A Cellular System for Spatial Signal Decoding in Chemical Gradients

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.

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.

Single-cell directional sensing from just a few receptor binding events

Identifying the directionality of signaling sources from noisy input to membrane receptors is an essential task performed by many cell types. A variety of models have been proposed to explain directional sensing in cells. However, many of these require significant computational and memory capacities for the cell. We propose and analyze a simple mechanism in which a cell adopts the direction associated with the first few membrane binding events. This model yields an accurate angular estimate to the source long before steady state is reached in biologically relevant scenarios. Our proposed mechanism allows for reliable estimates of the directionality of external signals using temporal information and assumes minimal computational capacities of the cell.

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.

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.

Localization of signaling receptors maximizes cellular information acquisition in spatially structured natural environments

Cells in natural environments, such as tissue or soil, sense and respond to extracellular ligands with intricately structured and non-monotonic spatial distributions, sculpted by processes such as fluid flow and substrate adhesion. In this work, we show that spatial sensing and navigation can be optimized by adapting the spatial organization of signaling pathways to the spatial structure of the environment. We develop an information-theoretic framework for computing the optimal spatial organization of a sensing system for a given signaling environment. We find that receptor localization previously observed in cells maximizes information acquisition in simulated natural contexts, including tissue and soil. Specifically, information acquisition is maximized when receptors form localized patches at regions of maximal ligand concentration. Receptor localization extends naturally to produce a dynamic protocol for continuously redistributing signaling receptors, which when implemented using simple feedback, boosts cell navigation efficiency by 30-fold.

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.

Gradient Tracking by Yeast GPCRs in a Microfluidics Chamber

Cells typically exist in a highly dynamic environment, which cannot easily be recreated in culture dishes or microwell plates. Microfluidic devices can provide precise control of the time, dose, and orientation of a stimulus, while simultaneously capturing quantitative single-cell data. The approach is particularly powerful when combined with the genetically tractable yeast model organism. The GPCR pathway in yeast is structurally conserved and functionally interchangeable with those in humans. We describe the implementation of a microfluidic device to investigate morphological and transcriptional responses of yeast to a gradient or pulse administration of a GPCR ligand, the peptide mating pheromone α-factor.

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.

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.

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.

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.

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.

Mechanical stress impairs pheromone signaling via Pkc1-mediated regulation of the MAPK scaffold Ste5

This study shows that Pkc1 inhibits yeast pheromone signaling upon intrinsic and extrinsic mechanical stress. Pkc1 phosphorylates the RING-H2 domains of the scaffolds Ste5 and Far1, thereby preventing their interaction with Gβγ at the plasma membrane. This crosstalk mechanism regulates polarized growth and cell–cell fusion during mating.

Cells continuously adapt cellular processes by integrating external and internal signals. In yeast, multiple stress signals regulate pheromone signaling to prevent mating under unfavorable conditions. However, the underlying crosstalk mechanisms remain poorly understood. Here, we show that mechanical stress activates Pkc1, which prevents lysis of pheromone-treated cells by inhibiting polarized growth. In vitro Pkc1 phosphorylates conserved residues within the RING-H2 domains of the scaffold proteins Far1 and Ste5, which are also phosphorylated in vivo. Interestingly, Pkc1 triggers dispersal of Ste5 from mating projections upon mechanically induced stress and during cell–cell fusion, leading to inhibition of the MAPK Fus3. Indeed, RING phosphorylation interferes with Ste5 membrane association by preventing binding to the receptor-linked Gβγ protein. Cells expressing nonphosphorylatable Ste5 undergo increased lysis upon mechanical stress and exhibit defects in cell–cell fusion during mating, which is exacerbated by simultaneous expression of nonphosphorylatable Far1. These results uncover a mechanical stress–triggered crosstalk mechanism modulating pheromone signaling, polarized growth, and cell–cell fusion during mating.

