**3. The hydrophobic effect**

346 Chromatography – The Most Versatile Method of Chemical Analysis

lipophilicity. In recent times to describe the molecules lipophilicity also used the

0

0 0 *st t <sup>k</sup> t*

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

log log *<sup>w</sup> k kS* = +

**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.

*φ*0 (with the same meaning) as the ratio of log*kw* and the slope from log*k* = *f*(*φ*) [9,10].

Similar as in the RP TLC analysis, in RP HPLC also can defined the chromatographic indices

ϕ

<sup>=</sup> − (6)

<sup>−</sup> <sup>=</sup> (7)

(8)

*RM S*

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-

chromatographic parameters *φ*0 which is the ratio of *RM*0 and the slope *S* (Fig. 2) [7,8].

0

ϕ

HPLC analysis is usually characterized by the retention coefficient (capacity factor):

zero volume fraction *φ* of organic modifier in aqueous mobile phase.

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

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

O

O OH

H OH

**convex plane side**

H H

**concave plane side**

H

chenodeoxycholic acid (**CDC**): R1=OH, R2=H, R3=OH, R4=H deoxycholic acid (**DC**): R1=OH, R2=H, R3=H, R4=OH hyodeoxycholic acid (**HDC**): R1=OH, R2=OH, R3=H, R4=H lithocholic acid (**LC**): R1=OH, R2=H, R3=H, R4=H

H

O OH

H

**Figure 5.** The bile acids general structure.

A B

**5 cholanic acid**

the literature often uses the term molecule with a hydrophilic edge.

C6 OH group from hyodeoxycholic acid (**HDA**).

C D

**primary secondary** R2

cholic acid (**C**): R1=OH, R2=H, R3=OH, R4=OH

skeleton is the polar surface – hydrophilic side, while the convex surface (β) is the nonpolar surface – hydrophobic side. Simultaneous presence of hydrophobic and hydrophilic regions in the molecule of bile acids is named as amphiphilic. Since the carboxyl group ionized under physiological conditions, bile acids in biochemical systems belong to the ionic amphiphile. Also, bile acids are a special group of amphiphilic compounds, the group of biplanar molecules [4.5]. This is most apparent in cholic acid molecules (Fig. 6) because the molecules oxygen atoms from the α OH groups are in the same plane, the polar plane. In chenodeoxycholic and deoxycholic acid cannot be talking about the true planar polarity, but

If it oxidation of C7 or C12 α axial hydroxy group in cholic acid (**C**) (or deoxycolic acid (**DC**) or chenodeocycholic acid (**CDC**)) molecule leads to oxo derivative whose oxigen atom is switched for 60° (Newman projection) in relation to its' starting axial orientation i.e forms an angle of 30° with steroid skeleton mean plain (SSMP) (Newman projection, **Fig. 7**) [11,14]. Oxigen atom from C7 or C12 oxo group has the same steric orientation as has the equatorial

Convergence of oxigen core (from oxo group) toward steroid sceleton β side means that there is the rise in number of stabilised water molecules (SWM, stabilised by hydrogen bonds) in hydratation layer of bile acids' steroid sceleton while hydrophobic surface of the

R1 R3

<sup>3</sup> <sup>6</sup> <sup>7</sup>

R4

12

**Figure 4.** The hydrophobic effect: SWM = stabilised water molecules, NSWM = nonstabilised water molecules.

system entropy. Amphiphilic molecules (ions) are oriented so that their (formally) desolvated hydrophobic sides are to the smallest extent exposed to water molecules. This is realized either in the form of self-association of the amphiphils via their hydrophobic surfaces (Fig. 4) (entropy decrease due to the amphiphil self-association is smaller than the increase in the entropy due to their release from the hydration layer) or by binding of the amphiphil to the hydrophobic surface of the system: hydrophobic stationary phase, proteins, distribution in the organic solvent, etc. [11]. Generally, the hydrophobicity of a particle (molecule, ion) can be expressed via the logarithm of the coefficient of its partition (log*P*) between 1-octanol and water (*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). If log*P* > 1, the particle is hydrophobic (lipophilic), and if log*P* < 1, the particle is hydrophilic [12]. Apart from the partition coefficient, the hydrophobicity of a particle can be also expressed via chromatographic parameters, either of the normal-phase or reversedphase chromatography.

## **4. Structure of bile acids**

Bile acid enzymatic produced in the liver of human and other mammals are the primary bile acids, and their intestinal microbial transformation to obtain the secondary bile acids. Both groups of bile acids are hydroxy derivatives of 5β-cholanic acid (cholic acid and chenodeoxycholic acid) [13]. The geometry of the 5β-cholanic acid largely determines of bile acids properties. The steroid skeleton of 5β-cholanic acid can be distinguished convex β and concave α surface (Fig. 5) [5].

Hydroxyl groups of bile acids are mostly oriented towards α side of steroid skeleton. X ray diffraction is demonstrated that the carboxyl group of the side chain from C17 carbon is also located on the α side of the steroid ring system. A concave (α) of bile acids steroid

**Figure 5.** The bile acids general structure.

348 Chromatography – The Most Versatile Method of Chemical Analysis

molecules.

phase chromatography.

**4. Structure of bile acids** 

concave α surface (Fig. 5) [5].

**Figure 4.** The hydrophobic effect: SWM = stabilised water molecules, NSWM = nonstabilised water

system entropy. Amphiphilic molecules (ions) are oriented so that their (formally) desolvated hydrophobic sides are to the smallest extent exposed to water molecules. This is realized either in the form of self-association of the amphiphils via their hydrophobic surfaces (Fig. 4) (entropy decrease due to the amphiphil self-association is smaller than the increase in the entropy due to their release from the hydration layer) or by binding of the amphiphil to the hydrophobic surface of the system: hydrophobic stationary phase, proteins, distribution in the organic solvent, etc. [11]. Generally, the hydrophobicity of a particle (molecule, ion) can be expressed via the logarithm of the coefficient of its partition (log*P*) between 1-octanol and water (*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). If log*P* > 1, the particle is hydrophobic (lipophilic), and if log*P* < 1, the particle is hydrophilic [12]. Apart from the partition coefficient, the hydrophobicity of a particle can be also expressed via chromatographic parameters, either of the normal-phase or reversed-

Bile acid enzymatic produced in the liver of human and other mammals are the primary bile acids, and their intestinal microbial transformation to obtain the secondary bile acids. Both groups of bile acids are hydroxy derivatives of 5β-cholanic acid (cholic acid and chenodeoxycholic acid) [13]. The geometry of the 5β-cholanic acid largely determines of bile acids properties. The steroid skeleton of 5β-cholanic acid can be distinguished convex β and

Hydroxyl groups of bile acids are mostly oriented towards α side of steroid skeleton. X ray diffraction is demonstrated that the carboxyl group of the side chain from C17 carbon is also located on the α side of the steroid ring system. A concave (α) of bile acids steroid skeleton is the polar surface – hydrophilic side, while the convex surface (β) is the nonpolar surface – hydrophobic side. Simultaneous presence of hydrophobic and hydrophilic regions in the molecule of bile acids is named as amphiphilic. Since the carboxyl group ionized under physiological conditions, bile acids in biochemical systems belong to the ionic amphiphile. Also, bile acids are a special group of amphiphilic compounds, the group of biplanar molecules [4.5]. This is most apparent in cholic acid molecules (Fig. 6) because the molecules oxygen atoms from the α OH groups are in the same plane, the polar plane. In chenodeoxycholic and deoxycholic acid cannot be talking about the true planar polarity, but the literature often uses the term molecule with a hydrophilic edge.

