Tracking shallow chemical gradients by actin-driven wandering of the polarization site

Cdc42 mobility and membrane flows regulate fission yeast cell shape and survival

Polarized exocytosis induced by local Cdc42 GTPase activity results in membrane flows that deplete low-mobility membrane-associated proteins. A reaction-diffusion particle model comprising Cdc42 positive feedback activation, hydrolysis by GTPase-activating proteins (GAPs), and flow-induced displacement by exo/endocytosis shows that flow-induced depletion of low mobility GAPs promotes polarization. We modified Cdc42 mobility in Schizosaccharomyces pombe by replacing its prenylation site with 1, 2 or 3 repeats of the Rit C-terminal membrane-binding domain (ritC), yielding alleles with progressively lower mobility and increased flow-coupling. While Cdc42-1ritC cells are viable and polarized, Cdc42-2ritC polarize poorly and Cdc42-3ritC are inviable, in agreement with model's predictions. Deletion of Cdc42 GAPs restores viability to Cdc42-3ritC cells, verifying the model's prediction that GAP deletion increases Cdc42 activity at the expense of polarization. Our work demonstrates how membrane flows are an integral part of Cdc42-driven pattern formation and require Cdc42-GTP to turn over faster than the surface on which it forms.

Multiscale Modeling of Bistability in the Yeast Polarity Circuit

Cell polarity refers to the asymmetric distribution of proteins and other molecules along a specified axis within a cell. Polarity establishment is the first step in many cellular processes. For example, directed growth or migration requires the formation of a cell front and back. In many cases, polarity occurs in the absence of spatial cues. That is, the cell undergoes symmetry breaking. Understanding the molecular mechanisms that allow cells to break symmetry and polarize requires computational models that span multiple spatial and temporal scales. Here, we apply a multiscale modeling approach to examine the polarity circuit of yeast. In addition to symmetry breaking, experiments revealed two key features of the yeast polarity circuit: bistability and rapid dismantling of the polarity site following a loss of signal. We used modeling based on ordinary differential equations (ODEs) to investigate mechanisms that generate these behaviors. Our analysis revealed that a model involving positive and negative feedback acting on different time scales captured both features. We then extend our ODE model into a coarse-grained reaction-diffusion equation (RDE) model to capture the spatial profiles of polarity factors. After establishing that the coarse-grained RDE model qualitatively captures key features of the polarity circuit, we expand it to more accurately capture the biochemical reactions involved in the system. We convert the expanded model to a particle-based model that resolves individual molecules and captures fluctuations that arise from the stochastic nature of biochemical reactions. Our models assume that negative regulation results from negative feedback. However, experimental observations do not rule out the possibility that negative regulation occurs through an incoherent feedforward loop. Therefore, we conclude by using our RDE model to suggest how negative feedback might be distinguished from incoherent feedforward regulation.

The roles of yeast formins and their regulators Bud6 and Bil2 in the pheromone response

In response to pheromone Saccharomyces cerevisiae extend a mating projection. This process depends on the formation of polarized actin cables which direct secretion to the mating tip and translocate the nucleus for karyogamy. Here, we demonstrate that proper mating projection formation requires the formin Bni1, as well as the actin nucleation promoting activities of Bud6, but not the formin Bnr1. Further, Bni1 is required for pheromone gradient tracking. Our work also reveals unexpected new functions for Bil2 in the pheromone response. Previously we identified Bil2 as a direct inhibitor of Bnr1 during vegetative cell growth. Here, we show that Bil2 has Bnr1-independent functions in spatially focusing Bni1-GFP at mating projection tips, and in vitro Bil2 and its binding partner Bud6 organize Bni1 into clusters that nucleate actin assembly. bil2∆ cells also display entangled Bni1-generated actin cable arrays and defects in secretory vesicle transport and nuclear positioning. At low pheromone concentrations, bil2∆ cells are delayed in establishing a polarity axis, and at high concentrations they prematurely form a second and a third mating projection. Together, these results suggest that Bil2 promotes the proper formation and timing of mating projections by organizing Bni1 and maintaining a persistent axis of polarized growth.

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.

Cytosolic concentrations of actin binding proteins and the implications for in vivo F-actin turnover

Understanding how numerous actin-binding proteins (ABPs) work in concert to control the assembly, organization, and turnover of the actin cytoskeleton requires quantitative information about the levels of each component. Here, we measured the cellular concentrations of actin and the majority of the conserved ABPs in Saccharomyces cerevisiae, as well as the free (cytosolic) fractions of each ABP. The cellular concentration of actin is estimated to be 13.2 µM, with approximately two-thirds in the F-actin form and one-third in the G-actin form. Cellular concentrations of ABPs range from 12.4 to 0.85 µM (Tpm1> Pfy1> Cof1> Abp1> Srv2> Abp140> Tpm2> Aip1> Cap1/2> Crn1> Sac6> Twf1> Arp2/3> Scp1). The cytosolic fractions of all ABPs are unexpectedly high (0.6-0.9) and remain so throughout the cell cycle. Based on these numbers, we speculate that F-actin binding sites are limited in vivo, which leads to high cytosolic levels of ABPs, and in turn helps drive the rapid assembly and turnover of cellular F-actin structures.

Particle-based simulations reveal two positive feedback loops allow relocation and stabilization of the polarity site during yeast mating

Many cells adjust the direction of polarized growth or migration in response to external directional cues. The yeast Saccharomyces cerevisiae orient their cell fronts (also called polarity sites) up pheromone gradients in the course of mating. However, the initial polarity site is often not oriented towards the eventual mating partner, and cells relocate the polarity site in an indecisive manner before developing a stable orientation. During this reorientation phase, the polarity site displays erratic assembly-disassembly behavior and moves around the cell cortex. The mechanisms underlying this dynamic behavior remain poorly understood. Particle-based simulations of the core polarity circuit revealed that molecular-level fluctuations are unlikely to overcome the strong positive feedback required for polarization and generate relocating polarity sites. Surprisingly, inclusion of a second pathway that promotes polarity site orientation generated relocating polarity sites with properties similar to those observed experimentally. This pathway forms a second positive feedback loop involving the recruitment of receptors to the cell membrane and couples polarity establishment to gradient sensing. This second positive feedback loop also allows cells to stabilize their polarity site once the site is aligned with the pheromone gradient.

