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The synthetic actin network arouses great interest as bio-material due to itssoft and wet nature that mimics many biological scaffolding structures. Insidethe cell, the actin network is regulated by tens of actin-binding proteins(ABP's), which make for a highly complex system with several emergentbehaviours. In particular, calponin is an ABP that was identified as an actinstabiliser, but whose mechanism is still poorly understood. Recent experimentsusing an in vitro model system of cross-linked actin with calponin and largedeformation bulk rheology, found that networks with basic calponin exhibited adelayed onset and were able to withstand a higher maximal strain beforesoftening.  In this work, we show that the difference between the two networks, with andwithout calponin, not only provides bundle flexibility. But, also encodesalterations in the pre-strain and the regulation of the crosslinks adhesionenergy to define the new yielding point. We verify these effects theoreticallyusing nonlinear continuum mechanics for the semiflexible and crosslinkednetwork. In addition, the alterations over the microstructure are described bythe definition of an interaction parameter $\Gamma$ according the formalism ofLandau. According to this simple model we demonstrates that the interactionparameter can describe the experimental observations following an scalingexponent as $\Gamma \sim \mid c-c_{cr} \mid^{1/2}$, where $c$ is the ratiobetween concentration of calponin and actin. This result provides interestingfeedback to improve our understanding of several mechano-biological pathways.

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