If it oxidation of C7 or C12 α axial hydroxy group in cholic acid (**C**) (or deoxycolic acid (**DC**) or chenodeocycholic acid (**CDC**)) molecule leads to oxo derivative whose oxigen atom is switched for 60° (Newman projection) in relation to its' starting axial orientation i.e forms an angle of 30° with steroid skeleton mean plain (SSMP) (Newman projection, **Fig. 7**) [11,14]. Oxigen atom from C7 or C12 oxo group has the same steric orientation as has the equatorial C6 OH group from hyodeoxycholic acid (**HDA**).

Convergence of oxigen core (from oxo group) toward steroid sceleton β side means that there is the rise in number of stabilised water molecules (SWM, stabilised by hydrogen bonds) in hydratation layer of bile acids' steroid sceleton while hydrophobic surface of the

350 Chromatography – The Most Versatile Method of Chemical Analysis

(9)

of the reaction (R2), taking also

ϕ(10)

This equilibrium is characterized by the equilibrium constant *Kad* = [BA(*s*)] / [BA(*aq*)], which is connected with the retention factor (capacity factor) (7) via the following relation [15]:

*ad hc*

*pf K V k K <sup>V</sup>* = =

the column. The change of the standard Gibbs energy Δ*Gad*

into account (9), is:

environment.

where *Vhc* represents the volume of hydrocarbon in the stationary phase, whereas *Vpf* is the volume of the polar phase. Their ratio is denoted as *φ*, and it represents a characteristic of

*ad* ln ln ln *G RT K RT k RT ad* Δ =− =− +

In both RPHPLC and RPTLC, in the adsorption of bile acids on the hydrophobic stationary phase, the water molecules from the solvation sheath that are not stabilized by hydrogen bonds (NSWM) pass to the hydrophilic mobile phase, giving a positive entropy contribution. Beside that, during the return of these water molecules in the bulk solution, NSWMs surface energy is released, which is then dissipated as a heat in the environment (solvophobic theory: according to this theory change in surface energy is a key factor in the reversed phase chromatographic processes energy). The formally dehydrated hydrophobic surfaces of bile acid molecules (ions) bind to the surface of the adsorbent by hydrophobic interactions (London dispersion forces, and dipol-induced dipole interactions). This makes a negative enthalpic contribution to the adsorption process, which is also dissipated as heat into the mobile phase (environment), giving rise to a positive change of the entropy of the

Hence, the overall entropy change is positive, i.e. the Gibbs energy is lowered. The decrease in the free enthalpy of adsorption (Δ*adGº*) of bile acids (molecules or ions) on the hydrophobic stationary phase is more pronounced if the solvation layer of the steroid skeleton contains a greater number of NSWM, since then, there exists a largest increase in the overall entropy. In the binding of bile acids (molecules or ions) to the hydrophobic stationary phase, their steroid skeletons orient in such a way that the formally desolvated surfaces are to the smallest possible extent exposed to the solvent molecules from the hydrophilic mobile phase (methanol and water). Since bile acids are biplanar compounds, their molecules bind to the hydrophobic stationary phase by the side of the steroid skeleton that is most hydrophobic. With natural bile acids and their oxo derivatives, this is usually the convex β side of the steroid skeleton (an exception is the enantiomer of cholic acid with β configurations of all three OH groups, where α side is more hydrophobic than the β side of the steroid skeleton). Thus, the ln*k* chromatographic parameter has the liner dependence of Δ*adGº*, which means that lnk has also linear depending on the hydrophobic surface of the β side of steroid nucleus. Similar is true for *RM* chromatographic parameter (RPTLC). Therefore, ln*k* could serve as a molecular descriptor for the hydrophobicity of bile acids. But the studies dealing with the hydrophobicity of bile acids as expressed via the retention coefficients (*k*), there is a problem of mutual comparability of the ln*k* values. Because of that

*ad*

ϕ

**Figure 6.** Two different side of cholic acid.

**Figure 7.** Introduction of oxo group in bile acids' steroid sceleton leads to rise in number of stabilised water molecules (SWM) i.e. the hydrophobic β side of the steroid sceleton decreases.

convex side of the steroid sceleton decreases (Fig. 7). Thus, the number of unstabilised water molecules (NSWM) declines [11].

$$\text{BA} \Big[ \text{NSWM} \Big]\_{\text{n(aq)}} \rightleftharpoons \text{BA}\_{\text{(s)}} + \text{nNSWM} \tag{\text{R1}}$$

If bile acids' hydrophobic surface deceases (B), i.e. the number of NSWM is lower, the observed molecule bonds to the hydrophobic stationary phase with lower intensity, i.e. reaction (R1) is moved to the right. This change in hydrophobic surface reflects in the values of retention coefficient *k* (RPHPLC) and retention parameter *RM*0 (RPTLC).

## **5. Discussion: bile acids and the hromatographic parametars (indices)**

In the RPHPLC(TLC), there is an equilibrium between the bile acid molecules (ions) from the polar mobile phase BA(*aq*) and the bile acid BA(*s*) adsorbed on the hydrophobic stationary phase.

$$\mathsf{BA}\_{(aq)} \rightleftharpoons \mathsf{BA}\_{(s)}\tag{\mathsf{R}2}$$

This equilibrium is characterized by the equilibrium constant *Kad* = [BA(*s*)] / [BA(*aq*)], which is connected with the retention factor (capacity factor) (7) via the following relation [15]:

350 Chromatography – The Most Versatile Method of Chemical Analysis

**Figure 6.** Two different side of cholic acid.

molecules (NSWM) declines [11].

phase.

α

**hydrophilic part**

β

**Figure 7.** Introduction of oxo group in bile acids' steroid sceleton leads to rise in number of stabilised

convex side of the steroid sceleton decreases (Fig. 7). Thus, the number of unstabilised water

n( ) ( ) BA NSWM BA NSWM *<sup>s</sup> aq*

If bile acids' hydrophobic surface deceases (B), i.e. the number of NSWM is lower, the observed molecule bonds to the hydrophobic stationary phase with lower intensity, i.e. reaction (R1) is moved to the right. This change in hydrophobic surface reflects in the values

**5. Discussion: bile acids and the hromatographic parametars (indices)** 

In the RPHPLC(TLC), there is an equilibrium between the bile acid molecules (ions) from the polar mobile phase BA(*aq*) and the bile acid BA(*s*) adsorbed on the hydrophobic stationary

+ *n* (R1)

SWM

SWM

( ) () BA BA *aq <sup>s</sup>* (R2)

water molecules (SWM) i.e. the hydrophobic β side of the steroid sceleton decreases.

SWM

β

α

of retention coefficient *k* (RPHPLC) and retention parameter *RM*0 (RPTLC).

