Feedback mechanisms in a mechanical model of cell polarization

Directed cell migration requires a spatially polarized distribution of polymerized actin. We develop and treat a mechanical model of cell polarization based on polymerization and depolymerization of actin filaments at the two ends of a cell, modulated by forces at either end that are coupled by the cell membrane. We solve this model using both a simulation approach that treats filament nucleation, polymerization, and depolymerization stochastically, and a rate-equation approach based on key properties such as the number of filaments N and the number of polymerized subunits F at either end of the cell. The rate-equation approach agrees closely with the stochastic approach at steady state and, when appropriately generalized, also predicts the dynamic behavior accurately. The calculated transitions from symmetric to polarized states show that polarization is enhanced by a high free-actin concentration, a large pointed-end off-rate, a small barbed-end off-rate, and a small spontaneous nucleation rate. The rate-equation approach allows us to perform a linear-stability analysis to pin down the key interactions that drive the polarization. The polarization is driven by a positive-feedback loop having two interactions. First, an increase in F at one side of the cell lengthens the filaments and thus reduces the decay rate of N (increasing N); second, increasing N enhances F because the force per growing filament tip is reduced. We find that the transitions induced by changing system properties result from supercritical pitchfork bifurcations. The filament lifetime depends strongly on the average filament length, and this effect is crucial for obtaining polarization correctly.