Diffusive coupling of two well-mixed compartments elucidates elementary principles of protein-based pattern formation

Spatial organization of proteins in cells is important for many biological functions. In general, the nonlinear, spatially coupled models protein-pattern formation are only accessible to numerical simulations, which has limited insight into general underlying principles. To overcome this limitation, we adopt setting two diffusively coupled, well-mixed compartments that represents elementary feature any pattern—an interface. For intracellular systems, total numbers conserved on relevant timescale pattern formation. Thus essential dynamics redistribution globally mass densities between compartments. We present a phase-portrait analysis phase-space redistributed masses provides insights physical mechanisms demonstrate approach several paradigmatic model systems. particular, show pole-to-pole Min oscillations Escherichia coli relaxation MinD polarity orientation. This reveals close relation cell oscillatory patterns cells. Critically, our findings suggest design principles found characteristic features these phase portraits (nullclines and fixed points). These not uniquely determined by topology protein-interaction network but depend parameters (kinetic rates, diffusion constants) distinct networks can give rise equivalent portrait features.3 MoreReceived 29 October 2020Accepted 25 February 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.013258Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasCell polarityPattern formationSelf-organizationPhysical SystemsProtein interaction networksTechniquesBifurcation analysisPhase space methodsSpatial modelingBiological PhysicsNonlinear Dynamics