[go: up one dir, main page]

Skip to main content
Log in

Mathematical Modeling of Cell Polarity Establishment of Budding Yeast

  • Review Article
  • Published:
Communications on Applied Mathematics and Computation Aims and scope Submit manuscript

Abstract

The budding yeast Saccharomyces cerevisiae is a powerful model system for studying the cell polarity establishment. The cell polarization process is regulated by signaling molecules, which are initially distributed in the cytoplasm and then recruited to a proper location on the cell membrane in response to spatial cues or spontaneously. Polarization of these signaling molecules involves complex regulation, so the mathematical models become a useful tool to investigate the mechanism behind the process. In this review, we discuss how mathematical modeling has shed light on different regulations in the cell polarization. We also propose future applications for the mathematical modeling of cell polarization and morphogenesis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Adams, A.E., Johnson, D.I., Longnecker, R.M., Sloat, B.F., Pringle, John R.: CDC42 and CDC43, two additional genes involved in budding and the establishment of cell polarity in the yeast Saccharomyces cerevisiae. J. Cell Biol. 111(1), 131–142 (1990)

    Google Scholar 

  2. Altschuler, S.J., Angenent, S.B., Wang, Y., Lani, F.W.: On the spontaneous emergence of cell polarity. Nature 454(7206), 886–889 (2008)

    Google Scholar 

  3. Banavar, S.P., Trogdon, M., Drawert, B., Yi, T.-M., Petzold, L.R., Campàs, O.: Coordinating cell polarization and morphogenesis through mechanical feedback. PLoS Comput. Biol. 17(1), e1007971 (2021)

    Google Scholar 

  4. Bi, E., Park, H.-O.: Cell polarization and cytokinesis in budding yeast. Genetics 191(2), 347–387 (2012)

    Google Scholar 

  5. Brinkmann, F., Mercker, M., Richter, T., Marciniak-Czochra, A.: Post-Turing tissue pattern formation: advent of mechanochemistry. PLoS Comput. Biol. 14(7), 1–21 (2018)

    Google Scholar 

  6. Bryant, D.M., Mostov, K.E.: From cells to organs: building polarized tissue. Nat. Rev. Mol. Cell Biol. 9(11), 887–901 (2008)

    Google Scholar 

  7. Caviston, J.P., Longtine, M., Pringle, J.R., Bi, E.: The role of Cdc42p GTPase-activating proteins in assembly of the septin ring in yeast. Mol. Biol. Cell 14(10), 4051–4066 (2003)

    Google Scholar 

  8. Champneys, A.R., Saadi, F.A., Breña-Medina, V.F., Grieneisen, V.A., Marée, A.F.M., Verschueren, N., Wuyts, B.: Bistability, wave pinning and localisation in natural reaction-diffusion systems. Phys. D 416, 132735 (2021)

    MathSciNet  Google Scholar 

  9. Chiou, J.-G., Ramirez, S.A., Elston, T.C., Witelski, T.P., Schaeffer, D.G., Lew, D.J.: Principles that govern competition or co-existence in Rho-GTPase driven polarization. PLoS Comput. Biol. 14(4), 1–23 (2018)

    Google Scholar 

  10. Choi, S.-C., Han, J.-K.: Xenopus Cdc42 regulates convergent extension movements during gastrulation through Wnt/Ca2+ signaling pathway. Dev. Biol. 244(2), 342–357 (2002)

    Google Scholar 

  11. Chollet, J., Dünkler, A., Bäuerle, A., Vivero-Pol, L., Mulaw, M.A., Gronemeyer, T., Johnsson, N.: Cdc24 interacts with septins to create a positive feedback loop during bud site assembly in yeast. J. Cell Sci. 133(11), jcs240283 (2020)

    Google Scholar 

  12. Clay, L., Caudron, F., Denoth-Lippuner, A., Boettcher, B., Frei, S.B., Snapp, E.L., Barral, Y.: A sphingolipid-dependent diffusion barrier confines ER stress to the yeast mother cell. Life 3, e01883 (2014)

