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

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

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

Modeling vesicle traffic reveals unexpected consequences for Cdc42p-mediated polarity establishment

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

Inhibitory GEF Phosphorylation Provides Negative Feedback in the Yeast Polarity Circuit

Cell polarity is critical for the form and function of many celltypes. During polarity establishment, cells define a cortical‘‘front’’ that behaves differently from the rest of the cortex.The front accumulates high levels of the active form ofa polarity-determining Rho-family GTPase (Cdc42, Rac, orRop) that then orients cytoskeletal elements through variouseffectors to generate the polarized morphology appropriateto the particular cell type [1, 2]. GTPase accumulation isthought to involve positive feedback, such that activeGTPase promotes further delivery and/or activation ofmore GTPase in its vicinity [3]. Recent studies suggest thatonce a front forms, the concentration of polarity factors atthe front can increase and decrease periodically, first clus-tering the factors at the cortex and then dispersing themback to the cytoplasm [4–7]. Such oscillatory behaviorimplies the presence of negative feedback in the polaritycircuit [8], but the mechanism of negative feedback wasnot known. Here we show that, in the budding yeastSaccha-romyces cerevisiae, the catalytic activity of the Cdc42-directed GEF is inhibited by Cdc42-stimulated effectorkinases, thus providing negative feedback. We furthershow that replacing the GEF with a phosphosite mutantGEF abolishes oscillations and leads to the accumulationof excess GTP-Cdc42 and other polarity factors at the front.These findings reveal a mechanism for negative feedbackand suggest that the function of negative feedback via GEFinhibition is to buffer the level of Cdc42 at the polarity site

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 up-gradient. How non-motile 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 non-motile cells to track shallow gradients

Parallel Actin-Independent Recycling Pathways Polarize Cdc42 in Budding Yeast

The highly conserved Rho-family GTPase Cdc42 is an essential regulator of polarity in many different cell types. During polarity establishment, Cdc42 becomes concentrated at a cortical site, where it interacts with downstream effectors to orient the cytoskeleton along the front-back axis. To concentrate Cdc42, loss of Cdc42 by diffusion must be balanced by recycling to the front. In Saccharomyces cerevisiae, the guanine nucleotide dissociation inhibitor (GDI) Rdi1 recycles Cdc42 through the cytoplasm. Loss of Rdi1 slowed but did not eliminate Cdc42 accumulation at the front, suggesting the existence of other recycling pathways. One proposed pathway involves actin-directed trafficking of vesicles carrying Cdc42 to the front. However, we found no role for F-actin in Cdc42 concentration, even in rdi1 Delta cells. Instead, Cdc42 was still able to exchange between the membrane and cytoplasm in rdi1 Delta cells, albeit at a reduced rate. Membrane-cytoplasm exchange of GDP-Cdc42 was faster than that of GTP-Cdc42, and computational modeling indicated that such exchange would suffice to promote polarization. We also uncovered a novel role for the Cdc42-directed GTPase-activating protein (GAP) Bem2 in Cdc42 polarization. Bem2 was known to act in series with Rdi1 to promote recycling of Cdc42, but we found that rdi1 Delta bem2 Delta mutants were synthetically lethal, suggesting that they also act in parallel. We suggest that GAP activity cooperates with the GDI to counteract the dissipative effect of a previously unappreciated pathway whereby GTP-Cdc42 escapes from the polarity site through the cytoplasm

‘The past was never simply there to begin with and the future is not simply what will unfold’ : a posthumanist performative approach to qualitative longitudinal research

Peer reviewedPostprin

Assessing secondary attack rates among household contacts at the beginning of the influenza A (H1N1) pandemic in Ontario, Canada, April-June 2009: A prospective, observational study

<p>Abstract</p> <p>Background</p> <p>Understanding transmission dynamics of the pandemic influenza A (H1N1) virus in various exposure settings and determining whether transmissibility differed from seasonal influenza viruses was a priority for decision making on mitigation strategies at the beginning of the pandemic. The objective of this study was to estimate household secondary attack rates for pandemic influenza in a susceptible population where control measures had yet to be implemented.</p> <p>Methods</p> <p>All Ontario local health units were invited to participate; seven health units volunteered. For all laboratory-confirmed cases reported between April 24 and June 18, 2009, participating health units performed contact tracing to detect secondary cases among household contacts. In total, 87 cases and 266 household contacts were included in this study. Secondary cases were defined as any household member with new onset of acute respiratory illness (fever or two or more respiratory symptoms) or influenza-like illness (fever plus one additional respiratory symptom). Attack rates were estimated using both case definitions.</p> <p>Results</p> <p>Secondary attack rates were estimated at 10.3% (95% CI 6.8-14.7) for secondary cases with influenza-like illness and 20.2% (95% CI 15.4-25.6) for secondary cases with acute respiratory illness. For both case definitions, attack rates were significantly higher in children under 16 years than adults (25.4% and 42.4% compared to 7.6% and 17.2%). The median time between symptom onset in the primary case and the secondary case was estimated at 3.0 days.</p> <p>Conclusions</p> <p>Secondary attack rates for pandemic influenza A (H1N1) were comparable to seasonal influenza estimates suggesting similarities in transmission. High secondary attack rates in children provide additional support for increased susceptibility to infection.</p

Positional Signaling and Expression of ENHANCER OF TRY AND CPC1 Are Tuned to Increase Root Hair Density in Response Phosphate Deficiency in Arabidopsis thaliana

Phosphate (Pi) deficiency induces a multitude of responses aimed at improving the acquisition of Pi, including an increased density of root hairs. To understand the mechanisms involved in Pi deficiency-induced alterations of the root hair phenotype in Arabidopsis (Arabidopsis thaliana), we analyzed the patterning and length of root epidermal cells under control and Pi-deficient conditions in wild-type plants and in four mutants defective in the expression of master regulators of cell fate, CAPRICE (CPC), ENHANCER OF TRY AND CPC 1 (ETC1), WEREWOLF (WER) and SCRAMBLED (SCM). From this analysis we deduced that the longitudinal cell length of root epidermal cells is dependent on the correct perception of a positional signal (‘cortical bias’) in both control and Pi-deficient plants; mutants defective in the receptor of the signal, SCM, produced short cells characteristic of root hair-forming cells (trichoblasts). Simulating the effect of cortical bias on the time-evolving probability of cell fate supports a scenario in which a compromised positional signal delays the time point at which non-hair cells opt out the default trichoblast pathway, resulting in short, trichoblast-like non-hair cells. Collectively, our data show that Pi-deficient plants increase root hair density by the formation of shorter cells, resulting in a higher frequency of hairs per unit root length, and additional trichoblast cell fate assignment via increased expression of ETC1