**hydrophobic part**

$$k = \frac{K\_{ad} V\_{hc}}{V\_{pf}} = K\_{ad} \varphi \tag{9}$$

where *Vhc* represents the volume of hydrocarbon in the stationary phase, whereas *Vpf* is the volume of the polar phase. Their ratio is denoted as *φ*, and it represents a characteristic of the column. The change of the standard Gibbs energy Δ*Gad* of the reaction (R2), taking also into account (9), is:

$$
\Delta G\_{al}^{\circ} = -RT\ln K\_{ad} = -RT\ln k + RT\ln \varphi \tag{10}
$$

In both RPHPLC and RPTLC, in the adsorption of bile acids on the hydrophobic stationary phase, the water molecules from the solvation sheath that are not stabilized by hydrogen bonds (NSWM) pass to the hydrophilic mobile phase, giving a positive entropy contribution. Beside that, during the return of these water molecules in the bulk solution, NSWMs surface energy is released, which is then dissipated as a heat in the environment (solvophobic theory: according to this theory change in surface energy is a key factor in the reversed phase chromatographic processes energy). The formally dehydrated hydrophobic surfaces of bile acid molecules (ions) bind to the surface of the adsorbent by hydrophobic interactions (London dispersion forces, and dipol-induced dipole interactions). This makes a negative enthalpic contribution to the adsorption process, which is also dissipated as heat into the mobile phase (environment), giving rise to a positive change of the entropy of the environment.

Hence, the overall entropy change is positive, i.e. the Gibbs energy is lowered. The decrease in the free enthalpy of adsorption (Δ*adGº*) of bile acids (molecules or ions) on the hydrophobic stationary phase is more pronounced if the solvation layer of the steroid skeleton contains a greater number of NSWM, since then, there exists a largest increase in the overall entropy. In the binding of bile acids (molecules or ions) to the hydrophobic stationary phase, their steroid skeletons orient in such a way that the formally desolvated surfaces are to the smallest possible extent exposed to the solvent molecules from the hydrophilic mobile phase (methanol and water). Since bile acids are biplanar compounds, their molecules bind to the hydrophobic stationary phase by the side of the steroid skeleton that is most hydrophobic. With natural bile acids and their oxo derivatives, this is usually the convex β side of the steroid skeleton (an exception is the enantiomer of cholic acid with β configurations of all three OH groups, where α side is more hydrophobic than the β side of the steroid skeleton). Thus, the ln*k* chromatographic parameter has the liner dependence of Δ*adGº*, which means that lnk has also linear depending on the hydrophobic surface of the β side of steroid nucleus. Similar is true for *RM* chromatographic parameter (RPTLC). Therefore, ln*k* could serve as a molecular descriptor for the hydrophobicity of bile acids. But the studies dealing with the hydrophobicity of bile acids as expressed via the retention coefficients (*k*), there is a problem of mutual comparability of the ln*k* values. Because of that

it is usually accustomed to give an order of hydrophobicity of the molecules, while the ln*k* values, though determined under identical experimental conditions, may vary because of the characteristic of the column (RPHPLC), which is in equation (9) denoted with *φ*. Because of that, Heuman introduced for bile acids a relative retention coefficient (*kr*) which is defined as the ratio of the retention coefficient of the given bile acid (*k*(BA)) and the retention coefficient of taurocholic acid (**TC**) (*k*(TC)) (Fig. 8) [16].

$$k\_r(\text{BA}) = \frac{k(\text{BA})}{k(\text{TC})} \tag{11}$$

Chromatographic Retention Parameters as Molecular Descriptors for Lipophilicity in QSA(P)R Studies of Bile Acid 353

(15)

*M*

*ad* (BA) (BA) ln (TL) (TC) ( ) *ad G HI RT k G <sup>r</sup>* Δ = ×− + Δ (14)

from which is evident that there is a linear relation between the hydrophobicity index of a

The *HI* value for taurocholic acid (**TC**) is zero since its relative retention coefficient equation (11) is equal to one, and the same value (one) holds also for taurolithocholic acid (**TL**). If a certain bile acid is more hydrophilic than taurocholic acid (**TC**), its retention constant (*k*) is smaller than the *k* value of taurocholic acid (**TC**), so that the relative retention coefficient of that bile acid is smaller than unity (ln*k*<0), which means that, according to equation (13), the *HI*(BA) is negative. In the opposite case, if a certain bile acid is more hydrophobic than taurocholic acid (**TC**), then the value of its retention coefficient is greater than the retention coefficient of taurochollic acd (**37**), and the relative retention coefficient for that bile acid is

Besides of Heumans hydrophobic index (based on data retention) log*k* is used to obtain predictive equations where log*k* is the independent variable while bile acid properties associated with its hydrophobicity is the dependent variable. Armstrong and Carey were given a linear regression equation, where log*k* is associated with the solubilized molar fraction of cholesterol *ϑ* (solubilized by micellar solutions of bile acid salts in the

**-1 -0.5 0 0.5 1**

**TU TU TC TD TL**

log log . *k S const* = − ϑ

In the plane of *ϑ* and log*k* is obtained of three linear congeneric groups of examined bile acids, a particular group form the non-conjugated bile acids, whereas the glyco- and tauroconjugated bile acids are also in separate groups. For each of the derived linear congeneric group is determined equation (15) whose regression coefficients (R) is range in 0993-0999. Armstrong and Carey were predicted the capacity of cholesterol solubilization by bile acids oxo derivatives using the equations (15) for each congeneric group of bile acid [17]. It can be shown that log*k* is indeed associated with a number of hydration layers non-stabilized water

( ) <sup>2</sup>

where Φ*mNaCl* is the product of the osmotic coefficient and the molality of NaCl, and *H O*<sup>2</sup>

is the molecular weight of water [11]. Therefore with the increasing of the number of the α

*d k n M*

*NSWM H O*

*d m* <sup>=</sup> <sup>Φ</sup> (16)

ln

*NaCl*

bile acid and the Gibbs energy of adsorption on the hydrophobic stationary phase.

larger than unity (ln*k*>0), that is *HI*>0 (Fig. 9).

**Figure 9.** Heumans scale of bile acids hydrophobicity.

molecules from β side of steroid skeleton:

equilibrium conditions) [17]:

*NSWM n*

Taurocholic acid (**37**) was chosen as a reference because its retention coefficient in the pH range of the mobile phase from 2.9 to 9.0 is practically constant (complete ionization) [16]. By combining equations (10) and (11), the free enthalpy of adsorpion of bile acid (BA) on the hydrophobic stationary phase is:

$$
\Delta G\_{\text{ul}}^{\circ}(\text{BA}) = -RT\ln k\_r(\text{BA}) + \Delta G\_{\text{ul}}^{\circ}(\text{TC}) \tag{12}
$$

In this way are eliminated the individual characteristics of the column, so that the relative retention coefficient depends only on the composition of the mobile phase and the degree of hydrophobicity of the stationary phase.

