A System of Counteracting Feedback Loops Regulates Cdc42p Activity during Spontaneous Cell Polarization

Oscillatory dynamics of Rac1 activity in Dictyostelium discoideum amoebae

Small GTPases of the Rho family play a central role in the regulation of cell motility by controlling the remodeling of the actin cytoskeleton. In the amoeboid cells of Dictyostelium discoideum, the active form of the Rho GTPase Rac1 regulates actin polymerases at the leading edge and actin filament bundling proteins at the posterior cortex of polarized cells. We monitored the spatiotemporal dynamics of Rac1 and its effector DGAP1 in vegetative amoebae using specific fluorescent probes. We observed that plasma membrane domains enriched in active Rac1 not only exhibited stable polarization, but also showed rotations and oscillations, whereas DGAP1 was depleted from these regions. To simulate the observed dynamics of the two proteins, we developed a mass-conserving reaction-diffusion model based on the circulation of Rac1 between the membrane and the cytoplasm coupled with its activation by GEFs, deactivation by GAPs and interaction with DGAP1. Our theoretical model accurately reproduced the experimentally observed dynamic patterns, including the predominant anti-correlation between active Rac1 and DGAP1. Significantly, the model predicted a new colocalization regime of these two proteins in polarized cells, which we confirmed experimentally. In summary, our results improve the understanding of Rac1 dynamics and reveal how the occurrence and transitions between different regimes depend on biochemical reaction rates, protein levels and cell size. This study not only expands our knowledge of the behavior of Rac1 GTPases in D. discoideum amoebae but also demonstrates how specific modes of interaction between Rac1 and its effector DGAP1 lead to their counterintuitively anti-correlated dynamics.

Change in RhoGAP and RhoGEF availability drives transitions in cortical patterning and excitability in Drosophila

Actin cortex patterning and dynamics are critical for cell shape changes. These dynamics undergo transitions during development, often accompanying changes in collective cell behavior. Although mechanisms have been established for individual cells' dynamic behaviors, the mechanisms and specific molecules that result in developmental transitions in vivo are still poorly understood. Here, we took advantage of two developmental systems in Drosophila melanogaster to identify conditions that altered cortical patterning and dynamics. We identified a Rho guanine nucleotide exchange factor (RhoGEF) and Rho GTPase activating protein (RhoGAP) pair required for actomyosin waves in egg chambers. Specifically, depletion of the RhoGEF, Ect2, or the RhoGAP, RhoGAP15B, disrupted actomyosin wave induction, and both proteins relocalized from the nucleus to the cortex preceding wave formation. Furthermore, we found that overexpression of a different RhoGEF and RhoGAP pair, RhoGEF2 and Cumberland GAP (C-GAP), resulted in actomyosin waves in the early embryo, during which RhoA activation precedes actomyosin assembly by ∼4 s. We found that C-GAP was recruited to actomyosin waves, and disrupting F-actin polymerization altered the spatial organization of both RhoA signaling and the cytoskeleton in waves. In addition, disrupting F-actin dynamics increased wave period and width, consistent with a possible role for F-actin in promoting delayed negative feedback. Overall, we showed a mechanism involved in inducing actomyosin waves that is essential for oocyte development and is general to other cell types, such as epithelial and syncytial cells.

Patterning of the cell cortex by Rho GTPases

The Rho GTPases - RHOA, RAC1 and CDC42 - are small GTP binding proteins that regulate basic biological processes such as cell locomotion, cell division and morphogenesis by promoting cytoskeleton-based changes in the cell cortex. This regulation results from active (GTP-bound) Rho GTPases stimulating target proteins that, in turn, promote actin assembly and myosin 2-based contraction to organize the cortex. This basic regulatory scheme, well supported by in vitro studies, led to the natural assumption that Rho GTPases function in vivo in an essentially linear matter, with a given process being initiated by GTPase activation and terminated by GTPase inactivation. However, a growing body of evidence based on live cell imaging, modelling and experimental manipulation indicates that Rho GTPase activation and inactivation are often tightly coupled in space and time via signalling circuits and networks based on positive and negative feedback. In this Review, we present and discuss this evidence, and we address one of the fundamental consequences of coupled activation and inactivation: the ability of the Rho GTPases to self-organize, that is, direct their own transition from states of low order to states of high order. We discuss how Rho GTPase self-organization results in the formation of diverse spatiotemporal cortical patterns such as static clusters, oscillatory pulses, travelling wave trains and ring-like waves. Finally, we discuss the advantages of Rho GTPase self-organization and pattern formation for cell function.

Change in RhoGAP and RhoGEF availability drives transitions in cortical patterning and excitability in Drosophila

Actin cortex patterning and dynamics are critical for cell shape changes. These dynamics undergo transitions during development, often accompanying changes in collective cell behavior. While mechanisms have been established for individual cells' dynamic behaviors, mechanisms and specific molecules that result in developmental transitions in vivo are still poorly understood. Here, we took advantage of two developmental systems in Drosophila melanogaster to identify conditions that altered cortical patterning and dynamics. We identified a RhoGEF and RhoGAP pair whose relocalization from nucleus to cortex results in actomyosin waves in egg chambers. Furthermore, we found that overexpression of a different RhoGEF and RhoGAP pair resulted in actomyosin waves in the early embryo, during which RhoA activation precedes actomyosin assembly and RhoGAP recruitment by ~4 seconds. Overall, we showed a mechanism involved in inducing actomyosin waves that is essential for oocyte development and is general to other cell types.

Redundancy and the role of protein copy numbers in the cell polarization machinery of budding yeast

How can a self-organized cellular function evolve, adapt to perturbations, and acquire new sub-functions? To make progress in answering these basic questions of evolutionary cell biology, we analyze, as a concrete example, the cell polarity machinery of Saccharomyces cerevisiae. This cellular module exhibits an intriguing resilience: it remains operational under genetic perturbations and recovers quickly and reproducibly from the deletion of one of its key components. Using a combination of modeling, conceptual theory, and experiments, we propose that multiple, redundant self-organization mechanisms coexist within the protein network underlying cell polarization and are responsible for the module's resilience and adaptability. Based on our mechanistic understanding of polarity establishment, we hypothesize that scaffold proteins, by introducing new connections in the existing network, can increase the redundancy of mechanisms and thus increase the evolvability of other network components. Moreover, our work gives a perspective on how a complex, redundant cellular module might have evolved from a more rudimental ancestral form.

Silencing Notch4 promotes tumorigenesis and inhibits metastasis of triple-negative breast cancer via Nanog and Cdc42

Elucidation of individual Notch protein biology in specific cancer is crucial to develop safe, effective, and tumor-selective Notch-targeting therapeutic reagents for clinical use [1]. Here, we explored the Notch4 function in triple-negative breast cancer (TNBC). We found that silencing Notch4 enhanced tumorigenic ability in TNBC cells via upregulating Nanog expression, a pluripotency factor of embryonic stem cells. Intriguingly, silencing Notch4 in TNBC cells suppressed metastasis via downregulating Cdc42 expression, a key molecular for cell polarity formation. Notably, downregulation of Cdc42 expression affected Vimentin distribution, but not Vimentin expression to inhibit EMT shift. Collectively, our results show that silencing Notch4 enhances tumorigenesis and inhibits metastasis in TNBC, indicating that targeting Notch4 may not be a potential strategy for drug discovery in TNBC.

