**1. Introduction**

Beside of separation and identification of chemical compounds, chromatography can be used to obtain molecular parameters that reflect their structural characteristics – molecular descriptors. Most often it is a parameter of hydrophobicity (lipophilicity) of molecules (ions) which is obtained by using retention parameters of reversed phase liquid chromatography or thin layer chromatography of high resolutions (RPHPLC and RPTLC) [1,2]. Hydrophobicity of molecules is an important feature in medical chemistry, and arbitrarily connected with the logarithm of the solute partition (distribution) coefficient log*P* (*P* stands for the ratio of the equilibrium concentration of the particle of the same electronic structure in 1-octanol and its equilibrium concentration in water). Partition coefficient is determined by the traditional shake flask method, which has drawbacks: long analysis (for reaching equilibrium) and the results often do not have adequate reproducibility [1,2,3]. While hydrophobicity obtained by chromatographic methods is obtained relatively quickly, it is possible to specify a number of compounds and achieved by high precision and reproducibility of results. Lipophilicity of chemical compounds (which is expressed either as a chromatographically i.e. retention parameters or as an *in silico* molecular descriptors of log*P*) is often included in the regression equations obtained in the QSA(P)R (Quantitative Structure Activity (Property) Relationship) studies [1,2,3].

Bile acids are amphiphilic molecules that have peculiar structure, because molecular descriptors that are obtained on the basis of the molecular graph or fragmentation methods often do not reflect their true structural features [4]. Therefore, the bile acid chromatographic lipophilicity play an important application in obtaining QSA(P)R models that connect biological and pharmacological or other physical-chemical properties

© 2012 Poša, 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 Poša, licensee InTech. This is a paper 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.

(solubility, critical micelle concentration, critical micelle temperature, etc.) for their structure [5]. In the QSA(P)R models chromatographic parameters are independent variables.

In the following section presents the introduction chromatographic parameters (TLC and HPLC) that are used to represent the hydrophobicity of compounds, and presents the main structural features of bile acids.

### **2. Chromatographic parameters**

The basic characteristic of the position of analytes spot on TLC chromatograms is the *Rf* value (retardaction factor). *Rf* value is the ratio of the path length that has crossed spot of solute from the start line *Ss* and path length *Sf* of the solvent front (Fig. 1).

$$R\_f = \frac{s\_s}{s\_f} \tag{1}$$

Chromatographic Retention Parameters as Molecular Descriptors for Lipophilicity in QSA(P)R Studies of Bile Acid 345

(4)

(5)

<sup>1</sup> log log 1

and the retention parameter log*k* usually indicates with *RM*. In the reverse phase thin layer chromatography, where the stationary phase is the hydrophobic environment, in the course of the chromatographic process chemical compounds that are more hydrophobic spend more time in the stationary phase than in the polar mobile phase, which resulting in less crossed paths of their chromatographic spots. Therefore, the more hydrophobic is solute its *Rf* value is more lower or its retention parameter *RM* value is more higher. In reverse phase thin-layer chromatography for each compound is determined the dependence of the chromatographic parameters *RM* of the volume fraction *φ* of organic modifier in aqueous mobile phase (i.e. for each of the tested compounds from one chromatographic experiment to another experiment varies of mobile phase volume fraction of organic modifier). The most common organic modifier is methanol. If increasing the volume fraction of the organic modifier in aqueous mobile phase results of decrease in hydrophobicity of mobile phase. This is manifested as the reduction of the difference between staying time of solute in the stationary and mobile phase during the chromatographic process – increased *Rf* values (decreasing value of *RM*). Usually between the chromatographic parameters *RM* and the volume fraction of organic modifier *φ* is linear relation (usually in the interval: 0.2 ≤ *φ* ≤ 0.8)

*RR S M M*<sup>0</sup> = +

In the above equation *RM*0 is the extrapolated value of the chromatographic parameters *RM* which is governed to the mobile phase contain only water (or buffered aqueous solution), i.e. mobile phase without an organic modifier, while *S* is the slope of the right (Fig. 2). *S* is

**Figure 2.** The linear dependence of *RM* chromatographic parameters of volume of organic modifier *φ*.

tg =-*S*

*RM*0 parameters value depends on the type of organic modifier on the basis of which is determined by the function (1.5). *RM*0 is usually in the good correlation of the compounds

directly related to the specific surface of the stationary phase.

