Effects of solvent on the conformation and the collective motions of a protein. 3. Free energy analysis by the extended RISM theory

Abstract

The equilibrium hydration properties of melittin, a small protein, are studied on the basis of the extended RISM (XRISM) theory, an integral equation method in liquid state. The radial distribution functions of water molecules around the 436 protein atoms are determined and are compared with those obtained by the molecular dynamics simulation. The free energy profiles along the first two normal modes of the protein are also calculated. The results show a clear multiminima feature in the potential profile not observed in vacuum, supporting the conclusion we have previously deduced from the molecular dynamics study. I. Introduction It has been well established that the hydration of a protein plays an essential role in its chemical and biological functions. Studies based on computer simulations have revealed the ways that solvent affects the structure and dynamics of protein.' In the preceding papers,2J we have reported on a molecular dynamics study of the solvent effect on concerted motions in a protein (melittin). When the trajectory of the protein is projected onto its low-frequency modes, the motion of the protein in solvent has shown a marked difference from that in vacuum in two respects: (1) a Brownian-like zigzag motion in solvent compared to smooth, more-or-less sinusoidal motion in vacuum and (2) a marked transition in the trajectory of the solvated protein in contrast to the absence of such a transition in vacuum. The former of the two solvent effects can be explained by the random collision exerted on the solute by solvent molecules. The latter, on the other hand, strongly suggests that the potential surfaceof the protein is altered due to solutesolvent interactions. It is therefore of great interest to see how the potential surface is changed by the solvent. Several semiempirical or phenomenological approaches to treat solvent effects have been proposed, including methods based on the accessible surface area (ASA)4 and the Poisson-Boltzmann (PB) equation.5 The ASA approach, which relies on experimentally determined free energy values for constituent atom groups in protein, has succeeded in predicting the cold denaturation for some proteins. However, this method may not be so successful in those cases where electrostatic interactions play a dominant role. On the other hand, the PB approach seems quite promising for these cases. It should be pointed out that neither of these approaches can give information of the solvent structure around proteins. However, changes in the potential surface of the protein shown in the refs 2 and 3 are closely related to a change of the hydration structure. To treat the solvent structure as well as the solute structure, we have to determine the potential energy function for solvent molecules as well as the solute molecule. Unfortunately, it is still a formidable task for molecular simulations to determine the free energy surface or the solvent-mediated potential, mainly due to the overwhelmingly large configuration space accessible to solvent. For a free energy change associated with a local structural change of the protein, including amino acid substitution and ligand binding, methods such as umbrella samplings and thermodynamic perturbation' have attained reasonable success. However, there is the serious problem that the sampling of the conformations is insufficient for the accurate calculation of the statistical average.