A focus on yeast mating: From pheromone signaling to cell-cell fusion

Cells live in a chemical environment and are able to orient towards chemical cues. Unicellular haploid fungal cells communicate by secreting pheromones to reproduce sexually. In the yeast models Saccharomyces cerevisiae and Schizosaccharomyces pombe, pheromonal communication activates similar pathways composed of cognate G-protein-coupled receptors and downstream small GTPase Cdc42 and MAP kinase cascades. Local pheromone release and sensing, at a mobile surface polarity patch, underlie spatial gradient interpretation to form pairs between two cells of distinct mating types. Concentration of secretion at the point of cell-cell contact then leads to local cell wall digestion for cell fusion, forming a diploid zygote that prevents further fusion attempts. A number of asymmetries between mating types may promote efficiency of the system. In this review, we present our current knowledge of pheromone signaling in the two model yeasts, with an emphasis on how cells decode the pheromone signal spatially and ultimately fuse together. Though overall pathway architectures are similar in the two species, their large evolutionary distance allows to explore how conceptually similar solutions to a general biological problem can arise from divergent molecular components.

Orientation of Cell Polarity by Chemical Gradients

Accurate decoding of spatial chemical landscapes is critical for many cell functions. Eukaryotic cells decode local chemical gradients to orient growth or movement in productive directions. Recent work on yeast model systems, whose gradient sensing pathways display much less complexity than those in animal cells, has suggested new paradigms for how these very small cells successfully exploit information in noisy and dynamic pheromone gradients to identify their mates. Pheromone receptors regulate a polarity circuit centered on the conserved Rho-family GTPase, Cdc42. The polarity circuit contains both positive and negative feedback pathways, allowing spontaneous symmetry breaking and also polarity site disassembly and relocation. Cdc42 orients the actin cytoskeleton, leading to focused vesicle traffic that promotes movement of the polarity site and also reshapes the cortical distribution of receptors at the cell surface. In this article, we review the advances from work on yeasts and compare them with the excitable signaling pathways that have been revealed in chemotactic animal cells. Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Noise-induced quasiperiod and period switching

We employ a typical genetic circuit model to explore how noise can influence dynamic structure. With the increase of a key interactive parameter, the model will deterministically go through two bifurcations and three dynamic structure regions. We find that a quasiperiodic component, which is not allowed by deterministic dynamics, will be generated by noise inducing in the first two regions, and this quasiperiod will be more and more stable along with the increase in noise. In particular, in the second region the quasiperiod will compete with a stable limit cycle and perform a new transient rhythm. Furthermore, we ascertain the entropy production rate and the heat dissipation rate, and discover a minimal value with theoretical elucidation. In the end, we unveil the mechanism of the formation of quasiperiods, and show a practical biological example. We expect this work to be helpful in solving some biological or ecological problems, such as the genetic origin of periodical cicadas and population dynamics with fluctuation.

Stress-dependent inhibition of polarized cell growth through unbalancing the GEF/GAP regulation of Cdc42

Cdc42 GTPase rules cell polarity and growth in fission yeast. It is negatively and positively regulated by GTPase-activating proteins (GAPs) and guanine nucleotide exchange factors (GEFs), respectively. Active Cdc42-GTP localizes to the poles, where it associates with numerous proteins constituting the polarity module. However, little is known about its downregulation. We describe here that oxidative stress causes Sty1-kinase-dependent Cdc42 inactivation at cell poles. Both the amount of active Cdc42 at tips and cell length inversely correlate with Sty1 activity, explaining the elongated morphology of Δsty1 cells. We have created stress-blinded cell poles either by eliminating two Cdc42 GAPs or through the constitutive tethering of Gef1 to cell tips, and we biochemically demonstrate that the GAPs Rga3/6 and the GEF Gef1 are direct substrates of Sty1. We propose that phosphorylation of Rga3/6 and Gef1 mediates the Sty1-dependent inhibition of Cdc42 at cell tips, halting polarized growth during stress adaptation.

Stress-Activated Protein Kinase Signalling Regulates Mycoparasitic Hyphal-Hyphal Interactions in Trichoderma atroviride

Trichoderma atroviride is a mycoparasitic fungus used as biological control agent against fungal plant pathogens. The recognition and appropriate morphogenetic responses to prey-derived signals are essential for successful mycoparasitism. We established microcolony confrontation assays using T. atroviride strains expressing cell division cycle 42 (Cdc42) and Ras-related C3 botulinum toxin substrate 1 (Rac1) interactive binding (CRIB) reporters to analyse morphogenetic changes and the dynamic displacement of localized GTPase activity during polarized tip growth. Microscopic analyses showed that Trichoderma experiences significant polarity stress when approaching its fungal preys. The perception of prey-derived signals is integrated via the guanosine triphosphatase (GTPase) and mitogen-activated protein kinase (MAPK) signalling network, and deletion of the MAP kinases Trichoderma MAPK 1 (Tmk1) and Tmk3 affected T. atroviride tip polarization, chemotropic growth, and contact-induced morphogenesis so severely that the establishment of mycoparasitism was highly inefficient to impossible. The responses varied depending on the prey species and the interaction stage, reflecting the high selectivity of the signalling process. Our data suggest that Tmk3 affects the polarity-stress adaptation process especially during the pre-contact phase, whereas Tmk1 regulates contact-induced morphogenesis at the early-contact phase. Neither Tmk1 nor Tmk3 loss-of-function could be fully compensated within the GTPase/MAPK signalling network underscoring the crucial importance of a sensitive polarized tip growth apparatus for successful mycoparasitism.

Coordinating cell polarization and morphogenesis through mechanical feedback

Many cellular processes require cell polarization to be maintained as the cell changes shape, grows or moves. Without feedback mechanisms relaying information about cell shape to the polarity molecular machinery, the coordination between cell polarization and morphogenesis, movement or growth would not be possible. Here we theoretically and computationally study the role of a genetically-encoded mechanical feedback (in the Cell Wall Integrity pathway) as a potential coordination mechanism between cell morphogenesis and polarity during budding yeast mating projection growth. We developed a coarse-grained continuum description of the coupled dynamics of cell polarization and morphogenesis as well as 3D stochastic simulations of the molecular polarization machinery in the evolving cell shape. Both theoretical approaches show that in the absence of mechanical feedback (or in the presence of weak feedback), cell polarity cannot be maintained at the projection tip during growth, with the polarization cap wandering off the projection tip, arresting morphogenesis. In contrast, for mechanical feedback strengths above a threshold, cells can robustly maintain cell polarization at the tip and simultaneously sustain mating projection growth. These results indicate that the mechanical feedback encoded in the Cell Wall Integrity pathway can provide important positional information to the molecular machinery in the cell, thereby enabling the coordination of cell polarization and morphogenesis.

