Graph-Based Ginzburg-Landau Energy Functional Theory For Soft Matter*

We consider a binary mixture of particles in equilibrium, and a nonequilibrium actomyosin network for investigating the phases and the mechanism of collective self-assembly. In our simulations, binary mixture becomes phase-separated above a critical temperature. Next, we study a dynamical system of actomyosin networks which undergo contraction and gelation. We developed a graph theory based model that examines and predicts the generic features in the dynamics and thermodynamics of self-assembly. First we translate a complex biophysical system into a graph, then extracting meaningful reaction coordinates and order parameters from the graph. We capture phase separation in a binary mixture when using its bipartite graph’s Min-Cut as an order parameter in a Landau Free Energy Functional. For actomyosin networks, we construct the graph from the adjacency matrix of the actin filaments’ monomers. Establishing this renormalization framework allows to build graphs from cytoskeleton super resolution experiments and to link together analytical, simulated, and experimental data.