    Google Scholar 

  13. Cusseddu, D., Edelstein-Keshet, L., Mackenzie, J.A., Portet, S., Madzvamuse, A.: A coupled bulk-surface model for cell polarisation. J. Theor. Biol. 481, 119–135 (2019)

    MathSciNet  Google Scholar 

  14. Davis, E.E., Katsanis, N.: Cell polarization defects in early heart development. Circ. Res. 101(2), 122–124 (2007)

    Google Scholar 

  15. Diekmann, D., Brill, S., Garrett, M.D., Totty, N., Hsuan, J., Monfries, C., Hall, C., Lim, L., Hall, A.: Bcr encodes a GTPase-activating protein for p21rac. Nature 351(6325), 400–402 (1991)

    Google Scholar 

  16. Dobbelaere, J., Gentry, M.S., Hallberg, R.L., Barral, Y.: Phosphorylation-dependent regulation of septin dynamics during the cell cycle. Dev. Cell 4(3), 345–357 (2003)

    Google Scholar 

  17. Etienne-Manneville, S.: Cdc42-the centre of polarity. J. Cell Sci. 117(8), 1291–1300 (2004)

    Google Scholar 

  18. Ewers, H., Tada, T., Petersen, J.D., Racz, B., Sheng, M., Choquet, D.: A septin-dependent diffusion barrier at dendritic spine necks. PLoS One 9(12), e113916 (2014)

    Google Scholar 

  19. Finger, F.P., Kopish, K.R., White, J.G.: A role for septins in cellular and axonal migration in C. elegans. Dev. Biol. 261(1), 220–234 (2003)

    Google Scholar 

  20. Gibson, M.A., Bruck, J.: Efficient exact stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. A 104(9), 1876–1889 (2000)

    Google Scholar 

  21. Giese, W., Eigel, M., Westerheide, S., Engwer, C., Klipp, E.: Influence of cell shape, inhomogeneities and diffusion barriers in cell polarization models. Phys. Biol. 12(6), 066014 (2015)

    Google Scholar 

  22. Gillespie, D.T.: A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22(4), 403–434 (1976)

    MathSciNet  Google Scholar 

  23. Gladfelter, A.S., Pringle, J.R., Lew, D.J.: The septin cortex at the yeast mother-bud neck. Curr. Opin. Microbiol. 4(6), 681–689 (2001)

    Google Scholar 

  24. Glise, B., Noselli, S.: Coupling of Jun amino-terminal kinase and Decapentaplegic signaling pathways in Drosophila morphogenesis. Genes Dev. 11(13), 1738–1747 (1997)

    Google Scholar 

  25. Goryachev, A.B., Leda, M.: Many roads to symmetry breaking: molecular mechanisms and theoretical models of yeast cell polarity. Mol. Biol. Cell 28(3), 370–380 (2017)

    Google Scholar 

  26. Goryachev, A.B., Pokhilko, A.V.: Dynamics of Cdc42 network embodies a Turing-type mechanism of yeast cell polarity. FEBS Lett. 582(10), 1437–1443 (2008)

    Google Scholar 

  27. Harden, N., Loh, H.Y., Chia, W., Lim, L.: A dominant inhibitory version of the small GTP-binding protein Rac disrupts cytoskeletal structures and inhibits developmental cell shape changes in Drosophila. Development 121(3), 903–914 (1995)

    Google Scholar 

  28. Hart, M.J., Eva, A., Evans, T., Aaronson, S.A., Cerione, R.A.: Catalysis of guanine nucleotide exchange on the CDC42Hs protein by the dbloncogene product. Nature 354(6351), 311–314 (1991)

    Google Scholar 

  29. Howell, A.S., Jin, M., Chi-Fang, W., Zyla, T.R., Elston, T.C., Lew, D.J.: Negative feedback enhances robustness in the yeast polarity establishment circuit. Cell 149(2), 322–333 (2012)

