Simple lattice model for biological gels

TL;DR

This paper introduces a 3D lattice model for biological gels, capturing their elastic properties and rigidity transitions by incorporating filamentous polymers, crosslinks, and bending forces, revealing a threshold for rigidity.

Contribution

It presents a novel lattice model that combines stretching and bending forces to study the elastic behavior and rigidity thresholds of biological gels.

Findings

Model exhibits a rigidity threshold at p=p_b<1.

Elastic response transitions from nonaffine to affine.

All elastic constants are nonzero despite zero modes.

Abstract

We construct a three-dimensional lattice model for biological gels in which straight lines of bonds correspond to filamentous semi-flexible polymers and lattice sites, which are exactly four-fold coordinated, to crosslinks. With only stretching central forces between nearest neighbors, this lattice is sub-isostatic with an extensive number of zero modes; but all of its elastic constants are nonzero, and its elastic response is affine. Removal of bonds with probability $1-p$ leads to a lattice with average coordination number less than four and a distribution of polymer lengths. When bending forces are added, the diluted lattice exhibits a rigidity threshold at $p=p_b<1$ and crossover from bending-dominated nonaffine to stretching-dominated affine response between $p_b$ and $p=1$.