Exploring the effects of actin-binding proteins on the percolation of actin networks using a mean field model

The actin cytoskeleton is a dynamical system that can exert forces and transmit forces between the cell and its environment. The dynamical and rheological properties of the actin cytoskeleton are modulated by actin binding proteins (ABPs). Some ABPs, such as α-actinin or Arp2/3, connect different actin filaments thereby changing the topology of the network. Other ABPs, such as myosin, can also exert forces on the network thus altering its dynamic behavior. In this work we model an actin system and its interaction with α-actinin, myosin and Arp2/3 using ordinary differential equations and stochastic mechanochemical simulations. We then use a mean field approach to quantify how the concentrations of different ABPs affect the connectivity and rigidity of the network. We find that the presence of Arp2/3 increases the connectivity of the network. We also discuss the conditions needed for force exertion and transmission in this system. We expect that this result may provide a theoretical insight into how ABPs affect the ability of the actin cytoskeleton to exert and transmit forces.