A Nonlinear Elasticity Model of Macromolecular Conformational Change Induced by Electrostatic Forces

TL;DR

This paper introduces a nonlinear elasticity model for macromolecular conformational changes driven by electrostatic forces, incorporating a new electrostatic force model and proving the existence of equilibrium configurations under certain conditions.

Contribution

It develops a continuous electrostatic force model integrated with nonlinear elasticity equations, ensuring solvability and applicability to complex molecular geometries.

Findings

Established existence of equilibrium configurations under small perturbations.

Derived estimates for electrostatic forces for various potential perturbations.

Model applicable to complex dielectric interfaces and large deformations.

Abstract

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.