Four different mechanisms for switching cell polarity.

The mechanisms and design principles of regulatory systems establishing stable polarized protein patterns within cells are well studied. However, cells can also dynamically control their cell polarity. Here, we ask how an upstream signaling system can switch the orientation of a polarized pattern. We use a mathematical model of a core polarity system based on three proteins as the basis to study different mechanisms of signal-induced polarity switching. The analysis of this model reveals four general classes of switching mechanisms with qualitatively distinct behaviors: the transient oscillator switch, the reset switch, the prime-release switch, and the push switch. Each of these regulatory mechanisms effectively implements the function of a spatial toggle switch, however with different characteristics in their nonlinear and stochastic dynamics. We identify these characteristics and also discuss experimental signatures of each type of switching mechanism.

Flow Induced Symmetry Breaking in a Conceptual Polarity Model.

Important cellular processes, such as cell motility and cell division, are coordinated by cell polarity, which is determined by the non-uniform distribution of certain proteins. Such protein patterns form via an interplay of protein reactions and protein transport. Since Turing's seminal work, the formation of protein patterns resulting from the interplay between reactions and diffusive transport has been widely studied. Over the last few years, increasing evidence shows that also advective transport, resulting from cytosolic and cortical flows, is present in many cells. However, it remains unclear how and whether these flows contribute to protein-pattern formation. To address this question, we use a minimal model that conserves the total protein mass to characterize the effects of cytosolic flow on pattern formation. Combining a linear stability analysis with numerical simulations, we find that membrane-bound protein patterns propagate against the direction of cytoplasmic flow with a speed that is maximal for intermediate flow speed. We show that the mechanism underlying this pattern propagation relies on a higher protein influx on the upstream side of the pattern compared to the downstream side. Furthermore, we find that cytosolic flow can change the membrane pattern qualitatively from a peak pattern to a mesa pattern. Finally, our study shows that a non-uniform flow profile can induce pattern formation by triggering a regional lateral instability.

Pattern localization to a domain edge.

The formation of protein patterns inside cells is generically described by reaction-diffusion models. The study of such systems goes back to Turing, who showed how patterns can emerge from a homogenous steady state when two reactive components have different diffusivities (e.g., membrane-bound and cytosolic states). However, in nature, systems typically develop in a heterogeneous environment, where upstream protein patterns affect the formation of protein patterns downstream. Examples for this are the polarization of Cdc42 adjacent to the previous bud site in budding yeast and the formation of an actin-recruiter ring that forms around a PIP3 domain in macropinocytosis. This suggests that previously established protein patterns can serve as a template for downstream proteins and that these downstream proteins can "sense" the edge of the template. A mechanism for how this edge sensing may work remains elusive. Here we demonstrate and analyze a generic and robust edge-sensing mechanism, based on a two-component mass-conserving reaction-diffusion (McRD) model. Our analysis is rooted in a recently developed theoretical framework for McRD systems, termed local equilibria theory. We extend this framework to capture the spatially heterogeneous reaction kinetics due to the template. This enables us to graphically construct the stationary patterns in the phase space of the reaction kinetics. Furthermore, we show that the protein template can trigger a regional mass-redistribution instability near the template edge, leading to the accumulation of protein mass, which eventually results in a stationary peak at the template edge. We show that simple geometric criteria on the reactive nullcline's shape predict when this edge-sensing mechanism is operational. Thus, our results provide guidance for future studies of biological systems and for the design of synthetic pattern forming systems.

Spatial control of the GTPase MglA by localized RomR-RomX GEF and MglB GAP activities enables Myxococcus xanthus motility.

The rod-shaped Myxococcus xanthus cells move with defined front-rear polarity using polarized motility systems. A polarity module consisting of the small GTPase MglA, its cognate GTPase activating protein (GAP) MglB and RomR establishes this polarity. Agl-Glt gliding motility complexes assemble and disassemble at the leading and lagging pole, respectively. These processes are stimulated by MglA-GTP at the leading and MglB at the lagging pole. Here, we identify RomX as an integral component of the polarity module. RomX and RomR form a complex that has MglA guanine nucleotide exchange factor (GEF) activity and also binds MglA-GTP. In vivo RomR recruits RomX to the leading pole forming the RomR-RomX complex that stimulates MglA-GTP formation and binding, resulting in a high local concentration of MglA-GTP. The spatially separated and opposing activities of the RomR-RomX GEF at the leading and the MglB GAP at the lagging cell pole establish front-rear polarity by allowing the spatially separated assembly and disassembly of Agl-Glt motility complexes. Our findings uncover a regulatory system for bacterial cell polarity that incorporates a nucleotide exchange factor as well as an NTPase activating protein for regulation of a nucleotide-dependent molecular switch and demonstrate a spatial organization that is conserved in eukaryotes.