Directing Min protein patterns with advective bulk flow
We theoretically predict and experimentally show that the propagation direction of in vitro Min protein patterns can be controlled by a hydrodynamic flow of the bulk solution. We find downstream propagation of Min wave patterns relative to the bulk flow direction for low MinE:MinD concentration ratios, but upstream propagation for large MinE:MinD ratios, with multistability of both propagation directions in between. A theoretical model for the Min system reveals the mechanism underlying the upstream propagation and links it to the fast conformational switching of MinE in the bulk. For high MinE:MinD ratios, upstream propagation can be reproduced by a reduced model in which increased MinD bulk concentrations on the upstream side promote protein attachment and hence, propagation in that direction. For low MinE:D ratios, downstream propagation is described by the minimal model, as additionally confirmed by experiments with a non-switching MinE mutant. No advection takes place on the membrane surface where the protein patterns form, but advective bulk flow shifts the protein-concentration profiles in the bulk relative to the membrane-bound pattern. From a broader perspective, differential flows in a bulk volume relative to a surface are a relevant general feature in bulk-surface coupled systems. Our study shows how such a differential flow can control surface-pattern propagation and demonstrates how the global pattern's response may depend on specific molecular features of the reaction kinetics.