Loss of Translational Entropy in Molecular Associations

Molecular associations in solution are opposed by the loss of entropy (ΔS) that results from the restriction of motion of each component in the complex. Theoretical estimates of ΔS are essential for rationalizing binding affinities, as well as for calculating entropic contribution to enzyme catalysis. Recently a statistical-mechanical framework has been proposed for estimating efficiently the translational entropy loss (ΔS^trsl), while taking explicitly into account the complex intermolecular interactions between the solute and the solvent. This framework relates the translational entropy of a solute in solution to its "free volume," defined as the volume accessible to the center of mass of the solute in the presence of the solvent and calculated by using an extension of the cell model (CM) for condensed phases. The translational entropy of pure water, estimated with the CM algorithm, shows good agreement with the experimental information. The free volume of various solutes in water, calculated within the CM by using molecular dynamics simulations with explicit solvent, displays a strong correlation with the solutes' polar and total surface areas. This correlation is used to propose a parameterization that can be used to calculate routinely the translational entropy of a solute in water. We also applied the CM formalism to calculate the free volume and translational entropy loss (ΔS^trsl) on binding of benzene to a cavity in a mutant T4-lysozyme. Our results agree with previously published estimates of the binding of benzene to this mutant T4-lysozyme. These and other considerations suggest that the cell model is a simple yet efficient theoretical framework to evaluate the translational entropy loss on molecular association in solution.