**Figure 8.** Tauro conjugated bile acids.

Besides, Heuman defined also the hydrophobicity index *HI* as the ratio of the logarithm of the relative retention coefficient of the given bile acid (BA) and of the relative retention coefficient of taurolithocholic acid (**TL**) (ln*kr*(TL)) (Fig. 7):

$$HI(\text{BA}) = \frac{\ln k\_r(\text{BA})}{\ln k\_r(\text{TL})} \tag{13}$$

By introducing equation (13) into (12), one obtains the following equation:

$$
\Delta G\_{ul}^{\circ}(\text{BA}) = H\text{I(BA)} \times \left( -RT\ln k\_r(\text{TL}) \right) + \Delta G\_{ul}^{\circ}(\text{TC}) \tag{14}
$$

from which is evident that there is a linear relation between the hydrophobicity index of a bile acid and the Gibbs energy of adsorption on the hydrophobic stationary phase.

The *HI* value for taurocholic acid (**TC**) is zero since its relative retention coefficient equation (11) is equal to one, and the same value (one) holds also for taurolithocholic acid (**TL**). If a certain bile acid is more hydrophilic than taurocholic acid (**TC**), its retention constant (*k*) is smaller than the *k* value of taurocholic acid (**TC**), so that the relative retention coefficient of that bile acid is smaller than unity (ln*k*<0), which means that, according to equation (13), the *HI*(BA) is negative. In the opposite case, if a certain bile acid is more hydrophobic than taurocholic acid (**TC**), then the value of its retention coefficient is greater than the retention coefficient of taurochollic acd (**37**), and the relative retention coefficient for that bile acid is larger than unity (ln*k*>0), that is *HI*>0 (Fig. 9).

**Figure 9.** Heumans scale of bile acids hydrophobicity.

352 Chromatography – The Most Versatile Method of Chemical Analysis

coefficient of taurocholic acid (**TC**) (*k*(TC)) (Fig. 8) [16].

hydrophobic stationary phase is:

hydrophobicity of the stationary phase.

**Figure 8.** Tauro conjugated bile acids.

coefficient of taurolithocholic acid (**TL**) (ln*kr*(TL)) (Fig. 7):

it is usually accustomed to give an order of hydrophobicity of the molecules, while the ln*k* values, though determined under identical experimental conditions, may vary because of the characteristic of the column (RPHPLC), which is in equation (9) denoted with *φ*. Because of that, Heuman introduced for bile acids a relative retention coefficient (*kr*) which is defined as the ratio of the retention coefficient of the given bile acid (*k*(BA)) and the retention

> (BA) (BA) (TC) *<sup>r</sup> <sup>k</sup> <sup>k</sup>*

Taurocholic acid (**37**) was chosen as a reference because its retention coefficient in the pH range of the mobile phase from 2.9 to 9.0 is practically constant (complete ionization) [16]. By combining equations (10) and (11), the free enthalpy of adsorpion of bile acid (BA) on the

In this way are eliminated the individual characteristics of the column, so that the relative retention coefficient depends only on the composition of the mobile phase and the degree of

Besides, Heuman defined also the hydrophobicity index *HI* as the ratio of the logarithm of the relative retention coefficient of the given bile acid (BA) and of the relative retention

> ln (BA) (BA) ln (TL) *r r*

*<sup>k</sup> HI*

By introducing equation (13) into (12), one obtains the following equation:

*<sup>k</sup>* <sup>=</sup> (11)

*<sup>k</sup>* <sup>=</sup> (13)

*ad* (BA) ln (BA) (TC) *ad G RT k G <sup>r</sup>* Δ =− + Δ (12)

Besides of Heumans hydrophobic index (based on data retention) log*k* is used to obtain predictive equations where log*k* is the independent variable while bile acid properties associated with its hydrophobicity is the dependent variable. Armstrong and Carey were given a linear regression equation, where log*k* is associated with the solubilized molar fraction of cholesterol *ϑ* (solubilized by micellar solutions of bile acid salts in the equilibrium conditions) [17]:

$$
\log k = S \log \vartheta - \text{const.} \tag{15}
$$

In the plane of *ϑ* and log*k* is obtained of three linear congeneric groups of examined bile acids, a particular group form the non-conjugated bile acids, whereas the glyco- and tauroconjugated bile acids are also in separate groups. For each of the derived linear congeneric group is determined equation (15) whose regression coefficients (R) is range in 0993-0999. Armstrong and Carey were predicted the capacity of cholesterol solubilization by bile acids oxo derivatives using the equations (15) for each congeneric group of bile acid [17]. It can be shown that log*k* is indeed associated with a number of hydration layers non-stabilized water molecules from β side of steroid skeleton: *NSWM n*

$$\frac{d\ln k}{d\left(\Phi m\_{\text{NaCl}}\right)} = n\_{\text{NSWM}} M\_{H\_2O} \tag{16}$$

where Φ*mNaCl* is the product of the osmotic coefficient and the molality of NaCl, and *H O*<sup>2</sup> *M* is the molecular weight of water [11]. Therefore with the increasing of the number of the α

axial OH groups which is replacement with equatorial OHs or oxo groups resulting in a decrease of NSWM number from the hydratation shell of bile acids, which are then reflected in the increase of log*k* values i.e. increasing hydrophobicity of bile acids. However, the cholesterol solubilization depends on the size of hydrophobic domain of micelles, which depends on the hydrophobic surface of the β side of steroid nucleus, that's all mean that the log*k* adequately describes of cholesterol (or any other hydrophobic guest molecules) solubilization. However it should be noted that the use of log*k* as molecular descriptors, log*k* for each molecule, as the molecules from teaching set and as the molecules from the control set must be obtained in an identical column. Contrary to the different values of *φ* (9) increases the error of prediction.

Chromatographic Retention Parameters as Molecular Descriptors for Lipophilicity in QSA(P)R Studies of Bile Acid 355

(19)

<sup>0</sup> *pCMC* = + 1.05 1.32 ϕ

(8) are away from the mobile phase without an organic modifier.

**Figure 11.** Dimeric micelles of cholic acids anion.

**Table 1.** Studied bile acids

R = 0.9380 Equations (18) and (19) have a good predictiveness in their congeneric groups, also with *φ*<sup>0</sup> is well described hydrophobicity of the bile acids steroid skeleton β side. The mutual association of bile acid salts, especially around the first critical micellar concentration, which is through to their hydrophobic β side of steroid skeleton (Fig. 11) indicated that the chromatographic parameter *φ*0 adequately be used to predict its critical micellar concentration. Advantages of chromatographic parameters *φ*0 (6) with respect to the parameters *RM*0 (5) and log*kw* (8) is reflected in the absence of appropriate extrapolation of retention coefficients. Extrapolation error can be large if the linear area of equations (5) and

Sarbu et al. in RPTLC experiments examined which chromatographic parameter the best describes the hydrophobicity of bile acids. In the studied bile acids (Table 1) between *RM*<sup>0</sup> parameter and the slope *S* (Equation 5) there is a good correlation, suggesting the presence

**Bile acids Abbreviation Position and orientation of OHs** 

of congeneric groups among chemical compounds in the tested assembly [3].

