β*-CD tethers and negatively charged carboxylate group of DCA and CA [33]. Accompanied with the more exothermic reaction enthalpies, the inclusion complexation of DCA and CA by aminated bridged *β*-CDs (**50**, **51**, and **53**–**55**) exhibits more unfavorable entropy changes compared to that for neutral bridged bis(*β*-CD) 2D ROESY NMR and circular dichroism spectroscopy experiments for the complexes of bile salts with bridged and metallobridged CDs with naphthalenecarboxyl linkers have been performed by Liu et al. to investigate the binding modes between host and guests [34]. The result of **57**/DCA complex showed that the guest DCA was included in the *β*-CD cavity with the D-ring and the carboxylic tail located near the narrow opening but the B-ring located near the wide opening and the naphthyl group was excluded from the *β*-CD cavity upon inclusion complexation. Moreover, the result of 2D ROESY NMR showed that the ethylenediamino moiety of the linker group was also partially self-included in the *β*-CD cavity from the narrow opening. Similar results were also found in other ROESY experiments of hosts **57** and **59** with bile salts.

## *4.3.2. Metallobridged β-CDs with biquinoline linkers*

2D NMR experiments in D2O and molecular modeling studies for the complexes of bridged and metallobridged *β*-CDs with biquinoline linkers and bile salts have been performed by Liu et al. to deduce the binding modes between the bile salts and *β*-CD dimers [35,36]. The results show that a cooperative "host-tether-guest" binding mode is operative in the association of *β*-CD dimers with a guest molecule; upon complexation with *β*-CD dimers, the guest steroid is embedded into one hydrophobic *β*-CD cavity from the primary side, while the tether group is partly self-included in the other cavity. In the metallobridged *β*-CDs, the tether group is entirely excluded from the *β*-CD cavities as a result of metal coordination. This arrangement allows two side groups of the guest molecule to be embedded into the hydrophobic *β*-CD cavities from the primary side of the *β*-CD to form a sandwich host–guest inclusion complex.

## *4.3.3. Metallobridged β-CDs with oxamidobisbenzoyl linkers*

1H ROESY experiments have been performed in D2O to investigate the binding modes between bridged and metallobridged *β*-CDs with oxamidobisbenzoyl linkers and bile salts [37]. The results show a "host-linker-guest" binding mode between **66** and CA. That is, upon inclusion complexation with *β*-CD dimer, the carboxylate tail and the D-ring of CA enter

into one CD cavity of **66** from the wide opening, while the linker group of **66** is partially selfincluded in the other CD cavity (Figure 9a). A similar binding mode is also observed for the inclusion complexation of **66** with DCA.

Thermodynamics of Resulting Complexes Between Cyclodextrins and Bile Salts 329

**57**–**59**) can form 1:1 complexes with bile salts CA and DCA. Thermodynamically, bridged *β*-CDs possess much stronger binding abilities compared with mono-modified *β*-CDs. These enhanced binding abilities should be attributed to cooperative binding of the *β*-CD cavity and the linker group towards the guest molecule, leading to greatly strengthened van der Waals and hydrophobic interactions between host and guest when compared with monomodified *β*-CDs. Furthermore, after metal coordination, the metallobridged bis(*β*-CD)s **58** and **59** significantly enhance the original binding ability of native *β*-CD **1**, mono-naphthylmodified *β*-CDs **27**–**29** and even parent bridged *β*-CD **57**. This enhancement may be subjected to a multiple recognition mechanism of metallobridged *β*-CDs towards model substrates. On one hand, the coordination of a metal ion to the linker group shortens the effective distance of two *β*-CD cavities to some extent and thus improves the size-fit degree between host and guest. On the other hand, the electrostatic attraction between the anionic carboxyl group of guest bile salt and the coordinated metal ion of metallobridged *β*-CD may

The interactions between host **51** and bile salts have been investigated by Liu et al. by the method of fluorescence [35]. The results show that all the bile salts can form 1:1 complexes with **51**. Thermodynamically, the binding constants obtained for CA and DCA are much larger than those reported for mono-modified *β*-CDs by Ueno et al. under practically the same experimental conditions [38]. This enhancement is probably due to the cooperative binding of the steroids by **51**. The complex stability decreases in the order: DCA > CA > GCA > TCA. The highest affinity for DCA is likely to arise from its more hydrophobic steroid skeleton. Host **51** shows comparable affinities toward CA and GCA, whereas TCA,

The stoichiometry for the inclusion complexation of hosts **60**–**64** with bile salts has also been determined by Job's method [36]. The results show that the stoichiometry of the inclusion complex formed by the **63**/CA system is likely to be 2:2, with intramolecular complexation. Stoichiometries of 1:1 (for bridged *β*-CD) or 2:2 (for metallobridged *β*-CD) were obtained in other similar cases of host–guest inclusion complexation. Thermodynamically, the stability constants of the complexes of bridged *β*-CDs **51**, **60** and **61** with bile salts are larger than those of the complexes formed by mono-modified *β*-CDs **27**–**29** by a factor of about 1.1 to around 200 benefitting from cooperative binding. In addition to inclusion complexation of the guest molecule within one hydrophobic CD cavity, the tether group located near the accommodated guest provides some additional interactions with the guest. In control experiments, the changes in the fluorescence spectra of **30**–**32** upon addition of guest steroids were too small to allow calculation of the stability constants, which may be attributed to strong self-inclusion of the substituted group preventing penetration of the guest into the CD cavity. Except **60**, the mono- and bridged-*β*-CDs display higher binding affinities for DCA than for CA. This stronger affinity for DCA is likely to arise from the

also favour the host–guest binding to some extent.

