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

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 behaviors. 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 exhibited a delayed onset and were able to withstand a higher maximal strain before softening. In this work, we show that at network scale the actin network with calponin furthermore the reduction of the persistence length allows: (i) The reduction in the network pre-strain. (ii) The increment of the crosslinks adhesion energy. 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 Γ according the formalism of Landau for phase transitions. According to this model we demonstrates that the interaction parameter can describe the experimental observations following a scaling exponent as Γ~|c−ccr|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.