Fast Analytical Continuum Treatments of Solvation

Successful applications of molecular dynamics ( MD ) to study the structure and function of a biomolecule depend on the quality of the underlying force fi eld and the sampling effi ciency of the simulation protocol. In particular, an accurate representation of the aqueous solvent environment is important to reproduce the structural, functional, and dynamic behavior of soluble biomolecule s. The most realistic and physically rigorous way to treat solvation effects is to include explicitly the solvent molecule s in the simulation system, at the price of high computational cost. In fact, the solvent molecules greatly increase the number of degrees of freedom and interaction centers. Even with today ’ s computational infrastructure, simulations of single domain proteins (about 100 residues) cannot sample more than 0.1 – 1 μ s. Such a short time scale prohibits the study of long time processes like protein folding , large scale structural transition s, multimeric assembly processes like complex formation and protein aggregation , as well as the derivation of accurate thermodynamic quantities. This computational drawback has motivated the development of fast implicit solvent models [1 – 3] , where the mean infl uence of solvent molecules around the solute is described by a potential of mean force that depends only on the atom coordinates of the solute [2, 4] . An implicit solvent model not only considerably reduces the system size, but also avoids the need to average over the extremely large number of solvent confi gurations, and reduces the viscosity of the solvent environment by eliminating the friction from the solvent molecules, thus accelerating molecular motions [5] . Furthermore, such a model directly yields the so called effective energy , which is the sum of the solute potential energy in vacuo and the solvation free energy . In contrast, explicit water simulations have to be post processed, for example by fi nite difference Poisson – Boltzmann calculations, to obtain the effective energy. The overall free energy cost of solvating a solute molecule ( ∆ G solv ) is decomposed into a non polar component and a polar component in most implicit solvent models [2] : ∆ G solv = ∆ G pol + ∆ G nonpol . The term ∆ G pol is the free energy change in 9