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.

[1]  Timothy C Elston,et al.  Role of competition between polarity sites in establishing a unique front , 2015, eLife.

[2]  K. Sawin,et al.  Remodeling of the Fission Yeast Cdc42 Cell-Polarity Module via the Sty1 p38 Stress-Activated Protein Kinase Pathway , 2016, Current Biology.

[3]  A. M. Turing,et al.  The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[4]  Jasmine A. Nirody,et al.  An introduction to linear stability analysis for deciphering spatial patterns in signaling networks , 2016, bioRxiv.

[5]  J. Sibarita,et al.  Robust polarity establishment occurs via an endocytosis-based cortical corralling mechanism , 2013, The Journal of cell biology.

[6]  I. Herskowitz,et al.  The role of Far1p in linking the heterotrimeric G protein to polarity establishment proteins during yeast mating. , 1998, Science.

[7]  Henry R. Bourne,et al.  Cell polarity: A chemical compass , 2002, Nature.

[8]  Jared L. Johnson,et al.  New Insights into How the Rho Guanine Nucleotide Dissociation Inhibitor Regulates the Interaction of Cdc42 with Membranes* , 2009, The Journal of Biological Chemistry.

[9]  A. Mogilner,et al.  Cell Polarity: Quantitative Modeling as a Tool in Cell Biology , 2012, Science.

[10]  E. Bi,et al.  Adjacent positioning of cellular structures enabled by a Cdc42 GTPase-activating protein–mediated zone of inhibition , 2007, The Journal of cell biology.

[11]  K. Kozminski,et al.  Cdc42 Interacts with the Exocyst and Regulates Polarized Secretion* , 2001, The Journal of Biological Chemistry.

[12]  Brian D. Slaughter,et al.  Flippase-mediated phospholipid asymmetry promotes fast Cdc42 recycling in dynamic maintenance of cell polarity , 2012, Nature Cell Biology.

[13]  Alexandra Jilkine,et al.  Asymptotic and Bifurcation Analysis of Wave-Pinning in a Reaction-Diffusion Model for Cell Polarization , 2010, SIAM J. Appl. Math..

[14]  M. Rao,et al.  Active Remodeling of Cortical Actin Regulates Spatiotemporal Organization of Cell Surface Molecules , 2012, Cell.

[15]  A. Bretscher,et al.  Polarization of cell growth in yeast. I. Establishment and maintenance of polarity states. , 2000, Journal of cell science.

[16]  E. Bi,et al.  Cell Polarization and Cytokinesis in Budding Yeast , 2012, Genetics.

[17]  Jonathon Howard,et al.  Turing's next steps: the mechanochemical basis of morphogenesis , 2011, Nature Reviews Molecular Cell Biology.

[18]  Lani Wu,et al.  Spontaneous Cell Polarization Through Actomyosin-Based Delivery of the Cdc42 GTPase , 2003, Science.

[19]  Yevgeny Berdichevsky,et al.  Dissociation of Rac1(GDP)·RhoGDI Complexes by the Cooperative Action of Anionic Liposomes Containing Phosphatidylinositol 3,4,5-Trisphosphate, Rac Guanine Nucleotide Exchange Factor, and GTP* , 2008, Journal of Biological Chemistry.

[20]  P. Nurse,et al.  Spatial control of Cdc42 activation determines cell width in fission yeast , 2011, Molecular biology of the cell.

[21]  Daniel J. Lew,et al.  A Morphogenesis Checkpoint Monitors the Actin Cytoskeleton in Yeast , 1998, The Journal of cell biology.

[22]  Brian D. Slaughter,et al.  Non-uniform membrane diffusion enables steady-state cell polarization via vesicular trafficking , 2013, Nature Communications.

[23]  A. Bretscher,et al.  Polarization of cell growth in yeast. , 2000, Journal of cell science.

[24]  Anna Payne-Tobin Jost,et al.  Probing Yeast Polarity with Acute, Reversible, Optogenetic Inhibition of Protein Function. , 2015, ACS synthetic biology.

[25]  M. Endo,et al.  The Cdc42 Binding and Scaffolding Activities of the Fission Yeast Adaptor Protein Scd2* , 2003, The Journal of Biological Chemistry.

[26]  Adriana T. Dawes,et al.  PAR-3 oligomerization may provide an actin-independent mechanism to maintain distinct par protein domains in the early Caenorhabditis elegans embryo. , 2011, Biophysical journal.

[27]  J. Davies,et al.  Molecular Biology of the Cell , 1983, Bristol Medico-Chirurgical Journal.