The Path towards Predicting Evolution as Illustrated in Yeast Cell Polarity

A bottom-up route towards predicting evolution relies on a deep understanding of the complex network that proteins form inside cells. In a rapidly expanding panorama of experimental possibilities, the most difficult question is how to conceptually approach the disentangling of such complex networks. These can exhibit varying degrees of hierarchy and modularity, which obfuscate certain protein functions that may prove pivotal for adaptation. Using the well-established polarity network in budding yeast as a case study, we first organize current literature to highlight protein entrenchments inside polarity. Following three examples, we see how alternating between experimental novelties and subsequent emerging design strategies can construct a layered understanding, potent enough to reveal evolutionary targets. We show that if you want to understand a cell’s evolutionary capacity, such as possible future evolutionary paths, seemingly unimportant proteins need to be mapped and studied. Finally, we generalize this research structure to be applicable to other systems of interest.

Robust banded protoxylem pattern formation through microtubule-based directional ROP diffusion restriction

In plant vascular tissue development, different cell wall patterns are formed, offering different mechanical properties optimised for different growth stages. Critical in these patterning processes are Rho of Plants (ROP) proteins, a class of evolutionarily conserved small GTPase proteins responsible for local membrane domain formation in many organisms. While te spotted metaxylem pattern can easily be understood as a result of a Turing-style reaction-diffusion mechanism, it remains an open question how the consistent orientation of evenly spaced bands and spirals as found in protoxylem is achieved. We hypothesise that this orientation results from an interaction between ROPs and an array of transversely oriented cortical microtubules that acts as a directional diffusion barrier. Here, we explore this hypothesis using partial differential equation models with anisotropic ROP diffusion and show that a horizontal microtubule array acting as a vertical diffusion barrier to active ROP can yield a horizontally banded ROP pattern. We then study the underlying mechanism in more detail, finding that it can only orient curved pattern features but not straight lines. This implies that, once formed, banded and spiral patterns cannot be reoriented by this mechanism. Finally, we observe that ROPs and microtubules together only form ultimately static patterns if the interaction is implemented with sufficient biological realism.

Secretory Vesicle Clustering in Fungal Filamentous Cells Does Not Require Directional Growth

During symmetry breaking, the highly conserved Rho GTPase Cdc42 becomes stabilized at a defined site via an amplification process. However, little is known about how a new polarity site is established in an already asymmetric cell-a critical process in a changing environment. The human fungal pathogen Candida albicans switches from budding to filamentous growth in response to external cues, a transition controlled by Cdc42. Here, we have used optogenetic manipulation of cell polarity to reset growth in asymmetric filamentous C. albicans cells. We show that increasing the level of active Cdc42 on the plasma membrane results in disruption of the exocyst subunit Sec3 localization and a striking de novo clustering of secretory vesicles. This new cluster of secretory vesicles is highly dynamic, moving by hops and jumps, until a new growth site is established. Our results reveal that secretory vesicle clustering can occur in the absence of directional growth.

Size-Regulated Symmetry Breaking in Reaction-Diffusion Models of Developmental Transitions

The development of multicellular organisms proceeds through a series of morphogenetic and cell-state transitions, transforming homogeneous zygotes into complex adults by a process of self-organisation. Many of these transitions are achieved by spontaneous symmetry breaking mechanisms, allowing cells and tissues to acquire pattern and polarity by virtue of local interactions without an upstream supply of information. The combined work of theory and experiment has elucidated how these systems break symmetry during developmental transitions. Given that such transitions are multiple and their temporal ordering is crucial, an equally important question is how these developmental transitions are coordinated in time. Using a minimal mass-conserved substrate-depletion model for symmetry breaking as our case study, we elucidate mechanisms by which cells and tissues can couple reaction-diffusion-driven symmetry breaking to the timing of developmental transitions, arguing that the dependence of patterning mode on system size may be a generic principle by which developing organisms measure time. By analysing different regimes of our model, simulated on growing domains, we elaborate three distinct behaviours, allowing for clock-, timer- or switch-like dynamics. Relating these behaviours to experimentally documented case studies of developmental timing, we provide a minimal conceptual framework to interrogate how developing organisms coordinate developmental transitions.

Regulation of Cdc42 for polarized growth in budding yeast

The Rho GTPase Cdc42 is a central regulator of cell polarity in diverse cell types. The activity of Cdc42 is dynamically controlled in time and space to enable distinct polarization events, which generally occur along a single axis in response to spatial cues. Our understanding of the mechanisms underlying Cdc42 polarization has benefited largely from studies of the budding yeast Saccharomyces cerevisiae, a genetically tractable model organism. In budding yeast, Cdc42 activation occurs in two temporal steps in the G1 phase of the cell cycle to establish a proper growth site. Here, we review findings in budding yeast that reveal an intricate crosstalk among polarity proteins for biphasic Cdc42 regulation. The first step of Cdc42 activation may determine the axis of cell polarity, while the second step ensures robust Cdc42 polarization for growth. Biphasic Cdc42 polarization is likely to ensure the proper timing of events including the assembly and recognition of spatial landmarks and stepwise assembly of a new ring of septins, cytoskeletal GTP-binding proteins, at the incipient bud site. Biphasic activation of GTPases has also been observed in mammalian cells, suggesting that biphasic activation could be a general mechanism for signal-responsive cell polarization. Cdc42 activity is necessary for polarity establishment during normal cell division and development, but its activity has also been implicated in the promotion of aging. We also discuss negative polarity signaling and emerging concepts of Cdc42 signaling in cellular aging.

Mechanistic insights into actin-driven polarity site movement in yeast

Directed cell growth or migration are critical for the development and function of many eukaryotic cells. These cells develop a dynamic "front" (also called "polarity site") that can change direction. Polarity establishment involves autocatalytic accumulation of polarity regulators, including the conserved Rho-family GTPase Cdc42, but the mechanisms underlying polarity reorientation remain poorly understood. The tractable model yeast, Saccharomyces cerevisiae, relocates its polarity site when searching for mating partners. Relocation requires polymerized actin, and is thought to involve actin-mediated vesicle traffic to the polarity site. In this study, we provide a quantitative characterization of spontaneous polarity site movement as a search process and use a mechanistic computational model that combines polarity protein biochemical interactions with vesicle trafficking to probe how various processes might affect polarity site movement. Our findings identify two previously documented features of yeast vesicle traffic as being particularly relevant to such movement: tight spatial focusing of exocytosis enhances the directional persistence of movement, and association of Cdc42-directed GTPase-Activating Proteins with secretory vesicles increases the distance moved. Furthermore, we suggest that variation in the rate of exocytosis beyond simple Poisson dynamics may be needed to fully account for the characteristics of polarity site movement in vivo.

