Nonlinear lattice models forbiopolymers: Dynamical coupling to a ionic cloud and application to actinfilaments

Cynthia Ferreira; Guillaume James; Michel Peyrard

doi:10.3934/dcdss.2011.4.1147

Article Contents

2011, Volume 4, Issue 5: 1147-1166. Doi: 10.3934/dcdss.2011.4.1147

This issue Previous Article Travelling waves of forced discrete nonlinear Schrödinger equations Next Article Complex spatiotemporal behavior in a chain of one-way nonlinearly coupled elements

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

1.
Institut de Mathématiques de Toulouse (UMR 5219), Département de Mathématiques, INSA-Toulouse, 135 avenue de Rangueil, 31077 Toulouse Cedex 4
2.
Laboratoire Jean Kuntzmann, Université de Grenoble and CNRS, BP 53, 38041 Grenoble Cedex 9
3.
Laboratoire de Physique, Ecole Normale Supérieure de Lyon, 46 allée d'Italie, 69364 Lyon Cedex 07

Received: August 31, 2009

Revised: December 31, 2009

Published: September 2011

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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.

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Mathematics Subject Classification: Primary: 92B99, 74J30, 70F99, 35Q99; Secondary: 74J35.

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