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

Daughter cell identity emerges from the interplay of Cdc42, septins, and exocytosis

Asymmetric cell division plays a crucial role in cell differentiation, unequal replicative senescence, and stem cell maintenance. In budding yeast, the identities of mother and daughter cells begin to diverge at bud emergence when distinct plasma-membrane domains are formed and separated by a septin ring. However, the mechanisms underlying this transformation remain unknown. Here, we show that septins recruited to the site of polarization by Cdc42-GTP inhibit Cdc42 activity in a negative feedback loop, and this inhibition depends on Cdc42 GTPase-activating proteins. Combining live-cell imaging and computational modeling, we demonstrate that the septin ring is sculpted by polarized exocytosis, which creates a hole in the accumulating septin density and relieves the inhibition of Cdc42. The nascent ring generates a sharp boundary that confines the Cdc42 activity and exocytosis strictly to its enclosure and thus clearly delineates the daughter cell identity. Our findings define a fundamental mechanism underlying eukaryotic cell fate differentiation.

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Septins provide negative feedback to Cdc42 activity that depends on Cdc42 GAPs

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Septin ring is formed by highly focused polarized exocytosis

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Suppression of exocytosis causes chasing behavior of septins

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Septin ring size is primarily determined by size of the underlying Cdc42 cluster

Beyond symmetry-breaking: competition and negative feedback in GTPase regulation

Cortical domains are often specified by the local accumulation of active GTPases. Such domains can arise through spontaneous symmetry-breaking, suggesting that GTPase accumulation occurs via positive feedback. Here, we focus on recent advances in fungal and plant cell models - where new work suggests that polarity-controlling GTPases develop only one 'front' because GTPase clusters engage in a winner-takes-all competition. However, in some circumstances two or more GTPase domains can coexist, and the basis for the switch from competition to coexistence remains an open question. Polarity GTPases can undergo oscillatory clustering and dispersal, suggesting that these systems contain negative feedback. Negative feedback may prevent polarity clusters from spreading too far, regulate the balance between competition and coexistence, and provide directional flexibility for cells tracking gradients.

Independence of symmetry breaking on Bem1-mediated autocatalytic activation of Cdc42

Rather than acting directly on Cdc42, Bem1 works in concert with the Cdc42 binding partner Rdi1 to relocalize Cdc42 to the cytosol during symmetry breaking in the absence of an intact actin cytoskeleton.

The ability to break symmetry and polarize through self-organization is a fundamental feature of cellular systems. A prevailing theory in yeast posits that symmetry breaking occurs via a positive feedback loop, wherein the adaptor protein Bem1 promotes local activation and accumulation of Cdc42 by directly tethering Cdc42^GTP with its guanine nucleotide exchange factor (GEF) Cdc24. In this paper, we find that neither Bem1 nor the ability of Bem1 to bind Cdc42^GTP is required for cell polarization. Instead, Bem1 functions primarily by boosting GEF activity, a role critical for polarization without actin filaments. In the absence of actin-based transport, polarization of Cdc42 is accomplished through Rdi1, the Cdc42 guanine nucleotide dissociation inhibitor. A mathematical model is constructed describing cell polarization as a product of distinct pathways controlling Cdc42 activation and protein localization. The model predicts a nonmonotonic dependence of cell polarization on the concentration of Rdi1 relative to that of Cdc42.

Interaction between bud-site selection and polarity-establishment machineries in budding yeast

Saccharomyces cerevisiae yeast cells polarize in order to form a single bud in each cell cycle. Distinct patterns of bud-site selection are observed in haploid and diploid cells. Genetic approaches have identified the molecular machinery responsible for positioning the bud site: during bud formation, specific locations are marked with immobile landmark proteins. In the next cell cycle, landmarks act through the Ras-family GTPase Rsr1 to promote local activation of the conserved Rho-family GTPase, Cdc42. Additional Cdc42 accumulates by positive feedback, creating a concentrated patch of GTP-Cdc42, which polarizes the cytoskeleton to promote bud emergence. Using time-lapse imaging and mathematical modelling, we examined the process of bud-site establishment. Imaging reveals unexpected effects of the bud-site-selection system on the dynamics of polarity establishment, raising new questions about how that system may operate. We found that polarity factors sometimes accumulate at more than one site among the landmark-specified locations, and we suggest that competition between clusters of polarity factors determines the final location of the Cdc42 cluster. Modelling indicated that temporally constant landmark-localized Rsr1 would weaken or block competition, yielding more than one polarity site. Instead, we suggest that polarity factors recruit Rsr1, effectively sequestering it from other locations and thereby terminating landmark activity.

Spatial stochastic dynamics enable robust cell polarization

Although cell polarity is an essential feature of living cells, it is far from being well-understood. Using a combination of computational modeling and biological experiments we closely examine an important prototype of cell polarity: the pheromone-induced formation of the yeast polarisome. Focusing on the role of noise and spatial heterogeneity, we develop and investigate two mechanistic spatial models of polarisome formation, one deterministic and the other stochastic, and compare the contrasting predictions of these two models against experimental phenotypes of wild-type and mutant cells. We find that the stochastic model can more robustly reproduce two fundamental characteristics observed in wild-type cells: a highly polarized phenotype via a mechanism that we refer to as spatial stochastic amplification, and the ability of the polarisome to track a moving pheromone input. Moreover, we find that only the stochastic model can simultaneously reproduce these characteristics of the wild-type phenotype and the multi-polarisome phenotype of a deletion mutant of the scaffolding protein Spa2. Significantly, our analysis also demonstrates that higher levels of stochastic noise results in increased robustness of polarization to parameter variation. Furthermore, our work suggests a novel role for a polarisome protein in the stabilization of actin cables. These findings elucidate the intricate role of spatial stochastic effects in cell polarity, giving support to a cellular model where noise and spatial heterogeneity combine to achieve robust biological function.