Cdc42 mobility and membrane flows regulate fission yeast cell shape and survival

Local Cdc42 GTPase activation promotes polarized exocytosis, resulting in membrane flows that deplete low-mobility membrane-associated proteins from the growth region. To investigate the self-organizing properties of the Cdc42 secretion-polarization system under membrane flow, we developed a reaction-diffusion particle model. The model includes positive feedback activation of Cdc42, hydrolysis by GTPase-activating proteins (GAPs), and flow-induced displacement by exo/endocytosis. Simulations show how polarization relies on flow-induced depletion of low mobility GAPs. To probe the role of Cdc42 mobility in the fission yeast Schizosaccharomyces pombe, we changed its membrane binding properties by replacing its prenylation site with 1, 2 or 3 repeats of the Rit1 C terminal membrane binding domain (ritC), yielding alleles with progressively lower unbinding and diffusion rates. Concordant modelling predictions and experimental observations show that lower Cdc42 mobility results in lower Cdc42 activation level and wider patches. Indeed, while Cdc42-1ritC cells are viable and polarized, Cdc42-2ritC polarize poorly and Cdc42-3ritC is inviable. The model further predicts that GAP depletion increases Cdc42 activity at the expense of loss of polarization. Experiments confirm this prediction, as deletion of Cdc42 GAPs restores viability to Cdc42-3ritC cells. Our combined experimental and modelling studies demonstrate how membrane flows are an integral part of Cdc42-driven pattern formation.

Cell wall dynamics stabilize tip growth in a filamentous fungus

Hyphal tip growth allows filamentous fungi to colonize space, reproduce, or infect. It features remarkable morphogenetic plasticity including unusually fast elongation rates, tip turning, branching, or bulging. These shape changes are all driven from the expansion of a protective cell wall (CW) secreted from apical pools of exocytic vesicles. How CW secretion, remodeling, and deformation are modulated in concert to support rapid tip growth and morphogenesis while ensuring surface integrity remains poorly understood. We implemented subresolution imaging to map the dynamics of CW thickness and secretory vesicles in Aspergillus nidulans. We found that tip growth is associated with balanced rates of CW secretion and expansion, which limit temporal fluctuations in CW thickness, elongation speed, and vesicle amount, to less than 10% to 20%. Affecting this balance through modulations of growth or trafficking yield to near-immediate changes in CW thickness, mechanics, and shape. We developed a model with mechanical feedback that accounts for steady states of hyphal growth as well as rapid adaptation of CW mechanics and vesicle recruitment to different perturbations. These data provide unprecedented details on how CW dynamics emerges from material secretion and expansion, to stabilize fungal tip growth as well as promote its morphogenetic plasticity.

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.

Polarization and cell-fate decision facilitated by the adaptor Ste50p in Saccharomyces cerevisiae

In response to pheromone, many proteins localize on the plasma membrane of yeast cell to reform it into a polarized shmoo structure. The adaptor protein Ste50p, known as a pheromone signal enhancer critical for shmoo polarization, has never been explored systematically for its localization and function in the polarization process. Time-lapse single-cell imaging and quantitation shown here characterizes Ste50p involvement in the establishment of cell polarity. We found that Ste50p patches on the cell cortex mark the point of shmoo initiation, these patches could move, and remain associated with the growing shmoo tip in a pheromone concentration time-dependent manner until shmoo maturation. A Ste50p mutant impaired in patch localization suffers a delay in polarization. By quantitative analysis we show that polarization correlates with the rising levels of Ste50p, enabling rapid cell responses to pheromone that correspond to a critical level of Ste50p at the initial G1 phase. We exploited the quantitative differences in the pattern of Ste50p expression to correlate with the cell-cell phenotypic heterogeneity, showing Ste50p involvement in the cellular differentiation choice. Taken together, these findings present Ste50p to be part of the early shmoo development phase, suggesting that Ste50p may be involved with the polarisome in the initiation of polarization, and plays a role in regulating the polarized growth of shmoo during pheromone response.

Phosphorylation of RGS regulates MAP kinase localization and promotes completion of cytokinesis

Phosphorylation of the RGS Sst2 alters its subcellular distribution, MAPK localization, and interaction with Kel1, which promotes coordination of polarized growth with completion of cytokinesis.

Yeast use the G-protein–coupled receptor signaling pathway to detect and track the mating pheromone. The G-protein–coupled receptor pathway is inhibited by the regulator of G-protein signaling (RGS) Sst2 which induces Gα GTPase activity and inactivation of downstream signaling. G-protein signaling activates the MAPK Fus3, which phosphorylates the RGS; however, the role of this modification is unknown. We found that pheromone-induced RGS phosphorylation peaks early; the phospho-state of RGS controls its localization and influences MAPK spatial distribution. Surprisingly, phosphorylation of the RGS promotes completion of cytokinesis before pheromone-induced growth. Completion of cytokinesis in the presence of pheromone is promoted by the kelch-repeat protein, Kel1 and antagonized by the formin Bni1. We found that RGS complexes with Kel1 and prefers the unphosphorylatable RGS mutant. We also found overexpression of unphosphorylatable RGS exacerbates cytokinetic defects, whereas they are rescued by overexpression of Kel1. These data lead us to a model where Kel1 promotes completion of cytokinesis before pheromone-induced polarity but is inhibited by unphosphorylated RGS binding.

Gradient tracking in mating yeast depends on Bud1 inactivation and actin-independent vesicle delivery

The mating of budding yeast depends on chemotropism, a fundamental cellular process. Haploid yeast cells of opposite mating type signal their positions to one another through mating pheromones. We have proposed a deterministic gradient sensing model that explains how these cells orient toward their mating partners. Using the cell-cycle determined default polarity site (DS), cells assemble a gradient tracking machine (GTM) composed of signaling, polarity, and trafficking proteins. After assembly, the GTM redistributes up the gradient, aligns with the pheromone source, and triggers polarized growth toward the partner. Since positive feedback mechanisms drive polarized growth at the DS, it is unclear how the GTM is released for tracking. What prevents the GTM from triggering polarized growth at the DS? Here, we describe two mechanisms that are essential for tracking: inactivation of the Ras GTPase Bud1 and positioning of actin-independent vesicle delivery upgradient.

