Modeling Composite Cytoskeletal Networks using Effective Medium Theory

The mechanical response of most living cells arises from their cytoskeleton, a polymeric scaffold made of different types of biopolymers and associated crosslinking proteins. We used rigidity percolation theory to devise a set of models using an effective medium approach to study the mechanical properties of cytoskeleton-like networks. We first successfully recreated a model which obtains the mechanical response of a disordered network of a single filament type, given the constitutive material properties of individual filaments and the network geometry. In this model, wherever two filaments cross they are crosslinked together, and these crosslinkers allow for energy free rotation of filaments but not translation, so the filaments cannot slide along one another. We then extended our approach for a model which involved ``phantom cosslinkers. At crosslinking nodes involving these crosslinkers, only a maximum of two filaments can be crosslinked together at a binding site, and if a third filament were to go through the connection, it would simply pass through and not be physically bound by the crosslinker. Although phantom cross-linkers have been used in computer simulations in the past, they have not been previously investigated analytically, including in a mean field theory. With both of these models involving only one filament and crosslinker type, we were then able to devise our main goal of extending the effective medium approach to composite networks of two types of filaments and crosslinkers. Specifically, this model involves two networks, for example an actin network and a microtubule network, and places weak spring-like interactions between filaments belonging to the two to resemble various types of interactions; for example weaker interactions represent entanglement and stronger springs to represent actual crosslinking between the two networks. With this new model we are able to define composite networks made of individual networks of stiff and soft filaments, and any combination of the two types of crosslinkers mentioned previously, with varying levels of interaction between the networks. Our results may provide new insights into the collective mechanical response of composite networks found in the cytoskeleton and design principles for engineered networks that mimic the cytoskeleton