Pattern formation in a coupled membrane-bulk reaction-diffusion model for intracellular polarization and oscillations

Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in cell biology, such as cell polarization. Coupled bulk-surface models naturally include compartmentalization of cytosolic and membrane-bound polarity molecules. Here we study the distribution of the polarity protein Cdc42 in a mass-conserved membrane-bulk model, and explore the effects of diffusion and spatial dimensionality on spatio-temporal pattern formation. We first analyze a one-dimensional (1-D) model for Cdc42 oscillations in fission yeast, consisting of two diffusion equations in the bulk domain coupled to nonlinear ODEs for binding kinetics at each end of the cell. In 1-D, our analysis reveals the existence of symmetric and asymmetric steady states, as well as anti-phase relaxation oscillations typical of slow-fast systems. We then extend our analysis to a two-dimensional (2-D) model with circular bulk geometry, for which species can either diffuse inside the cell or become bound to the membrane and undergo a nonlinear reaction-diffusion process. We also consider a nonlocal system of PDEs approximating the dynamics of the 2-D membrane-bulk model in the limit of fast bulk diffusion. In all three model variants we find that mass conservation selects perturbations of spatial modes that simply redistribute mass. In 1-D, only anti-phase oscillations between the two ends of the cell can occur, and in-phase oscillations are excluded. In higher dimensions, no radially symmetric oscillations are observed. Instead, the only instabilities are symmetry-breaking, either corresponding to stationary Turing instabilities, leading to the formation of stationary patterns, or to oscillatory Turing instabilities, leading to traveling and standing waves. Codimension-two Bogdanov-Takens bifurcations occur when the two distinct instabilities coincide, causing traveling waves to slow down and to eventually become stationary patterns. Our work clarifies the effect of geometry and dimensionality on behaviors observed in mass-conserved cell polarity models.

Autoactivation of small GTPases by the GEF-effector positive feedback modules

Small GTPases are organizers of a plethora of cellular processes. The time and place of their activation are tightly controlled by the localization and activation of their regulators, guanine-nucleotide exchange factors (GEFs) and GTPase-activating proteins (GAPs). Remarkably, in some systems, the upstream regulators of GTPases are also found downstream of their activity. Resulting feedback loops can generate complex spatiotemporal dynamics of GTPases with important functional consequences. Here we discuss the concept of positive autoregulation of small GTPases by the GEF-effector feedback modules and survey recent developments in this exciting area of cell biology.

Temporal regulation of cell polarity via the interaction of the Ras GTPase Rsr1 and the scaffold protein Bem1

The Cdc42 guanosine triphosphatase (GTPase) plays a central role in polarity development in species ranging from yeast to humans. In budding yeast, a specific growth site is selected in the G1 phase. Rsr1, a Ras GTPase, interacts with Cdc42 and its associated proteins to promote polarized growth at the proper bud site. Yet how Rsr1 regulates cell polarization is not fully understood. Here, we show that Rsr1-GDP interacts with the scaffold protein Bem1 in early G1, likely hindering the role of Bem1 in Cdc42 polarization and polarized secretion. Consistent with these in vivo observations, mathematical modeling predicts that Bem1 is unable to promote Cdc42 polarization in early G1 in the presence of Rsr1-GDP. We find that a part of the Bem1 Phox homology domain, which overlaps with a region interacting with the exocyst component Exo70, is necessary for the association of Bem1 with Rsr1-GDP. Overexpression of the GDP-locked Rsr1 interferes with Bem1-dependent Exo70 polarization. We thus propose that Rsr1 functions in spatial and temporal regulation of polarity establishment by associating with distinct polarity factors in its GTP- and GDP-bound states.

The shared role of the Rsr1 GTPase and Gic1/Gic2 in Cdc42 polarization

The Cdc42 GTPase plays a central role in polarity development in many species. In budding yeast, Cdc42 is essential for polarized growth at the proper site and also for spontaneous cell polarization in the absence of spatial cues. Cdc42 polarization is critical for multiple events in the G1 phase prior to bud emergence, including bud-site assembly, polarization of the actin cytoskeleton, and septin filament assembly to form a ring at the new bud site. Yet the mechanism by which Cdc42 polarizes is not fully understood. Here we report that biphasic Cdc42 polarization in the G1 phase is coupled to stepwise assembly of the septin ring for bud emergence. We show that the Rsr1 GTPase shares a partially redundant role with Gic1 and Gic2, two related Cdc42 effectors, in the first phase of Cdc42 polarization in haploid cells. We propose that the first phase of Cdc42 polarization is mediated by positive feedback loops that function in parallel-one involving Rsr1 via local activation of Cdc42 in response to spatial cues and another involving Gic1 or Gic2 via reduction of diffusion of active Cdc42.

Principles that govern competition or co-existence in Rho-GTPase driven polarization

Rho-GTPases are master regulators of polarity establishment and cell morphology. Positive feedback enables concentration of Rho-GTPases into clusters at the cell cortex, from where they regulate the cytoskeleton. Different cell types reproducibly generate either one (e.g. the front of a migrating cell) or several clusters (e.g. the multiple dendrites of a neuron), but the mechanistic basis for unipolar or multipolar outcomes is unclear. The design principles of Rho-GTPase circuits are captured by two-component reaction-diffusion models based on conserved aspects of Rho-GTPase biochemistry. Some such models display rapid winner-takes-all competition between clusters, yielding a unipolar outcome. Other models allow prolonged co-existence of clusters. We investigate the behavior of a simple class of models and show that while the timescale of competition varies enormously depending on model parameters, a single factor explains a large majority of this variation. The dominant factor concerns the degree to which the maximal active GTPase concentration in a cluster approaches a "saturation point" determined by model parameters. We suggest that both saturation and the effect of saturation on competition reflect fundamental properties of the Rho-GTPase polarity machinery, regardless of the specific feedback mechanism, which predict whether the system will generate unipolar or multipolar outcomes.

Particle-based simulations of polarity establishment reveal stochastic promotion of Turing pattern formation

Polarity establishment, the spontaneous generation of asymmetric molecular distributions, is a crucial component of many cellular functions. Saccharomyces cerevisiae (yeast) undergoes directed growth during budding and mating, and is an ideal model organism for studying polarization. In yeast and many other cell types, the Rho GTPase Cdc42 is the key molecular player in polarity establishment. During yeast polarization, multiple patches of Cdc42 initially form, then resolve into a single front. Because polarization relies on strong positive feedback, it is likely that the amplification of molecular-level fluctuations underlies the generation of multiple nascent patches. In the absence of spatial cues, these fluctuations may be key to driving polarization. Here we used particle-based simulations to investigate the role of stochastic effects in a Turing-type model of yeast polarity establishment. In the model, reactions take place either between two molecules on the membrane, or between a cytosolic and a membrane-bound molecule. Thus, we developed a computational platform that explicitly simulates molecules at and near the cell membrane, and implicitly handles molecules away from the membrane. To evaluate stochastic effects, we compared particle simulations to deterministic reaction-diffusion equation simulations. Defining macroscopic rate constants that are consistent with the microscopic parameters for this system is challenging, because diffusion occurs in two dimensions and particles exchange between the membrane and cytoplasm. We address this problem by empirically estimating macroscopic rate constants from appropriately designed particle-based simulations. Ultimately, we find that stochastic fluctuations speed polarity establishment and permit polarization in parameter regions predicted to be Turing stable. These effects can operate at Cdc42 abundances expected of yeast cells, and promote polarization on timescales consistent with experimental results. To our knowledge, our work represents the first particle-based simulations of a model for yeast polarization that is based on a Turing mechanism.

