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Electrostatic Free Energy and its Variations in Implicit
Solvent Models

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Bo Li

Department of Mathematics and Center for Theoretical Biological Physics

University of California, San Diego

# Abstract

In this talk, I will first recall a mean field approximation of
electrostatic free energy for an ionic solution, and discuss
two issues:
(1) Rigorous mathematical justification
of the existence of equilibrium concentrations and their
Boltzmann relations;
(2) The effect of inhomogeneous Dirichlet
boundary condition to the solution of the related Poisson-Boltzmann
equation for the electrostatic potential.
I will then consider a class of variational implicit solvent models
for the solvation of biomolecules, and present a formal
derivation of the first variation of the electrostatic free energy
with respect to the location change of the dielectric boundary.
This result is needed for level-set relaxation and force calculations
of biomolecular structures and dynamics.