*4.4.2. Metallobridged β-CDs with biquinoline linkers* 

possessing a highly polar anionic tail gives the lowest binding constant.

**Figure 9.** The possible binding modes of **66** (a) and **67** (b) with CA, and the possible binding modes of **69**–**72** with bile salts

With a shallowly self-included conformation, *β*-CD dimers **65**, **67**, and **68** show a binding mode different from that of **66**. For example, for **67**/CA complex, the carboxylate tail and Dring of CA enter the CD cavity from the wide opening, and the carboxylate tail is located close to the linker group. On the other hand, the linker group is mostly moved out from the CD cavity after complexation with CA (Figure 9b). **65**/CA, **65**/DCA, **67**/DCA, **68**/CA, and **68**/DCA complexes show a similar binding mode to the **67**/CA complex.

In the cases of the metallobridged *β*-CDs **69**–**72**, the strong electrostatic attraction from the coordinated CuII ions in the linker group may also favor the penetration of the carboxylate tail of bile salt into the CD cavity through the wide opening. Moreover, the 1:2 or 2:4 binding stoichiometry indicates that each CD cavity of a metallobridged *β*-CD is occupied by a bile salt (Figure 9c).

## **4.4. Complexation thermodynamics for bile salts and metallobridged CD series**

## *4.4.1. Metallobridged β-CDs with naphthalenecarboxyl linkers*

The interactions between hosts (**27**–**29**, **57**–**59**) and bile salts have been studied by Liu and Ueno et al. by the method of fluorescence [34,38]. The results show that all the hosts (**27**–**29**, **57**–**59**) can form 1:1 complexes with bile salts CA and DCA. Thermodynamically, bridged *β*-CDs possess much stronger binding abilities compared with mono-modified *β*-CDs. These enhanced binding abilities should be attributed to cooperative binding of the *β*-CD cavity and the linker group towards the guest molecule, leading to greatly strengthened van der Waals and hydrophobic interactions between host and guest when compared with monomodified *β*-CDs. Furthermore, after metal coordination, the metallobridged bis(*β*-CD)s **58** and **59** significantly enhance the original binding ability of native *β*-CD **1**, mono-naphthylmodified *β*-CDs **27**–**29** and even parent bridged *β*-CD **57**. This enhancement may be subjected to a multiple recognition mechanism of metallobridged *β*-CDs towards model substrates. On one hand, the coordination of a metal ion to the linker group shortens the effective distance of two *β*-CD cavities to some extent and thus improves the size-fit degree between host and guest. On the other hand, the electrostatic attraction between the anionic carboxyl group of guest bile salt and the coordinated metal ion of metallobridged *β*-CD may also favour the host–guest binding to some extent.

#### *4.4.2. Metallobridged β-CDs with biquinoline linkers*

328 Thermodynamics – Fundamentals and Its Application in Science

inclusion complexation of **66** with DCA.

**69**–**72** with bile salts

by a bile salt (Figure 9c).

into one CD cavity of **66** from the wide opening, while the linker group of **66** is partially selfincluded in the other CD cavity (Figure 9a). A similar binding mode is also observed for the

**Figure 9.** The possible binding modes of **66** (a) and **67** (b) with CA, and the possible binding modes of

With a shallowly self-included conformation, *β*-CD dimers **65**, **67**, and **68** show a binding mode different from that of **66**. For example, for **67**/CA complex, the carboxylate tail and Dring of CA enter the CD cavity from the wide opening, and the carboxylate tail is located close to the linker group. On the other hand, the linker group is mostly moved out from the CD cavity after complexation with CA (Figure 9b). **65**/CA, **65**/DCA, **67**/DCA, **68**/CA, and

In the cases of the metallobridged *β*-CDs **69**–**72**, the strong electrostatic attraction from the coordinated CuII ions in the linker group may also favor the penetration of the carboxylate tail of bile salt into the CD cavity through the wide opening. Moreover, the 1:2 or 2:4 binding stoichiometry indicates that each CD cavity of a metallobridged *β*-CD is occupied

**4.4. Complexation thermodynamics for bile salts and metallobridged CD series** 

The interactions between hosts (**27**–**29**, **57**–**59**) and bile salts have been studied by Liu and Ueno et al. by the method of fluorescence [34,38]. The results show that all the hosts (**27**–**29**,