Mechanism of commitment to a mating partner in Saccharomyces cerevisiae

Many cells detect and follow gradients of chemical signals to perform their functions. Yeast cells use gradients of extracellular pheromones to locate mating partners, providing a tractable model to understand how cells decode the spatial information in gradients. To mate, yeast cells must orient polarity toward the mating partner. Polarity sites are mobile, exploring the cell cortex until they reach the proper position, where they stop moving and "commit" to the partner. A simple model to explain commitment posits that a high concentration of pheromone is only detected upon alignment of partner cells' polarity sites, and causes polarity site movement to stop. Here we explore how yeast cells respond to partners that make different amounts of pheromone. Commitment was surprisingly robust to varying pheromone levels, ruling out the simple model. We also tested whether adaptive pathways were responsible for the robustness of commitment, but our results show that cells lacking those pathways were still able to accommodate changes in pheromone. To explain this robustness, we suggest that the steep pheromone gradients near each mating partner's polarity site trap the polarity site in place.

Chemophoresis engine: A general mechanism of ATPase-driven cargo transport

Cell polarity regulates the orientation of the cytoskeleton members that directs intracellular transport for cargo-like organelles, using chemical gradients sustained by ATP or GTP hydrolysis. However, how cargo transports are directly mediated by chemical gradients remains unknown. We previously proposed a physical mechanism that enables directed movement of cargos, referred to as chemophoresis. According to the mechanism, a cargo with reaction sites is subjected to a chemophoresis force in the direction of the increased concentration. Based on this, we introduce an extended model, the chemophoresis engine, as a general mechanism of cargo motion, which transforms chemical free energy into directed motion through the catalytic ATP hydrolysis. We applied the engine to plasmid motion in a ParABS system to demonstrate the self-organization system for directed plasmid movement and pattern dynamics of ParA-ATP concentration, thereby explaining plasmid equi-positioning and pole-to-pole oscillation observed in bacterial cells and in vitro experiments. We mathematically show the existence and stability of the plasmid-surfing pattern, which allows the cargo-directed motion through the symmetry-breaking transition of the ParA-ATP spatiotemporal pattern. We also quantitatively demonstrate that the chemophoresis engine can work even under in vivo conditions. Finally, we discuss the chemophoresis engine as one of the general mechanisms of hydrolysis-driven intracellular transport.

The formation of organelle/macromolecule patterns depending on chemical concentration under non-equilibrium conditions, first observed during macroscopic morphogenesis, has recently been observed at the intracellular level as well, and its relevance as intracellular morphogen has been demonstrated in the case of bacterial cell division. These studies have discussed how cargos maintain positional information provided by chemical concentration gradients/localization. However, how cargo transports are directly mediated by chemical gradients remains unknown. Based on the previously proposed mechanism of chemotaxis-like behavior of cargos (referred to as chemophoresis), we introduce a chemophoresis engine as a physicochemical mechanism of cargo motion, which transforms chemical free energy to directed motion. The engine is based on the chemophoresis force to make cargoes move in the direction of the increasing ATPase(-ATP) concentration and an enhanced catalytic ATPase hydrolysis at the positions of the cargoes. Applying the engine to ATPase-driven movement of plasmid-DNAs in bacterial cells, we constructed a mathematical model to demonstrate the self-organization for directed plasmid motion and pattern dynamics of ATPase concentration, as is consistent with in vitro and in vivo experiments. We propose that this chemophoresis engine works as a general mechanism of hydrolysis-driven intracellular transport.

Empowering the Voiceless: Securing the Participation of Marginalised Groups in Climate Change Governance in South Africa

For many of the world’s poor people, adaptation to climate change is not a choice but a reality. Existing evidence suggests that the poor, particularly those in the developing world, are the most vulnerable to any changes in climate variability and change. Using research methods inspired by the tradition of participatory research, we explore and discuss community perceptions on climate change adaptation governance in South Africa. We examine the myriad ways in which climate change adaptation policies and strategies are developed, and we systematically discuss the factors which either facilitate or hamper the involvement of all stakeholders in the development of these intervention measures. Our findings indicate that women seem to be the group of people who are mostly unaware of community initiatives, policies, and strategies for the adaptation to climate change. Thus, it is argued that, although South Africa has developed good climate change initiatives, policies, and strategies, the implementation of these policies seems to present difficulties, as those for whom they have been developed do not seem to have any knowledge of their effectiveness in helping them build resilience against extreme weather events. This study recommends that, in order to achieve successful public participation in climate change adaptation policy development, there must be an all-inclusive system which incorporates all stakeholders, including vulnerable groups.

Pheromone Guidance of Polarity Site Movement in Yeast

Cells' ability to track chemical gradients is integral to many biological phenomena, including fertilization, development, accessing nutrients, and combating infection. Mating of the yeast Saccharomyces cerevisiae provides a tractable model to understand how cells interpret the spatial information in chemical gradients. Mating yeast of the two different mating types secrete distinct peptide pheromones, called a-factor and α-factor, to communicate with potential partners. Spatial gradients of pheromones are decoded to guide mobile polarity sites so that polarity sites in mating partners align towards each other, as a prerequisite for cell-cell fusion and zygote formation. In ascomycetes including S. cerevisiae, one pheromone is prenylated (a-factor) while the other is not (α-factor). The difference in physical properties between the pheromones, combined with associated differences in mechanisms of secretion and extracellular pheromone metabolism, suggested that the pheromones might differ in the spatial information that they convey to potential mating partners. However, as mating appears to be isogamous in this species, it is not clear why any such signaling difference would be advantageous. Here we report assays that directly track movement of the polarity site in each partner as a way to understand the spatial information conveyed by each pheromone. Our findings suggest that both pheromones convey very similar information. We speculate that the different pheromones were advantageous in ancestral species with asymmetric mating systems and may represent an evolutionary vestige in yeasts that mate isogamously.