Generating kinetic environments to study dynamic cellular processes in single cells

Cells of any organism are consistently exposed to changes over time in their environment. The kinetics by which these changes occur are critical for the cellular response and fate decision. It is therefore important to control the temporal changes of extracellular stimuli precisely to understand biological mechanisms in a quantitative manner. Most current cell culture and biochemical studies focus on instant changes in the environment and therefore neglect the importance of kinetic environments. To address these shortcomings, we developed two experimental methodologies to precisely control the environment of single cells. These methodologies are compatible with standard biochemistry, molecular, cell and quantitative biology assays. We demonstrate applicability by obtaining time series and time point measurements in both live and fixed cells. We demonstrate the feasibility of the methodology in yeast and mammalian cell culture in combination with widely used assays such as flow cytometry, time-lapse microscopy and single-molecule RNA Fluorescent in-situ Hybridization (smFISH). Our experimental methodologies are easy to implement in most laboratory settings and allows the study of kinetic environments in a wide range of assays and different cell culture conditions.

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.

Comparison of Deterministic and Stochastic Regime in a Model for Cdc42 Oscillations in Fission Yeast

Oscillations occur in a wide variety of essential cellular processes, such as cell cycle progression, circadian clocks and calcium signaling in response to stimuli. It remains unclear how intrinsic stochasticity can influence these oscillatory systems. Here, we focus on oscillations of Cdc42 GTPase in fission yeast. We extend our previous deterministic model by Xu and Jilkine to construct a stochastic model, focusing on the fast diffusion case. We use SSA (Gillespie's algorithm) to numerically explore the low copy number regime in this model, and use analytical techniques to study the long-time behavior of the stochastic model and compare it to the equilibria of its deterministic counterpart. Numerical solutions suggest noisy limit cycles exist in the parameter regime in which the deterministic system converges to a stable limit cycle, and quasi-cycles exist in the parameter regime where the deterministic model has a damped oscillation. Near an infinite period bifurcation point, the deterministic model has a sustained oscillation, while stochastic trajectories start with an oscillatory mode and tend to approach deterministic steady states. In the low copy number regime, metastable transitions from oscillatory to steady behavior occur in the stochastic model. Our work contributes to the understanding of how stochastic chemical kinetics can affect a finite-dimensional dynamical system, and destabilize a deterministic steady state leading to oscillations.

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.

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.

Spatial focalization of pheromone/MAPK signaling triggers commitment to cell-cell fusion

Here, Dudin et al. show that cell fusion does not require a dedicated signal but is triggered by spatial focalization of the same pheromone–GPCR–MAPK signaling cascade that drives earlier mating events in Schizosaccharomyces pombe.

Cell fusion is universal in eukaryotes for fertilization and development, but what signals this process is unknown. Here, we show in Schizosaccharomyces pombe that fusion does not require a dedicated signal but is triggered by spatial focalization of the same pheromone–GPCR (G-protein-coupled receptor)–MAPK signaling cascade that drives earlier mating events. Autocrine cells expressing the receptor for their own pheromone trigger fusion attempts independently of cell–cell contact by concentrating pheromone release at the fusion focus, a dynamic actin aster underlying the secretion of cell wall hydrolases. Pheromone receptor and MAPK cascade are similarly enriched at the fusion focus, concomitant with fusion commitment in wild-type mating pairs. This focalization promotes cell fusion by immobilizing the fusion focus, thus driving local cell wall dissolution. We propose that fusion commitment is imposed by a local increase in MAPK concentration at the fusion focus, driven by a positive feedback between fusion focus formation and focalization of pheromone release and perception.

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.

Yeast chemotropism: A paradigm shift in chemical gradient sensing

The ability of cells to direct their movement and growth in response to shallow chemical gradients is essential in the life cycles of all eukaryotic organisms. The signaling mechanisms underlying directional sensing in chemotactic cells have been well studied; however, relatively little is known about how chemotropic cells interpret chemical gradients. Recent studies of chemotropism in budding and fission yeast have revealed 2 quite different mechanisms-biased wandering of the polarity complex, and differential internalization of the receptor and G protein. Each of these mechanisms has been proposed to play a key role in decoding mating pheromone gradients. Here we explore how they may work together as 2 essential components of one gradient sensing machine.

