Building mathematical model of cell leading edge from multiplex data

Many cells in our body migrate - 'good' examples are wound healing, embryogenesis and immune response; 'bad' example is metastasis. Migration starts with leading edge protrusion, which is enabled by branching growth of actin network and resisted by membrane tension. Two main molecular players in this process are actin fibers and Arp2/3 protein, which works as a branching agent. Several mathematical models of actin-Arp2/3-velocity dynamics at the leading edge were  proposed in the last few decades, all of them based on traditional modeling routine. I will present the modern approach of using phase plane analysis to reconstruct such model directly from the multiplex microscopy data in the form of spatial-temporal series of natural fluctuations of the leading edge velocity and Arp2/3 and actin densities. We treat these data as linear perturbations of stochastic integro-PDEs and derive these PDEs. The resulting model gives three nontrivial biological insights, which I will discuss.