**68**/DCA complexes show a similar binding mode to the **67**/CA complex.

*4.4.1. Metallobridged β-CDs with naphthalenecarboxyl linkers* 

The interactions between host **51** and bile salts have been investigated by Liu et al. by the method of fluorescence [35]. The results show that all the bile salts can form 1:1 complexes with **51**. Thermodynamically, the binding constants obtained for CA and DCA are much larger than those reported for mono-modified *β*-CDs by Ueno et al. under practically the same experimental conditions [38]. This enhancement is probably due to the cooperative binding of the steroids by **51**. The complex stability decreases in the order: DCA > CA > GCA > TCA. The highest affinity for DCA is likely to arise from its more hydrophobic steroid skeleton. Host **51** shows comparable affinities toward CA and GCA, whereas TCA, possessing a highly polar anionic tail gives the lowest binding constant.

The stoichiometry for the inclusion complexation of hosts **60**–**64** with bile salts has also been determined by Job's method [36]. The results show that the stoichiometry of the inclusion complex formed by the **63**/CA system is likely to be 2:2, with intramolecular complexation. Stoichiometries of 1:1 (for bridged *β*-CD) or 2:2 (for metallobridged *β*-CD) were obtained in other similar cases of host–guest inclusion complexation. Thermodynamically, the stability constants of the complexes of bridged *β*-CDs **51**, **60** and **61** with bile salts are larger than those of the complexes formed by mono-modified *β*-CDs **27**–**29** by a factor of about 1.1 to around 200 benefitting from cooperative binding. In addition to inclusion complexation of the guest molecule within one hydrophobic CD cavity, the tether group located near the accommodated guest provides some additional interactions with the guest. In control experiments, the changes in the fluorescence spectra of **30**–**32** upon addition of guest steroids were too small to allow calculation of the stability constants, which may be attributed to strong self-inclusion of the substituted group preventing penetration of the guest into the CD cavity. Except **60**, the mono- and bridged-*β*-CDs display higher binding affinities for DCA than for CA. This stronger affinity for DCA is likely to arise from the

more hydrophobic steroid skeleton of this compound compared with that of CA. The abilities of both the short-tethered compound **60** and the long-tethered host **61** to bind CA and DCA are unexpectedly limited compared to the binding abilities of mono-modified CDs **27**–**29** due to the self-inclusion of the tether group for the short-tethered *β*-CD dimer **60** and the steric hinderance from the relatively large 5-amino-3-azapentyl-2-quinoline-4 carboxyamide fragment on the exterior of the CD cavity for the long-tethered *β*-CD dimer **61**, respectively.

Thermodynamics of Resulting Complexes Between Cyclodextrins and Bile Salts 331

consequently gives strong van der Waals and hydrophobic interactions between host and

Significantly, metallobridged *β*-CDs **69**–**72** show greatly enhanced binding abilities with regard to the bridged *β*-CDs **65**–**68** [37]. These significant enhancements in the binding abilities may be attributable to a more complicated multiple recognition mechanism involving the cooperative binding of several CD cavities, conformation adjustment by the metal coordination, and additional binding interactions between the metal-coordinated

Except for **66**, all of the hosts examined display higher binding abilities for CA than for DCA [37]. One possible reason for the stronger affinities for CA may involve hydrogen bond interactions between the 7-hydroxy group of CA and the 2- and 3-hydroxy groups of CD.

The microcalorimetric experiments of *β*-CD **1** and modified *β*-CDs **2**, **5**, **6**, **7** with bile acids showed typical titration curves of 1:1 complex formation [18]. However, metallobridged *β*-CD **56** displays a 1:2 host–guest binding stoichiometry. Thermodynamically, as compared with native *β*-CD **1**, most oligo(ethylenediamino)-*β*-CDs **2**, **5 6**, and their CuII complexes **7** and **56** show enhanced molecular binding abilities and guest selectivities towards bile acids. The inclusion complexation of bile acids with native *β*-CD **1** and their derivatives (**2**, **5**, **6**, **7**, and **56**) is absolutely driven by favorable enthalpy changes accompanying with moderate unfavorable or slightly favorable entropy changes. The favorable enthalpy change is attributed to the dominant contribution of the hydrophobic interactions. Meanwhile, the unfavorable entropy given by most of the complexes is due to the decrease of rotational and

As compared with native *β*-CD **1**, **5** shows increased binding abilities toward negatively charged bile acids guest molecules, which should be mainly due to the additional electrostatic interactions between the amino tether moiety of hosts and anionic carboxylate or sulfonate tail of guests [18]. Moreover, *β*-CD dimer **56** shows a larger binding constant upon inclusion complexation with CA and DCA than **5**. This may be attributed to that the coordination of copper ion onto the amino tether of CD affords a more positive charged environment as compared with its precursor **5**. Compared with **5**, host **6** also shows stronger binding abilities toward guest molecules. However, the introduction of copper actually decreases the original binding ability of **6** towards DCA and gives comparable stability constant upon complexation with CA. All the hosts, including native *β*-CD **1** and modified *β*-CDs **2**, **5**, **6**, **7**, and **56**, show the weaker binding abilities upon inclusion complexation with GCA and TCA than those of CA and DCA. It is also found that complexes stabilities enhance with the extended length of spacer for the same guest except for **2**/CA to **5**/CA. It is reasonable to believe that the increased stability is due to the enlarged hydrogen binding

linker group and the accommodated guest molecules.