Cell polarity is the fundamental process of breaking symmetry to create asymmetric cellular structures. It is an open question how randomness (stochasticity) in the cell hinders or helps cell polarity. In this work, we focus on the ability of yeast cells to sense a spatial gradient of mating pheromone and respond by forming a projection in the direction of the mating partner. A key element is the polarisome, which is at the tip of the mating projection. We introduce the first model of polarisome formation in yeast. The model is well-supported by experimental data. We perform modeling to explore the role of noise in the formation of the polarisome. By running simulations with and without noise, we arrive at the surprising conclusion, that gradient-dependent polarization is enhanced by stochasticity. Both the tight localization (amplification) and the ability to respond to directional change of the input (tracking) are enhanced by stochastic dynamics, resulting in a more robust behavior. Mutants in which key polarisome proteins have been deleted exhibit broader, noisier polarisome than the wild type. The mutant phenotype is accurately captured by our stochastic simulations. These results demonstrate the importance of stochasticity in the study of cell polarity.

Heritable change caused by transient transcription errors

Transmission of cellular identity relies on the faithful transfer of information from the mother to the daughter cell. This process includes accurate replication of the DNA, but also the correct propagation of regulatory programs responsible for cellular identity. Errors in DNA replication (mutations) and protein conformation (prions) can trigger stable phenotypic changes and cause human disease, yet the ability of transient transcriptional errors to produce heritable phenotypic change ('epimutations') remains an open question. Here, we demonstrate that transcriptional errors made specifically in the mRNA encoding a transcription factor can promote heritable phenotypic change by reprogramming a transcriptional network, without altering DNA. We have harnessed the classical bistable switch in the lac operon, a memory-module, to capture the consequences of transient transcription errors in living Escherichia coli cells. We engineered an error-prone transcription sequence (A9 run) in the gene encoding the lac repressor and show that this 'slippery' sequence directly increases epigenetic switching, not mutation in the cell population. Therefore, one altered transcript within a multi-generational series of many error-free transcripts can cause long-term phenotypic consequences. Thus, like DNA mutations, transcriptional epimutations can instigate heritable changes that increase phenotypic diversity, which drives both evolution and disease.

Polarization of diploid daughter cells directed by spatial cues and GTP hydrolysis of Cdc42 budding yeast

Cell polarization occurs along a single axis that is generally determined by a spatial cue. Cells of the budding yeast exhibit a characteristic pattern of budding, which depends on cell-type-specific cortical markers, reflecting a genetic programming for the site of cell polarization. The Cdc42 GTPase plays a key role in cell polarization in various cell types. Although previous studies in budding yeast suggested positive feedback loops whereby Cdc42 becomes polarized, these mechanisms do not include spatial cues, neglecting the normal patterns of budding. Here we combine live-cell imaging and mathematical modeling to understand how diploid daughter cells establish polarity preferentially at the pole distal to the previous division site. Live-cell imaging shows that daughter cells of diploids exhibit dynamic polarization of Cdc42-GTP, which localizes to the bud tip until the M phase, to the division site at cytokinesis, and then to the distal pole in the next G1 phase. The strong bias toward distal budding of daughter cells requires the distal-pole tag Bud8 and Rga1, a GTPase activating protein for Cdc42, which inhibits budding at the cytokinesis site. Unexpectedly, we also find that over 50% of daughter cells lacking Rga1 exhibit persistent Cdc42-GTP polarization at the bud tip and the distal pole, revealing an additional role of Rga1 in spatiotemporal regulation of Cdc42 and thus in the pattern of polarized growth. Mathematical modeling indeed reveals robust Cdc42-GTP clustering at the distal pole in diploid daughter cells despite random perturbation of the landmark cues. Moreover, modeling predicts different dynamics of Cdc42-GTP polarization when the landmark level and the initial level of Cdc42-GTP at the division site are perturbed by noise added in the model.

Calcium oscillations-coupled conversion of actin travelling waves to standing oscillations

Dynamic spatial patterns of signaling factors or macromolecular assemblies in the form of oscillations or traveling waves have emerged as important themes in cell physiology. Feedback mechanisms underlying these processes and their modulation by signaling events and reciprocal cross-talks remain poorly understood. Here we show that antigen stimulation of mast cells triggers cyclic changes in the concentration of actin regulatory proteins and actin in the cell cortex that can be manifested in either spatial pattern. Recruitment of FBP17 and active Cdc42 at the plasma membrane, leading to actin polymerization, are involved in both events, whereas calcium oscillations, which correlate with global fluctuations of plasma membrane PI(4,5)P(2), are tightly linked to standing oscillations and counteract wave propagation. These findings demonstrate the occurrence of a calcium-independent oscillator that controls the collective dynamics of factors linking the actin cytoskeleton to the plasma membrane. Coupling between this oscillator and the one underlying global plasma membrane PI(4,5)P2 and calcium oscillations spatially regulates actin dynamics, revealing an unexpected pattern-rendering mechanism underlying plastic changes occurring in the cortical region of the cell.

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

BACKGROUND

Many cells are remarkably proficient at tracking very shallow chemical gradients, despite considerable noise from stochastic receptor-ligand interactions. Motile cells appear to undergo a biased random walk: spatial noise in receptor activity may determine the instantaneous direction, but because noise is spatially unbiased, it is filtered out by time averaging, resulting in net movement upgradient. How nonmotile cells might filter out noise is unknown.

RESULTS

Using yeast chemotropic mating as a model, we demonstrate that a polarized patch of polarity regulators "wanders" along the cortex during gradient tracking. Computational and experimental findings suggest that actin-directed membrane traffic contributes to wandering by diluting local polarity factors. The pheromone gradient appears to bias wandering via interactions between receptor-activated Gβγ and polarity regulators. Artificially blocking patch wandering impairs gradient tracking.

CONCLUSIONS

We suggest that the polarity patch undergoes an intracellular biased random walk that enables noise filtering by time averaging, allowing nonmotile cells to track shallow gradients.