Chemotropism and Cell-Cell Fusion in Fungi

Fungi exhibit an enormous variety of morphologies, including yeast colonies, hyphal mycelia, and elaborate fruiting bodies. This diversity arises through a combination of polar growth, cell division, and cell fusion. Because fungal cells are nonmotile and surrounded by a protective cell wall that is essential for cell integrity, potential fusion partners must grow toward each other until they touch and then degrade the intervening cell walls without impacting cell integrity. Here, we review recent progress on understanding how fungi overcome these challenges. Extracellular chemoattractants, including small peptide pheromones, mediate communication between potential fusion partners, promoting the local activation of core cell polarity regulators to orient polar growth and cell wall degradation. However, in crowded environments, pheromone gradients can be complex and potentially confusing, raising the question of how cells can effectively find their partners. Recent findings suggest that the cell polarity circuit exhibits searching behavior that can respond to pheromone cues through a remarkably flexible and effective strategy called exploratory polarization.

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.

A novel stochastic simulation approach enables exploration of mechanisms for regulating polarity site movement

Cells polarize their movement or growth toward external directional cues in many different contexts. For example, budding yeast cells grow toward potential mating partners in response to pheromone gradients. Directed growth is controlled by polarity factors that assemble into clusters at the cell membrane. The clusters assemble, disassemble, and move between different regions of the membrane before eventually forming a stable polarity site directed toward the pheromone source. Pathways that regulate clustering have been identified but the molecular mechanisms that regulate cluster mobility are not well understood. To gain insight into the contribution of chemical noise to cluster behavior we simulated clustering using the reaction-diffusion master equation (RDME) framework to account for molecular-level fluctuations. RDME simulations are a computationally efficient approximation, but their results can diverge from the underlying microscopic dynamics. We implemented novel concentration-dependent rate constants that improved the accuracy of RDME-based simulations, allowing us to efficiently investigate how cluster dynamics might be regulated. Molecular noise was effective in relocating clusters when the clusters contained low numbers of limiting polarity factors, and when Cdc42, the central polarity regulator, exhibited short dwell times at the polarity site. Cluster stabilization occurred when abundances or binding rates were altered to either lengthen dwell times or increase the number of polarity molecules in the cluster. We validated key results using full 3D particle-based simulations. Understanding the mechanisms cells use to regulate the dynamics of polarity clusters should provide insights into how cells dynamically track external directional cues.

Cells localize polarity molecules in a small region of the plasma membrane forming a polarity cluster that directs functions such as migration, reproduction, and growth. Guided by external signals, these clusters move across the membrane allowing cells to reorient growth or motion. The polarity molecules continuously and randomly shuttle between the cluster and the cell cytosol and, as a result, the number and distribution of molecules at the cluster constantly changes. Here we present an improved stochastic simulation algorithm to investigate how such molecular-scale fluctuations induce cluster movement across the cell membrane. Unexpectedly, cluster mobility does not correlate with variations in total molecule abundance within the cluster, but rather with changes in the spatial distribution of molecules that form the cluster. Cluster motion is faster when polarity molecules are scarce and when they shuttle rapidly between the cluster and the cytosol. Our results suggest that cells control cluster mobility by regulating the abundance of polarity molecules and biochemical reactions that affect the time molecules spend at the cluster. We provide insights into how cells harness random molecular behavior to perform functions important for survival, such as detecting the direction of external signals.

Chemotactic movement of a polarity site enables yeast cells to find their mates

How small eukaryotic cells can interpret dynamic, noisy, and spatially complex chemical gradients to orient growth or movement is poorly understood. We address this question using Saccharomyces cerevisiae, where cells orient polarity up pheromone gradients during mating. Initial orientation is often incorrect, but polarity sites then move around the cortex in a search for partners. We find that this movement is biased by local pheromone gradients across the polarity site: that is, movement of the polarity site is chemotactic. A bottom-up computational model recapitulates this biased movement. The model reveals how even though pheromone-bound receptors do not mimic the shape of external pheromone gradients, nonlinear and stochastic effects combine to generate effective gradient tracking. This mechanism for gradient tracking may be applicable to any cell that searches for a target in a complex chemical landscape.

Phosphorylated Gβ is a directional cue during yeast gradient tracking

Budding yeast cells interpret shallow pheromone gradients from cells of the opposite mating type, polarize their growth toward the pheromone source, and fuse at the chemotropic growth site. We previously proposed a deterministic, gradient-sensing model that explains how yeast cells switch from the intrinsically positioned default polarity site (DS) to the gradient-aligned chemotropic site (CS) at the plasma membrane. Because phosphorylation of the mating-specific Gβ subunit is thought to be important for this process, we developed a biosensor that bound to phosphorylated but not unphosphorylated Gβ and monitored its spatiotemporal dynamics to test key predictions of our gradient-sensing model. In mating cells, the biosensor colocalized with both Gβ and receptor reporters at the DS and then tracked with them to the CS. The biosensor concentrated on the leading side of the tracking Gβ and receptor peaks and was the first to arrive and stop tracking at the CS. Our data showed that the concentrated localization of phosphorylated Gβ correlated with the tracking direction and final position of the G protein and receptor, consistent with the idea that gradient-regulated phosphorylation and dephosphorylation of Gβ contributes to gradient sensing. Cells expressing a nonphosphorylatable mutant form of Gβ exhibited defects in gradient tracking, orientation toward mating partners, and mating efficiency.

Exploratory polarization facilitates mating partner selection in Saccharomyces cerevisiae

Yeast decode pheromone gradients to locate mating partners, providing a model for chemotropism. How yeast polarize toward a single partner in crowded environments is unclear. Initially, cells often polarize in unproductive directions, but then they relocate the polarity site until two partners’ polarity sites align, whereupon the cells “commit” to each other by stabilizing polarity to promote fusion. Here we address the role of the early mobile polarity sites. We found that commitment by either partner failed if just one partner was defective in generating, orienting, or stabilizing its mobile polarity sites. Mobile polarity sites were enriched for pheromone receptors and G proteins, and we suggest that such sites engage in an exploratory search of the local pheromone landscape, stabilizing only when they detect elevated pheromone levels. Mobile polarity sites were also enriched for pheromone secretion factors, and simulations suggest that only focal secretion at polarity sites would produce high pheromone concentrations at the partner’s polarity site, triggering commitment.