*4.4.4. Metallobridged β-CDs with aminated linkers* 

structural freedom upon complex construction.

interactions.

guest.

The metal-ligated oligomeric *β*-CDs **62**–**64** have significantly enhanced (around 50–4100 higher) binding affinities for the tested guest molecules compared with those of the monomodified *β*-CDs [36]. These results can be explained by considering a mechanism involving an uncommon multiple recognition behavior of metallobridged *β*-CDs. A metallobridged *β*-CD affords four hydrophobic binding sites (four CD cavities) and one (or three) metal coordination center(s), which jointly contribute to the cooperative binding of the oligomeric host with the guest molecule upon inclusion complexation. In addition, ligation of a CuII ion shortens the effective length of the tether to some extent and thus improves the size fit of the host with the guest. The cumulative result of these factors is that the metal-ligated *β*-CD oligomers have binding abilities around 6–200 times higher than those of their parent bridged *β*-CDs.

## *4.4.3. Metallobridged β-CDs with oxamidobisbenzoyl linkers*

The stoichiometry for the inclusion complexation of hosts **65**–**72** with bile salts has been determined by Job's method [37]. The results indicate that each of the Job's plots for the inclusion complexation of **65**–**68** with bile salts shows a maximum at a *β*-CD dimer molar fraction of 0.5, confirming the 1:1 binding stoichiometry between host and guest. For the inclusion complexation of metallobridged *β*-CDs **69**–**72** with bile salts, however, each of the Job's plots shows a maximum at a bridged *β*-CD unit molar fraction of 0.33, which indicates 1:2 stoichiometry between each bridged *β*-CD unit and guest. The metallobridged *β*-CDs **69** and **70** may only bind two bile salts to form a stoichiometric 1:2 inclusion complex. However, the metallobridged *β*-CDs **71** and **72** may adopt intramolecular 2:4 stoichiometry upon inclusion complexation with bile salts. Thermodynamically, the binding constants for the inclusion complexation of CA and DCA with bridged *β*-CDs **65**–**68** are higher than the *K*S values reported for the inclusion complexation of these bile salts with native or mono-modified *β*-CDs [33,38]. These enhanced binding abilities highlight the inherent advantage of the cooperative "hostlinker-guest" binding mode of bridged *β*-CDs **65**–**68**. In addition to the association of the CD cavity with a guest molecule, the linker group provides some additional binding interactions towards the accommodated guest.

The bile salts CA and DCA are better bound by bridged *β*-CD **65**, which possesses the shortest linker group, than by the long-linked bridged *β*-CDs [37]. This may be attributable to the strict size-fit between these bile salts and the short-linked bridged *β*-CD **65**, which consequently gives strong van der Waals and hydrophobic interactions between host and guest.

Significantly, metallobridged *β*-CDs **69**–**72** show greatly enhanced binding abilities with regard to the bridged *β*-CDs **65**–**68** [37]. These significant enhancements in the binding abilities may be attributable to a more complicated multiple recognition mechanism involving the cooperative binding of several CD cavities, conformation adjustment by the metal coordination, and additional binding interactions between the metal-coordinated linker group and the accommodated guest molecules.

Except for **66**, all of the hosts examined display higher binding abilities for CA than for DCA [37]. One possible reason for the stronger affinities for CA may involve hydrogen bond interactions between the 7-hydroxy group of CA and the 2- and 3-hydroxy groups of CD.

## *4.4.4. Metallobridged β-CDs with aminated linkers*

330 Thermodynamics – Fundamentals and Its Application in Science

*4.4.3. Metallobridged β-CDs with oxamidobisbenzoyl linkers* 

interactions towards the accommodated guest.

**61**, respectively.

bridged *β*-CDs.

more hydrophobic steroid skeleton of this compound compared with that of CA. The abilities of both the short-tethered compound **60** and the long-tethered host **61** to bind CA and DCA are unexpectedly limited compared to the binding abilities of mono-modified CDs **27**–**29** due to the self-inclusion of the tether group for the short-tethered *β*-CD dimer **60** and the steric hinderance from the relatively large 5-amino-3-azapentyl-2-quinoline-4 carboxyamide fragment on the exterior of the CD cavity for the long-tethered *β*-CD dimer

The metal-ligated oligomeric *β*-CDs **62**–**64** have significantly enhanced (around 50–4100 higher) binding affinities for the tested guest molecules compared with those of the monomodified *β*-CDs [36]. These results can be explained by considering a mechanism involving an uncommon multiple recognition behavior of metallobridged *β*-CDs. A metallobridged *β*-CD affords four hydrophobic binding sites (four CD cavities) and one (or three) metal coordination center(s), which jointly contribute to the cooperative binding of the oligomeric host with the guest molecule upon inclusion complexation. In addition, ligation of a CuII ion shortens the effective length of the tether to some extent and thus improves the size fit of the host with the guest. The cumulative result of these factors is that the metal-ligated *β*-CD oligomers have binding abilities around 6–200 times higher than those of their parent

