SUMMARY Many cells undergo symmetry-breaking polarization toward a randomly oriented “front” in the absence of spatial cues. In budding yeast, such polarization involves a positive feedback loop that enables amplification of stochastically arising clusters of polarity factors. Previous mathematical modeling suggested that, if more than one cluster were amplified, the clusters would compete for limiting resources and the largest would “win,” explaining why yeast cells always make one and only one bud. Here, using imaging with improved spatiotemporal resolution, we show the transient coexistence of multiple clusters during polarity establishment, as predicted by the model. Unexpectedly, we also find that initial polarity factor clustering is oscillatory, revealing the presence of a negative feedback loop that disperses the factors. Mathematical modeling predicts that negative feedback would confer robustness to the polarity circuit and make the kinetics of competition between polarity factor clusters relatively insensitive to polarity factor concentration. These predictions are confirmed experimentally.

Summary Background In 1952, Alan Turing suggested that spatial patterns could arise from homogeneous starting conditions by feedback amplification of stochastic fluctuations. One example of such self-organization, called symmetry breaking, involves spontaneous cell polarization in the absence of spatial cues. The conserved GTPase Cdc42p is essential for both guided and spontaneous polarization, and in budding yeast cells Cdc42p concentrates at a single site (the presumptive bud site) at the cortex. Cdc42p concentrates at a random cortical site during symmetry breaking in a manner that requires the scaffold protein Bem1p. The mechanism whereby Bem1p promotes this polarization was unknown. Results Here we show that Bem1p promotes symmetry breaking by assembling a complex in which both a Cdc42p-directed guanine nucleotide exchange factor (GEF) and a Cdc42p effector p21-activated kinase (PAK) associate with Bem1p. Analysis of Bem1p mutants indicates that both GEF and PAK must bind to the same molecule of Bem1p, and a protein fusion linking the yeast GEF and PAK bypasses the need for Bem1p. Although mammalian cells lack a Bem1p ortholog, they contain more complex multidomain GEFs that in some cases can directly interact with PAKs, and we show that yeast containing an artificial GEF with similar architecture can break symmetry even without Bem1p. Conclusions Yeast symmetry-breaking polarization involves a GEF-PAK complex that binds GTP-Cdc42p via the PAK and promotes local Cdc42p GTP-loading via the GEF. By generating fresh GTP-Cdc42p near pre-existing GTP-Cdc42p, the complex amplifies clusters of GTP-Cdc42p at the cortex. Our findings provide mechanistic insight into an evolutionarily conserved pattern-forming positive-feedback pathway.

Summary Robust dendrite morphogenesis is a critical step in the development of reproducible neural circuits. However, little is known about the extracellular cues that pattern complex dendrite morphologies. In the model nematode C. elegans, the sensory neuron PVD establishes stereotypical, highly-branched dendrite morphology. Here, we report the identification of a tripartite ligand-receptor complex of membrane adhesion molecules that is both necessary and sufficient to instruct spatially restricted growth and branching of PVD dendrites. The ligand complex SAX-7/L1CAM and MNR-1 function at defined locations in the surrounding hypodermal tissue, while DMA-1 acts as the cognate receptor on PVD. Mutations in this complex lead to dramatic defects in the formation, stabilization, and organization of the dendritic arbor. Ectopic expression of SAX-7 and MNR-1 generates a predictable, unnaturally patterned dendritic tree in a DMA-1 dependent manner. Both in vivo and in vitro experiments indicate that all three molecules are needed for interaction.

Summary For migrating cells, budding yeast, and many other cells, it is critical that polarization occur towards one, and only one, site (the singularity rule). Polarity establishment involves amplification of Cdc42 foci via positive feedback, but the basis for singularity was unclear. To assess whether or not singularity is linked to Cdc42 amplification, we disabled the yeast cell’s endogenous amplification mechanism and synthetically re-wired the cells to employ a different positive feedback loop to generate Cdc42 foci. Re-wired cells violated the singularity rule, occasionally making two buds. Mathematical modeling indicated that, given sufficient time, competition between foci would promote singularity. In re-wired cells, slower competition sometimes resulted in a failure to develop a single “winning” focus before budding. Manipulations predicted to slow competition in normal cells also allowed occasional formation of two buds, suggesting that singularity is enforced by rapid competition between Cdc42 foci.