Lithocholic acid **LC** 3α Deoxycholic acid **DC** 3α, 12α Chenodeoxycholic acid **CDC** 3α, 7α Ursodeoxycholic acid **UDC** 3α, 7β Hyodeoxycholic acid **HDC** 3α, 6α Hyocholic acid **HC** 3α, 6α, 7α Cholic acid **C** 3α, 7α, 12α Glycolithocholic acid **GLC** 3α Taurolithocholic acid **TLC** 3α Glycochenodeoxycholic acid **GCDC** 3α, 7α Taurochenodeoxycholic acid **TCDC** 3α, 7α Glycodeoxycholic acid **GDC** 3α, 12α Taurodeoxycholic acid **TDC** 3α, 12α Glycocholic acid **GC** 3α, 7α, 12α Taurocholic acid **TC** 3α, 7α, 12α

**Figure 10.** Micellar solubilization of cholesterol: cholesterol is in the contact with the hydrophobic surfaces of β side of bile acids steroid skeleton.

Natalini et al. as an experimental molecular descriptor used chromatographic parameter *φ*<sup>0</sup> (6) for modeling the negative logarithm of the critical micellar concentration (*pCMC* = log*CMC*) [9,10]. The study was included 20 non-conjugated and conjugated bile acids. For the full set of bile acids were obtained following linear regression equation:

$$p\text{CMC} = 3.85\varphi\_0 - 0.82\tag{17}$$

R = 0.8246

Regression coefficient is improved if the equations of linear regression obtained separately for conjugated (18) and for non-conjugated bile acids (19):

$$p\text{CMC} = 4.78\varphi\_0 - 1.57\tag{18}$$

R = 0.9643

$$p\text{CMC} = 1.05\varphi\_0 + 1.32\tag{19}$$

$$\mathbb{R} = 0.9380$$

Equations (18) and (19) have a good predictiveness in their congeneric groups, also with *φ*<sup>0</sup> is well described hydrophobicity of the bile acids steroid skeleton β side. The mutual association of bile acid salts, especially around the first critical micellar concentration, which is through to their hydrophobic β side of steroid skeleton (Fig. 11) indicated that the chromatographic parameter *φ*0 adequately be used to predict its critical micellar concentration. Advantages of chromatographic parameters *φ*0 (6) with respect to the parameters *RM*0 (5) and log*kw* (8) is reflected in the absence of appropriate extrapolation of retention coefficients. Extrapolation error can be large if the linear area of equations (5) and (8) are away from the mobile phase without an organic modifier.

**Figure 11.** Dimeric micelles of cholic acids anion.

354 Chromatography – The Most Versatile Method of Chemical Analysis

increases the error of prediction.

surfaces of β side of bile acids steroid skeleton.

axial OH groups which is replacement with equatorial OHs or oxo groups resulting in a decrease of NSWM number from the hydratation shell of bile acids, which are then reflected in the increase of log*k* values i.e. increasing hydrophobicity of bile acids. However, the cholesterol solubilization depends on the size of hydrophobic domain of micelles, which depends on the hydrophobic surface of the β side of steroid nucleus, that's all mean that the log*k* adequately describes of cholesterol (or any other hydrophobic guest molecules) solubilization. However it should be noted that the use of log*k* as molecular descriptors, log*k* for each molecule, as the molecules from teaching set and as the molecules from the control set must be obtained in an identical column. Contrary to the different values of *φ* (9)

**Figure 10.** Micellar solubilization of cholesterol: cholesterol is in the contact with the hydrophobic

the full set of bile acids were obtained following linear regression equation:

for conjugated (18) and for non-conjugated bile acids (19):

Natalini et al. as an experimental molecular descriptor used chromatographic parameter *φ*<sup>0</sup> (6) for modeling the negative logarithm of the critical micellar concentration (*pCMC* = log*CMC*) [9,10]. The study was included 20 non-conjugated and conjugated bile acids. For

> <sup>0</sup> *pCMC* = − 3.85 0.82 ϕ

R = 0.8246 Regression coefficient is improved if the equations of linear regression obtained separately

> <sup>0</sup> *pCMC* = − 4.78 1.57 ϕ

> > R = 0.9643

(17)

(18)

Sarbu et al. in RPTLC experiments examined which chromatographic parameter the best describes the hydrophobicity of bile acids. In the studied bile acids (Table 1) between *RM*<sup>0</sup> parameter and the slope *S* (Equation 5) there is a good correlation, suggesting the presence of congeneric groups among chemical compounds in the tested assembly [3].


**Table 1.** Studied bile acids

Application of PCA on the matrix of *RM* values (**D**) of the studied bile acids are obtained space of principal components with smaller dimensions then matrix **D**. Screen plot showed that the significant first and second principal components (PC1 and PC2) that explained 99.75% of variance in the starting matrix of retention parameters. Bartlett's statistic shows that PC1, PC2 and PC3 are significant which explained of 99.92% of the total variance. In the set of studied bile acids (Table 1) there is a good correlation between *RM*0 chromatographic parameters and scores of PC1:

$$R\_{M0} = 5.379 - 2.624 \,\text{PC1} \tag{20}$$

Chromatographic Retention Parameters as Molecular Descriptors for Lipophilicity in QSA(P)R Studies of Bile Acid 357

R = 0.8751

log 3.995 2.195PC1 *HA P* = − (23)

R = 0.8675

log 3.824 3.807 PC1 *AP* = − (24)

R = 0.9379

log 4.407 2.122PC1 2.168PC2 *HA P* =− − (25)

R = 0.8715

log 3.387 3.885PC1 2.290PC2 *AP* =− + (26)

R = 0.9395

Linear regression equations (23 and 24) in which the chromatographic parameter *RM*<sup>0</sup> replaced with a score of PC1 has correlation coefficients with larger values compared to the equations (21 and 23). Correlation coefficient is slightly increased in the multiple linear regression equation for log*P* (molecular and ionized form) when the equations involved scores of PC1 and PC2. Increasing the coefficient of correlation in the above equations can be explained with Wolds assumption according to which measurement errors are contained in the principal components with small eigenvalues, so the scores of PC1 is purified from the errors. In Fig. 12 bile acids are shown from the Table 2 in the plane of the scores of principal components. It can be seen to form three linear congeneric groups: nonconjugated bile acids (**BA**), glyco-conjugate (**G-BA**) and tauro-conjugated (**T-BA**). Grouping of bile acids on the basis of the scores of PC as the appropriate regression equation for log*P* (from 23 to 26), indicating that the PC1 scores is adequate replacement for *RM*0 chromatographic parameters to describe the lipophilicity (hydrophobicity) of bile acids, namely the scores of PC1 can be used as molecular descriptors for hydrophobicity of

If increase the set of bile acids from Table 1 by including oxo and acetoxy derivatives, *RM*<sup>0</sup> chromatographic parameter also included in the multiple linear regressions for the log*P*HA and the log*P*A with molecular descriptors such as polarizability and molar specific sum of absolute values of the charges on each atom of the molecule (electronic parameter), molecular volume, the third order of the connectivity index and Wiener index (shape parameter). Based on the loadings of PC can be concluded that *RM*0 carries different information about the structure of the studied bile acids than the above *in silico* molecular

Effect of temperature on the chromatographic process in reverse phase chromatography can also be applied to obtain chromatographic parameters that have properties of molecular

the steroid skeleton β (bile acids).