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."

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.

Local Ras activation, PTEN pattern, and global actin flow in the chemotactic responses of oversized cells

Chemotactic responses of eukaryotic cells require a signal processing system that translates an external gradient of attractant into directed motion. To challenge the response system to its limits, we increased the size of Dictyostelium discoideum cells by using electric-pulse-induced fusion. Large cells formed multiple protrusions at different sites along the gradient of chemoattractant, independently turned towards the gradient and competed with each other. Finally, these cells succeeded to re-establish polarity by coordinating front and tail activities. To analyse the responses, we combined two approaches, one aimed at local responses by visualising the dynamics of Ras activation at the front regions of reorientating cells, the other at global changes of polarity by monitoring front-to-tail-directed actin flow. Asymmetric Ras activation in turning protrusions underscores that gradients can be sensed locally and translated into orientation. Different to cells of normal size, the polarity of large cells is not linked to an increasing front-to-tail gradient of the PIP3-phosphatase PTEN. But even in large cells, the front communicates with the tail through an actin flow that might act as carrier of a protrusion inhibitor.

Gβ promotes pheromone receptor polarization and yeast chemotropism by inhibiting receptor phosphorylation

Gradient-directed cell migration (chemotaxis) and growth (chemotropism) are processes that are essential to the development and life cycles of all species. Cells use surface receptors to sense the shallow chemical gradients that elicit chemotaxis and chemotropism. Slight asymmetries in receptor activation are amplified by downstream signaling systems, which ultimately induce dynamic reorganization of the cytoskeleton. During the mating response of budding yeast, a model chemotropic system, the pheromone receptors on the plasma membrane polarize to the side of the cell closest to the stimulus. Although receptor polarization occurs before and independently of actin cable-dependent delivery of vesicles to the plasma membrane (directed secretion), it requires receptor internalization. Phosphorylation of pheromone receptors by yeast casein kinase 1 or 2 (Yck1/2) stimulates their internalization. We showed that the pheromone-responsive Gβγ dimer promotes the polarization of the pheromone receptor by interacting with Yck1/2 and locally inhibiting receptor phosphorylation. We also found that receptor phosphorylation is essential for chemotropism, independently of its role in inducing receptor internalization. A mathematical model supports the idea that the interaction between Gβγ and Yck1/2 results in differential phosphorylation and internalization of the pheromone receptor and accounts for its polarization before the initiation of directed secretion.

Local Pheromone Release from Dynamic Polarity Sites Underlies Cell-Cell Pairing during Yeast Mating

Cell pairing is central for many processes, including immune defense, neuronal connection, hyphal fusion, and sexual reproduction. How does a cell orient toward a partner, especially when faced with multiple choices? Fission yeast Schizosaccharomyces pombe P and M cells, which respectively express P and M factor pheromones [1, 2], pair during the mating process induced by nitrogen starvation. Engagement of pheromone receptors Map3 and Mam2 [3, 4] with their cognate pheromone ligands leads to activation of the Gα protein Gpa1 to signal sexual differentiation [3, 5, 6]. Prior to cell pairing, the Cdc42 GTPase, a central regulator of cell polarization, forms dynamic zones of activity at the cell periphery at distinct locations over time [7]. Here we show that Cdc42-GTP polarization sites contain the M factor transporter Mam1, the general secretion machinery, which underlies P factor secretion, and Gpa1, suggesting that these are sub-cellular zones of pheromone secretion and signaling. Zone lifetimes scale with pheromone concentration. Computational simulations of pair formation through a fluctuating zone show that the combination of local pheromone release and sensing, short pheromone decay length, and pheromone-dependent zone stabilization leads to efficient pair formation. Consistently, pairing efficiency is reduced in the absence of the P factor protease. Similarly, zone stabilization at reduced pheromone levels, which occurs in the absence of the predicted GTPase-activating protein for Ras, leads to reduction in pairing efficiency. We propose that efficient cell pairing relies on fluctuating local signal emission and perception, which become locked into place through stimulation.