# A mesoscopic theory to describe the flexibility regulation in F-actin networks: An approach of phase transitions with nonlinear elasticity

## TL;DR

This paper develops a mesoscopic nonlinear elasticity model to explain how calponin regulates the flexibility and mechanical response of F-actin networks, linking microstructural changes to phase transition behavior.

## Contribution

It introduces a phase transition framework using Landau formalism to describe calponin's effect on actin network mechanics, supported by experimental validation.

## Key findings

- Calponin increases network strain tolerance and delays softening.
- The interaction parameter scales as |c - c_{cr}|^{1/2}, indicating a phase transition.
- Microstructural alterations are linked to changes in pre-strain and crosslink adhesion energy.

## Abstract

The synthetic actin network arouses great interest as bio-material due to its soft and wet nature that mimics many biological scaffolding structures. Inside the cell, the actin network is regulated by tens of actin-binding proteins (ABP's), which make for a highly complex system with several emergent behaviours. In particular, calponin is an ABP that was identified as an actin stabiliser, but whose mechanism is still 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 show that the difference between the two networks, with and without calponin, not only provides bundle flexibility. But, also encodes alterations in the pre-strain and the regulation of the crosslinks adhesion energy to define the new yielding point. We verify these effects theoretically using nonlinear continuum mechanics for the semiflexible and crosslinked network. In addition, the alterations over the microstructure are described by the definition of an interaction parameter $\Gamma$ according the formalism of Landau. According to this simple model we demonstrates that the interaction parameter can describe the experimental observations following an scaling exponent as $\Gamma \sim \mid c-c_{cr} \mid^{1/2}$, where $c$ is the ratio between concentration of calponin and actin. This result provides interesting feedback to improve our understanding of several mechano-biological pathways.