Bulk-surface coupling reconciles Min-protein pattern formation <i>in vitro</i> and <i>in vivo</i>

The Min system of E. coli exhibits a rich variety of protein patterns whose phenomenology differs qualitatively and quantitatively between in vitro and in vivo settings. Here, we combine experiments and theory to show that this variety of patterns originates from distinct pattern-forming mechanisms (oscillation modes) that operate at different ratios of cytosolic volume to membrane surface area. Experiments in vitro, using laterally wide microchambers show qualitatively distinct patterns at different bulk heights, from standing waves, and sustained large-scale oscillations, to traveling waves. Our theoretical analysis shows that in vitro patterns at low bulk height are driven by the same lateral oscillation mechanism as in vivo pole-to-pole oscillations. Two distinct vertical oscillation modes – anti-phase oscillations between the opposite membrane surfaces and membrane-to-bulk oscillations – set in at larger bulk heights, marking the transition from the in vivo to the in vitro regime. We predict and experimentally confirm vertical pattern-synchronization (in-phase and anti-phase) between the microchambers' top and bottom surface and multistability of patterns in the transition regime.