Discrete-to-continuum models of pre-stressed cytoskeletal filament networks

TL;DR

This paper develops a multiscale mathematical framework for modeling the mechanical response of pre-stressed cytoskeletal filament networks, linking microscopic filament properties to macroscopic cell rheology and validating predictions with vimentin network data.

Contribution

It introduces a discrete-to-continuum modeling approach for pre-stressed cytoskeletal networks, providing analytical tools to predict cell mechanics from filament properties.

Findings

Network stiffness increases sublinearly with filament pre-stress.

Net force scales logarithmically with bead size.

Models show good agreement with experimental data on vimentin networks.

Abstract

We introduce a mathematical model for the mechanical behaviour of the eukaryotic cell cytoskeleton. This discrete model involves a regular array of pre-stressed protein filaments that exhibit resistance to enthalpic stretching, joined at crosslinks to form a network. Assuming that the inter-crosslink distance is much shorter than the lengthscale of the cell, we upscale the discrete force balance to form a continuum system of governing equations and deduce the corresponding macroscopic stress tensor. We use these discrete and continuum models to analyse the imposed displacement of a bead placed in the domain, characterising the cell rheology through the force-displacement curve. We further derive an analytical approximation to the stress and strain fields in the limit of small bead radius, predicting the net force required to generate a given deformation and elucidating the dependency on the microscale properties of the filaments. We apply these models to networks of the intermediate filament vimentin and demonstrate good agreement between predictions of the discrete, continuum and analytical approaches. In particular, our model predicts that the network stiffness increases sublinearly with the filament pre-stress and scales logarithmically with the bead size.