Disordered elastic systems theory as a framework to study collective cell migration

Solving interface dynamics and statics in realistic systems beyond the elastic approximation is still a largely open theoretical/analytical problem. In this work, we propose to address this problem by analyzing a Ginzburg-Landau model, where interfaces with overhangs may be studied. We make the connection between the Ginzburg-Landau model and the elastic Hamiltonian, and propose a new observable to probe the validity of the elastic theory as a function of "defects". We approach the problem numerically and analytically, and our simulations, in addition to making contact with experiments, also allow us to test and provide insight to develop new analytical approaches to this so far intractable problem. We apply these tools to unravel properties of migrating cells-fronts, by treating its boundaries as interfaces moving in a disordered landscape. In particular, we analyze the roughness, defined as the height-height correlations in space of the interface. For experiments done on extended moving fronts of epithelial rat cells under different sets of conditions, we show how by using this framework it is possible to distinguish short-range correlations (intra-cell) and long-range correlations (inter-cell), which depend on the internal mechanisms dominating the cell colony dynamics.