descriptors [6].


$$\mathbb{R} = \text{ - } 0.9203$$

**Table 2.** Chromatographic parameters

Sarbu for assessing whether *R*M0 or score of PC adequate to describe lipophilicity of bile acids using the experimental data of particion coefficients between 1-octanol and water of bile acids in molecular (HA) and ionized (A) forms. Between the logarithm partition coefficients and chromatographic parameters on the basis of Table 1 are obtained by the following equation of linear regression:

$$\log P\_{HA} = 0.366 + 0.620 R\_{M0} \tag{21}$$

$$\mathbb{R} = 0.8559$$

$$
\log P\_A = -2.255 + 1.017 R\_{M0} \tag{22}
$$

$$\begin{aligned} \text{R = 0.8751} \\\\ \log P\_{\text{fIA}} &= 3.995 - 2.195 \text{PC1} \\\\ \text{R = 0.8675} \\\\ \log P\_A &= 3.824 - 3.807 \text{PC1} \\\\ \text{R = 0.9379} \\\\ \log P\_{\text{fIA}} &= 4.407 - 2.122 \text{PC1} - 2.168 \text{PC2} \\\\ \text{R = 0.8715} \\\\ \log P\_A &= 3.387 - 3.885 \text{PC1} + 2.290 \text{PC2} \\\\ \text{(26)} \end{aligned} \tag{26}$$

$$\mathbf{R} = 0.9395$$

parameters and scores of PC1:

**Compound** *RM***<sup>0</sup>**

**Table 2.** Chromatographic parameters

following equation of linear regression:

Application of PCA on the matrix of *RM* values (**D**) of the studied bile acids are obtained space of principal components with smaller dimensions then matrix **D**. Screen plot showed that the significant first and second principal components (PC1 and PC2) that explained 99.75% of variance in the starting matrix of retention parameters. Bartlett's statistic shows that PC1, PC2 and PC3 are significant which explained of 99.92% of the total variance. In the set of studied bile acids (Table 1) there is a good correlation between *RM*0 chromatographic

R = - 0.9203

**2 DC** 4.78 0.346 0.179 0.111 3.50 2.65 **3 CDC** 5.01 0.340 0.177 0.082 3.28 2.25 **4 UDC** 3.65 0.545 0.226 0.114 3.00 2.20 **5 HDC** 3.88 0.488 0.208 0.110 3.08 2.28 **6 HC** 3.66 0.559 0.229 0.107 2.80 1.84 **7 C** 3.84 0.533 0.217 0.105 2.02 1.10

**10 GCDC** 2.87 0.819 0.237 0.088 2.12 0.45

**12 GDC** 2.90 0.850 0.247 0.087 2.25 0.80

**14 GC** 2.30 1.102 0.186 0.090 1.65 -0.40

Sarbu for assessing whether *R*M0 or score of PC adequate to describe lipophilicity of bile acids using the experimental data of particion coefficients between 1-octanol and water of bile acids in molecular (HA) and ionized (A) forms. Between the logarithm partition coefficients and chromatographic parameters on the basis of Table 1 are obtained by the

R = 0.8559

**1 LC** 5.33 0.195 0.122 0.080

**8 GLC** 3.39 0.674 0.246 0.119 **9 TLC** 2.12 1.000 0.249 0.077

**11 TCDC** 2.27 1.249 0.194 0.082

**13 TDC** 2.30 1.165 0.191 0.090

**15 TC** 2.29 1.524 0.137 0.125

<sup>0</sup> *RM* = − 5.379 2.624PC1 (20)

**PC1 PC2 PC3 Rodas data:** 

<sup>0</sup> log 0.366 0.620 *P R HA* = + *<sup>M</sup>* (21)

<sup>0</sup> log 2.255 1.017 *P R <sup>A</sup>* =− + *<sup>M</sup>* (22)

*scores* **logPHA logPHA**

Linear regression equations (23 and 24) in which the chromatographic parameter *RM*<sup>0</sup> replaced with a score of PC1 has correlation coefficients with larger values compared to the equations (21 and 23). Correlation coefficient is slightly increased in the multiple linear regression equation for log*P* (molecular and ionized form) when the equations involved scores of PC1 and PC2. Increasing the coefficient of correlation in the above equations can be explained with Wolds assumption according to which measurement errors are contained in the principal components with small eigenvalues, so the scores of PC1 is purified from the errors. In Fig. 12 bile acids are shown from the Table 2 in the plane of the scores of principal components. It can be seen to form three linear congeneric groups: nonconjugated bile acids (**BA**), glyco-conjugate (**G-BA**) and tauro-conjugated (**T-BA**). Grouping of bile acids on the basis of the scores of PC as the appropriate regression equation for log*P* (from 23 to 26), indicating that the PC1 scores is adequate replacement for *RM*0 chromatographic parameters to describe the lipophilicity (hydrophobicity) of bile acids, namely the scores of PC1 can be used as molecular descriptors for hydrophobicity of the steroid skeleton β (bile acids).

If increase the set of bile acids from Table 1 by including oxo and acetoxy derivatives, *RM*<sup>0</sup> chromatographic parameter also included in the multiple linear regressions for the log*P*HA and the log*P*A with molecular descriptors such as polarizability and molar specific sum of absolute values of the charges on each atom of the molecule (electronic parameter), molecular volume, the third order of the connectivity index and Wiener index (shape parameter). Based on the loadings of PC can be concluded that *RM*0 carries different information about the structure of the studied bile acids than the above *in silico* molecular descriptors [6].

Effect of temperature on the chromatographic process in reverse phase chromatography can also be applied to obtain chromatographic parameters that have properties of molecular

**Figure 12.** Sore of PC: bile acids from Table 1.

descriptors [15]. Namely, the reaction (R2) is exothermic (*Had* <0), then based on the van' t Hoff equation, the equilibrium constant of reaction (R2) decreases

$$\frac{d\ln K\_{ad}}{dT} = \frac{dH\_{ad}}{RT^2} \tag{27}$$

Chromatographic Retention Parameters as Molecular Descriptors for Lipophilicity in QSA(P)R Studies of Bile Acid 359

**and oxo groups** 

**Bile acids Abbreviation Position and orientation of OH** 

12-Monoketocholic acid **12-MKC** 3α-OH, 7α-OH, 12α-Oxo 7-Monoketocholic acid **7-MKC** 3α-OH, 7α-Oxo, 12α-OH 7,12-Diketocholic acid **7,12-DKC** 3α-OH, 7α-Oxo, 12α-Oxo 3,7-Diketocholic acid **3,7-DKC** 3α-Oxo, 7α-Oxo, 12α-OH 3,12-Diketocholic acid **3,12-DKC** 3α-Oxo, 7α-OH, 12α-Oxo Dehydrocholic acid **TKC** 3α-Oxo, 7α-Oxo, 12α-Oxo 12-Monoketodeoxycholic acid **12-MKD** 3α-OH, 12α-Oxo Diketodeoxycholic acid **DKD** 3α-Oxo, 12α-Oxo 7-Monoketochenodeoxycholic acid **7-MKCD** 3α-OH, 7α-Oxo Diketochenodeoxycholic acid **DKCD** 3α-Oxo, 7α-Oxo 6-Monoketohyodeoxycholic acid **6-MKHD** 3α-OH, 6α-Oxo **Table 3.** Tested bile acids in the experiment the influence of temperature on the values of retention