*RM*<sup>0</sup>

*RM*

0

ϕ

*k*

[3,6-8].

*f*

*R* = −

If the solute spends more time in the mobile phase, then its chromatographic spot position is closer to the front of solvent and its *Rf* value is even higher (maximum value of the *Rf* parameter is 1). Whereas if the solute spends more time in the stationary phase, then the position of his spots closer to the start line, and its *Rf* value is less (Fig. 1 (a)).

**Figure 1.** Chromatograms: (1) TLC with *Rf* values of the solute over their spots, (2) HPLC.

The ratio of time spent by the solute in the stationary phase *ts* and the time by spend in the mobile phase *tm* is the capacitance factor.

$$k = \frac{t\_s}{t\_m} \tag{2}$$

The connection between *Rf* values and capacitive factor has the equation:

$$k = \frac{1}{R\_f} - 1\tag{3}$$

The logarithm of the above expression is:

$$\log k = \log \left(\frac{1}{R\_f} - 1\right) \tag{4}$$

and the retention parameter log*k* usually indicates with *RM*. In the reverse phase thin layer chromatography, where the stationary phase is the hydrophobic environment, in the course of the chromatographic process chemical compounds that are more hydrophobic spend more time in the stationary phase than in the polar mobile phase, which resulting in less crossed paths of their chromatographic spots. Therefore, the more hydrophobic is solute its *Rf* value is more lower or its retention parameter *RM* value is more higher. In reverse phase thin-layer chromatography for each compound is determined the dependence of the chromatographic parameters *RM* of the volume fraction *φ* of organic modifier in aqueous mobile phase (i.e. for each of the tested compounds from one chromatographic experiment to another experiment varies of mobile phase volume fraction of organic modifier). The most common organic modifier is methanol. If increasing the volume fraction of the organic modifier in aqueous mobile phase results of decrease in hydrophobicity of mobile phase. This is manifested as the reduction of the difference between staying time of solute in the stationary and mobile phase during the chromatographic process – increased *Rf* values (decreasing value of *RM*). Usually between the chromatographic parameters *RM* and the volume fraction of organic modifier *φ* is linear relation (usually in the interval: 0.2 ≤ *φ* ≤ 0.8) [3,6-8].

344 Chromatography – The Most Versatile Method of Chemical Analysis

structural features of bile acids.

**2. Chromatographic parameters** 

mobile phase *tm* is the capacitance factor.

*increase of*

*lipophilicity*

The logarithm of the above expression is:

(solubility, critical micelle concentration, critical micelle temperature, etc.) for their structure

In the following section presents the introduction chromatographic parameters (TLC and HPLC) that are used to represent the hydrophobicity of compounds, and presents the main

The basic characteristic of the position of analytes spot on TLC chromatograms is the *Rf* value (retardaction factor). *Rf* value is the ratio of the path length that has crossed spot of

*f*

*<sup>s</sup> <sup>R</sup>*

If the solute spends more time in the mobile phase, then its chromatographic spot position is closer to the front of solvent and its *Rf* value is even higher (maximum value of the *Rf* parameter is 1). Whereas if the solute spends more time in the stationary phase, then the

*s*

*<sup>s</sup>* <sup>=</sup> (1)

*<sup>t</sup>* <sup>=</sup> (2)

*<sup>R</sup>* = − (3)

*f*

solute from the start line *Ss* and path length *Sf* of the solvent front (Fig. 1).

position of his spots closer to the start line, and its *Rf* value is less (Fig. 1 (a)).