The stoichiometry for the inclusion complexation of hosts **65**–**72** with bile salts has been determined by Job's method [37]. The results indicate that each of the Job's plots for the inclusion complexation of **65**–**68** with bile salts shows a maximum at a *β*-CD dimer molar fraction of 0.5, confirming the 1:1 binding stoichiometry between host and guest. For the inclusion complexation of metallobridged *β*-CDs **69**–**72** with bile salts, however, each of the Job's plots shows a maximum at a bridged *β*-CD unit molar fraction of 0.33, which indicates 1:2 stoichiometry between each bridged *β*-CD unit and guest. The metallobridged *β*-CDs **69** and **70** may only bind two bile salts to form a stoichiometric 1:2 inclusion complex. However, the metallobridged *β*-CDs **71** and **72** may adopt intramolecular 2:4 stoichiometry upon inclusion complexation with bile salts. Thermodynamically, the binding constants for the inclusion complexation of CA and DCA with bridged *β*-CDs **65**–**68** are higher than the *K*S values reported for the inclusion complexation of these bile salts with native or mono-modified *β*-CDs [33,38]. These enhanced binding abilities highlight the inherent advantage of the cooperative "hostlinker-guest" binding mode of bridged *β*-CDs **65**–**68**. In addition to the association of the CD cavity with a guest molecule, the linker group provides some additional binding

The bile salts CA and DCA are better bound by bridged *β*-CD **65**, which possesses the shortest linker group, than by the long-linked bridged *β*-CDs [37]. This may be attributable to the strict size-fit between these bile salts and the short-linked bridged *β*-CD **65**, which The microcalorimetric experiments of *β*-CD **1** and modified *β*-CDs **2**, **5**, **6**, **7** with bile acids showed typical titration curves of 1:1 complex formation [18]. However, metallobridged *β*-CD **56** displays a 1:2 host–guest binding stoichiometry. Thermodynamically, as compared with native *β*-CD **1**, most oligo(ethylenediamino)-*β*-CDs **2**, **5 6**, and their CuII complexes **7** and **56** show enhanced molecular binding abilities and guest selectivities towards bile acids. The inclusion complexation of bile acids with native *β*-CD **1** and their derivatives (**2**, **5**, **6**, **7**, and **56**) is absolutely driven by favorable enthalpy changes accompanying with moderate unfavorable or slightly favorable entropy changes. The favorable enthalpy change is attributed to the dominant contribution of the hydrophobic interactions. Meanwhile, the unfavorable entropy given by most of the complexes is due to the decrease of rotational and structural freedom upon complex construction.

As compared with native *β*-CD **1**, **5** shows increased binding abilities toward negatively charged bile acids guest molecules, which should be mainly due to the additional electrostatic interactions between the amino tether moiety of hosts and anionic carboxylate or sulfonate tail of guests [18]. Moreover, *β*-CD dimer **56** shows a larger binding constant upon inclusion complexation with CA and DCA than **5**. This may be attributed to that the coordination of copper ion onto the amino tether of CD affords a more positive charged environment as compared with its precursor **5**. Compared with **5**, host **6** also shows stronger binding abilities toward guest molecules. However, the introduction of copper actually decreases the original binding ability of **6** towards DCA and gives comparable stability constant upon complexation with CA. All the hosts, including native *β*-CD **1** and modified *β*-CDs **2**, **5**, **6**, **7**, and **56**, show the weaker binding abilities upon inclusion complexation with GCA and TCA than those of CA and DCA. It is also found that complexes stabilities enhance with the extended length of spacer for the same guest except for **2**/CA to **5**/CA. It is reasonable to believe that the increased stability is due to the enlarged hydrogen binding interactions.



Hosts Guests pH *K*s *H TS* Methods Refs.