Cdc42 explores the cell periphery for mate selection in fission yeast

How cells polarize in response to external cues is a fundamental biological problem. For mating, yeast cells orient growth toward the source of a pheromone gradient produced by cells of the opposite mating type. Polarized growth depends on the small GTPase Cdc42, a central eukaryotic polarity regulator that controls signaling, cytoskeleton polarization, and vesicle trafficking. However, the mechanisms of polarity establishment and mate selection in complex cellular environments are poorly understood. Here we show that, in fission yeast, low-level pheromone signaling promotes a novel polarization state, where active Cdc42, its GEF Scd1, and scaffold Scd2 form colocalizing dynamic zones that sample the periphery of the cell. Two direct Cdc42 effectors--actin cables marked by myosin V Myo52 and the exocyst complex labeled by Sec6 and Sec8--also dynamically colocalize with active Cdc42. However, these cells do not grow due to a block in the exocytosis of cell wall synthases Bgs1 and Bgs4. High-level pheromone stabilizes active Cdc42 zones and promotes cell wall synthase exocytosis and polarized growth. However, in the absence of prior low-level pheromone signaling, exploration fails, and cells polarize growth at cell poles by default. Consequently, these cells show altered partner choice, mating preferentially with sister rather than nonsister cells. Thus, Cdc42 exploration serves to orient growth for partner selection. This process may also promote genetic diversification.

Designing synthetic regulatory networks capable of self-organizing cell polarization

How cells form global, self-organized structures using genetically encoded molecular rules remains elusive. Here, we take a synthetic biology approach to investigate the design principles governing cell polarization. First, using a coarse-grained computational model, we searched for all possible simple networks that can achieve polarization. All solutions contained one of three minimal motifs: positive feedback, mutual inhibition, or inhibitor with positive feedback. These minimal motifs alone could achieve polarization under limited conditions; circuits that combined two or more of these motifs were significantly more robust. With these design principles as a blueprint, we experimentally constructed artificial polarization networks in yeast, using a toolkit of chimeric signaling proteins that spatially direct the synthesis and degradation of phosphatidylinositol (3,4,5)-trisphosphate (PIP(3)). Circuits with combinatorial motifs yielded clear foci of synthetic PIP(3) that can persist for nearly an hour. Thus, by harnessing localization-regulated signaling molecules, we can engineer simple molecular circuits that reliably execute spatial self-organized programs.

Cell polarity: quantitative modeling as a tool in cell biology

Among a number of innovative approaches that have modernized cell biology, modeling has a prominent yet unusual place. One popular view is that we progress linearly, from conceptual to ever more detailed models. We review recent discoveries of cell polarity mechanisms, in which modeling played an important role, to demonstrate that the experiment-theory feedback loop requires diverse models characterized by varying levels of biological detail and mathematical complexity. We argue that a quantitative model is a tool that has to fit an experimental study, and the model's value should be judged not by how complex and detailed it is, but by what could be learned from it.

Negative feedback enhances robustness in the yeast polarity establishment circuit

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

Cell polarization and cytokinesis in budding yeast

Asymmetric cell division, which includes cell polarization and cytokinesis, is essential for generating cell diversity during development. The budding yeast Saccharomyces cerevisiae reproduces by asymmetric cell division, and has thus served as an attractive model for unraveling the general principles of eukaryotic cell polarization and cytokinesis. Polarity development requires G-protein signaling, cytoskeletal polarization, and exocytosis, whereas cytokinesis requires concerted actions of a contractile actomyosin ring and targeted membrane deposition. In this chapter, we discuss the mechanics and spatial control of polarity development and cytokinesis, emphasizing the key concepts, mechanisms, and emerging questions in the field.

Oscillatory dynamics of Cdc42 GTPase in the control of polarized growth

Cells promote polarized growth by activation of Rho-family protein Cdc42 at the cell membrane. We combined experiments and modeling to study bipolar growth initiation in fission yeast. Concentrations of a fluorescent marker for active Cdc42, Cdc42 protein, Cdc42-activator Scd1, and scaffold protein Scd2 exhibited anticorrelated fluctuations and oscillations with a 5-minute average period at polarized cell tips. These dynamics indicate competition for active Cdc42 or its regulators and the presence of positive and delayed negative feedbacks. Cdc42 oscillations and spatial distribution were sensitive to the amounts of Cdc42-activator Gef1 and to the activity of Cdc42-dependent kinase Pak1, a negative regulator. Feedbacks regulating Cdc42 oscillations and spatial self-organization appear to provide a flexible mechanism for fission yeast cells to explore polarization states and to control their morphology.

Mechanistic mathematical model of polarity in yeast

The establishment of cell polarity involves positive-feedback mechanisms that concentrate polarity regulators, including the conserved GTPase Cdc42p, at the "front" of the polarized cell. Previous studies in yeast suggested the presence of two parallel positive-feedback loops, one operating as a diffusion-based system, and the other involving actin-directed trafficking of Cdc42p on vesicles. F-actin (and hence directed vesicle traffic) speeds fluorescence recovery of Cdc42p after photobleaching, suggesting that vesicle traffic of Cdc42p contributes to polarization. We present a mathematical modeling framework that combines previously developed mechanistic reaction-diffusion and vesicle-trafficking models. Surprisingly, the combined model recapitulated the observed effect of vesicle traffic on Cdc42p dynamics even when the vesicles did not carry significant amounts of Cdc42p. Vesicle traffic reduced the concentration of Cdc42p at the front, so that fluorescence recovery mediated by Cdc42p flux from the cytoplasm took less time to replenish the bleached pool. Simulations in which Cdc42p was concentrated into vesicles or depleted from vesicles yielded almost identical predictions, because Cdc42p flux from the cytoplasm was dominant. These findings indicate that vesicle-mediated delivery of Cdc42p is not required to explain the observed Cdc42p dynamics, and raise the question of whether such Cdc42p traffic actually contributes to polarity establishment.

Import oligomers induce positive feedback to promote peroxisome differentiation and control organelle abundance

A fundamental question in cell biology is how cells control organelle composition and abundance. Woronin bodies are fungal peroxisomes centered on a crystalline core of the self-assembled HEX protein. Despite using the canonical peroxisome import machinery for biogenesis, Woronin bodies are scarce compared to the overall peroxisome population. Here, we show that HEX oligomers promote the differentiation of a subpopulation of peroxisomes, which become enlarged and highly active in matrix protein import. HEX physically associates with the essential matrix import peroxin, PEX26, and promotes its enrichment in the membrane of differentiated peroxisomes. In addition, a PEX26 mutant that disrupts differentiation produces increased numbers of aberrantly small Woronin bodies. Our data suggest a mechanism where HEX oligomers recruit a key component of the import machinery, which promotes the import of additional HEX. This type of positive feedback provides a basic mechanism for the production of an organelle subpopulation of distinct composition and abundance.