[28]  Michelle D. Larrea,et al.  Regulation of cell diameter, For3p localization, and cell symmetry by fission yeast Rho-GAP Rga4p. , 2007, Molecular biology of the cell.

[29]  Leah Edelstein-Keshet,et al.  Synthetic spatially graded Rac activation drives cell polarization and movement , 2012, Proceedings of the National Academy of Sciences.

[30]  Timothy C Elston,et al.  Role of Polarized G Protein Signaling in Tracking Pheromone Gradients. , 2015, Developmental cell.

[31]  M. Peter,et al.  A Cellular System for Spatial Signal Decoding in Chemical Gradients. , 2015, Developmental cell.

[32]  M. Peter,et al.  Phosphorylation of the Cdc42 exchange factor Cdc24 by the PAK-like kinase Cla4 may regulate polarized growth in yeast. , 2000, Molecular cell.

[33]  J. Tyson,et al.  Design principles of biochemical oscillators , 2008, Nature Reviews Molecular Cell Biology.

[34]  A. R. Khan,et al.  Structural biology of Arf and Rab GTPases' effector recruitment and specificity. , 2013, Structure.

[35]  H. Bourne,et al.  A chemical compass. , 2002, Nature.

[36]  Chun-Chen Kuo,et al.  Cdc42p regulation of the yeast formin Bni1p mediated by the effector Gic2p , 2012, Molecular biology of the cell.

[37]  D. Lew,et al.  Interaction between bud-site selection and polarity-establishment machineries in budding yeast , 2013, Philosophical Transactions of the Royal Society B: Biological Sciences.

[38]  Alexandra V. Pokhilko,et al.  Computational Model Explains High Activity and Rapid Cycling of Rho GTPases within Protein Complexes , 2006, PLoS Comput. Biol..

[39]  K. Rittinger,et al.  Interactions between Cdc42 and the scaffold protein Scd2: requirement of SH3 domains for GTPase binding. , 2005, The Biochemical journal.

[40]  J. Pringle,et al.  Molecular characterization of CDC42, a Saccharomyces cerevisiae gene involved in the development of cell polarity , 1990, The Journal of cell biology.

[41]  K. Shiozaki,et al.  Pom1 DYRK Regulates Localization of the Rga4 GAP to Ensure Bipolar Activation of Cdc42 in Fission Yeast , 2008, Current Biology.

[42]  Bruce Bowerman,et al.  Symmetry breaking in biology. , 2010, Cold Spring Harbor perspectives in biology.

[43]  K. Knobeloch,et al.  Cell-Intrinsic Adaptation Arising from Chronic Ablation of a Key Rho GTPase Regulator. , 2016, Developmental cell.

[44]  Amy S. Gladfelter,et al.  Scaffold-mediated symmetry breaking by Cdc42p , 2003, Nature Cell Biology.

[45]  A. Seminara,et al.  Phosphatidylinositol-4-phosphate-dependent membrane traffic is critical for fungal filamentous growth , 2015, Proceedings of the National Academy of Sciences.

[46]  Arezki Boudaoud,et al.  Symmetry breaking in spore germination relies on an interplay between polar cap stability and spore wall mechanics. , 2014, Developmental cell.

[47]  Albert-László Barabási,et al.  Control Principles of Complex Networks , 2015, ArXiv.

[48]  Hay-Oak Park,et al.  Mathematical Analysis of Spontaneous Emergence of Cell Polarity , 2014, Bulletin of mathematical biology.

[49]  Andrew B. Goryachev,et al.  Daughter Cell Identity Emerges from the Interplay of Cdc42, Septins, and Exocytosis , 2013, Developmental cell.

[50]  I. Prigogine,et al.  On symmetry-breaking instabilities in dissipative systems , 1967 .

[51]  Sophie G. Martin Spontaneous cell polarization: Feedback control of Cdc42 GTPase breaks cellular symmetry , 2015, BioEssays : news and reviews in molecular, cellular and developmental biology.

[52]  K. Ogura,et al.  Solution Structure of a Novel Cdc42 Binding Module of Bem1 and Its Interaction with Ste20 and Cdc42* , 2010, The Journal of Biological Chemistry.

[53]  Timothy C. Elston,et al.  Negative Feedback Enhances Robustness in the Yeast Polarity Establishment Circuit , 2012, Cell.

[54]  Sophie G. Martin,et al.  The Tea4–PP1 landmark promotes local growth by dual Cdc42 GEF recruitment and GAP exclusion , 2014, Journal of Cell Science.