**46** CA 7.2 (PBS) 15310 Fluorescence 31

**47** CA 7.2 (PBS) 39900 Fluorescence 31

**48** CA 7.2 (PBS) 25930 Fluorescence 31

**49** CA 7.2 (PBS) 26200 Fluorescence 32

**50** CA 7.2 (PBS) 7351 –33.0 –10.9 ITC 33

**51** CA 7.2 (PBS) 5559 –49.3 –27.9 ITC 33

**52** CA 7.2 (PBS) 5039 –28.2 –7.1 ITC 33

**53** CA 7.2 (PBS) 10700 –30.6 –7.6 ITC 33

**54** CA 7.2 (PBS) 9899 –37.5 –14.7 ITC 33

DCA 7.2 (PBS) 7900 –31.6 –9.4 ITC 33 GCA 7.2 (PBS) 4262 –21.5 –0.8 ITC 33 TCA 7.2 (PBS) 1975 –22.0 –3.2 ITC 33

DCA 7.2 (PBS) 8912 –38.1 –15.6 ITC 33 GCA 7.2 (PBS) 5689 –22.7 –1.3 ITC 33 TCA 7.2 (PBS) 2762 –37.3 –17.6 ITC 33

DCA 7.2 (PBS) 11150 –39.9 –16.8 ITC 33 GCA 7.2 (PBS) 4061 –23.5 –2.9 ITC 33 TCA 7.2 (PBS) 2502 –20.2 0.8 ITC 33

GCA 7.2 (PBS) 7200 Fluorescence 30 TCA 7.2 (PBS) 17610 Fluorescence 30

DCA 7.2 (PBS) 8790 Fluorescence 31 GCA 7.2 (PBS) 3040 Fluorescence 31 TCA 7.2 (PBS) 4100 Fluorescence 31

DCA 7.2 (PBS) 31880 Fluorescence 31 GCA 7.2 (PBS) 10400 Fluorescence 31 TCA 7.2 (PBS) 5360 Fluorescence 31

DCA 7.2 (PBS) 14330 Fluorescence 31 GCA 7.2 (PBS) 7950 Fluorescence 31 TCA 7.2 (PBS) 4590 Fluorescence 31

DCA 7.2 (PBS) 10140 Fluorescence 32 GCA 7.2 (PBS) 3150 Fluorescence 32 TCA 7.2 (PBS) 7730 Fluorescence 32

DCA 7.2 (PBS) 5504 –42.7 –21.4 ITC 33 GCA 7.2 (PBS) 5936 –15.1 6.4 ITC 33 TCA 7.2 (PBS) 3058 –24.5 –4.6 ITC 33

CA 7.2 (PBS) 11300 Fluorescence 35 DCA 7.2 (PBS) 8372 –48.1 –25.7 ITC 33 DCA 7.2 (PBS) 21730 Fluorescence 35 GCA 7.2 (PBS) 2979 –18.1 4.2 ITC 33 GCA 7.2 (PBS) 11040 Fluorescence 35 TCA 7.2 (PBS) 4441 –19.7 1.1 ITC 33 TCA 7.2 (PBS) 6040 Fluorescence 35


332 Thermodynamics – Fundamentals and Its Application in Science

**<sup>33</sup>**CA 7.4

**<sup>35</sup>**CA 7.4

**<sup>36</sup>**CA 7.4

**<sup>37</sup>**CA 7.4

**<sup>39</sup>**CA 7.4

**<sup>40</sup>**CA 7.4

**<sup>41</sup>**CA 7.4

DCA 7.4

DCA 7.4

DCA 7.4

DCA 7.4

DCA 7.4

DCA 7.4

DCA 7.4

Hosts Guests pH *K*s *H TS* Methods Refs.