Neuronal (bi)polarity as a self-organized process enhanced by growing membrane

Early in vitro and recent in vivo studies demonstrated that neuronal polarization occurs by the sequential formation of two oppositely located neurites. This early bipolar phenotype is of crucial relevance in brain organization, determining neuronal migration and brain layering. It is currently considered that the place of formation of the first neurite is dictated by extrinsic cues, through the induction of localized changes in membrane and cytoskeleton dynamics leading to deformation of the cells' curvature followed by the growth of a cylindrical extension (neurite). It is unknown if the appearance of the second neurite at the opposite pole, thus the formation of a bipolar cell axis and capacity to undergo migration, is defined by the growth at the first place, therefore intrinsic, or requires external determinants. We addressed this question by using a mathematical model based on the induction of dynamic changes in one pole of a round cell. The model anticipates that a second area of growth can spontaneously form at the opposite pole. Hence, through mathematical modeling we prove that neuronal bipolar axis of growth can be due to an intrinsic mechanism.

Polarized growth in fungi: symmetry breaking and hyphal formation

Cell shape is a critical determinant for function. The baker's yeast Saccharomyces cerevisiae changes shape in response to its environment, growing by budding in rich nutrients, forming invasive pseudohyphal filaments in nutrient poor conditions and pear shaped shmoos for growth towards a partner during mating. The human opportunistic pathogen Candida albicans can switch from budding to hyphal growth, in response to numerous environmental stimuli to colonize and invade its host. Hyphal growth, typical of filamentous fungi, is not observed in S. cerevisiae. A number of internal cues regulate when and where yeast cells break symmetry leading to polarized growth and ultimately distinct cell shapes. This review discusses how cells break symmetry using the yeast S. cerevisiae paradigm and how polarized growth is initiated and maintained to result in dramatic morphological changes during C. albicans hyphal growth.

A comparison of mathematical models for polarization of single eukaryotic cells in response to guided cues

Polarization, a primary step in the response of an individual eukaryotic cell to a spatial stimulus, has attracted numerous theoretical treatments complementing experimental studies in a variety of cell types. While the phenomenon itself is universal, details differ across cell types, and across classes of models that have been proposed. Most models address how symmetry breaking leads to polarization, some in abstract settings, others based on specific biochemistry. Here, we compare polarization in response to a stimulus (e.g., a chemoattractant) in cells typically used in experiments (yeast, amoebae, leukocytes, keratocytes, fibroblasts, and neurons), and, in parallel, responses of several prototypical models to typical stimulation protocols. We find that the diversity of cell behaviors is reflected by a diversity of models, and that some, but not all models, can account for amplification of stimulus, maintenance of polarity, adaptation, sensitivity to new signals, and robustness.

Models at the single cell level

Many cellular behaviors cannot be completely captured or appropriately described at the cell population level. Noise induced by stochastic chemical reactions, spatially polarized signaling networks, and heterogeneous cell-cell communication are among the many phenomena that require fine-grained analysis. Accordingly, the mathematical models used to describe such systems must be capable of single cell or subcellular resolution. Here, we review techniques for modeling single cells, including models of stochastic chemical kinetics, spatially heterogeneous intracellular signaling, and spatial stochastic systems. We also briefly discuss applications of each type of model.

Bimodal analysis reveals a general scaling law governing nondirected and chemotactic cell motility

Cell motility is a fundamental process with relevance to embryonic development, immune response, and metastasis. Cells move either spontaneously, in a nondirected fashion, or in response to chemotactic signals, in a directed fashion. Even though they are often studied separately, both forms of motility share many complex processes at the molecular and subcellular scale, e.g., orchestrated cytoskeletal rearrangements and polarization. In addition, at the cellular level both types of motility include persistent runs interspersed with reorientation pauses. Because there is a great range of variability in motility among different cell types, a key challenge in the field is to integrate these multiscale processes into a coherent framework. We analyzed the motility of Dictyostelium cells with bimodal analysis, a method that compares time spent in persistent versus reorientation mode. Unexpectedly, we found that reorientation time is coupled with persistent time in an inverse correlation and, surprisingly, the inverse correlation holds for both nondirected and chemotactic motility, so that the full range of Dictyostelium motility can be described by a single scaling relationship. Additionally, we found an identical scaling relationship for three human cell lines, indicating that the coupling of reorientation and persistence holds across species and making it possible to describe the complexity of cell motility in a surprisingly general and simple manner. With this new perspective, we analyzed the motility of Dictyostelium mutants, and found four in which the coupling between two modes was altered. Our results point to a fundamental underlying principle, described by a simple scaling law, unifying mechanisms of eukaryotic cell motility at several scales.

Reorganization of the growth pattern of Schizosaccharomyces pombe in invasive filament formation

The organization and control of polarized growth through the cell cycle of Schizosaccharomyces pombe, a single-celled eukaryote, have been studied extensively. We have investigated the changes in these processes when S. pombe differentiates to form multicellular invasive mycelia and have found striking alterations to the behavior of some of the key regulatory proteins. Cells at the tips of invading filaments are considerably more elongated than cells growing singly and grow at one pole only. The filament tip follows a strict direction of growth through multiple cell cycles. A group of proteins involved in the growth process and actin regulation, comprising Spo20, Bgs4, activated Cdc42, and Crn1, are all concentrated at the growing tip, unlike their distribution at both ends of single cells. In contrast, several proteins implicated in microtubule-dependent organization of growth, including Tea1, Tea4, Mod5, and Pom1, all show the opposite effect and are relatively depleted at the growing end and enriched at the nongrowing end, although Tea1 appears to continue to be delivered to both ends. A third group acting at different stages of the cell cycle, including Bud6, Rga4, and Mid1, localize similarly in filaments and single cells, while Nif1 shows a reciprocal localization to Pom1.

Cytoskeletal dynamics in fission yeast: a review of models for polarization and division

We review modeling studies concerning cytoskeletal activity of fission yeast. Recent models vary in length and time scales, describing a range of phenomena from cellular morphogenesis to polymer assembly. The components of cytoskeleton act in concert to mediate cell-scale events and interactions such as polarization. The mathematical models reduce these events and interactions to their essential ingredients, describing the cytoskeleton by its bulk properties. On a smaller scale, models describe cytoskeletal subcomponents and how bulk properties emerge.