Many cells need to generate and maintain biochemical signals in specific subcellular regions. This phenomenon is broadly called polarity establishment, and is important in fundamental processes such as cell migration and differentiation. A key polarity factor found in diverse organisms, including yeast and humans, is the protein Cdc42. In yeast, Cdc42-dependent polarization occurs through a self-reinforcing biochemical signaling loop. Directional cues can guide polarity establishment, but interestingly, yeast can polarize in the absence of such a cue. The mechanism thought to underlie this symmetry breaking involves the amplification of inhomogeneities in molecular distributions that arise from molecular-level fluctuations. We investigated the effects of random fluctuations on polarization by performing particle-based simulations of the Cdc42 signaling network. We found that fluctuations can facilitate polarization, allowing faster polarization, and polarization over a broader range of concentrations. Our observations may help understand how polarity works in other systems.

A compartmentalized signaling network mediates crossover control in meiosis

During meiosis, each pair of homologous chromosomes typically undergoes at least one crossover (crossover assurance), but these exchanges are strictly limited in number and widely spaced along chromosomes (crossover interference). The molecular basis for this chromosome-wide regulation remains mysterious. A family of meiotic RING finger proteins has been implicated in crossover regulation across eukaryotes. Caenorhabditis elegans expresses four such proteins, of which one (ZHP-3) is known to be required for crossovers. Here we investigate the functions of ZHP-1, ZHP-2, and ZHP-4. We find that all four ZHP proteins, like their homologs in other species, localize to the synaptonemal complex, an unusual, liquid crystalline compartment that assembles between paired homologs. Together they promote accumulation of pro-crossover factors, including ZHP-3 and ZHP-4, at a single recombination intermediate, thereby patterning exchanges along paired chromosomes. These proteins also act at the top of a hierarchical, symmetry-breaking process that enables crossovers to direct accurate chromosome segregation.

A compartmentalized signaling network mediates crossover control in meiosis

During meiosis, each pair of homologous chromosomes typically undergoes at least one crossover (crossover assurance), but these exchanges are strictly limited in number and widely spaced along chromosomes (crossover interference). The molecular basis for this chromosome-wide regulation remains mysterious. A family of meiotic RING finger proteins has been implicated in crossover regulation across eukaryotes. Caenorhabditis elegans expresses four such proteins, of which one (ZHP-3) is known to be required for crossovers. Here we investigate the functions of ZHP-1, ZHP-2, and ZHP-4. We find that all four ZHP proteins, like their homologs in other species, localize to the synaptonemal complex, an unusual, liquid crystalline compartment that assembles between paired homologs. Together they promote accumulation of pro-crossover factors, including ZHP-3 and ZHP-4, at a single recombination intermediate, thereby patterning exchanges along paired chromosomes. These proteins also act at the top of a hierarchical, symmetry-breaking process that enables crossovers to direct accurate chromosome segregation.

Inhibition of Ras activity coordinates cell fusion with cell-cell contact during yeast mating

In the fission yeast Schizosaccharomyces pombe, pheromone signaling engages a signaling pathway composed of a G protein-coupled receptor, Ras, and a mitogen-activated protein kinase (MAPK) cascade that triggers sexual differentiation and gamete fusion. Cell-cell fusion requires local cell wall digestion, which relies on an initially dynamic actin fusion focus that becomes stabilized upon local enrichment of the signaling cascade on the structure. We constructed a live-reporter of active Ras1 (Ras1-guanosine triphosphate [GTP]) that shows Ras activity at polarity sites peaking on the fusion structure before fusion. Remarkably, constitutive Ras1 activation promoted fusion focus stabilization and fusion attempts irrespective of cell pairing, leading to cell lysis. Ras1 activity was restricted by the guanosine triphosphatase-activating protein Gap1, which was itself recruited to sites of Ras1-GTP and was essential to block untimely fusion attempts. We propose that negative feedback control of Ras activity restrains the MAPK signal and couples fusion with cell-cell engagement.

Clathrin Assembly Defines the Onset and Geometry of Cortical Patterning

Assembly of the endocytic machinery is a constitutively active process that is important for the organization of the plasma membrane, signal transduction, and membrane trafficking. Existing research has focused on the stochastic nature of endocytosis. Here, we report the emergence of the collective dynamics of endocytic proteins as periodic traveling waves on the cell surface. Coordinated clathrin assembly provides the earliest spatial cue for cortical waves and sets the direction of propagation. Surprisingly, the onset of clathrin waves, but not individual endocytic events, requires feedback from downstream factors, including FBP17, Cdc42, and N-WASP. In addition to the localized endocytic assembly at the plasma membrane, intracellular clathrin and phosphatidylinositol-3,4-bisphosphate predict the excitability of the plasma membrane and modulate the geometry of traveling waves. Collectively, our data demonstrate the multiplicity of clathrin functions in cortical pattern formation and provide important insights regarding the nucleation and propagation of single-cell patterns.

Fine-tuning the orientation of the polarity axis by Rga1, a Cdc42 GTPase-activating protein

In vivo and in vitro analyses reveal how a Cdc42 GTPase-activating protein (GAP) interacts with other negative polarity cues at old division sites in budding yeast. Mathematical modeling suggests that spatial distribution of a Cdc42 GAP in coordination with G1 progression is critical for fine-tuning the orientation of the polarity axis.

In yeast and animal cells, signaling pathways involving small guanosine triphosphatases (GTPases) regulate cell polarization. In budding yeast, selection of a bud site directs polarity establishment and subsequently determines the plane of cell division. Rga1, a Cdc42 GTPase-activating protein, prevents budding within the division site by inhibiting Cdc42 repolarization. A protein complex including Nba1 and Nis1 is involved in preventing rebudding at old division sites, yet how these proteins and Rga1 might function in negative polarity signaling has been elusive. Here we show that Rga1 transiently localizes to the immediately preceding and older division sites by interacting with Nba1 and Nis1. The LIM domains of Rga1 are necessary for its interaction with Nba1, and loss of this interaction results in premature delocalization of Rga1 from the immediately preceding division site and, consequently, abnormal bud-site selection in daughter cells. However, such defects are minor in mother cells of these mutants, likely because the G1 phase is shorter and a new bud site is established prior to delocalization of Rga1. Indeed, our biphasic mathematical model of Cdc42 polarization predicts that premature delocalization of Rga1 leads to more frequent Cdc42 repolarization within the division site when the first temporal step in G1 is assumed to last longer. Spatial distribution of a Cdc42 GAP in coordination with G1 progression may thus be critical for fine-tuning the orientation of the polarity axis in yeast.

Cell Polarity in Yeast

A conserved molecular machinery centered on the Cdc42 GTPase regulates cell polarity in diverse organisms. Here we review findings from budding and fission yeasts that reveal both a conserved core polarity circuit and several adaptations that each organism exploits to fulfill the needs of its lifestyle. The core circuit involves positive feedback by local activation of Cdc42 to generate a cluster of concentrated GTP-Cdc42 at the membrane. Species-specific pathways regulate the timing of polarization during the cell cycle, as well as the location and number of polarity sites.