(Tris–NaCl) 6860 –30.5 –8.6 ITC 27

(Tris–NaCl) 9700 –37.0 –14.3 ITC 27

(Tris–NaCl) 2700 –27.1 –7.5 ITC 27

(Tris–NaCl) 3300 –35.7 –15.7 ITC 27

(Tris–NaCl) 4100 –24.9 –4.3 ITC 28

(Tris–NaCl) 5400 –35.0 –13.7 ITC 28

(Tris–NaCl) 5030 –29.1 –8.0 ITC 28

(Tris–NaCl) 6100 –40.2 –18.6 ITC 28

(Tris–NaCl) 12700 –32.4 –9.0 ITC 28

(Tris–NaCl) 12400 –45.4 –22.0 ITC 28

(Tris–NaCl) 12400 –25.5 –2.2 ITC 28

(Tris–NaCl) 13100 –31.9 –8.3 ITC 28

(Tris–NaCl) 6800 –25.4 –3.5 ITC 28

(Tris–NaCl) 7500 –35.2 –13.1 ITC 28

**42** CA 7.2 (PBS) 21065 –32.8 –8.1 ITC 29

**43** CA 7.2 (PBS) 5868 –39.3 –17.7 ITC 29

**44** CA 7.2 (PBS) 5606 –41.0 –19.6 ITC 29

**45** CA 7.2 (PBS) 27050 Fluorescence 30

DCA 7.2 (PBS) 22780 –42.7 –17.9 ITC 29 GCA 7.2 (PBS) 9707 –23.0 –0.3 ITC 29 TCA 7.2 (PBS) 6848 –22.4 –0.5 ITC 29

DCA 7.2 (PBS) 7017 –47.4 –25.5 ITC 29 GCA 7.2 (PBS) 4031 –25.8 –5.2 ITC 29 TCA 7.2 (PBS) 2947 –26.9 –7.1 ITC 29

DCA 7.2 (PBS) 5511 –52.1 –30.7 ITC 29 GCA 7.2 (PBS) 2847 –26.5 –6.9 ITC 29 TCA 7.2 (PBS) 1877 –29.0 –10.3 ITC 29

DCA 7.2 (PBS) 22930 Fluorescence 30



(Tris–HCl) 11900 Fluorescence 37

(Tris–HCl) 11500 Fluorescence 37

(Tris–HCl) 8820 Fluorescence 37

(Tris–HCl) 1870 Fluorescence 37

(Tris–HCl) 5.73 × 107 Fluorescence 37

(Tris–HCl) 2.03 × 107 Fluorescence 37

(Tris–HCl) 9.93 × 107 Fluorescence 37

(Tris–HCl) 3.47 × 107 Fluorescence 37

(Tris–HCl) 3.96 × 107 Fluorescence 37

(Tris–HCl) 3.78 × 107 Fluorescence 37

(Tris–HCl) 2.95 × 107 Fluorescence 37

(Tris–HCl) 6.2 × 106 Fluorescence 37

–: The guest-induced variations in the fluorescence intensities are too small for these values to be determined.

In conclusion, the binding modes, binding abilities, and molecular selectivities of four typical bile salts (CA, DCA, GCA, and TCA) upon complexation with CDs and their derivatives are summarized in this chapter from thermodynamic viewpoints. Generally, native and mono-modified CDs display relatively limited binding ability towards guest molecules, probably because of weak interactions between hosts and guests, which would result in a relative small negative enthalpy change, and then, a relative weak binding. However, bridged and metallobridged CDs have greatly enhanced the binding abilities in

**Table 2.** Complex stability constants (*K*s/M1), enthalpy (*H*°/(kJmol1)), and entropy changes (*TS*°/(kJmol1)) for intermolecular complexation of bile salts with bridged *β*-CDs in aqueous solution

Hosts Guests pH *K*s *H TS* Methods Refs.

(Tris–HCl)

**<sup>67</sup>**CA 7.2

**<sup>68</sup>**CA 7.2

**<sup>69</sup>**CA*<sup>a</sup>* 7.2

**<sup>70</sup>**CA*<sup>a</sup>* 7.2

**<sup>71</sup>**CA*<sup>a</sup>* 7.2

**<sup>72</sup>**CA*<sup>a</sup>* 7.2

Tris: Tris(hydroxymethyl)aminomethane;

*a*

: Unit of *K*s is in M–2.

**5. Conclusion** 

DCA 7.2

DCA 7.2

DCA*<sup>a</sup>* 7.2

DCA*<sup>a</sup>* 7.2

DCA*<sup>a</sup>* 7.2

DCA*<sup>a</sup>* 7.2

PBS: Phosphate Buffer Solution; ITC: Isothermal Titration Calorimetry;



PBS: Phosphate Buffer Solution; ITC: Isothermal Titration Calorimetry;

Tris: Tris(hydroxymethyl)aminomethane;

–: The guest-induced variations in the fluorescence intensities are too small for these values to be determined.

*a* : Unit of *K*s is in M–2.

334 Thermodynamics – Fundamentals and Its Application in Science

**<sup>57</sup>**CA 7.4

**<sup>58</sup>**CA 7.4

**<sup>59</sup>**CA 7.4

**<sup>65</sup>**CA 7.2

**<sup>66</sup>**CA 7.2

DCA 7.2

DCA 7.4

DCA 7.4

DCA 7.4

Hosts Guests pH *K*s *H TS* Methods Refs. **55** CA 7.2 (PBS) 6196 –39.3 –17.6 ITC 33

**56** CA 7.2 (PBS) 13330 –29.77 –6.23 ITC 18

**60** CA aqueous solution 5380 Fluorescence 36

**61** CA aqueous solution 3380 Fluorescence 36

**62** CA aqueous solution 30500 Fluorescence 36

**63** CA aqueous solution 196000 Fluorescence 36

**64** CA aqueous solution 246000 Fluorescence 36

DCA aqueous solution 2790 Fluorescence 36 GCA aqueous solution – Fluorescence 36

DCA aqueous solution 3710 Fluorescence 36 GCA aqueous solution – Fluorescence 36

DCA aqueous solution 529000 Fluorescence 36 GCA aqueous solution 1745000 Fluorescence 36

DCA aqueous solution 283700 Fluorescence 36 GCA aqueous solution 13000 Fluorescence 36

DCA aqueous solution 54000 Fluorescence 36 GCA aqueous solution 891000 Fluorescence 36

DCA 7.2 – Fluorescence 37

(Tris–HCl) 18500 Fluorescence 37

(Tris–HCl) 12200 Fluorescence 37

(Tris–HCl) 8130 Fluorescence 37

DCA 7.2 (PBS) 10325 –39.4 –16.5 ITC 33 GCA 7.2 (PBS) 2891 –23.3 –3.5 ITC 33 TCA 7.2 (PBS) 2189 –20.0 –0.9 ITC 33

DCA 7.2 (PBS) 12065 –34.02 –10.72 ITC 18 GCA 7.2 (PBS) 2925 –23.36 –3.58 ITC 18 TCA 7.2 (PBS) 2478 –21.46 –2.09 ITC 18

(Tris–HCl) 10540 Fluorescence 34

(Tris–HCl) 12400 Fluorescence 34

(Tris–HCl) 15500 Fluorescence 34

(Tris–HCl) 15700 Fluorescence 34

(Tris–HCl) 31400 Fluorescence 34

(Tris–HCl) 95900 Fluorescence 34

**Table 2.** Complex stability constants (*K*s/M1), enthalpy (*H*°/(kJmol1)), and entropy changes (*TS*°/(kJmol1)) for intermolecular complexation of bile salts with bridged *β*-CDs in aqueous solution