Quantitative time-lapse fluorescence microscopy in single cells

The cloning of green fluorescent protein (GFP) 15 years ago revolutionized cell biology by permitting visualization of a wide range of molecular mechanisms within living cells. Though initially used to make largely qualitative assessments of protein levels and localizations, fluorescence microscopy has since evolved to become highly quantitative and high-throughput. Computational image analysis has catalyzed this evolution, enabling rapid and automated processing of large datasets. Here, we review studies that combine time-lapse fluorescence microscopy and automated image analysis to investigate dynamic events at the single-cell level. We highlight examples where single-cell analysis provides unique mechanistic insights into cellular processes that cannot be otherwise resolved in bulk assays. Additionally, we discuss studies where quantitative microscopy facilitates the assembly of detailed 4D lineages in developing organisms. Finally, we describe recent advances in imaging technology, focusing especially on platforms that allow the simultaneous perturbation and quantitative monitoring of biological systems.

Pollen-tube tip growth requires a balance of lateral propagation and global inhibition of Rho-family GTPase activity

Rapid tip growth allows for efficient development of highly elongated cells (e.g. neuronal axons, fungal hyphae and pollen tubes) and requires an elaborate spatiotemporal regulation of the growing region. Here, we use the pollen tube as a model to investigate the mechanism regulating the growing region. ROPs (Rho-related GTPases from plants) are essential for pollen tip growth and display oscillatory activity changes in the apical plasma membrane (PM). By manipulating the ROP activity level, we showed that the PM distribution of ROP activity as an apical cap determines the tip growth region and that efficient tip growth requires an optimum level of the apical ROP1 activity. Excessive ROP activation induced the enlargement of the tip growth region, causing growth depolarization and reduced tube elongation. Time-lapse analysis suggests that the apical ROP1 cap is generated by lateral propagation of a localized ROP activity. Subcellular localization and gain- and loss-of-function analyses suggest that RhoGDI- and RhoGAP-mediated global inhibition limits the lateral propagation of apical ROP1 activity. We propose that the balance between the lateral propagation and the global inhibition maintains an optimal apical ROP1 cap and generates the apical ROP1 activity oscillation required for efficient pollen-tube elongation.

Compete globally, bud locally

How cells generate a single axis of polarity for mating, division, and movement is unknown. In this issue, Howell et al. (2009) use a synthetic biology approach to demonstrate that rapid competition for a soluble signaling component (Bem1) is essential to ensure a unique axis of polarity in budding yeast.

Phosphoinositides, exocytosis and polarity in yeast: all about actin?

Cell polarity is necessary for cell division, morphogenesis and motility in eukaryotes, and is determined by dynamic control of the cytoskeleton and secretory pathway to promote directional growth. In yeast, three essential and tightly-regulated processes orchestrate polarization and facilitate bud growth. These processes include phosphoinositide (PI) signaling, Rho GTPase regulation of the actin cytoskeleton, and exocytosis. As yet, the interplay between these different processes is unclear, and two main models (Spatial Landmark and Allosteric Local Activation) have been proposed for Rho GTPase control of polarization in yeast. Here, we summarize the inter-relationship between these growth processes and present a more unified model, the Exocytic Signal model, which proposes that exocytosis and actin regulation are fully integrated events mediated by PI signaling.

Symmetry breaking in the life cycle of the budding yeast

The budding yeast Saccharomyces cerevisiae has been an invaluable model system for the study of the establishment of cellular asymmetry and growth polarity in response to specific physiological cues. A large body of experimental observations has shown that yeast cells are able to break symmetry and establish polarity through two coupled and partially redundant intrinsic mechanisms, even in the absence of any pre-existing external asymmetry. One of these mechanisms is dependent upon interplay between the actin cytoskeleton and the Rho family GTPase Cdc42, whereas the other relies on a Cdc42 GTPase signaling network. Integral to these mechanisms appear to be positive feedback loops capable of amplifying small and stochastic asymmetries. Spatial cues, such as bud scars and pheromone gradients, orient cell polarity by modulating the regulation of the Cdc42 GTPase cycle, thereby biasing the site of asymmetry amplification.

The yeast endocytic protein Epsin 2 functions in a cell-division signaling pathway

The epsins are a family of adaptors involved in recruiting other endocytic proteins, binding of ubiquitylated cargo and induction of membrane curvature. These molecules bear a characteristic epsin N-terminal homology (ENTH) domain and multiple peptide motifs that mediate protein-protein interactions. We have previously demonstrated that the ENTH domain of epsin is involved in Cdc42 signaling regulation. Here, we present evidence that yeast epsin 2 (Ent2) plays a signaling role during cell division. We observed that overexpression of the ENTH domain of Ent2 (ENTH2), but not Ent1, promoted the formation of chains of cells and aberrant septa. This dominant-negative effect resulted from ENTH2-mediated interference with septin assembly pathways. We mapped the ENTH2 determinants responsible for induction of the phenotype and found them to be important for efficient binding to the septin regulatory protein, Bem3. Supporting a physiological role for epsin 2 in cell division, the protein localized to sites of polarized growth and cytokinesis and rescued a defect in cell division induced by Bem3 misregulation. Collectively, our findings provide a potential molecular mechanism linking endocytosis (via epsin 2) with signaling pathways regulating cell division.

Calling heads from tails: the role of mathematical modeling in understanding cell polarization

Theorists have long speculated on the mechanisms driving directed and spontaneous cell polarization. Recently, experimentalists have uncovered many of the mechanisms underlying polarization, enabling these models to be directly tested. In the process, they have demonstrated the explanatory and predictive value of these models and, at the same time, uncovered additional complexities not currently explained by them. In this review, we discuss some of main theories regarding cell polarization and highlight how the intersection of mathematical and experimental biology has yielded new insights into these mechanisms in the case of budding yeast and eukaryotic chemotaxis.

