  In this paper we propose a nonlinear elasticity model of macromolecular
conformational change (deformation) induced by electrostatic forces generated
by an implicit solvation model. The Poisson-Boltzmann equation for the
electrostatic potential is analyzed in a domain varying with the elastic
deformation of molecules, and a new continuous model of the electrostatic
forces is developed to ensure solvability of the nonlinear elasticity
equations. We derive the estimates of electrostatic forces corresponding to
four types of perturbations to an electrostatic potential field, and establish
the existance of an equilibrium configuration using a fixed-point argument,
under the assumption that the change in the ionic strength and charges due to
the additional molecules causing the deformation are sufficiently small. The
results are valid for elastic models with arbitrarily complex dielectric
interfaces and cavities, and can be generalized to large elastic deformation
caused by high ionic strength, large charges, and strong external fields by
using continuation methods.