Cell polarisation in a bulk-surface model can be driven by both classic and non-classic Turing instability

The GTPase Cdc42 is the master regulator of eukaryotic cell polarisation. During this process, the active form of Cdc42 is accumulated at a particular site on the cell membrane called the pole. It is believed that the accumulation of the active Cdc42 resulting in a pole is driven by a combination of activation–inactivation reactions and diffusion. It has been proposed using mathematical modelling that this is the result of diffusion-driven instability, originally proposed by Alan Turing. In this study, we developed, analysed and validated a 3D bulk-surface model of the dynamics of Cdc42. We show that the model can undergo both classic and non-classic Turing instability by deriving necessary conditions for which this occurs and conclude that the non-classic case can be viewed as a limit case of the classic case of diffusion-driven instability. Using three-dimensional Spatio-temporal simulation we predicted pole size and time to polarisation, suggesting that cell polarisation is mainly driven by the reaction strength parameter and that the size of the pole is determined by the relative diffusion.

Mechanisms that ensure monogamous mating in Saccharomyces cerevisiae

Haploid cells of the budding yeast Saccharomyces cerevisiae communicate using secreted pheromones and mate to form diploid zygotes. Mating is monogamous, resulting in the fusion of precisely one cell of each mating type. Monogamous mating in crowded conditions, where cells have access to more than one potential partner, raises the question of how multiple-mating outcomes are prevented. Here we identify mutants capable of mating with multiple partners, revealing the mechanisms that ensure monogamous mating. Before fusion, cells develop polarity foci oriented toward potential partners. Competition between these polarity foci within each cell leads to disassembly of all but one focus, thus favoring a single fusion event. Fusion promotes the formation of heterodimeric complexes between subunits that are uniquely expressed in each mating type. One complex shuts off haploid-specific gene expression, and the other shuts off the ability to respond to pheromone. Zygotes able to form either complex remain monogamous, but zygotes lacking both can re-mate.

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.

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.

GPCR receptor phosphorylation and endocytosis are not necessary to switch polarized growth between internal cues during pheromone response in S. cerevisiae

Chemotactic/chemotropic cells follow accurately the direction of gradients of regulatory molecules. Many G-protein-coupled receptors (GPCR) function as chemoattractant receptors to guide polarized responses. In "a" mating type yeast, the GPCR Ste2 senses the α-cell's pheromone. Previously, phosphorylation and trafficking of this receptor have been implicated in the process of gradient sensing, where cells dynamically correct growth. Correction is often necessary since yeast have intrinsic polarity sites that interfere with a correct initial gradient decoding. We have recently showed that when actively dividing (not in G1) yeast are exposed to a uniform pheromone concentration, they initiate a pheromone-induced polarization next to the mother-daughter cytokinesis site. Then, they reorient their growth to the intrinsic polarity site. Here, to study if Ste2 phosphorylation and internalization are involved in this process, we generated receptor variants combining three types of mutated signals for the first time: phosphorylation, ubiquitylation and the NPFX1,2D Sla1-binding motif. We first characterized their effect on endocytosis and found that these processes regulate internalization in a more complex manner than previously shown. Interestingly, we showed that receptor phosphorylation can drive internalization independently of ubiquitylation and the NPFX1,2D motif. When tested in our assays, cells expressing either phosphorylation or endocytosis-deficient receptors were able to switch away from the cytokinesis site to find the intrinsic polarity site as efficiently as their WT counterparts. Thus, we conclude that these processes are not necessary for the reorientation of polarization.

Fission Yeast Polarization: Modeling Cdc42 Oscillations, Symmetry Breaking, and Zones of Activation and Inhibition

Cells polarize for growth, motion, or mating through regulation of membrane-bound small GTPases between active GTP-bound and inactive GDP-bound forms. Activators (GEFs, GTP exchange factors) and inhibitors (GAPs, GTPase activating proteins) provide positive and negative feedbacks. We show that a reaction-diffusion model on a curved surface accounts for key features of polarization of model organism fission yeast. The model implements Cdc42 membrane diffusion using measured values for diffusion coefficients and dissociation rates and assumes a limiting GEF pool (proteins Gef1 and Scd1), as in prior models for budding yeast. The model includes two types of GAPs, one representing tip-localized GAPs, such as Rga3; and one representing side-localized GAPs, such as Rga4 and Rga6, that we assume switch between fast and slow diffusing states. After adjustment of unknown rate constants, the model reproduces active Cdc42 zones at cell tips and the pattern of GEF and GAP localization at cell tips and sides. The model reproduces observed tip-to-tip oscillations with periods of the order of several minutes, as well as asymmetric to symmetric oscillations transitions (corresponding to NETO "new end take off"), assuming the limiting GEF amount increases with cell size.

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.

Regulation of intrinsic polarity establishment by a differentiation-type MAPK pathway in S. cerevisiae

All cells establish and maintain an axis of polarity that is critical for cell shape and progression through the cell cycle. A well-studied example of polarity establishment is bud emergence in the yeast Saccharomyces cerevisiae, which is controlled by the Rho GTPase Cdc42p. The prevailing view of bud emergence does not account for regulation by extrinsic cues. Here, we show that the filamentous growth mitogen activated protein kinase (fMAPK) pathway regulates bud emergence under nutrient-limiting conditions. The fMAPK pathway regulated the expression of polarity targets including the gene encoding a direct effector of Cdc42p, Gic2p. The fMAPK pathway also stimulated GTP-Cdc42p levels, which is a critical determinant of polarity establishment. The fMAPK pathway activity was spatially restricted to bud sites and active during the period of the cell cycle leading up to bud emergence. Time-lapse fluorescence microscopy showed that the fMAPK pathway stimulated the rate of bud emergence during filamentous growth. Unregulated activation of the fMAPK pathway induced multiple rounds of symmetry breaking inside the growing bud. Collectively, our findings identify a new regulatory aspect of bud emergence that sensitizes this essential cellular process to external cues.