Organelle positioning and cell polarity

In spite of conspicuous differences in their polarized architecture, swimming unicellular eukaryotes and migrating cells from metazoa display a conserved hierarchical interlocking of the main cellular compartments, in which the microtubule network has a dominant role. A microtubule array can organize the distribution of endomembranes owing to a cell-wide and polarized extension around a unique nucleus-associated structure. The nucleus-associated structure in animal cells contains a highly conserved organelle, the centriole or basal body. This organelle has a defined polarity that can be transmitted to the cell. Its conservative mode of duplication seems to be a core mechanism for the transmission of polarities through cell division.

A genetic timer through noise-induced stabilization of an unstable state

Stochastic fluctuations affect the dynamics of biological systems. Typically, such noise causes perturbations that can permit genetic circuits to escape stable states, triggering, for example, phenotypic switching. In contrast, studies have shown that noise can surprisingly also generate new states, which exist solely in the presence of fluctuations. In those instances noise is supplied externally to the dynamical system. Here, we present a mechanism in which noise intrinsic to a simple genetic circuit effectively stabilizes a deterministically unstable state. Furthermore, this noise-induced stabilization represents a unique mechanism for a genetic timer. Specifically, we analyzed the effect of noise intrinsic to a prototypical two-component gene-circuit architecture composed of interacting positive and negative feedback loops. Genetic circuits with this topology are common in biology and typically regulate cell cycles and circadian clocks. These systems can undergo a variety of bifurcations in response to parameter changes. Simulations show that near one such bifurcation, noise induces oscillations around an unstable spiral point and thus effectively stabilizes this unstable fixed point. Because of the periodicity of these oscillations, the lifetime of the noise-dependent stabilization exhibits a polymodal distribution with multiple, well defined, and regularly spaced peaks. Therefore, the noise-induced stabilization presented here constitutes a minimal mechanism for a genetic circuit to function as a timer that could be used in the engineering of synthetic circuits.

On the spontaneous emergence of cell polarity

Diverse cell polarity networks require positive feedback for locally amplifying distributions of signalling molecules at the plasma membrane. Additional mechanisms, such as directed transport or coupled inhibitors, have been proposed to be required for reinforcing a unique axis of polarity. Here we analyse a simple model of positive feedback, with strong analogy to the 'stepping stone' model of population genetics, in which a single species of diffusible, membrane-bound signalling molecules can self-recruit from a cytoplasmic pool. We identify an intrinsic stochastic mechanism through which positive feedback alone is sufficient to account for the spontaneous establishment of a single site of polarity. We find that the polarization frequency has an inverse dependence on the number of signalling molecules: the frequency of polarization decreases as the number of molecules becomes large. Experimental observation of polarizing Cdc42 in budding yeast is consistent with this prediction. Our work suggests that positive feedback can work alone or with additional mechanisms to create robust cell polarity.

Building the cell: design principles of cellular architecture

The astounding structural complexity of a cell arises from the action of a relatively small number of genes, raising the question of how this complexity is achieved. Self-organizing processes combined with simple physical constraints seem to have key roles in controlling organelle size, number, shape and position, and these factors then combine to produce the overall cell architecture. By examining how these parameters are controlled in specific cell biological examples we can identify a handful of simple design principles that seem to underlie cellular architecture and assembly.

Coherent coupling of feedback loops: a design principle of cell signaling networks

MOTIVATION

It is widely accepted that cell signaling networks have been evolved to be robust against perturbations. To investigate the topological characteristics resulting in such robustness, we have examined large-scale signaling networks and found that a number of feedback loops are present mostly in coupled structures. In particular, the coupling was made in a coherent way implying that same types of feedback loops are interlinked together.

RESULTS

We have investigated the role of such coherently coupled feedback loops through extensive Boolean network simulations and found that a high proportion of coherent couplings can enhance the robustness of a network against its state perturbations. Moreover, we found that the robustness achieved by coherently coupled feedback loops can be kept evolutionarily stable. All these results imply that the coherent coupling of feedback loops might be a design principle of cell signaling networks devised to achieve the robustness.

Pom1 DYRK regulates localization of the Rga4 GAP to ensure bipolar activation of Cdc42 in fission yeast

BACKGROUND

In the fission yeast Schizosaccharomyces pombe, cell growth takes place exclusively at both ends of the cylindrical cell. During this highly polarized growth, microtubules are responsible for the placement of the cell-end marker proteins, the Tea1-Tea4/Wsh3 complex, which recruits the Pom1 DYRK-family protein kinase. Pom1 is required for proper positioning of growth sites, and the Deltapom1 mutation brings about monopolar cell growth.

RESULTS

Pom1 kinase physically interacts with Rga4, which has a GAP (GTPase-activating protein) domain for Rho-family GTPase. Genetic and biochemical evidence indicates that Rga4 functions as GAP for the Cdc42 GTPase, an evolutionarily conserved regulator of F-actin. CRIB (Cdc42/Rac interactive binding)-GFP microscopy has revealed that GTP-bound, active Cdc42 is concentrated to growing cell ends accompanied by developed F-actin structures, where the Rga4 GAP is excluded. The monopolar Deltapom1 mutant fails to eliminate Rga4 from the nongrowing cell end, resulting in monopolar distribution of GTP-Cdc42 to the growing cell end. However, mutational inactivation of Rga4 allows Cdc42 to be active at both ends of Deltapom1 cells, suggesting that mislocalization of Rga4 in the Deltapom1 mutant contributes to its monopolar phenotype.

CONCLUSIONS

Pom1 kinase recruited to cell ends by the Tea1-Tea4/Wsh3 complex is essential for proper localization of a GAP for Cdc42, Rga4, which ensures bipolar localization of GTP-bound, active Cdc42. Because of the established role of Cdc42 in F-actin formation, these observations provide a new insight into how the microtubule system achieves localized formation of F-actin to generate cell polarity.

Quantitative analysis of robustness and fragility in biological networks based on feedback dynamics

MOTIVATION

It has been widely reported that biological networks are robust against perturbations such as mutations. On the contrary, it has also been known that biological networks are often fragile against unexpected mutations. There is a growing interest in these intriguing observations and the underlying design principle that causes such robust but fragile characteristics of biological networks. For relatively small networks, a feedback loop has been considered as an important motif for realizing the robustness. It is still, however, not clear how a number of coupled feedback loops actually affect the robustness of large complex biological networks. In particular, the relationship between fragility and feedback loops has not yet been investigated till now.