Many roads to symmetry breaking: molecular mechanisms and theoretical models of yeast cell polarity

Mathematical modeling has been instrumental in identifying common principles of cell polarity across diverse systems. These principles include positive feedback loops that are required to destabilize a spatially uniform state of the cell. The conserved small G-protein Cdc42 is a master regulator of eukaryotic cellular polarization. Here we discuss recent developments in studies of Cdc42 polarization in budding and fission yeasts and demonstrate that models describing symmetry-breaking polarization can be classified into six minimal classes based on the structure of positive feedback loops that activate and localize Cdc42. Owing to their generic system-independent nature, these model classes are also likely to be relevant for the G-protein–based symmetry-breaking systems of higher eukaryotes. We review experimental evidence pro et contra different theoretically plausible models and conclude that several parallel and non–mutually exclusive mechanisms are likely involved in cellular polarization of yeasts. This potential redundancy needs to be taken into consideration when interpreting the results of recent cell-rewiring studies.

Cell cycle entry triggers a switch between two modes of Cdc42 activation during yeast polarization

Cell polarization underlies many cellular and organismal functions. The GTPase Cdc42 orchestrates polarization in many contexts. In budding yeast, polarization is associated with a focus of Cdc42•GTP which is thought to self sustain by recruiting a complex containing Cla4, a Cdc42-binding effector, Bem1, a scaffold, and Cdc24, a Cdc42 GEF. Using optogenetics, we probe yeast polarization and find that local recruitment of Cdc24 or Bem1 is sufficient to induce polarization by triggering self-sustaining Cdc42 activity. However, the response to these perturbations depends on the recruited molecule, the cell cycle stage, and existing polarization sites. Before cell cycle entry, recruitment of Cdc24, but not Bem1, induces a metastable pool of Cdc42 that is sustained by positive feedback. Upon Cdk1 activation, recruitment of either Cdc24 or Bem1 creates a stable site of polarization that induces budding and inhibits formation of competing sites. Local perturbations have therefore revealed unexpected features of polarity establishment.

DOI:http://dx.doi.org/10.7554/eLife.26722.001

Living cells are not always symmetrical. Instead they are often polarized, with a distinct front and back or top and bottom. Cell polarization influences many processes, including how a cell moves and grows, and where it will divide. Breaking symmetry – in other words, making one part of a cell different from the rest – regularly involves a small protein called Cdc42, which can switch between an active and inactive form. This protein is found in a range of organisms from fungi to animals.

Budding yeast is a valuable model to study cell polarization. This single-celled fungus polarizes in order to produce a daughter cell or ‘bud’ that emerges out of one end of the mother cell. To become polarized, the mother cell accumulates active Cdc42 in a small area of the cell membrane. This region then becomes the front of the cell, from where the future bud will emerge. However, it is not fully understood how active Cdc42 accumulates at only one place. One model proposed that some molecules of active Cdc42 that are already present on the membrane, recruit polarity proteins that in turn activate other, inactive Cdc42 molecules. This self-amplifying loop could eventually build up a local pool of active Cdc42. However, it has proved challenging to directly test this model.

Optogenetics is a technique in which a beam of light is used to manipulate proteins inside cells in a precise manner. The method was first developed in the field of neuroscience over a decade ago, and has more recently been applied to cell biology. Now, Witte et al. have used optogenetics to move polarity proteins to defined places on the membrane of yeast cells and analyse how this change affected the pattern of Cdc42 activation. The experiments showed that polarity proteins not only activate Cdc42 but they also recruit more polarity proteins to the same place. The resulting positive feedback loop leads to active Cdc42 accumulating at one site on the membrane. Further work showed that this mechanism only operates in this manner just before the mother cell replicates its DNA, which is when a yeast cell will normally polarize.

These results provide a new perspective on how cells can make one part of the cell different from the rest. Beyond yeast, cell polarization plays a major role when animals, including humans, are developing as embryos or healing wounds. These processes are often controlled by a protein that is equivalent to Cdc42 or by other highly related switch-like proteins. This means that yeast will continue to provide a useful model to study these processes in the laboratory. Lastly, the optogenetics approach developed Witte et al. will be useful to dissect other processes that involve molecules being located at specific place in a cell at specific time.

DOI:http://dx.doi.org/10.7554/eLife.26722.002

Local sampling paints a global picture: Local concentration measurements sense direction in complex chemical gradients

Detecting and interpreting extracellular spatial signals is essential for cellular orientation within complex environments, such as during directed cell migration or growth in multicellular development. Although the molecular understanding of how cells read spatial signals like chemical gradients is still lacking, recent work has revealed that stochastic processes at different temporal and spatial scales are at the core of this gradient sensing process in a wide range of eukaryotes. Fast biochemical reactions like those underlying GTPase activity dynamics form a functional module together with slower cell morphological changes driven by membrane remodelling. This biochemical-morphological module explores the environment by stochastic local concentration sampling to determine the source of the gradient signal, enabling efficient signal detection and interpretation before polarised growth or migration towards the gradient source is initiated. Here we review recent data describing local sampling and propose a model of local fast and slow feedback counteracted by gradient-dependent substrate limitation to be at the core of gradient sensing by local sampling.

A Two-Tiered Mechanism Enables Localized Cdc42 Signaling during Enterocyte Polarization

Signaling by the small GTPase Cdc42 governs a diverse set of cellular processes that contribute to tissue morphogenesis. Since these processes often require highly localized signaling, Cdc42 activity must be clustered in order to prevent ectopic signaling. During cell polarization, apical Cdc42 signaling directs the positioning of the nascent apical membrane. However, the molecular mechanisms that drive Cdc42 clustering during polarity establishment are largely unknown. Here, we demonstrate that during cell polarization localized Cdc42 signaling is enabled via activity-dependent control of Cdc42 mobility. By performing photoconversion experiments, we show that inactive Cdc42-GDP is 30-fold more mobile than active Cdc42-GTP. This switch in apical mobility originates from a dual mechanism involving RhoGDI-mediated membrane dissociation of Cdc42-GDP and Tuba-mediated immobilization of Cdc42-GTP. Interference with either mechanism affects Cdc42 clustering and as a consequence impairs Cdc42-mediated apical membrane clustering. We therefore identify a molecular network, comprised of Cdc42, the guanine nucleotide exchange factor (GEF) Tuba, and RhoGDI, that enables differential diffusion of inactive and active Cdc42 and is required to establish localized Cdc42 signaling during enterocyte polarization.

Polarity establishment by Cdc42: Key roles for positive feedback and differential mobility

Cell polarity is fundamental to the function of most cells. The evolutionarily conserved molecular machinery that controls cell polarity is centered on a family of GTPases related to Cdc42. Cdc42 becomes activated and concentrated at polarity sites, but studies in yeast model systems led to controversy on the mechanisms of polarization. Here we review recent studies that have clarified how Cdc42 becomes polarized in yeast. On one hand, findings that appeared to support a key role for the actin cytoskeleton and vesicle traffic in polarity establishment now appear to reflect the action of stress response pathways induced by cytoskeletal perturbations. On the other hand, new findings strongly support hypotheses on the polarization mechanism whose origins date back to the mathematician Alan Turing. The key features of the polarity establishment mechanism in yeasts include a positive feedback pathway in which active Cdc42 recruits a Cdc42 activator to polarity sites, and differential mobility of polarity "activators" and "substrates."

