Probabilistic Interpretation for the Nonlinear Poisson-Boltzmann Equation in Molecular Dynamics

Abstract

The Poisson-Boltzmann (PB) equation describes the electrostatic potential of a biomolecular system composed by a molecule in a solvent. The electrostatic potential is involved in biomolecular models which are used in molecular simulation. In consequence, finding an efficient method to simulate the numerical solution of PB equation is very useful. In this paper, we establish a probabilistic interpretation of the nonlinear PB equation with Backward Stochastic Differential Equations (BSDEs). This interpretation requires an adaptation of existing results on BSDEs.