The mechanics of phantom Mikado networks

Dl Humphries,Ea Gaffney,Ja Grogan

doi:10.1088/2399-6528/aac07a

Abstract

The elasticity of networks comprised of semi-flexible polymers plays a vital role in regulating the mechanics of both intra- and extra-cellular matrices. The behaviour of this polymer scaffold will depend on the nature and density of cross-linking between constituent fibres. While modelling efforts have investigated the effects of cross-link density in biopolymer networks, this is often accompanied by changes in both the fibre density and the network structure. We investigate the elasticity of a quasi two-dimensional Mikado network of elastic rods, in which cross-link density is allowed to vary while polymer density is held constant. In particular, this model is extended by allowing constituent rods to cross without forming cross-links, while polymer density and network geometry are preserved. In doing so, the competing contributions to the shear modulus from cross-link density, mesh size, geometry and polymer density are decoupled. We find that previous scaling laws fail to capture the well-studied transition from bend- to stretch- dominated elasticity as cross-link density is varied. We identify a length scale which relates cross-link density to the transition between affine and nonaffine regimes, and which provides a collapse of simulation data curves for varying cross-link densities.

Highlights

Biopolymer networks are ubiquitous in living matter, from the collagen-dominant extracellular matrix (ECM) to the actin cortex of eukaryotic cells
Biopolymer networks exist in many forms, and across many scales, the physics governing their mechanics being fundamental to their biological function
As the above transition is predicted to occur for constant network geometry and constitutive choices, we predict that knowledge of the fibre elastic moduli and network fibre density will not be sufficient to determine the elastic regime in which a fibre network resides in the presence of variable crosslinking

Summary

Introduction

Biopolymer networks are ubiquitous in living matter, from the collagen-dominant extracellular matrix (ECM) to the actin cortex of eukaryotic cells. The mechanics of such networks is vital to the proper functioning of many processes, including cellular motility [1, 2], mechanical cell-cell communication [3, 4] and stress management in articular cartilage [5]. Dynamically shifting networks allow for structural stability in the presence of a fluctuating extracellular environment [9]. As stresses derived from the environment are transmitted to the cell membrane, rearrangements in stress fibres allow cells to adapt to various substrate mechanics and geometries [10]. Despite the ubiquity of these polymer assemblies in vivo, a complete understanding of how network structural properties and polymer behaviours can produce the observed local and bulk mechanics is challenging

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