Probing Cdc42 Polarization Dynamics in Budding Yeast Using a Biosensor

Cdc42 is a small guanosine triphosphatase (GTPase) that plays a central role in polarity development in diverse cell types. Since the activity of Cdc42 is dynamically controlled in time and space, it is required to develop a biosensor to monitor its activation in vivo. In this chapter, we describe the construction and usage of a simple and robust biosensor for monitoring active Cdc42 in budding yeast. This affinity-based biosensor uses a red fluorescent protein fused to a Cdc42- and Rac-interactive binding motif from one of the Cdc42 effector proteins. Because it binds specifically to the GTP-bound Cdc42, this biosensor can be used to monitor Cdc42 activation in vivo. This or similar biosensors can be widely used for studying GTPase signaling in other cell types because of the conserved CRIB motif present among GTPase targets.

Spatial and temporal signal processing and decision making by MAPK pathways

Mitogen-activated protein kinase (MAPK) pathways are conserved from yeast to man and regulate a variety of cellular processes, including proliferation and differentiation. Recent developments show how MAPK pathways perform exquisite spatial and temporal signal processing and underscores the importance of studying the dynamics of signaling pathways to understand their physiological response. The importance of dynamic mechanisms that process input signals into graded downstream responses has been demonstrated in the pheromone-induced and osmotic stress-induced MAPK pathways in yeast and in the mammalian extracellular signal-regulated kinase MAPK pathway. Particularly, recent studies in the yeast pheromone response have shown how positive feedback generates switches, negative feedback enables gradient detection, and coherent feedforward regulation underlies cellular memory. More generally, a new wave of quantitative single-cell studies has begun to elucidate how signaling dynamics determine cell physiology and represents a paradigm shift from descriptive to predictive biology.

Relocation sensors to quantify signaling dynamics in live single cells

All cells are different. Even isogenic cells can possess diverse shapes, reside in different cell-cycle stages or express various sets of proteins. These variations can modulate the cell response to environmental stimuli and thereby provide key insights into the regulation of signal transduction cascades. Fluorescence microscopy allows to visualize these differences and monitor in real-time the responses of live single cells. In order to observe key cellular events, fluorescent biosensors have been developed. Among many assays, relocation reporters play an important role since they enable the quantification of the signal transduction dynamics. Fluorescently tagged endogenous proteins, as well as synthetic constructs, have allowed the measurement of kinase activity, transcription factor activation, transcription and protein expression in live single cells.

Role of Polarized G Protein Signaling in Tracking Pheromone Gradients

Yeast cells track gradients of pheromones to locate mating partners. Intuition suggests that uniform distribution of pheromone receptors over the cell surface would yield optimal gradient sensing. However, yeast cells display polarized receptors. The benefit of such polarization was unknown. During gradient tracking, cell growth is directed by a patch of polarity regulators that wanders around the cortex. Patch movement is sensitive to pheromone dose, with wandering reduced on the up-gradient side of the cell, resulting in net growth in that direction. Mathematical modeling suggests that active receptors and associated G proteins lag behind the polarity patch and act as an effective drag on patch movement. In vivo, the polarity patch is trailed by a G protein-rich domain, and this polarized distribution of G proteins is required to constrain patch wandering. Our findings explain why G protein polarization is beneficial and illuminate a novel mechanism for gradient tracking.

Spontaneous cell polarization: Feedback control of Cdc42 GTPase breaks cellular symmetry

Spontaneous polarization without spatial cues, or symmetry breaking, is a fundamental problem of spatial organization in biological systems. This question has been extensively studied using yeast models, which revealed the central role of the small GTPase switch Cdc42. Active Cdc42-GTP forms a coherent patch at the cell cortex, thought to result from amplification of a small initial stochastic inhomogeneity through positive feedback mechanisms, which induces cell polarization. Here, I review and discuss the mechanisms of Cdc42 activity self-amplification and dynamic turnover. A robust Cdc42 patch is formed through the combined effects of Cdc42 activity promoting its own activation and active Cdc42-GTP displaying reduced membrane detachment and lateral diffusion compared to inactive Cdc42-GDP. I argue the role of the actin cytoskeleton in symmetry breaking is not primarily to transport Cdc42 to the active site. Finally, negative feedback and competition mechanisms serve to control the number of polarization sites.

Regulation of Cdc42 polarization by the Rsr1 GTPase and Rga1, a Cdc42 GTPase-activating protein, in budding yeast

Cdc42 plays a central role in establishing polarity in yeast and animals, yet how polarization of Cdc42 is achieved in response to spatial cues is poorly understood. Using live-cell imaging, we found distinct dynamics of Cdc42 polarization in haploid budding yeast in correlation with two temporal steps of the G1 phase. The position at which the Cdc42-GTP cluster develops changes rapidly around the division site during the first step but becomes stabilized in the second step, suggesting that an axis of polarized growth is determined in mid G1. Cdc42 polarization in the first step and its proper positioning depend on Rsr1 and its GTPase-activating protein (GAP) Bud2. Interestingly, Rga1, a Cdc42 GAP, exhibits transient localization to a site near the bud neck and to the division site during cytokinesis and G1, and this temporal change of Rga1 distribution is necessary for determination of a proper growth site. Mathematical modeling suggests that a proper axis of Cdc42 polarization in haploid cells might be established through a biphasic mechanism involving sequential positive feedback and transient negative feedback.

Quantitative analysis of membrane trafficking in regulation of Cdc42 polarity

Vesicle delivery of Cdc42 has been proposed as an important mechanism for generating and maintaining Cdc42 polarity at the plasma membrane. This mechanism requires the density of Cdc42 on secretory vesicles to be equal to or higher than the plasma membrane polarity cap. Using a novel method to estimate Cdc42 levels on post-Golgi secretory vesicles in intact yeast cells, we: (1) determined that endocytosis plays an important role in Cdc42's association with secretory vesicles (2) found that a GFP-tag placed on the N-terminus of Cdc42 negatively impacts this vesicle association and (3) quantified the surface densities of Cdc42 on post-Golgi vesicles which revealed that the vesicle density of Cdc42 is three times more dilute than that at the polarity cap. This work suggests that the immediate consequence of secretory vesicle fusion with the plasma membrane polarity cap is to dilute the local Cdc42 surface density. This provides strong support for the model in which vesicle trafficking acts to negatively regulate Cdc42 polarity on the cell surface while also providing a means to recycle Cdc42 between the cell surface and internal membrane locations.

Bud3 activates Cdc42 to establish a proper growth site in budding yeast

Cell polarization occurs along a single axis that is generally determined by a spatial cue, yet the underlying mechanism is poorly understood. Using biochemical assays and live-cell imaging, we show that cell polarization to a proper growth site requires activation of Cdc42 by Bud3 in haploid budding yeast. Bud3 catalyzes the release of guanosine diphosphate (GDP) from Cdc42 and elevates intracellular Cdc42-guanosine triphosphate (GTP) levels in cells with inactive Cdc24, which has as of yet been the sole GDP-GTP exchange factor for Cdc42. Cdc42 is activated in two temporal steps in the G1 phase: the first depends on Bud3, whereas subsequent activation depends on Cdc24. Mutational analyses suggest that biphasic activation of Cdc42 in G1 is necessary for assembly of a proper bud site. Biphasic activation of Cdc42 or Rac GTPases may be a general mechanism for spatial cue-directed cell polarization in eukaryotes.

