Title: Pulses, waves, and mesas in dissipative mass-conserved reaction-diffusion systems and their implications to cell motility
Abstract: The transition from random walk to directional motion (and back) is one of the intriguing phenomena observed in motile eukaryotic cells. However, typical theoretical studies distinguish between the two phenomena and focus either on dissipative models or models obeying gradient flows, respectively. Using a three-variable dissipative reaction-diffusion system with mass conservation, we show how pulses, waves, and (stationary) mesas generically organize about high codimension bifurcations. Specifically, we demonstrate the novelty of mass conservation, which enters via a long-wavenumber bifurcation of a large-scale mode. Following the biological interest, we address the bistability between travelling wave and mesa solution branches, which emerge from a codimension-2 bifurcation to a finite wavenumber Hopf and a conserved large-scale mode. Lastly, through simulations of the reaction-diffusion system coupled to a model of cell deformations, we show how these solution types affect cell motility.