RESULTS

Through extensive computational experiments, we found that networks with a larger number of positive feedback loops and a smaller number of negative feedback loops are likely to be more robust against perturbations. Moreover, we found that the nodes of a robust network subject to perturbations are mostly involved with a smaller number of feedback loops compared with the other nodes not usually subject to perturbations. This topological characteristic eventually makes the robust network fragile against unexpected mutations at the nodes not previously exposed to perturbations.

Wave-pinning and cell polarity from a bistable reaction-diffusion system

Motile eukaryotic cells polarize in response to external signals. Numerous mechanisms have been suggested to account for this symmetry breaking and for the ensuing robust polarization. Implicated in this process are various proteins that are recruited to the plasma membrane and segregate at an emergent front or back of the polarizing cell. Among these are PI3K, PTEN, and members of the Rho family GTPases such as Cdc42, Rac, and Rho. Many such proteins, including the Rho GTPases, cycle between active membrane-bound forms and inactive cytosolic forms. In previous work, we have shown that this property, together with appropriate crosstalk, endows a biochemical circuit (Cdc42, Rac, and Rho) with the property of inherent polarizability. Here we show that this property is present in an even simpler system comprised of a single active/inactive protein pair with positive feedback to its own activation. The simplicity of this minimal system also allows us to explain the mechanism using insights from mathematical analysis. The basic idea resides in a well-known property of reaction-diffusion systems with bistable kinetics, namely, propagation of fronts. However, it crucially depends on exchange between active and inactive forms of the chemicals with unequal rates of diffusion, and overall conservation to pin the waves into a stable polar distribution. We refer to these dynamics as wave-pinning and we show that this phenomenon is distinct from Turing-instability-generated pattern formation that occurs in reaction-diffusion systems that appear to be very similar. We explain the mathematical basis of the phenomenon, relate it to spatial segregation of Rho GTPases, and show how it can account for spatial amplification and maintenance of polarity, as well as sensitivity to new stimuli typical in polarization of eukaryotic cells.

Analysis of feedback loops and robustness in network evolution based on Boolean models

BACKGROUND

Many biological networks such as protein-protein interaction networks, signaling networks, and metabolic networks have topological characteristics of a scale-free degree distribution. Preferential attachment has been considered as the most plausible evolutionary growth model to explain this topological property. Although various studies have been undertaken to investigate the structural characteristics of a network obtained using this growth model, its dynamical characteristics have received relatively less attention.

RESULTS

In this paper, we focus on the robustness of a network that is acquired during its evolutionary process. Through simulations using Boolean network models, we found that preferential attachment increases the number of coupled feedback loops in the course of network evolution. Whereas, if networks evolve to have more coupled feedback loops rather than following preferential attachment, the resulting networks are more robust than those obtained through preferential attachment, although both of them have similar degree distributions.

CONCLUSION

The presented analysis demonstrates that coupled feedback loops may play an important role in network evolution to acquire robustness. The result also provides a hint as to why various biological networks have evolved to contain a number of coupled feedback loops.

Spatial regulation of Fus3 MAP kinase activity through a reaction-diffusion mechanism in yeast pheromone signalling

Signal transduction through mitogen-activated protein kinase (MAPK) cascades is thought to occur through the assembly of macromolecular complexes. We quantified the abundance of complexes in the cytoplasm among the MAPKs Ste11, Ste7, Fus3 and the scaffold protein Ste5 in yeast pheromone signalling using fluorescence cross-correlation spectroscopy (FCCS). Significant complex concentrations were observed that remained unchanged on pheromone stimulation, demonstrating that global changes in complex abundances do not contribute to the transmission of signal through the cytoplasm. On the other hand, investigation of the distribution of active Fus3 (Fus3(PP)) across the cytoplasm using fluorescence lifetime imaging microscopy (FLIM) revealed a gradient of Fus3(PP) activity emanating from the tip of the mating projection. Spatial partitioning of Fus3 activating kinases to this site and deactivating phosphatases in the cytoplasm maintain this Fus3(PP)-activity distribution. Propagation of signalling from the shmoo is, therefore, spatially constrained by a gradient-generating reaction-diffusion mechanism.

Phosphorylation of Bem2p and Bem3p may contribute to local activation of Cdc42p at bud emergence

Site-specific activation of the Rho-type GTPase Cdc42p is critical for the establishment of cell polarity. Here we investigated the role and regulation of the GTPase-activating enzymes (GAPs) Bem2p and Bem3p for Cdc42p activation and actin polarization at bud emergence in Saccharomyces cerevisiae. Bem2p and Bem3p are localized throughout the cytoplasm and the cell cortex in unbudded G1 cells, but accumulate at sites of polarization after bud emergence. Inactivation of Bem2p results in hyperactivation of Cdc42p and polarization toward multiple sites. Bem2p and Bem3p are hyperphosphorylated at bud emergence most likely by the Cdc28p-Cln2p kinase. This phosphorylation appears to inhibit their GAP activity in vivo, as non-phosphorylatable Bem3p mutants are hyperactive and interfere with Cdc42p activation. Taken together, our results indicate that Bem2p and Bem3p may function as global inhibitors of Cdc42p activation during G1, and their inactivation by the Cdc28p/Cln kinase contributes to site-specific activation of Cdc42p at bud emergence.

Identification of novel membrane-binding domains in multiple yeast Cdc42 effectors

The Rho-type GTPase Cdc42 is a central regulator of eukaryotic cell polarity and signal transduction. In budding yeast, Cdc42 regulates polarity and mitogen-activated protein (MAP) kinase signaling in part through the PAK-family kinase Ste20. Activation of Ste20 requires a Cdc42/Rac interactive binding (CRIB) domain, which mediates its recruitment to membrane-associated Cdc42. Here, we identify a separate domain in Ste20 that interacts directly with membrane phospholipids and is critical for its function. This short region, termed the basic-rich (BR) domain, can target green fluorescent protein to the plasma membrane in vivo and binds PIP(2)-containing liposomes in vitro. Mutation of basic or hydrophobic residues in the BR domain abolishes polarized localization of Ste20 and its function in both MAP kinase-dependent and independent pathways. Thus, Cdc42 binding is required but is insufficient; instead, direct membrane binding by Ste20 is also required. Nevertheless, phospholipid specificity is not essential in vivo, because the BR domain can be replaced with several heterologous lipid-binding domains of varying lipid preferences. We also identify functionally important BR domains in two other yeast Cdc42 effectors, Gic1 and Gic2, suggesting that cooperation between protein-protein and protein-membrane interactions is a prevalent mechanism during Cdc42-regulated signaling and perhaps for other dynamic localization events at the cell cortex.