**Figure 1.** Chromatograms: (1) TLC with *Rf* values of the solute over their spots, (2) HPLC.

The connection between *Rf* values and capacitive factor has the equation:

The ratio of time spent by the solute in the stationary phase *ts* and the time by spend in the

*s m <sup>t</sup> <sup>k</sup>*

> <sup>1</sup> <sup>1</sup> *f*

*k*

[5]. In the QSA(P)R models chromatographic parameters are independent variables.

$$R\_M = R\_{M0} + S\varphi \tag{5}$$

In the above equation *RM*0 is the extrapolated value of the chromatographic parameters *RM* which is governed to the mobile phase contain only water (or buffered aqueous solution), i.e. mobile phase without an organic modifier, while *S* is the slope of the right (Fig. 2). *S* is directly related to the specific surface of the stationary phase.

**Figure 2.** The linear dependence of *RM* chromatographic parameters of volume of organic modifier *φ*.

*RM*0 parameters value depends on the type of organic modifier on the basis of which is determined by the function (1.5). *RM*0 is usually in the good correlation of the compounds

lipophilicity. In recent times to describe the molecules lipophilicity also used the chromatographic parameters *φ*0 which is the ratio of *RM*0 and the slope *S* (Fig. 2) [7,8].

$$\varphi\_0 = \frac{R\_{M0}}{\left| -S \right|} \tag{6}$$

Chromatographic Retention Parameters as Molecular Descriptors for Lipophilicity in QSA(P)R Studies of Bile Acid 347

There is a possibility of application principal component analysis (PCA) on chromatographic data to the thin layer and the liquid chromatography. PCA is applied to the data matrix **D** of retention parameters *RM*, log*k* (or *k*). The columns of the matrix **D** corresponding retention parameters for different volume fraction *φ* of organic modifier (columns represent the organic modifier) while the matrix rows represent the different types of chemical compounds. PCA is usually applied directly on the covariance matrix **DTD** retention parameters. As a result of PCAs mathematical procedure (orthogonal diagonalization) are obtained orthonorms PC score vectors of whose number is 2 (PC1, PC2) or 3 (PC1, PC2, PC3), depending on the percentage of variance explained from the data matrix **D**. Accordingly objects (tested molecules) from a multidimensional space matrix of retention parameters **D** mapped to 2d or 3d space of PC. In the graphs of PC scores can be found congeneric group of chemical compounds by their lipophilicity. As a parameter of lipophilicity of chemical compounds in the QSA(P)R studies can be applied also to the

Generally, the dissolution of an amphiphilic object in water is accompanied by the disruption of the hydrogen bonds between water molecules and formation of a hydration sheath (hydration layer) around the particles of the dissolved substance. If we observe such a system (amphiphilic solution), which consists of two subsystems: hydrophobic part (**a**) and hydrophilic part (**b**), then the thermodynamic functions can be considered separately for each subsystem (Fig. 4). For both subsystems it holds that in the formation of the solvation sheaths (around the amphiphilic objects) approximately the same number of hydrogen bonds are formed as existed between the water molecules in the bulk water, i.e. before introducing the amphiphilic object. Hence the change of the enthalpy for each of the subsystems is equal to zero: Δ*H*(**a**)≈Δ*H*(**b**)≈0. Also, in the formation of the solvation sheath, the entropy (translational and rotational) of both subsystems decreases, that is: Δ*S*(**a**)≈Δ*S*(**b**)<0. However, the water molecules from the hydrophilic side (**b**) of the amphiphilic molecule form additional hydrogen bonds; hence for this subsystem there is an additional negative enthalpy (Δ*Hɛ*<0), which is dissipated as heath in the environment (bulk of the solution), thus giving rise to a positive change of the entropy (of the environment). Therefore, the free enthalpy change for the hydrophilic subsystem is: Δ*G*(**b**)<0, on the basis of which the water molecules from the hydrophilic side (**b**) of the amphiphil can be denoted as stabilized water molecules (SWM), while the water molecules from the hydrophobic side