#### **5. Conclusion**

In conclusion, the binding modes, binding abilities, and molecular selectivities of four typical bile salts (CA, DCA, GCA, and TCA) upon complexation with CDs and their derivatives are summarized in this chapter from thermodynamic viewpoints. Generally, native and mono-modified CDs display relatively limited binding ability towards guest molecules, probably because of weak interactions between hosts and guests, which would result in a relative small negative enthalpy change, and then, a relative weak binding. However, bridged and metallobridged CDs have greatly enhanced the binding abilities in relation to the parent CDs, owing to a multiple recognition mechanism, which would lead to a relative large negative enthalpy change, and then a strong binding. This summary of the binding modes and thermodynamic data for the complexation of bile salts with CDs and their derivatives is quite important to improve the understanding of molecular recognition mechanism in supramolecular systems and further guide the design and synthesis of new supramolecular systems based on different kinds of CDs in the future.

Thermodynamics of Resulting Complexes Between Cyclodextrins and Bile Salts 337

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## **Author details**

Yu Liu\* and Kui Wang

*Department of Chemistry, State Key Laboratory of Elemento-Organic Chemistry, Nankai University, Tianjin, P. R. China* 

## **Acknowledgement**

This work was supported by the 973 Program (2011CB932502) and NSFC (20932004), which are gratefully acknowledged.

## **6. References**


<sup>\*</sup> Corresponding Author

[10] Holm R, Madsen J.C, Shi W, Larsen K.L, Städe L.W, Westh P (2011) Thermodynamics of Complexation of Tauro- and Glyco-Conjugated Bile Salts with Two Modified *β*-Cyclodextrins. J. Incl. Phenom. Macrocycl. Chem. 69: 201–211.

336 Thermodynamics – Fundamentals and Its Application in Science

**Author details** 

*Tianjin, P. R. China* 

**6. References** 

**Acknowledgement** 

are gratefully acknowledged.

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Chem. Rev. 97: 1567–1608.

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Salts. Langmuir 26: 17949–17957.

 \*

Corresponding Author

β-Cyclodextrin. Phys. Chem. Chem. Phys. 11: 5070–5078.

97: 1325–1357.

and Kui Wang

Yu Liu\*

relation to the parent CDs, owing to a multiple recognition mechanism, which would lead to a relative large negative enthalpy change, and then a strong binding. This summary of the binding modes and thermodynamic data for the complexation of bile salts with CDs and their derivatives is quite important to improve the understanding of molecular recognition mechanism in supramolecular systems and further guide the design and synthesis of new

*Department of Chemistry, State Key Laboratory of Elemento-Organic Chemistry, Nankai University,* 

This work was supported by the 973 Program (2011CB932502) and NSFC (20932004), which

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supramolecular systems based on different kinds of CDs in the future.

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**Chapter 13** 

© 2012 Vieillard, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

**Thermodynamics of Hydration in Minerals:** 

Many papers have suggested that several specific "types" of H2O exist. These have been labelled variously as " zeolitic", " loosely held", "structural", "crystal", "tightly bound" and "external" [1-3]. These labels suggest both the differing apparent energies of H2O as well as their differing apparent structural roles. Three useful distinctions can be made about H2O in

The first type (continuously varying H2O) is characteristic of the zeolites and clay minerals and considers that most of the zeolites and clay minerals lose or gain H2O in response to small changes in temperature and pressure over an extended temperature, relative humidity

The second type of H2O is similar in nature to that found in hydrates of salts and considers that dehydration occurs over narrow temperature intervals in some compounds. Some zeolites, like analcime and laumontite, do not exchange water at room temperature. This type can be called "hydrate" H2O and has a specific position in the crystal structure. Hydroxides are excluded from this chapter because the H2O molecule is not identified but is

The third type of H2O is externally sorbed to the crystal and may be referred to as external. This type is present in quantities much smaller than the H2O present within the structure of any zeolite grain size. In the clay minerals, whose specific surfaces are greater than those of zeolites, the water located in inter-particle spaces, in inter-aggregate spaces and at the

1. H2O that varies in content as a continuous function of temperature and pressure 2. H2O that changes discontinuously at a unique temperature for a given pressure

**How to Predict These Entities** 

Additional information is available at the end of the chapter

3. H2O that is sorbed to external surfaces

or the nature of cations in exchanged sites.

only virtually present as a hydroxyl OH.

Philippe Vieillard

**1. Introduction** 

compounds:

http://dx.doi.org/10.5772/51567