The ESCRT System Plays an Important Role in the Germination in Candida albicans by Regulating the Expression of Hyphal-Specific Genes and the Localization of Polarity-Related Proteins

Candida albicans is an important opportunistic fungal pathogen, and its pathogenicity is closely related to its ability to form hyphae. ESCRT system was initially discovered as a membrane-budding machinery involved in the formation of multivesicular bodies. More recently, the role of ESCRT is vastly expanded. Early reports showed that the ESCRT system is involved in inducing hyphae under neutral-alkaline environment via the Rim101 pathway. We previously found that in the environment that contains serum, one ESCRT protein, Vps4, is essential for polarity maintenance during hyphal formation, as its deletion causes the formation of multiple hyphae. In this study, we found that Vps4 is also essential for the proper localization of Cdc42 and Cdc3, which may be related to its role in polarity maintenance. We also discovered that deletions of the ESCRT proteins significantly delay germination and cause downregulation of hyphal-specific genes, most prominent of which is HGC1. Since Hgc1 is essential for many aspects of hyphal growth, its downregulation could explain our observed phenotypes. Our further studies show that ESCRT proteins are involved in the dynamics of Ras1. Deletions of VPS4 or SNF7 significantly decrease the recovery rate of GFP-Ras1 in the fluorescence recovery after photobleaching experiment. The decreased Ras1 dynamics may disrupt the signaling pathway and lead to downregulation of hyphal-specific genes. Therefore, in this study we discovered a novel and Rim101 independent mechanism used by the ESCRT system to regulate hyphal induction and polarity maintenance, which could provide insights on the pathogenicity mechanism of Candia albicans.

Mitotic and pheromone-specific intrinsic polarization cues interfere with gradient sensing in Saccharomyces cerevisiae

Polarity decisions are central to many processes, including mitosis and chemotropism. In Saccharomyces cerevisiae, budding and mating projection (MP) formation use an overlapping system of cortical landmarks that converges on the small G protein Cdc42. However, pheromone-gradient sensing must override the Rsr1-dependent internal polarity cues used for budding. Using this model system, we asked what happens when intrinsic and extrinsic spatial cues are not aligned. Is there competition, or collaboration? By live-cell microscopy and microfluidics techniques, we uncovered three previously overlooked features of this signaling system. First, the cytokinesis-associated polarization patch serves as a polarity landmark independently of all known cues. Second, the Rax1-Rax2 complex functions as a pheromone-promoted polarity cue in the distal pole of the cells. Third, internal cues remain active during pheromone-gradient tracking and can interfere with this process, biasing the location of MPs. Yeast defective in internal-cue utilization align significantly better than wild type with artificially generated pheromone gradients.

Ratiometric GPCR signaling enables directional sensing in yeast

Accurate detection of extracellular chemical gradients is essential for many cellular behaviors. Gradient sensing is challenging for small cells, which can experience little difference in ligand concentrations on the up-gradient and down-gradient sides of the cell. Nevertheless, the tiny cells of the yeast Saccharomyces cerevisiae reliably decode gradients of extracellular pheromones to find their mates. By imaging the behavior of polarity factors and pheromone receptors, we quantified the accuracy of initial polarization during mating encounters. We found that cells bias the orientation of initial polarity up-gradient, even though they have unevenly distributed receptors. Uneven receptor density means that the gradient of ligand-bound receptors does not accurately reflect the external pheromone gradient. Nevertheless, yeast cells appear to avoid being misled by responding to the fraction of occupied receptors rather than simply the concentration of ligand-bound receptors. Such ratiometric sensing also serves to amplify the gradient of active G protein. However, this process is quite error-prone, and initial errors are corrected during a subsequent indecisive phase in which polarity clusters exhibit erratic mobile behavior.

Cells use surface receptors to decode spatial information from chemical gradients, but accurate decoding is hampered by small cell size and the presence of molecular noise. This study shows that yeast cells decode pheromone gradients by measuring the local ratio of bound to unbound receptors. This mechanism corrects for uneven receptor density at the surface and amplifies the gradient transmitted to downstream components.

Mating yeast cells use an intrinsic polarity site to assemble a pheromone-gradient tracking machine

The mating of budding yeast depends on chemotropism, a fundamental cellular process. The two yeast mating types secrete peptide pheromones that bind to GPCRs on cells of the opposite type. Cells find and contact a partner by determining the direction of the pheromone source and polarizing their growth toward it. Actin-directed secretion to the chemotropic growth site (CS) generates a mating projection. When pheromone-stimulated cells are unable to sense a gradient, they form mating projections where they would have budded in the next cell cycle, at a position called the default polarity site (DS). Numerous models have been proposed to explain yeast gradient sensing, but none address how cells reliably switch from the intrinsically determined DS to the gradient-aligned CS, despite a weak spatial signal. Here we demonstrate that, in mating cells, the initially uniform receptor and G protein first polarize to the DS, then redistribute along the plasma membrane until they reach the CS. Our data indicate that signaling, polarity, and trafficking proteins localize to the DS during assembly of what we call the gradient tracking machine (GTM). Differential activation of the receptor triggers feedback mechanisms that bias exocytosis upgradient and endocytosis downgradient, thus enabling redistribution of the GTM toward the pheromone source. The GTM stabilizes when the receptor peak centers at the CS and the endocytic machinery surrounds it. A computational model simulates GTM tracking and stabilization and correctly predicts that its assembly at a single site contributes to mating fidelity.

Systematic analysis of F-box proteins reveals a new branch of the yeast mating pathway

The mating pathway in yeast Saccharomyces cerevisiae has long been used to reveal new mechanisms of signal transduction. The pathway comprises a pheromone receptor, a heterotrimeric G protein, and intracellular effectors of morphogenesis and transcription. Polarized cell growth, in the direction of a potential mating partner, is accomplished by the G-protein βγ subunits and the small G-protein Cdc42. Transcription induction, needed for cell-cell fusion, is mediated by Gβγ and the mitogen-activated protein kinase (MAPK) scaffold protein Ste5. A potential third pathway is initiated by the G-protein α subunit Gpa1. Gpa1 signaling was shown previously to involve the F-box adaptor protein Dia2 and an endosomal effector protein, the phosphatidylinositol 3-kinase Vps34. Vps34 is also required for proper vacuolar sorting and autophagy. Here, using a panel of reporter assays, we demonstrate that mating pheromone stimulates vacuolar targeting of a cytoplasmic reporter protein and that this process depends on Vps34. Through a systematic analysis of F-box deletion mutants, we show that Dia2 is required to sustain pheromone-induced vacuolar targeting. We also found that other F-box proteins selectively regulate morphogenesis (Ydr306, renamed Pfu1) and transcription (Ucc1). These findings point to the existence of a new and distinct branch of the pheromone-signaling pathway, one that likely leads to vacuolar engulfment of cytoplasmic proteins and recycling of cellular contents in preparation for mating.