The ratio of the hydrophilic-to-hydrophobic surface area of an amphiphilic molecule determines the overall change of the Gibbs energy of formation of the hydration sheath (Δ*G*), and, since the hydrophobic surface of the amphiphilic molecule is larger, then Δ*G*>0. The larger the amount of the amphiphil present in the solution, the more water molecules participate in the formation of the hydration sheath, and the more negative is the overall entropy change. This results in the changes in the system (solution) due to the passing of NSMW from the amphiphil hydration sheath to the bulk of the solution, giving rise to the

scores of PC [3,6].

**3. The hydrophobic effect** 

(**a**) are nonstabilized water molecules (NSWM) [4,11].

The chromatographic parameters *φ*0 corresponding volume ratio of organic modifier in aqueous mobile phase in which the same amount of solute in the mobile phase and in the stationary phase. Indeed solute in the above mobile phase composition, during the chromatographic process, spends at the same time in the stationary phase and the mobile phase, therefore capacitive factor (2) is *k* = 1, respectively *Rf* value (3) is 0.5. This *Rf* values corresponding to *RM* chromatographic parameter (4) whose value is zero. Which means that equation (5) is: 0=*RM*0 + *Sφ*0 from which follows the expression (6). If the solute is more hydrophobic then a larger quantity of organic modifier is needed to equalize the amount of solute in two phases, i.e. the chromatographic parameter *φ*0 has higher value. With a high efficient reverse phase liquid chromatography, stationary phase is also hydrophobic environment. Solute is characterized by retention time *ts*, which represents the elapsed time from injection to the occurrence of the same solute in detectors, i.e. the retention time of solute in the column. Chemical compounds in RP-HPLC analysis is usually characterized by the retention coefficient (capacity factor):

$$k = \frac{t\_s - t\_0}{t\_0} \tag{7}$$

where *t*0 is the retention time of solvent from the mobile phase (Fig. 1 (a)). If a chemical compound is more hydrophobic, then more time is spent in the hydrophobic stationary phase, i.e. it takes more time to pass the column and the retention time or retention factor even greater. The logarithm of the retention coefficient log*k* is used as a parameter of hydrophobicity of chemical compound. An important chromatographic parameter of lipophilicity is log*kw* which were obtained an extrapolation of the linear equations (8) to the zero volume fraction *φ* of organic modifier in aqueous mobile phase.

$$
\log k = \log k\_w + S\varphi \tag{8}
$$

Similar as in the RP TLC analysis, in RP HPLC also can defined the chromatographic indices *φ*0 (with the same meaning) as the ratio of log*kw* and the slope from log*k* = *f*(*φ*) [9,10].

**Figure 3.** Application of principal component analysis on the retention data matrix D, n = number of different volume fraction of organic modifier, m = number of different compounds, n> 3.

There is a possibility of application principal component analysis (PCA) on chromatographic data to the thin layer and the liquid chromatography. PCA is applied to the data matrix **D** of retention parameters *RM*, log*k* (or *k*). The columns of the matrix **D** corresponding retention parameters for different volume fraction *φ* of organic modifier (columns represent the organic modifier) while the matrix rows represent the different types of chemical compounds. PCA is usually applied directly on the covariance matrix **DTD** retention parameters. As a result of PCAs mathematical procedure (orthogonal diagonalization) are obtained orthonorms PC score vectors of whose number is 2 (PC1, PC2) or 3 (PC1, PC2, PC3), depending on the percentage of variance explained from the data matrix **D**. Accordingly objects (tested molecules) from a multidimensional space matrix of retention parameters **D** mapped to 2d or 3d space of PC. In the graphs of PC scores can be found congeneric group of chemical compounds by their lipophilicity. As a parameter of lipophilicity of chemical compounds in the QSA(P)R studies can be applied also to the scores of PC [3,6].