[55]  D. Lew,et al.  Beyond symmetry-breaking: competition and negative feedback in GTPase regulation. , 2013, Trends in cell biology.

[56]  Erik E. Griffin,et al.  Regulation of the MEX-5 Gradient by a Spatially Segregated Kinase/Phosphatase Cycle , 2011, Cell.

[57]  James E Ferrell,et al.  Feedback loops and reciprocal regulation: recurring motifs in the systems biology of the cell cycle. , 2013, Current opinion in cell biology.

[58]  S. Molshanski-Mor,et al.  Liposomes Comprising Anionic but Not Neutral Phospholipids Cause Dissociation of Rac(1 or 2)·RhoGDI Complexes and Support Amphiphile-independent NADPH Oxidase Activation by Such Complexes* , 2006, Journal of Biological Chemistry.

[59]  S. Glashow,et al.  Spontaneous Breakdown of Elementary Particle Symmetries , 1962 .

[60]  I. Herskowitz,et al.  Two active states of the Ras-related Bud1/Rsr1 protein bind to different effectors to determine yeast cell polarity. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[61]  J. Thorner,et al.  Pheromone-induced anisotropy in yeast plasma membrane phosphatidylinositol-4,5-bisphosphate distribution is required for MAPK signaling , 2010, Proceedings of the National Academy of Sciences.

[62]  S. Fields,et al.  A protein interaction map for cell polarity development , 2001, The Journal of cell biology.

[63]  M. Leonetti,et al.  Emergence of symmetry breaking in fucoid zygotes. , 2007, Trends in plant science.

[64]  Elsen Tjhung,et al.  Spontaneous symmetry breaking in active droplets provides a generic route to motility , 2012, Proceedings of the National Academy of Sciences.

[65]  A. Hall,et al.  A Conserved Binding Motif Defines Numerous Candidate Target Proteins for Both Cdc42 and Rac GTPases (*) , 1995, The Journal of Biological Chemistry.

[66]  Erwin Frey,et al.  Establishment of a robust single axis of cell polarity by coupling multiple positive feedback loops , 2013, Nature Communications.

[67]  Patrick Brennwald,et al.  Quantitative Analysis of Membrane Trafficking in Regulation of Cdc42 Polarity , 2014, Traffic.

[68]  J. Gerhart,et al.  Molecular “Vitalism” , 2000, Cell.

[69]  J. Chant,et al.  A localized GTPase exchange factor, Bud5, determines the orientation of division axes in yeast , 2001, Current Biology.

[70]  Eugenio Marco,et al.  Endocytosis Optimizes the Dynamic Localization of Membrane Proteins that Regulate Cortical Polarity , 2007, Cell.

[71]  K. Hahn,et al.  FRET binding antenna reports spatiotemporal dynamics of GDI-Cdc42 GTPase interactions , 2016, Nature chemical biology.

[72]  Stephan W. Grill,et al.  Parameter-space topology of models for cell polarity , 2014 .

[73]  Sophie G. Martin,et al.  Regulation of the formin for3p by cdc42p and bud6p. , 2007, Molecular biology of the cell.

[74]  I. Prigogine,et al.  Symmetry Breaking Instabilities in Biological Systems , 1969, Nature.

[75]  Daniel J. Lew,et al.  Parallel Actin-Independent Recycling Pathways Polarize Cdc42 in Budding Yeast , 2016, Current Biology.

[76]  D. Pellman,et al.  Symmetry Breaking: Scaffold Plays Matchmaker for Polarity Signaling Proteins , 2008, Current Biology.

[77]  Alexandra Jilkine,et al.  Wave-pinning and cell polarity from a bistable reaction-diffusion system. , 2008, Biophysical journal.

[78]  Kay Hofmann,et al.  A positive feedback loop stabilizes the guanine‐nucleotide exchange factor Cdc24 at sites of polarization , 2002, The EMBO journal.

[79]  C. Der,et al.  GEF means go: turning on RHO GTPases with guanine nucleotide-exchange factors , 2005, Nature Reviews Molecular Cell Biology.

[80]  Sophie G. Martin,et al.  Spontaneous Cdc42 Polarization Independent of GDI-Mediated Extraction and Actin-Based Trafficking , 2015, PLoS biology.

[81]  R. Goody,et al.  RabGDI displacement by DrrA from Legionella is a consequence of its guanine nucleotide exchange activity. , 2009, Molecular cell.