Quantitative analysis of the yeast pheromone pathway

The pheromone response pathway of the yeast Saccharomyces cerevisiae is a well-established model for the study of G proteins and mitogen-activated protein kinase (MAPK) cascades. Our longstanding ability to combine sophisticated genetic approaches with established functional assays has provided a thorough understanding of signalling mechanisms and regulation. In this report, we compare new and established methods used to quantify pheromone-dependent MAPK phosphorylation, transcriptional induction, mating morphogenesis, and gradient tracking. These include both single-cell and population-based assays of activity. We describe several technical advances, provide example data for benchmark mutants, highlight important differences between newer and established methodologies, and compare the advantages and disadvantages of each as applied to the yeast model. Quantitative measurements of pathway activity have been used to develop mathematical models and reveal new regulatory mechanisms in yeast. It is our expectation that experimental and computational approaches developed in yeast may eventually be adapted to human systems biology and pharmacology.

Molecular mechanisms of chemotropism and cell fusion in unicellular fungi

In all eukaryotic phyla, cell fusion is important for many aspects of life, from sexual reproduction to tissue formation. Fungal cells fuse during mating to form the zygote, and during vegetative growth to connect mycelia. Prior to fusion, cells first detect gradients of pheromonal chemoattractants that are released by their partner and polarize growth in their direction. Upon pairing, cells digest their cell wall at the site of contact and merge their plasma membrane. In this Review, I discuss recent work on the chemotropic response of the yeast models Saccharomyces cerevisiae and Schizosaccharomyces pombe, which has led to a novel model of gradient sensing: the cell builds a motile cortical polarized patch, which acts as site of communication where pheromones are released and sensed. Initial patch dynamics serve to correct its position and align it with the gradient from the partner cell. Furthermore, I highlight the transition from cell wall expansion during growth to cell wall digestion, which is imposed by physical and signaling changes owing to hyperpolarization that is induced by cell proximity. To conclude, I discuss mechanisms of membrane fusion, whose characterization remains a major challenge for the future.

Cell fusion in yeast is negatively regulated by components of the cell wall integrity pathway

During mating, Saccharomyces cerevisiae cells must degrade the intervening cell wall to allow fusion of the partners. Because improper timing or location of cell wall degradation would cause lysis, the initiation of cell fusion must be highly regulated. Here, we find that yeast cell fusion is negatively regulated by components of the cell wall integrity (CWI) pathway. Loss of the cell wall sensor, MID2, specifically causes “mating-induced death” after pheromone exposure. Mating-induced death is suppressed by mutations in cell fusion genes (FUS1, FUS2, RVS161, CDC42), implying that mid2Δ cells die from premature fusion without a partner. Consistent with premature fusion, mid2Δ shmoos had thinner cell walls and lysed at the shmoo tip. Normally, Cdc42p colocalizes with Fus2p to form a focus only when mating cells are in contact (prezygotes) and colocalization is required for cell fusion. However, Cdc42p was aberrantly colocalized with Fus2p to form a focus in mid2Δ shmoos. A hyperactive allele of the CWI kinase Pkc1p (PKC1*) caused decreased cell fusion and Cdc42p localization in prezygotes. In shmoos, PKC1* increased Cdc42p localization; however, it was not colocalized with Fus2p or associated with cell death. We conclude that Mid2p and Pkc1p negatively regulate cell fusion via Cdc42p and Fus2p.

Differential GAP requirement for Cdc42-GTP polarization during proliferation and sexual reproduction

The formation of a local zone of Cdc42 GTPase activity, which governs cell polarization in many cell types, requires not only local activation but also switch-off mechanisms. In this study, we identify Rga3, a paralog of Rga4, as a novel Cdc42 GTPase-activating protein (GAP) in the fission yeast Schizosaccharomyces pombe Contrary to Rga4, Rga3 localizes with Cdc42-GTP to sites of polarity. Rga3 is dispensable for cell polarization during mitotic growth, but it limits the lifetime of unstable Cdc42-GTP patches that underlie cell pairing during sexual reproduction, masking a partly compensatory patch-wandering motion. In consequence, cells lacking rga3 hyperpolarize and lose out in mating competition. Rga3 synergizes with the Cdc42 GAPs Rga4 and Rga6 to restrict Cdc42-GTP zone sizes during mitotic growth. Surprisingly, triple-mutant cells, which are almost fully round, retain pheromone-dependent dynamic polarization of Cdc42-GTP, extend a polarized projection, and mate. Thus, the requirement for Cdc42-GTP hydrolysis by GAPs is distinct during polarization by intrinsic or extrinsic cues.

Exploration and stabilization of Ras1 mating zone: A mechanism with positive and negative feedbacks

In mating fission yeast cells, sensing and response to extracellular pheromone concentrations occurs through an exploratory Cdc42 patch that stochastically samples the cell cortex before stabilizing towards a mating partner. Active Ras1 (Ras1-GTP), an upstream regulator of Cdc42, and Gap1, the GTPase-activating protein for Ras1, localize at the patch. We developed a reaction-diffusion model of Ras1 patch appearance and disappearance with a positive feedback by a Guanine nucleotide Exchange Factor (GEF) and Gap1 inhibition. The model is based on new estimates of Ras1-GDP, Ras1-GTP and Gap1 diffusion coefficients and rates of cytoplasmic exchange studied by FRAP. The model reproduces exploratory patch behavior and lack of Ras1 patch in cells lacking Gap1. Transition to a stable patch can occur by change of Gap1 rates constants or local increase of the positive feedback rate constants. The model predicts that the patch size and number of patches depend on the strength of positive and negative feedbacks. Measurements of Ras1 patch size and number in cells overexpressing the Ras1 GEF or Gap1 are consistent with the model.

Unicellular fission yeasts mate by fusing with partners of the opposite mating type. Each pair member grows towards its selected partner that signals its presence through secreted pheromone. The process of partner selection occurs through an exploratory patch (containing activated signaling protein Cdc42 and upstream regulator Ras1) that assembles and disassembles on the cell cortex, stabilizing in regions of higher opposite pheromone concentration. We present a computational model of the molecular mechanisms driving the dynamical pattern of patch exploration and stabilization. The model is based on reaction and diffusion along the curved cell membrane, with diffusion coefficients measured experimentally. In the model, a positive Ras1 activation feedback loop generates a patch containing most of the activating protein (Ras1 GEF). The fast diffusing inhibitor Gap1 that is recruited locally from the cytoplasm spreads on the cell membrane, limiting patch size and causing its decay. Spontaneous reinitiation of Ras1 activation elsewhere on the cortex provides a mechanism for exploration. Transition of the system’s behavior to that of a single stable patch is possible upon simulated pheromone sensing. The computational model provides predictions for the number of patches and patch size dependence on parameters that we tested experimentally.

