Oligomerization of peripheral membrane proteins provides tunable control of cell surface polarity

Abstract

Asymmetric distributions of peripheral membrane proteins define cell polarity across all kingdoms of life. These asymmetries are shaped by membrane binding, diffusion and transport. Theoretical studies have revealed a general requirement for non-linear positive feedback to spontaneously amplify and/or stabilize asymmetries against dispersion by diffusion and dissociation. But how specific molecular sources of non-linearity shape polarization dynamics remains poorly understood. Here we study how oligomerization of peripheral membrane proteins shapes polarization dynamics in simple feedback circuits. We show that size dependent binding avidity and mobility of membrane bound oligomers endow polarity circuits generically with several key properties. Size-dependent binding avidity confers a form of positive feedback in which the effective rate constant for subunit dissociation decreases with increasing subunit density. This combined with additional weak linear positive feedback is sufficient for spontaneous emergence of stably polarized states. Size-dependent oligomer mobility makes symmetry-breaking and stable polarity more robust with respect to variation in subunit diffusivities and cell sizes, and slows the approach to a final stable spatial distribution, allowing cells to "remember" polarity boundaries imposed by transient external cues. Together, these findings reveal how oligomerization of peripheral membrane proteins can provide powerful and highly tunable sources of non-linear feedback in biochemical circuits that govern cell-surface polarity. Given its prevalence and widespread involvement in cell polarity, we speculate that self-oligomerization may have provided an accessible path to evolving simple polarity circuits. Author summaryAll cells organize their activities with respect to one or more axes of polarity. Cell polarity is often defined by the asymmetric enrichment of specific polarity proteins at the cell membrane. Absent external cues, stable polarity requires positive feedback in which proteins locally promote their own accumulation at the membrane, and the strength of feedback must depend non-linearly on local protein concentration. Here, we show that this kind of non-linear dependence arises when peripheral membrane proteins form small oligomers that dissociate from the membrane more slowly than single protein monomers. Combining this effect with a little additional linear feedback allows cells to form and stabilize asymmetric distributions of polarity proteins. In addition, we find that size-dependent reduction in oligomer mobility makes the ability to polarize more robust to variation in monomer diffusivity and cell size and makes polarity protein distributions more responsive to external inputs. Since many polarity proteins form small oligomers at the cell membrane, and there are many ways for weak linear feedback to arise in biochemical systems, the combination of oligomerization with a small amount of additional positive feedback may provide a general mechanism for polarizing a wide variety of unrelated cell types.