Pseudo-time coupled smooth interface models for biomolecular solvation calculations

Shan Zhao (April 26, 2011)

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Recently, we have introduced a differential geometry based model, the minimal molecular surface, to characterize the dielectric boundary between biomolecules and the surrounding aqueous environment. The mean curvature flow is used to minimize a surface free energy functional to drive the surface formation and evolution. More recently, several potential driven geometric flow models have been introduced in the literature for the analysis and computation of the equilibrium property of solvation, by appropriately coupling polar and nonpolar contributions in the free energy functional. The solvent-solute interface is usually treated as a sharp interface with discontinuous dielectric profile in a Lagrangian formulation, while in an Eulerian formulation a smeared interface model with continuous dielectric profile provides a convenient setting for solvation calculations. In the present study, we further extend the smeared interface model by considering a generalized nonlinear Poisson-Boltzmann (PB) equation in order to account for the salt effect. A new pseudo-time coupling between the surface geometric flows and electrostatic PB potential is introduced. Such a coupling allows for a fast numerical solution of governing nonlinear partial differential equations. Example solvation analysis of both small compounds and proteins are carried out to examine the proposed models and numerical approaches. Numerical results are compared to the experimental measurements and to those obtained by using other theoretical methods in the literature.