[82]  Indrani Bose,et al.  Singularity in Polarization: Rewiring Yeast Cells to Make Two Buds , 2009, Cell.

[83]  Anita T. Layton,et al.  Mechanistic mathematical model of polarity in yeast , 2012, Molecular biology of the cell.

[84]  Sophie G. Martin,et al.  Actin cables and the exocyst form two independent morphogenesis pathways in the fission yeast , 2011, Molecular biology of the cell.

[85]  D. Drubin Development of cell polarity in budding yeast , 1991, Cell.

[86]  Joan E. Adamo,et al.  Yeast Cdc42 functions at a late step in exocytosis, specifically during polarized growth of the emerging bud , 2001, The Journal of cell biology.

[87]  J. Pringle,et al.  CDC42 and CDC43, two additional genes involved in budding and the establishment of cell polarity in the yeast Saccharomyces cerevisiae , 1990, The Journal of cell biology.

[88]  A. Levchenko,et al.  Models of eukaryotic gradient sensing: application to chemotaxis of amoebae and neutrophils. , 2001, Biophysical journal.

[89]  M. Ahmadian,et al.  Liposome Reconstitution and Modulation of Recombinant Prenylated Human Rac1 by GEFs, GDI1 and Pak1 , 2014, PloS one.

[90]  Herbert Waldmann,et al.  Membrane targeting mechanism of Rab GTPases elucidated by semisynthetic protein probes. , 2010, Nature chemical biology.

[91]  Matthias Peter,et al.  The nucleotide exchange factor Cdc24p may be regulated by auto‐inhibition , 2004, The EMBO journal.

[92]  Jian Zhang,et al.  Membrane association and functional regulation of Sec3 by phospholipids and Cdc42 , 2008, The Journal of cell biology.

[93]  K. Mostov,et al.  Regulation of cell polarity during epithelial morphogenesis. , 2008, Current opinion in cell biology.

[94]  Alexander van Oudenaarden,et al.  A system of counteracting feedback loops regulates Cdc42p activity during spontaneous cell polarization. , 2005, Developmental cell.

[95]  Gregory R. Hoffman,et al.  Structure of the Rho Family GTP-Binding Protein Cdc42 in Complex with the Multifunctional Regulator RhoGDI , 2000, Cell.

[96]  Sigurd B. Angenent,et al.  On the spontaneous emergence of cell polarity , 2008, Nature.

[97]  J. Pringle,et al.  Multicopy suppression of the cdc24 budding defect in yeast by CDC42 and three newly identified genes including the ras-related gene RSR1. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[98]  References , 1971 .

[99]  E. Bi,et al.  Central Roles of Small GTPases in the Development of Cell Polarity in Yeast and Beyond , 2007, Microbiology and Molecular Biology Reviews.

[100]  I. Macara,et al.  Signaling pathways in cell polarity. , 2012, Cold Spring Harbor perspectives in biology.

[101]  Nicolas Minc,et al.  Electrochemical control of cell and tissue polarity. , 2014, Annual review of cell and developmental biology.

[102]  Leah Edelstein-Keshet,et al.  Analysis of a minimal Rho-GTPase circuit regulating cell shape , 2016, Physical biology.

[103]  A. Ridley,et al.  Rho GTPase signalling in cell migration , 2015, Current opinion in cell biology.

[104]  Andrew B Goryachev,et al.  Dynamics of Cdc42 network embodies a Turing‐type mechanism of yeast cell polarity , 2008, FEBS letters.

[105]  Jean-François Rupprecht,et al.  Actin Flows Mediate a Universal Coupling between Cell Speed and Cell Persistence , 2015, Cell.

[106]  Timothy C. Elston,et al.  Tracking Shallow Chemical Gradients by Actin-Driven Wandering of the Polarization Site , 2013, Current Biology.

[107]  Erwin Frey,et al.  GDI-Mediated Cell Polarization in Yeast Provides Precise Spatial and Temporal Control of Cdc42 Signaling , 2013, PLoS Comput. Biol..

[108]  Alexandra Jilkine,et al.  A Comparison of Mathematical Models for Polarization of Single Eukaryotic Cells in Response to Guided Cues , 2011, PLoS Comput. Biol..

[109]  Patrick Brennwald,et al.  The Exo70 Subunit of the Exocyst Is an Effector for Both Cdc42 and Rho3 Function in Polarized Exocytosis , 2010, Molecular biology of the cell.