Fig. 13 shows that the tested bile acids in the plane of parameters of equation (23) formed by three congeneric groups. The first group (**I**) formed by bile acids with oxo groups in the steroid nucleus and the bile acids that in addition to C3 have one more equatorial OH groups. The α equatorial OH groups have the same position relative to the steroid skeleton mean plane such have the α oxo groups. However, in this group also includes the cholic acid and the glycocholic acid which is structurally not fit into the above mentioned group. The second group (**II**) formed deoxycholic acid and chenodeoxycholic acid with its conjugates. The third group (**III**) forms lithocholic acid and its conjugates. Question may arise as whether can be improved with grouping of bile acid gained by in the plane of *a* and *b*, especially in terms of group **I** which provides the vendor cholic acid? The answer may be the application of methods of principal components of the matrix of the data of retention factor dependence on temperature. The first principal component (PC1) explains 99.99715%

factor *k*

Lithocholic acid **LC** 3α-OH Deoxycholic acid **DC** 3α-OH, 12α-OH Chenodeoxycholic acid **CDC** 3α-OH, 7α-OH Cholic acid **C** 3α-OH, 7α-OH, 12α-OH Ursodeoxycholic acid **UDC** 3α-OH, 7β-OH Hyodeoxycholic acid **HDC** 3α-OH, 6α-OH Hyocholic acid **HC** 3α-OH, 6α-OH, 7α-OH Glycochenodeoxycholic acid **GCDC** 3α-OH, 7α-OH Taurodeoxycholic acid **TDC** 3α-OH, 12α-OH Glycocholic acid **GC** 3α-OH, 7α-OH, 12α-OH Glycodeoxycholic acid **GDC** 3α-OH, 12α-OH Taurolithocholic acid **TLC** 3α-OH Taurochenodeoxycholic acid **TCDC** 3α-OH, 7α-OH Glycolithocholic acid **GLC** 3α-OH

This means that the retention factor *k* (9) also decreases. Thus, the increase in temperature has the same effect on the value of *k* as there are increasing the volume fraction of organic modifier in aqueous mobile phase (reversed phase chromatography). In the experiment, the influence of temperature with an the retention factor at constant mobile phase included 25 different bile acids (conjugated and non-conjugated) (Table 3) [18].

For each tested bile acids between retention factor *k* and temperature *t* there is a linear relation:

$$k = a + bt\tag{28}$$

The linear model (28) explains from 96% to 99% of the variance at tested bile acids (Table 4). In the set of the studied bile acids (Table 3) between the parameters of equation (28) (*a* and *b*) there is a good correlation, indicating the formation of congeneric groups in the plane of *a* and *b*:

$$a = 0.7683 + 58.8522b \tag{29}$$

R=0.9996


**23**

**BA**

Hoff equation, the equilibrium constant of reaction (R2) decreases

different bile acids (conjugated and non-conjugated) (Table 3) [18].

**4**

**6 7**

**<sup>8</sup> <sup>9</sup> 10**

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 *score* **PC1**

descriptors [15]. Namely, the reaction (R2) is exothermic (*Had* <0), then based on the van' t

ln *ad ad d K dH*

This means that the retention factor *k* (9) also decreases. Thus, the increase in temperature has the same effect on the value of *k* as there are increasing the volume fraction of organic modifier in aqueous mobile phase (reversed phase chromatography). In the experiment, the influence of temperature with an the retention factor at constant mobile phase included 25

For each tested bile acids between retention factor *k* and temperature *t* there is a linear relation:

The linear model (28) explains from 96% to 99% of the variance at tested bile acids (Table 4). In the set of the studied bile acids (Table 3) between the parameters of equation (28) (*a* and *b*) there is a good correlation, indicating the formation of congeneric groups in the plane of *a* and *b*:

0.7683 58.8522 *a b* = + (29)

R=0.9996

2

**12**

**G-BA**

**11**

*dT RT* <sup>=</sup> (27)

*k a bt* = + (28)

**T-BA**

**15**

**13 14**

**5**

**1**

**Figure 12.** Sore of PC: bile acids from Table 1.

0.10

0.12

0.14

0.16

0.18

*score* **PC2**

0.20

0.22

0.24

0.26

**Table 3.** Tested bile acids in the experiment the influence of temperature on the values of retention factor *k*

Fig. 13 shows that the tested bile acids in the plane of parameters of equation (23) formed by three congeneric groups. The first group (**I**) formed by bile acids with oxo groups in the steroid nucleus and the bile acids that in addition to C3 have one more equatorial OH groups. The α equatorial OH groups have the same position relative to the steroid skeleton mean plane such have the α oxo groups. However, in this group also includes the cholic acid and the glycocholic acid which is structurally not fit into the above mentioned group. The second group (**II**) formed deoxycholic acid and chenodeoxycholic acid with its conjugates. The third group (**III**) forms lithocholic acid and its conjugates. Question may arise as whether can be improved with grouping of bile acid gained by in the plane of *a* and *b*, especially in terms of group **I** which provides the vendor cholic acid? The answer may be the application of methods of principal components of the matrix of the data of retention factor dependence on temperature. The first principal component (PC1) explains 99.99715%

of variance in the starting data matrix, while the remaining variance explained by PC2. In Table 4 presents the scores of principal components of bile acids studied.

Chromatographic Retention Parameters as Molecular Descriptors for Lipophilicity in QSA(P)R Studies of Bile Acid 361

**12**

**2**


**Figure 13.** Grouping the bile (Table 4) acid on the basis of linear regression parameters of the retention

In the plane of principal component scores are obtained by analogous groups such as Fig. 14. However in the group **I** the oxo derivatives and the derivatives with α equatorial OH groups forming linear congeneric group, while based on Cooks distance cholic acid and glycocholic acid may be considered as outliners. With loadings of principal component can be determined by mutual correlation of different *in silico* descriptors (topological and electronic) and obtained experimental descriptors *a*, *b*, and PC1 on the set of 25 bile acids (Table 4). It may be concluded that chromatographic parameters *a* and PC1 are more or less orthogonal to most topological descriptors (Winers index, Balabans index, shape attributes, konectivities, etc.), while PC1 and *a* are mutually parallel so that explain the same structural characteristics of bile acids. Namely, as flat molecules nitrazepan guest molecule is incorporated in the hydrophobic domain of micelles. Therefore, if the β side of bile acids steroid skeleton more hydrophobic then nitrazepans partition coefficient has a higher value. Using the method of partial least square (PLS) regression equation was obtained for the nitrazepans partition coefficients in which experimentally determined variables *a* and PC1 are the most significant with respect to *in silico* descriptors. Which means that PC1 and *a* can be used as molecular descriptors of bile acids lipophilicity, and that the temperature dependence of retention factors may obtain information regarding the structure of bile acids

**3**

**9**

**11**

**II**

**8**

**13**

**4**

**10**

**21**

**5 67**

**I**

**1615 1820917**


(lipophilicity).

factor temperatures dependence.