The effect of cell geometry on polarization in budding yeast

The localization (or polarization) of proteins on the membrane during the mating of budding yeast (Saccharomyces cerevisiae) is an important model system for understanding simple pattern formation within cells. While there are many existing mathematical models of polarization, for both budding and mating, there are still many aspects of this process that are not well understood. In this paper we set out to elucidate the effect that the geometry of the cell can have on the dynamics of certain models of polarization. Specifically, we look at several spatial stochastic models of Cdc42 polarization that have been adapted from published models, on a variety of tip-shaped geometries, to replicate the shape change that occurs during the growth of the mating projection. We show here that there is a complex interplay between the dynamics of polarization and the shape of the cell. Our results show that while models of polarization can generate a stable polarization cap, its localization at the tip of mating projections is unstable, with the polarization cap drifting away from the tip of the projection in a geometry dependent manner. We also compare predictions from our computational results to experiments that observe cells with projections of varying lengths, and track the stability of the polarization cap. Lastly, we examine one model of actin polarization and show that it is unlikely, at least for the models studied here, that actin dynamics and vesicle traffic are able to overcome this effect of geometry.

Heterogeneity and Robustness in Plant Morphogenesis: From Cells to Organs

Development is remarkably reproducible, producing organs with the same size, shape, and function repeatedly from individual to individual. For example, every flower on the Antirrhinum stalk has the same snapping dragon mouth. This reproducibility has allowed taxonomists to classify plants and animals according to their morphology. Yet these reproducible organs are composed of highly variable cells. For example, neighboring cells grow at different rates in Arabidopsis leaves, sepals, and shoot apical meristems. This cellular variability occurs in normal, wild-type organisms, indicating that cellular heterogeneity (or diversity in a characteristic such as growth rate) is either actively maintained or, at a minimum, not entirely suppressed. In fact, cellular heterogeneity can contribute to producing invariant organs. Here, we focus on how plant organs are reproducibly created during development from these highly variable cells.

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.

Membrane shape-mediated wave propagation of cortical protein dynamics

Immune cells exhibit stimulation-dependent traveling waves in the cortex, much faster than typical cortical actin waves. These waves reflect rhythmic assembly of both actin machinery and peripheral membrane proteins such as F-BAR domain-containing proteins. Combining theory and experiments, we develop a mechanochemical feedback model involving membrane shape changes and F-BAR proteins that render the cortex an interesting dynamical system. We show that such cortical dynamics manifests itself as ultrafast traveling waves of cortical proteins, in which the curvature sensitivity-driven feedback always constrains protein lateral diffusion in wave propagation. The resulting protein wave propagation mainly reflects the spatial gradient in the timing of local protein recruitment from cytoplasm. We provide evidence that membrane undulations accompany these protein waves and potentiate their propagation. Therefore, membrane shape change and protein curvature sensitivity may have underappreciated roles in setting high-speed cortical signal transduction rhythms.

Traveling waves in the cell cortex can propagate much faster than actin waves, and the mechanism is unknown. Here the authors propose a mechanochemical feedback model for traveling waves that incorporates membrane shape changes and recruitment of F-BAR proteins that enables fast wave propagation.

Invading, Leading and Navigating Cells in Caenorhabditis elegans: Insights into Cell Movement in Vivo

Highly regulated cell migration events are crucial during animal tissue formation and the trafficking of cells to sites of infection and injury. Misregulation of cell movement underlies numerous human diseases, including cancer. Although originally studied primarily in two-dimensional in vitro assays, most cell migrations in vivo occur in complex three-dimensional tissue environments that are difficult to recapitulate in cell culture or ex vivo Further, it is now known that cells can mobilize a diverse repertoire of migration modes and subcellular structures to move through and around tissues. This review provides an overview of three distinct cellular movement events in Caenorhabditis elegans-cell invasion through basement membrane, leader cell migration during organ formation, and individual cell migration around tissues-which together illustrate powerful experimental models of diverse modes of movement in vivo We discuss new insights into migration that are emerging from these in vivo studies and important future directions toward understanding the remarkable and assorted ways that cells move in animals.

In Situ Assays of Chemotropism During Yeast Mating

Virtually all eukaryotic cells can grow in a polarized fashion in response to external signals. Cells can respond to gradients of chemoattractants or chemorepellents by directional growth, a process referred to as chemotropism. The budding yeast Saccharomyces cerevisiae undergoes chemotropic growth during mating, in which two haploid cells of opposite mating type grow towards one another. Mating pheromone gradients are essential for efficient mating in yeast and different yeast mutants are defective in chemotropism. Two methods of assessing the ability of yeast strains to respond to pheromone gradients are presented here.

Membrane curvature directs the localization of Cdc42p to novel foci required for cell-cell fusion

Cell fusion is ubiquitous in eukaryotic fertilization and development. The highly conserved Rho-GTPase Cdc42p promotes yeast fusion through interaction with Fus2p, a pheromone-induced amphiphysin-like protein. We show that in prezygotes, Cdc42p forms a novel Fus2p-dependent focus at the center of the zone of cell fusion (ZCF) and remains associated with remnant cell walls after initial fusion. At the ZCF and during fusion, Cdc42p and Fus2p colocalized. In contrast, in shmoos, both proteins were near the cortex but spatially separate. Cdc42p focus formation depends on ZCF membrane curvature: mutant analysis showed that Cdc42p localization is negatively affected by shmoo-like positive ZCF curvature, consistent with the flattening of the ZCF during fusion. BAR-domain proteins such as the fusion proteins Fus2p and Rvs161p are known to recognize membrane curvature. We find that mutations that disrupt binding of the Fus2p/Rvs161p heterodimer to membranes affect Cdc42p ZCF localization. We propose that Fus2p localizes Cdc42p to the flat ZCF to promote cell wall degradation.

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.

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.