A theoretical model for the critical micelle concentration of bile salts

Critical micelle concentration (CMC) is a fundamental parameter in the evaluation of the biological activity of natural and synthetic bile salts. The CMC is logarithmically related to the free energy of solute micellization in aqueous solution. Hydrophobic and hydrogen bonding interaction energies were identified as the primary contributors to this free energy and the logarithm of the CMC was modeled as a linear function of relevant chemical group contributions to the solvent accessible molecular surface area of the solute. The structures (three-dimensional atomic coordinates) of 23 mono-, di-, and tri-hydroxyl bile acids were generated and optimized by energy minimization. The accessible surface area for each structure was computed and partitioned according to calculated charge distribution and polar group orientation. Experimental CMC values were fitted to these computed quantities by least squares multiple linear regression. Two regression equations, based on slightly different surface area partition schemes, were derived and compared. Their significance in explaining the aggregation process and in predicting the CMC of new bile salts is discussed.