UNC-6 (netrin) stabilizes oscillatory clustering of the UNC-40 (DCC) receptor to orient polarity

The receptor deleted in colorectal cancer (DCC) directs dynamic polarizing activities in animals toward its extracellular ligand netrin. How DCC polarizes toward netrin is poorly understood. By performing live-cell imaging of the DCC orthologue UNC-40 during anchor cell invasion in Caenorhabditis elegans, we have found that UNC-40 clusters, recruits F-actin effectors, and generates F-actin in the absence of UNC-6 (netrin). Time-lapse analyses revealed that UNC-40 clusters assemble, disassemble, and reform at periodic intervals in different regions of the cell membrane. This oscillatory behavior indicates that UNC-40 clusters through a mechanism involving interlinked positive (formation) and negative (disassembly) feedback. We show that endogenous UNC-6 and ectopically provided UNC-6 orient and stabilize UNC-40 clustering. Furthermore, the UNC-40-binding protein MADD-2 (a TRIM family protein) promotes ligand-independent clustering and robust UNC-40 polarization toward UNC-6. Together, our data suggest that UNC-6 (netrin) directs polarized responses by stabilizing UNC-40 clustering. We propose that ligand-independent UNC-40 clustering provides a robust and adaptable mechanism to polarize toward netrin.

PANET: a GPU-based tool for fast parallel analysis of robustness dynamics and feed-forward/feedback loop structures in large-scale biological networks

It has been a challenge in systems biology to unravel relationships between structural properties and dynamic behaviors of biological networks. A Cytoscape plugin named NetDS was recently proposed to analyze the robustness-related dynamics and feed-forward/feedback loop structures of biological networks. Despite such a useful function, limitations on the network size that can be analyzed exist due to high computational costs. In addition, the plugin cannot verify an intrinsic property which can be induced by an observed result because it has no function to simulate the observation on a large number of random networks. To overcome these limitations, we have developed a novel software tool, PANET. First, the time-consuming parts of NetDS were redesigned to be processed in parallel using the OpenCL library. This approach utilizes the full computing power of multi-core central processing units and graphics processing units. Eventually, this made it possible to investigate a large-scale network such as a human signaling network with 1,609 nodes and 5,063 links. We also developed a new function to perform a batch-mode simulation where it generates a lot of random networks and conducts robustness calculations and feed-forward/feedback loop examinations of them. This helps us to determine if the findings in real biological networks are valid in arbitrary random networks or not. We tested our plugin in two case studies based on two large-scale signaling networks and found interesting results regarding relationships between coherently coupled feed-forward/feedback loops and robustness. In addition, we verified whether or not those findings are consistently conserved in random networks through batch-mode simulations. Taken together, our plugin is expected to effectively investigate various relationships between dynamics and structural properties in large-scale networks. Our software tool, user manual and example datasets are freely available at http://panet-csc.sourceforge.net/.

CDC-42 and RAC-1 regulate opposite chemotropisms in Neurospora crassa

Cell polarization and fusion are crucial developmental processes that occur in response to intracellular and extracellular signals. Asexual spores (conidia) of the mold Neurospora crassa differentiate two types of polarized cell protrusions, germ tubes and conidial anastomosis tubes (CATs), which exhibit negative and positive chemotropism, respectively. We provide the first evidence that shared and separate functions of the Rho-type GTPases CDC-42 and RAC-1 regulate these opposite chemotropisms. We demonstrate that RAC-1 is essential for CAT formation and cell fusion, whereas CDC-42 is necessary and sufficient for normal germ tube development. Cdc42-Rac-interactive-binding (CRIB) reporters were constructed to exclusively label locally activated GTP-bound GTPases. Time course analyses showed that repositioning of these activated GTPase clusters within germ tube and CAT tip apices controls directional growth in the absence of a tip-localized vesicle supply center (Spitzenkörper). We propose a model in which the local assembly of a plasma-membrane-associated GTPase–PAK–MAPK signaling platform regulates chemoattractant perception and secretion in order to synchronize oscillatory cell–cell communication and directional CAT tip growth.

Inhibitory GEF phosphorylation provides negative feedback in the yeast polarity circuit

Cell polarity is critical for the form and function of many cell types. During polarity establishment, cells define a cortical "front" that behaves differently from the rest of the cortex. The front accumulates high levels of the active form of a polarity-determining Rho-family GTPase (Cdc42, Rac, or Rop) that then orients cytoskeletal elements through various effectors to generate the polarized morphology appropriate to the particular cell type [1, 2]. GTPase accumulation is thought to involve positive feedback, such that active GTPase promotes further delivery and/or activation of more GTPase in its vicinity [3]. Recent studies suggest that once a front forms, the concentration of polarity factors at the front can increase and decrease periodically, first clustering the factors at the cortex and then dispersing them back to the cytoplasm [4-7]. Such oscillatory behavior implies the presence of negative feedback in the polarity circuit [8], but the mechanism of negative feedback was not known. Here we show that, in the budding yeast Saccharomyces cerevisiae, the catalytic activity of the Cdc42-directed GEF is inhibited by Cdc42-stimulated effector kinases, thus providing negative feedback. We further show that replacing the GEF with a phosphosite mutant GEF abolishes oscillations and leads to the accumulation of excess GTP-Cdc42 and other polarity factors at the front. These findings reveal a mechanism for negative feedback and suggest that the function of negative feedback via GEF inhibition is to buffer the level of Cdc42 at the polarity site.

Establishment of a robust single axis of cell polarity by coupling multiple positive feedback loops

Establishment of cell polarity—or symmetry breaking—relies on local accumulation of polarity regulators. Although simple positive feedback is sufficient to drive symmetry breaking, it is highly sensitive to stochastic fluctuations typical for living cells. Here, by integrating mathematical modelling with quantitative experimental validations, we show that in the yeast Saccharomyces cerevisiae a combination of actin- and guanine nucleotide dissociation inhibitor-dependent recycling of the central polarity regulator Cdc42 is needed to establish robust cell polarity at a single site during yeast budding. The guanine nucleotide dissociation inhibitor pathway consistently generates a single-polarization site, but requires Cdc42 to cycle rapidly between its active and inactive form, and is therefore sensitive to perturbations of the GTPase cycle. Conversely, actin-mediated recycling of Cdc42 induces robust symmetry breaking but cannot restrict polarization to a single site. Our results demonstrate how cells optimize symmetry breaking through coupling between multiple feedback loops.

A positive feedback loop which results in localized accumulation of the small GTPase Cdc42 generates cell polarity in budding yeast; however, such loops are inherently susceptible to noise. Here the authors demonstrate how two pathways that mediate Cdc42 recycling work together to ensure the robustness of symmetry breaking.