Singularity in polarization:rewiring yeast cells to make two buds

SummaryFor budding yeast to ensure formation of only one bud, cells must polarize toward one, and only one, site. Polarity establishment involves the Rho family GTPase Cdc42, which concentrates at polarization sites via a positive feedback loop. To assess whether singularity is linked to the specific Cdc42 feedback loop, we disabled the yeast cell's endogenous amplification mechanism and synthetically rewired the cells to employ a different positive feedback loop. Rewired cells violated singularity, occasionally making two buds. Even cells that made only one bud sometimes initiated two clusters of Cdc42, but then one cluster became dominant. Mathematical modeling indicated that, given sufficient time, competition between clusters would promote singularity. In rewired cells, competition occurred slowly and sometimes failed to develop a single “winning” cluster before budding. Slowing competition in normal cells also allowed occasional formation of two buds, suggesting that singularity is enforced by rapid competition between Cdc42 clusters

Turing instabilities in a mathematical model for signaling networks

GTPase molecules are important regulators in cells that continuously run through an activation/deactivation and membrane-attachment/membrane-detachment cycle. Activated GTPase is able to localize in parts of the membranes and to induce cell polarity. As feedback loops contribute to the GTPase cycle and as the coupling between membrane-bound and cytoplasmic processes introduces different diffusion coefficients a Turing mechanism is a natural candidate for this symmetry breaking. We formulate a mathematical model that couples a reaction-diffusion system in the inner volume to a reaction-diffusion system on the membrane via a flux condition and an attachment/detachment law at the membrane. We present a reduction to a simpler non-local reaction-diffusion model and perform a stability analysis and numerical simulations for this reduction. Our model in principle does support Turing instabilities but only if the lateral diffusion of inactivated GTPase is much faster than the diffusion of activated GTPase.Comment: 23 pages, 5 figures; The final publication is available at http://www.springerlink.com http://dx.doi.org/10.1007/s00285-011-0495-

Polarized Growth in the Absence of F-Actin in Saccharomyces cerevisiae Exiting Quiescence

Polarity establishment and maintenance are crucial for morphogenesis and development. In budding yeast, these two intricate processes involve the superposition of regulatory loops between polarity landmarks, RHO GTPases, actin-mediated vesicles transport and endocytosis. Deciphering the chronology and the significance of each molecular step of polarized growth is therefore very challenging.We have taken advantage of the fact that yeast quiescent cells display actin bodies, a non polarized actin structure, to evaluate the role of F-actin in bud emergence. Here we show that upon exit from quiescence, actin cables are not required for the first steps of polarized growth. We further show that polarized growth can occur in the absence of actin patch-mediated endocytosis. We finally establish, using latrunculin-A, that the first steps of polarized growth do not require any F-actin containing structures. Yet, these structures are required for the formation of a bona fide daughter cell and cell cycle completion. We propose that upon exit from quiescence in the absence of F-actin, secretory vesicles randomly reach the plasma membrane but preferentially dock and fuse where polarity cues are localized, this being sufficient to trigger polarized growth

The Rho GDI Rdi1 regulates Rho GTPases by distinct mechanisms

© 2008 by The American Society for Cell Biology. Under the License and Publishing Agreement, authors grant to the general public, effective two months after publication of (i.e.,. the appearance of) the edited manuscript in an online issue of MBoC, the nonexclusive right to copy, distribute, or display the manuscript subject to the terms of the Creative Commons–Noncommercial–Share Alike 3.0 Unported license (http://creativecommons.org/licenses/by-nc-sa/3.0).The small guanosine triphosphate (GTP)-binding proteins of the Rho family are implicated in various cell functions, including establishment and maintenance of cell polarity. Activity of Rho guanosine triphosphatases (GTPases) is not only regulated by guanine nucleotide exchange factors and GTPase-activating proteins but also by guanine nucleotide dissociation inhibitors (GDIs). These proteins have the ability to extract Rho proteins from membranes and keep them in an inactive cytosolic complex. Here, we show that Rdi1, the sole Rho GDI of the yeast Saccharomyces cerevisiae, contributes to pseudohyphal growth and mitotic exit. Rdi1 interacts only with Cdc42, Rho1, and Rho4, and it regulates these Rho GTPases by distinct mechanisms. Binding between Rdi1 and Cdc42 as well as Rho1 is modulated by the Cdc42 effector and p21-activated kinase Cla4. After membrane extraction mediated by Rdi1, Rho4 is degraded by a novel mechanism, which includes the glycogen synthase kinase 3β homologue Ygk3, vacuolar proteases, and the proteasome. Together, these results indicate that Rdi1 uses distinct modes of regulation for different Rho GTPases.Deutsche Forschungsgemeinschaf

A Density-Dependent Switch Drives Stochastic Clustering and Polarization of Signaling Molecules