From segment to somite: segmentation to epithelialization analyzed within quantitative frameworks

One of the most visually striking patterns in the early developing embryo is somite segmentation. Somites form as repeated, periodic structures in pairs along nearly the entire caudal vertebrate axis. The morphological process involves short- and long-range signals that drive cell rearrangements and cell shaping to create discrete, epithelialized segments. Key to developing novel strategies to prevent somite birth defects that involve axial bone and skeletal muscle development is understanding how the molecular choreography is coordinated across multiple spatial scales and in a repeating temporal manner. Mathematical models have emerged as useful tools to integrate spatiotemporal data and simulate model mechanisms to provide unique insights into somite pattern formation. In this short review, we present two quantitative frameworks that address the morphogenesis from segment to somite and discuss recent data of segmentation and epithelialization.

Combinatorial promoter design for engineering noisy gene expression

Understanding the behavior of basic biomolecular components as parts of larger systems is one of the goals of the developing field of synthetic biology. A multidisciplinary approach, involving mathematical and computational modeling in parallel with experimentation, is often crucial for gaining such insights and improving the efficiency of artificial gene network design. Here we used such an approach and developed a combinatorial promoter design strategy to characterize how the position and multiplicity of tetO(2) operator sites within the GAL1 promoter affect gene expression levels and gene expression noise in Saccharomyces cerevisiae. We observed stronger transcriptional repression and higher gene expression noise as a single operator site was moved closer to the TATA box, whereas for multiple operator-containing promoters, we found that the position and number of operator sites together determined the dose-response curve and gene expression noise. We developed a generic computational model that captured the experimentally observed differences for each of the promoters, and more detailed models to successively predict the behavior of multiple operator-containing promoters from single operator-containing promoters. Our results suggest that the independent binding of single repressors is not sufficient to explain the more complex behavior of the multiple operator-containing promoters. Taken together, our findings highlight the importance of joint experimental-computational efforts and some of the challenges of using a bottom-up approach based on well characterized, isolated biomolecular components for predicting the behavior of complex, synthetic gene networks, e.g., the whole can be different from the sum of its parts.

Drosophila hemopoiesis and cellular immunity

In Drosophila melanogaster larvae, three classes of circulating cellular immune surveillance cells (hemocytes) can be identified: plasmatocytes, crystal cells, and lamellocytes. Plasmatocytes are professional phagocytes most similar to the mammalian monocyte/macrophage lineage and make up approximately 95% of circulating hemocytes. The other approximately 5% of circulating hemocytes consists of crystal cells, which secrete components necessary for the melanization of invading organisms, as well as for wound repair. A third cell type known as lamellocytes are rarely seen in healthy larvae and are involved in the encapsulation of invading pathogens. There are no obvious mammalian counterparts for crystal cells or lamellocytes, and there is no equivalent to the lymphoid lineage in insects. In this review, I will discuss what is currently known about Drosophila hemopoiesis and the cellular immune response and where possible compare it to vertebrate mechanisms.

Endocytosis optimizes the dynamic localization of membrane proteins that regulate cortical polarity

Diverse cell types require the ability to maintain dynamically polarized membrane-protein distributions through balancing transport and diffusion. However, design principles underlying dynamically maintained cortical polarity are not well understood. Here we constructed a mathematical model for characterizing the morphology of dynamically polarized protein distributions. We developed analytical approaches for measuring all model parameters from single-cell experiments. We applied our methods to a well-characterized system for studying polarized membrane proteins: budding yeast cells expressing activated Cdc42. We found that a balance of diffusion, directed transport, and endocytosis was sufficient for accurately describing polarization morphologies. Surprisingly, the model predicts that polarized regions are defined with a precision that is nearly optimal for measured endocytosis rates and that polarity can be dynamically stabilized through positive feedback with directed transport. Our approach provides a step toward understanding how biological systems shape spatially precise, unambiguous cortical polarity domains using dynamic processes.

Central roles of small GTPases in the development of cell polarity in yeast and beyond

SUMMARY

The establishment of cell polarity is critical for the development of many organisms and for the function of many cell types. A large number of studies of diverse organisms from yeast to humans indicate that the conserved, small-molecular-weight GTPases function as key signaling proteins involved in cell polarization. The budding yeast Saccharomyces cerevisiae is a particularly attractive model because it displays pronounced cell polarity in response to intracellular and extracellular cues. Cells of S. cerevisiae undergo polarized growth during various phases of their life cycle, such as during vegetative growth, mating between haploid cells of opposite mating types, and filamentous growth upon deprivation of nutrition such as nitrogen. Substantial progress has been made in deciphering the molecular basis of cell polarity in budding yeast. In particular, it becomes increasingly clear how small GTPases regulate polarized cytoskeletal organization, cell wall assembly, and exocytosis at the molecular level and how these GTPases are regulated. In this review, we discuss the key signaling pathways that regulate cell polarization during the mitotic cell cycle and during mating.

Coupled positive and negative feedback circuits form an essential building block of cellular signaling pathways

Cellular circuits have positive and negative feedback loops that allow them to respond properly to noisy external stimuli. It is intriguing that such feedback loops exist in many cases in a particular form of coupled positive and negative feedback loops with different time delays. As a result of our mathematical simulations and investigations into various experimental evidences, we found that such coupled feedback circuits can rapidly turn on a reaction to a proper stimulus, robustly maintain its status, and immediately turn off the reaction when the stimulus disappears. In other words, coupled feedback loops enable cellular systems to produce perfect responses to noisy stimuli with respect to signal duration and amplitude. This suggests that coupled positive and negative feedback loops form essential signal transduction motifs in cellular signaling systems.