Nonlinear lattice models for biopolymers: Dynamical coupling to a ionic cloud and application to actin filaments

Abstract

This paper is a first attempt to derive a qualitatively simple model coupling the dynamics of a charged biopolymer and its diffuse cloud of counterions. We consider here the case of a single actin filament. A zig-zag chain model introduced by Zolotaryuk et al [28] is used to represent the actin helix, and calibrated using experimental data on the stiffness constant of actin. Starting from the continuum drift-diffusion model describing counterion dynamics, we derive a discrete damped diffusion equation for the quantity of ionic charges in a one-dimensional grid along actin. The actin and ionic cloud models are coupled via electrostatic effects. Numerical simulations of the coupled system show that mechanical waves propagating along the polymer can generate charge density waves with intensities in the $pA$ range, in agreement with experimental measurements of ionic currents along actin.