Positive feedback plays a key role in the ability of signaling molecules to form highly localized clusters in the membrane or cytosol of cells. Such clustering can occur in the absence of localizing mechanisms such as pre-existing spatial cues, diffusional barriers, or molecular cross-linking. What prevents positive feedback from amplifying inevitable biological noise when an un-clustered “off” state is desired? And, what limits the spread of clusters when an “on” state is desired? Here, we show that a minimal positive feedback circuit provides the general principle for both suppressing and amplifying noise: below a critical density of signaling molecules, clustering switches off; above this threshold, highly localized clusters are recurrently generated. Clustering occurs only in the stochastic regime, suggesting that finite sizes of molecular populations cannot be ignored in signal transduction networks. The emergence of a dominant cluster for finite numbers of molecules is partly a phenomenon of random sampling, analogous to the fixation or loss of neutral mutations in finite populations. We refer to our model as the “neutral drift polarity model.” Regulating the density of signaling molecules provides a simple mechanism for a positive feedback circuit to robustly switch between clustered and un-clustered states. The intrinsic ability of positive feedback both to create and suppress clustering is a general mechanism that could operate within diverse biological networks to create dynamic spatial organization

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

De Novo Growth Zone Formation from Fission Yeast Spheroplasts

Eukaryotic cells often form polarized growth zones in response to internal or external cues. To understand the establishment of growth zones with specific dimensions we used fission yeast, which grows as a rod-shaped cell of near-constant width from growth zones located at the cell tips. Removing the cell wall creates a round spheroplast with a disorganized cytoskeleton and depolarized growth proteins. As spheroplasts recover, new growth zones form that resemble normal growing cell tips in shape and width, and polarized growth resumes. Regulators of the GTPase Cdc42, which control width in exponentially growing cells, also control spheroplast growth zone width. During recovery the Cdc42 scaffold Scd2 forms a polarized patch in the rounded spheroplast, demonstrating that a growth zone protein can organize independent of cell shape. Rga4, a Cdc42 GTPase activating protein (GAP) that is excluded from cell tips, is initially distributed throughout the spheroplast membrane, but is excluded from the growth zone after a stable patch of Scd2 forms. These results provide evidence that growth zones with normal width and protein localization can form de novo through sequential organization of cellular domains, and that the size of these growth zones is genetically controlled, independent of preexisting cell shape

Rho GTPase Cdc42 Is a Direct Interacting Partner of Adenomatous Polyposis Coli Protein and Can Alter Its Cellular Localization

Adenomatous Polyposis Coli (APC) is a tumor suppressor gene product involved in colon cancer. APC is a large multidomain molecule of 2843 amino acid residues and connects cell-cell adhesion, the F-actin/microtubule cytoskeleton and the nucleus. Here we show that Cdc42 interacts directly with the first three armadillo repeats of APC by yeast two-hybrid screens. We confirm the Cdc42-APC interaction using pulldown assays in vitro and FRET assays in vivo. Interestingly, Cdc42 interacts with APC at leading edge sites where F-actin is enriched. In contrast, Cdc42 interacts with the truncated mutant APC1–1638 in cellular puncta associated with the golgi-lysozome pathway in transfected CHO cells. In HCT116 and SW480 cells, Cdc42 induces the relocalization of endogenous APC and the mutant APC1–1338 to the plasma membrane and cellular puncta, respectively. Taken together, these data indicate that the Cdc42-APC interaction induces localization of both APC and mutant APC and may thus play a direct role in the functions of these proteins

Modeling Robustness Tradeoffs in Yeast Cell Polarization Induced by Spatial Gradients

Cells localize (polarize) internal components to specific locations in response to external signals such as spatial gradients. For example, yeast cells form a mating projection toward the source of mating pheromone. There are specific challenges associated with cell polarization including amplification of shallow external gradients of ligand to produce steep internal gradients of protein components (e.g. localized distribution), response over a broad range of ligand concentrations, and tracking of moving signal sources. In this work, we investigated the tradeoffs among these performance objectives using a generic model that captures the basic spatial dynamics of polarization in yeast cells, which are small. We varied the positive feedback, cooperativity, and diffusion coefficients in the model to explore the nature of this tradeoff. Increasing the positive feedback gain resulted in better amplification, but also produced multiple steady-states and hysteresis that prevented the tracking of directional changes of the gradient. Feedforward/feedback coincidence detection in the positive feedback loop and multi-stage amplification both improved tracking with only a modest loss of amplification. Surprisingly, we found that introducing lateral surface diffusion increased the robustness of polarization and collapsed the multiple steady-states to a single steady-state at the cost of a reduction in polarization. Finally, in a more mechanistic model of yeast cell polarization, a surface diffusion coefficient between 0.01 and 0.001 µm2/s produced the best polarization performance, and this range is close to the measured value. The model also showed good gradient-sensitivity and dynamic range. This research is significant because it provides an in-depth analysis of the performance tradeoffs that confront biological systems that sense and respond to chemical spatial gradients, proposes strategies for balancing this tradeoff, highlights the critical role of lateral diffusion of proteins in the membrane on the robustness of polarization, and furnishes a framework for future spatial models of yeast cell polarization