Investigating local negative feedback of Rac activity by mathematical models and cell-motility simulations

How do cells maintain robust, yet flexible polarization for directed motion? Recent optogenetic experiments by Town and Weiner on neutrophil-like HL-60 cells strongly point to the essential role of a Rac-inhibitor (downstream of the small GTPase Rac) in shaping requisite negative feedback that allows cells to respond to rapidly changing directional cues. Here we adapt a previous mathematical model for cell polarity to model interactions of Rac, its putative inhibitor, and upstream PIP3 (a product of the optogenetically stimulated PI3K). We fit parameters in our partial differential equation (PDE) model to temporal and spatial experimental data. Cell shapes, motility, and stimulus responses are modeled in 2D simulations, with PDEs solved along the cell edge. We show that the Rac-inhibitor-PIP3 circuit accounts for the optogenetic data (including exotic cell trajectories), that it is the minimal circuit to do so, and that it improves gradient sensing under noisy or dynamic conditions.