[110]  Bruno Antonny,et al.  Dissociation of GDP Dissociation Inhibitor and Membrane Translocation Are Required for Efficient Activation of Rac by the Dbl Homology-Pleckstrin Homology Region of Tiam* , 2003, The Journal of Biological Chemistry.

[111]  H. Begthel,et al.  ATP8B1-mediated spatial organization of Cdc42 signaling maintains singularity during enterocyte polarization , 2015, The Journal of cell biology.

[112]  F. Tostevin,et al.  Modeling the establishment of PAR protein polarity in the one-cell C. elegans embryo. , 2008, Biophysical journal.

[113]  T. Höfken,et al.  The Rho GDI Rdi1 regulates Rho GTPases by distinct mechanisms. , 2008, Molecular biology of the cell.

[114]  A. Hyman,et al.  Polarization of PAR Proteins by Advective Triggering of a Pattern-Forming System , 2011, Science.

[115]  Brian D. Slaughter,et al.  Independence of symmetry breaking on Bem1-mediated autocatalytic activation of Cdc42 , 2013, The Journal of cell biology.

[116]  D. Lew,et al.  Stress-specific Activation Mechanisms for the “Cell Integrity” MAPK Pathway* , 2004, Journal of Biological Chemistry.

[117]  D. Drubin,et al.  Origins of Cell Polarity , 1996, Cell.

[118]  Hay-Oak Park,et al.  Polarization of Diploid Daughter Cells Directed by Spatial Cues and GTP Hydrolysis of Cdc42 in Budding Yeast , 2013, PloS one.

[119]  R. Goody,et al.  bMERB domains are bivalent Rab8 family effectors evolved by gene duplication , 2016, eLife.

[120]  Daniel J. Lew,et al.  Symmetry-Breaking Polarization Driven by a Cdc42p GEF-PAK Complex , 2008, Current Biology.

[121]  Matthias Peter,et al.  Phosphorylation of Bem2p and Bem3p may contribute to local activation of Cdc42p at bud emergence , 2007, The EMBO journal.

[122]  J. Moskow,et al.  Assembly of Scaffold-mediated Complexes Containing Cdc42p, the Exchange Factor Cdc24p, and the Effector Cla4p Required for Cell Cycle-regulated Phosphorylation of Cdc24p* , 2001, The Journal of Biological Chemistry.

[123]  Matteo Semplice,et al.  A Bistable Model of Cell Polarity , 2012, PloS one.

[124]  Brian D. Slaughter,et al.  Dual modes of cdc42 recycling fine-tune polarized morphogenesis. , 2009, Developmental cell.

[125]  A. Goryachev,et al.  CDC-42 and RAC-1 regulate opposite chemotropisms in Neurospora crassa , 2014, Journal of Cell Science.

[126]  M. Wigler,et al.  Cooperative interaction of S. pombe proteins required for mating and morphogenesis , 1994, Cell.

[127]  Hay-Oak Park,et al.  Regulation of Cdc42 polarization by the Rsr1 GTPase and Rga1, a Cdc42 GTPase-activating protein, in budding yeast , 2015, Journal of Cell Science.

[128]  I. Herskowitz,et al.  Genetic control of bud site selection in yeast by a set of gene products that constitute a morphogenetic pathway , 1991, Cell.

[129]  K. Hahn,et al.  Activation of Endogenous Cdc42 Visualized in Living Cells , 2004, Science.

[130]  J. Caviston,et al.  The role of Cdc42p GTPase-activating proteins in assembly of the septin ring in yeast. , 2003, Molecular biology of the cell.

[131]  R. Martín-García,et al.  Rga6 is a fission yeast Rho GAP involved in Cdc42 regulation of polarized growth , 2016, Molecular biology of the cell.

[132]  Daniel J. Lew,et al.  Polarity establishment requires localized activation of Cdc42 , 2015, The Journal of cell biology.

[133]  Navin Pokala,et al.  High Rates of Actin Filament Turnover in Budding Yeast and Roles for Actin in Establishment and Maintenance of Cell Polarity Revealed Using the Actin Inhibitor Latrunculin-A , 1997, The Journal of cell biology.

[134]  Pablo A Iglesias,et al.  Navigating through models of chemotaxis. , 2008, Current opinion in cell biology.

[135]  Hay-Oak Park,et al.  A GDP/GTP Exchange Factor Involved in Linking a Spatial Landmark to Cell Polarity , 2001, Science.

[136]  Anita T. Layton,et al.  Modeling Vesicle Traffic Reveals Unexpected Consequences for Cdc42p-Mediated Polarity Establishment , 2011, Current Biology.