0

5

10

15

20

*a*

25

30

35

40

45

**22 23 24 25** **1**

**III**

**14**


**Table 4.** The parameters of the linear model (28) and scores of principal components

of variance in the starting data matrix, while the remaining variance explained by PC2. In

**Compound** *a b* **R2 PC1 PC2** 

**1 LC** 43.0501 0.7200 0.9879 5.37637 0.023150 **2 DC** 21.8893 0.3518 0.9906 1.79015 -0.051081 **3 CDC** 18.4260 0.3021 0.9807 1.05575 0.020646 **4 C** 8.4873 0.1319 0.9828 -0.66245 0.016292 **5 UDC** 4.4884 0.0680 0.9843 -1.40668 0.031446 **6 HDC** 5.6203 0.0804 0.9538 -1.11512 -0.034642 **7 HC** 5.5477 0.0864 0.9836 -1.23205 0.041543 **8 GCDC** 16.6862 0.2651 0.9946 0.85970 -0.024730 **9 TDC** 19.5503 0.3165 0.9802 1.30724 -0.001736 **10 GC** 7.8569 0.1213 0.9841 -0.77443 0.014749 **11 GDC** 20.6286 0.3336 0.9786 1.51098 -0.012582 **12 TLC** 39.1628 0.6544 0.9728 4.65836 0.029036 **13 TCDC** 16.3808 0.2671 0.9796 0.70668 0.007651 **14 GLC** 41.1016 0.6926 0.9750 4.95053 0.026326 **15 12-MKC** 3.1340 0.0402 0.9704 -1.58139 -0.004996 **16 7-MKC** 2.8202 0.0353 0.9676 -1.64238 -0.002356 **17 7,12-DKC** 0.7141 0.0078 0.9769 -2.12906 0.056420 **18 3,7-DKC** 0.6100 0.0054 0.9974 -2.11715 0.056756 **19 3,12-DKC** 0.6237 0.0060 0.9752 -2.12981 0.056122 **20 TKC** 0.5042 0.0056 0.9738 -2.17086 0.066570 **21 12-MKD** 7.7659 0.1040 0.9652 -0.57871 -0.116428 **22 DKD** 4.1490 0.0511 0.9681 -1.32315 -0.048688 **23 7-MKCD** 6.1746 0.0817 0.9665 -0.91824 -0.078586 **24 DKCD** 3.4944 0.0423 0.9704 -1.46618 -0.031508 **25 6-MKHD** 6.3614 0.0913 0.9667 -0.96809 -0.039373

*score* 

Table 4 presents the scores of principal components of bile acids studied.

**Table 4.** The parameters of the linear model (28) and scores of principal components

**Figure 13.** Grouping the bile (Table 4) acid on the basis of linear regression parameters of the retention factor temperatures dependence.

In the plane of principal component scores are obtained by analogous groups such as Fig. 14. However in the group **I** the oxo derivatives and the derivatives with α equatorial OH groups forming linear congeneric group, while based on Cooks distance cholic acid and glycocholic acid may be considered as outliners. With loadings of principal component can be determined by mutual correlation of different *in silico* descriptors (topological and electronic) and obtained experimental descriptors *a*, *b*, and PC1 on the set of 25 bile acids (Table 4). It may be concluded that chromatographic parameters *a* and PC1 are more or less orthogonal to most topological descriptors (Winers index, Balabans index, shape attributes, konectivities, etc.), while PC1 and *a* are mutually parallel so that explain the same structural characteristics of bile acids. Namely, as flat molecules nitrazepan guest molecule is incorporated in the hydrophobic domain of micelles. Therefore, if the β side of bile acids steroid skeleton more hydrophobic then nitrazepans partition coefficient has a higher value. Using the method of partial least square (PLS) regression equation was obtained for the nitrazepans partition coefficients in which experimentally determined variables *a* and PC1 are the most significant with respect to *in silico* descriptors. Which means that PC1 and *a* can be used as molecular descriptors of bile acids lipophilicity, and that the temperature dependence of retention factors may obtain information regarding the structure of bile acids (lipophilicity).

This study was supported by the Secretariat for Science and Technological Development of

AP Vojvodina, Republic of Serbia (Grant No. 114-451-2113/2012).

QSA(P)R = Quantitative Structure Activity (Property) Relationship

RPTLC = Reversed Phase Thin Layer Chromarography

PCA = Principal Component Analysis

SWM = Stabilised Water Molecules NSWM = Non Stabilised Water Molecules SSMP = steroid skeleton mean plane

Chromatogr. A 917: 361-366.

33(20): 3110-3118.

regression methods. Talanta 75: 651-657.

PC = Principal Component

RPHPLC = Reversed Phase High Pressure (Resolutions) Liquid Chromatography

[1] Camile W (2003) The Practice of Medicinal Chemistry. Oxford: Academic Press. [2] King F.D (2002) Medicinal Chemistry Principles and Practice. Cambridge: R.S.C.

critical micellar concentrations of bile acids. Steroids 76(1-2): 85-93.

bile acids and their derivatives. Rev. Roum. Chim. 56(3): 217-229.

process of bile acids. J. Pharm. Biomed. Anal. 50: 613-621.

cholic, deoxycholic and chenodeoxycholic acids. Steroids 75(6): 424-431.

[3] Sârbu C, Kuhajda K, Kevrešan S (2001) Evaulation of the lipofilicity of bile acids and their derivatives by thin-layer chromatography and principal component analysis. J.

[4] Poša M (2011) QSPR study of the effect of steroidal hydroxy and oxo substituents on the

[5] Poša M, Kuhajda K (2010) Hydrophobiciti and haemolytic potential of oxo derivatives of

[6] Sârbu C, Onişor C, Poša M, Kuhajda K, Kevrešan S (2008) Modeling and prediction (correction) of partition coefficients of bile acids and their derivatives by multivariate

[7] Onişor C, Poša M, Sârbu C (2011) Modeling of chromatographic lipophilicity indices of

[8] Onişor C, Poša M, Kevrešan S, Kuhajda K, Sârbu C (2010) Modeling chromatographic lipophilicity of bile acids and their derivatives estimated by HP-RPTLC. J. Sep. Sci.

[9] Natalini B, Sardella R, Camaioni E, Gioiello A, Pellicciari R (2007) Correlation between CMC and chromatographic index: simple and effective evaluation of the hydrophobic/hydrophilic balance of bile acids. Anal. Bioanal. Chem. 388: 1681-1688. [10] Natalini B, Sardella R, Camaioni E, Macchiarulo A, Gioiello A, Carbone G, Pellicciari R (2009) Derived chromatographic indices as effective tools to study the self-aggregation

[11] Poša M, Pilipović A, Lalić M (2010) The influence of NaCl on hydrophobicity of selected, pharmacologically active bile acids expressed with chromatographic retention index and critical micellar concentration. Colloids Surf. B: Biointerfaces 81: 336-343.

**Acknowledgement** 

**Abbreviations** 

**7. References** 

**Figure 14.** Grouping of bile acids (Table 4) based on the scores of principal component.
