Research Colloquium with Arik Yochelis (Ben-Gurion University)

Multiple cellular motility modes driven by actin waves: Mechanisms revealed by bifurcation theory

Eukaryotic cells exhibit a wide range of dynamic patterns involving filamentous actin (F-actin) and its regulators. Because many of these patterns underlie key cellular functions, including distinct modes of motility, they provide the motivation for this study. We develop a mass-conserved reaction-diffusion model of the actin cortex in which active and inactive Rho-GTPase are interconverted, active Rho-GTPase promotes F-actin assembly, and F-actin feeds back to inactivate active Rho-GTPase. We analyze the model on a one-dimensional periodic domain, representing the edge of a thin sheet-like cell, using bifurcation theory complemented by numerical simulations.
Among the bifurcations considered, our analysis focuses on the unfolding of a codimension-two instability involving both a long-wavelength mode and a finite-wavenumber Hopf mode. This unfolding reveals a rich organization of steady wave-pinning states, also known as mesas and governed by the Maxwell construction; propagating coherent structures, including fronts and excitable pulses; and traveling and standing waves. These patterns are distinguished by their mass-conservation regimes and classified according to domain size. In particular, we identify unexpected conditions under which steady wave-pinning states and traveling waves can coexist bistably on moderate-sized domains.

These results reveal possible mechanisms for the coexistence of, and transitions between, different cellular motility modes, including cell polarization, crawling, ruffling, and disordered dynamics. More broadly, they suggest that dissipative reaction-diffusion systems with mass conservation possess distinctive pattern-formation mechanisms, motivating further studies of higher-codimension structures such as codimension-three instabilities and T-points.