Studies of the processes leading to the construction of a bud and its separation from the mother cell in Saccharomyces cerevisiae have provided foundational paradigms for the mechanisms of polarity establishment, cytoskeletal organization, and cytokinesis. Here we review our current understanding of how these morphogenetic events occur and how they are controlled by the cellcycle-regulatory cyclin-CDK system. In addition, defects in morphogenesis provide signals that feed back on the cyclin-CDK system, and we review what is known regarding regulation of cell-cycle progression in response to such defects, primarily acting through the kinase Swe1p. The bidirectional communication between morphogenesis and the cell cycle is crucial for successful proliferation, and its study has illuminated many elegant and often unexpected regulatory mechanisms. Despite considerable progress, however, many of the most puzzling mysteries in this field remain to be resolved.

Summary Background Polarization in yeast has been proposed to involve a positive feedback loop whereby the polarity regulator Cdc42p orients actin cables, which deliver vesicles carrying Cdc42p to the polarization site. Previous mathematical models treating Cdc42p traffic as a membrane-free flux suggested that directed traffic would polarize Cdc42p, but it remained unclear whether Cdc42p would become polarized without the membrane-free simplifying assumption. Results We present mathematical models that explicitly consider stochastic vesicle traffic via exocytosis and endocytosis, providing several new insights. Our findings suggest that endocytic cargo influences the timing of vesicle internalization in yeast. Moreover, our models provide quantitative support for the view that integral membrane cargo proteins would become polarized by directed vesicle traffic given the experimentally determined rates of vesicle traffic and diffusion. However, such traffic cannot effectively polarize the more rapidly-diffusing Cdc42p in the model, without making additional assumptions that seem implausible and lack experimental support. Conclusions Our findings suggest that actin-directed vesicle traffic would perturb, rather than reinforce, polarization in yeast.

Cells of the budding yeast Saccharomyces cerevisiae are born carrying localized transmembrane landmark proteins that guide the subsequent establishment of a polarity axis and hence polarized growth to form a bud in the next cell cycle. In haploid cells, the relevant landmark proteins are concentrated at the site of the preceding cell division, to which they recruit Cdc24, the guanine nucleotide exchange factor for the conserved polarity regulator Cdc42. However, instead of polarizing at the division site, the new polarity axis is directed next to but not overlapping that site. Here, we show that the Cdc42 guanosine triphosphatase–activating protein (GAP) Rga1 establishes an exclusion zone at the division site that blocks subsequent polarization within that site. In the absence of localized Rga1 GAP activity, new buds do in fact form within the old division site. Thus, Cdc42 activators and GAPs establish concentric zones of action such that polarization is directed to occur adjacent to but not within the previous cell division site.

Somatosensory information from the face is transmitted to the brain by trigeminal sensory neurons. It was previously unknown whether neurons innervating distinct areas of the face possess molecular differences. We have identified a set of genes differentially expressed along the dorsoventral axis of the embryonic mouse trigeminal ganglion and thus can be considered trigeminal positional identity markers. Interestingly, establishing some of the spatial patterns requires signals from the developing face. We identified bone morphogenetic protein 4 (BMP4) as one of these target-derived factors and showed that spatially defined retrograde BMP signaling controls the differential gene expressions in trigeminal neurons through both Smad4-independent and Smad4-dependent pathways. Mice lacking one of the BMP4-regulated transcription factors, Onecut2 (OC2), have defects in the trigeminal central projections representing the whiskers. Our results provide molecular evidence for both spatial patterning and retrograde regulation of gene expression in sensory neurons during the development of the somatosensory map.