# Microstructural model for calponin stabilization of crosslinked actin networks

## TL;DR

This paper develops a nonlinear continuum mechanics model to explain how Calponin stabilizes crosslinked actin networks, aligning well with experimental findings and shedding light on the molecular mechanisms involved.

## Contribution

It introduces a novel mathematical model that links Calponin's stabilizing effect to changes in pre-strain and crosslink adhesion energy in actin networks.

## Key findings

- Model accurately predicts delayed softening in Calponin-stabilized networks
- Theoretical results match experimental rheology data
- Highlights the role of pre-strain and crosslink regulation in stabilization

## Abstract

The synthetic actin network demands great interest as bio-material due to its soft and wet nature that mimic many biological scaffolding structures. The study of these structures can contribute to a better understanding of this new micro/nano technology and the cytoskeleton like structural building blocks. Inside the cell the actin network is regulated by tens of actin-binding proteins (ABP's), which makes for a highly complex system with several emergent behavior. In particular Calponin is an ABP that was identified as an actin stabiliser, but its mechanism is poorly understood. Recent experiments using an in vitro model system of cross-linked actin with Calponin and large deformation bulk rheology, found that networks with basic calponin exhibited a delayed onset and were able to withstand a higher maximal strain before softening. In this work we propose a mathematical model into the framework of nonlinear continuum mechanics to explain the observation of Jansen, where we introduce the hypothesis by which the difference between the two networks, with and without Calponin, is interpreted as a alterations in the pre-strain developed by the network entanglement and the regulation of the crosslinks adhesion energy. The mechanics of the F-actin is modelled using the wormlike chain model for semi-flexible filaments and the gelation process is described as mesoscale dynamics for the crosslinks. The model has been validated with reported experimental results from literature, showing a good agreement between theory and experiments.