A Standard Structure for Bile Acids and Derivatives

Analysis of the Electron Density of a Water Molecule Encapsulated by Two Cholic Acid Residues

Cholic acid is a trihydroxy bile acid with a nice peculiarity: the average distance between the oxygen atoms (O7 and O12) of the hydroxy groups located at C7 and C12 carbon atoms is 4.5 Å, a value which perfectly matches with the O/O tetrahedral edge distance in Ih ice. In the solid phase, they are involved in the formation of hydrogen bonds with other cholic acid units and solvents. This fact was satisfactorily used for designing a cholic dimer which encapsulates one single water molecule between two cholic residues, its oxygen atom (Ow) being exactly located at the centroid of a distorted tetrahedron formed by the four steroid hydroxy groups. The water molecule participates in four hydrogen bonds, with the water simultaneously being an acceptor from the 2 O12 (hydrogen lengths are 2.177 Å and 2.114 Å) and a donor towards the 2 O7 (hydrogen bond lengths are 1.866 Å and 1.920 Å). These facts suggest that this system can be a nice model for the theoretical study of the formation of ice-like structures. These are frequently proposed to describe the water structure found in a plethora of systems (water interfaces, metal complexes, solubilized hydrophobic species, proteins, and confined carbon nanotubes). The above tetrahedral structure is proposed as a reference model for those systems, and the results obtained from the application of the atoms in molecules theory are presented here. Furthermore, the structure of the whole system allows a division into two interesting subsystems in which water is the acceptor of one hydrogen bond and the donor of another. The analysis of the calculated electron density is performed through its gradient vector and the Laplacian. The calculation of the complexation energy used correction of the basis set superposition error (BSSE) with the counterpoise method. As expected, four critical points located in the H…O bond paths were identified. All calculated parameters obey the proposed criteria for hydrogen bonds. The total energy for the interaction in the tetrahedral structure is 54.29 kJ/mol, while the summation obtained of the two independent subsystems and the one between the alkyl rings without water is only 2.5 kJ/mol higher. This concordance, together with the calculated values for the electron density, the Laplacian of the electron density, and the lengths of the oxygen atom and the hydrogen atom (involved in the formation of each hydrogen bond) to the hydrogen bond critical point, suggests that each pair of hydrogen bonds can be considered independent of each other.

Highly Hydrophilic and Lipophilic Derivatives of Bile Salts

Lipophilicity of 15 derivatives of sodium cholate, defined by the octan-1-ol/water partition coefficient (log P), has been theoretically determined by the Virtual log P method. These derivatives bear highly hydrophobic or highly hydrophilic substituents at the C3 position of the steroid nucleus, being linked to it through an amide bond. The difference between the maximum value of log P and the minimum one is enlarged to 3.5. The partition coefficient and the critical micelle concentration (cmc) are tightly related by a double-logarithm relationship (VirtuallogP=-(1.00±0.09)log(cmcmM)+(2.79±0.09)), meaning that the Gibbs free energies for the transfer of a bile anion from water to either a micelle or to octan-1-ol differ by a constant. The equation also means that cmc can be used as a measurement of lipophilicity. The demicellization of the aggregates formed by three derivatives of sodium cholate bearing bulky hydrophobic substituents has been studied by surface tension and isothermal titration calorimetry. Aggregation numbers, enthalpies, free energies, entropies, and heat capacities, ΔCP,demic, were obtained. ΔCP,demic, being positive, means that the interior of the aggregates is hydrophobic.