Reconstructing actin dynamics of the leading edge from observational data

Mesenchymal cell migration starts with the protrusion of the cell's leading edge, enabled by the branching growth of the actin network. Two crucial molecular players in protrusion are actin filaments and the Arp2/3 complex, the branching agent. Traditionally, protrusion models are intuited from several perturbative experiments. Recent multiplex microscopy imaging data promise to change this paradigm by providing measurements of naturally fluctuating densities of key proteins at the leading edge of unperturbed cells. We report an attempt to reconstruct the mechanistic protrusion model from such data. We analyze fluctuations of densities of actin filaments and Arp2/3 complex and cell edge velocity using phase space and regression analysis to reconstruct linearized dynamics of the coupled actin-Arp2/3-velocity system. We then build a nonlinear model of these dynamics based on previous knowledge of this system and parsimony. The resulting models recover the rates of reactions and mechanical and transport processes in the lamellipodium from a single nonperturbative experiment. The models posit that the dominant nonlinear term in the lamellipodial dynamics corresponds to the retrograde flow of the actin network in the cell frame. The models suggest that the protrusion is dominated by a damped oscillatory cycle resulting from a combination of positive feedback from the Arp2/3 complex to protrusion velocity and negative feedback from actin density to the velocity.