    Google Scholar 

  30. Howell, A.S., Savage, N.S., Johnson, S.A., Bose, I., Wagner, A.W., Zyla, T.R., Frederik, N.H., Reed, M.C., Goryachev, A.B., Lew, D.J.: Singularity in polarization: rewiring yeast cells to make two buds. Cell 139(4), 731–743 (2009)

    Google Scholar 

  31. Hsu, C.L., Muerdter, C.P., Knickerbocker, A.D., Walsh, R.M., Zepeda-Rivera, M.A., Depner, K.H., Sangesland, M., Cisneros, T.B., Kim, J.Y., Sanchez-Vazquez, P., Cherezova, L., Regan, R.D., Bahrami, N.M., Gray, E.A., Chan, A.Y., Chen, T., Rao, M.Y., Hille, M.B.: Cdc42 GTPase and Rac1 GTPase act downstream of p120 catenin and require GTP exchange during gastrulation of zebrafish mesoderm. Dev. Dyn. 241(10), 1545–1561 (2012)

    Google Scholar 

  32. Hu, Q., Milenkovic, L., Jin, H., Scott, M.P., Nachury, M.V., Spiliotis, E.T., James Nelson, W.: A septin diffusion barrier at the base of the primary cilium maintains ciliary membrane protein distribution. Science 329(5990), 436–439 (2010)

    Google Scholar 

  33. Iwase, M., Luo, J., Nagaraj, S., Longtine, M., Kim, H.B., Haarer, B.K., Caruso, C., Tong, Z., Pringle, J.R., Bi, E.: Role of a Cdc42p effector pathway in recruitment of the yeast septins to the presumptive bud site. Mole. Biol. Cell 17(3), 1110–1125 (2006)

    Google Scholar 

  34. Jilkine, A., Angenent, S.B., Wu, L.F., Altschuler, S.J.: A density-dependent switch drives stochastic clustering and polarization of signaling molecules. PLoS Comput. Biol. 7(11), e1002271 (2011)

    Google Scholar 

  35. Johnson, D.I., Pringle, J.R.: Molecular characterization of CDC42, a Saccharomyces cerevisiae gene involved in the development of cell polarity. J. Cell Biol. 111(1), 143–152 (1990)

    Google Scholar 

  36. Kozubowski, L., Larson, J.R., Tatchell, K.: Role of the septin ring in the asymmetric localization of proteins at the mother-bud neck in Saccharomyces cerevisiae. Mol. Biol. Cell 16(8), 3455–3466 (2005)

    Google Scholar 

  37. Kozubowski, L., Saito, K., Johnson, J.M., Howell, A.S., Zyla, T.R., Lew, D.J.: Symmetry-breaking polarization driven by a Cdc42p GEF-PAK complex. Curr. Biol. 18(22), 1719–1726 (2008)

    Google Scholar 

  38. Kwitny, S., Klaus, A.V., Hunnicutt, G.R.: The annulus of the mouse sperm tail is required to establish a membrane diffusion barrier that is engaged during the late steps of spermiogenesis. Biol. Reprod. 82(4), 669–678 (2010)

    Google Scholar 

  39. Lawson, M.J., Drawert, B., Khammash, M., Petzold, L., Yi, T.-M.: Spatial stochastic dynamics enable robust cell polarization. PLoS Comput. Biol. 9(7), 1–12 (2013)

    Google Scholar 

  40. Lee, M.E., Lo, W.-C., Miller, K.E., Chou, C.-S., Park, H.-O.: Regulation of Cdc42 polarization by the Rsr1 GTPase and Rga1, a Cdc42 GTPase-activating protein, in budding yeast. J. Cell Sci. 128(11), 2106–2117 (2015)

    Google Scholar 

  41. Liu, Y., Lo, W.-C.: Analysis of spontaneous emergence of cell polarity with delayed negative feedback. Math. Biosci. Eng. 16(3), 1392–1413 (2019)

    MathSciNet  Google Scholar 

  42. Liu, Y., Lo, W.-C.: Deterministic and stochastic analysis for different types of regulations in the spontaneous emergence of cell polarity. Chaos, Solitons and Fractals 144, 110620 (2021)

    MathSciNet  Google Scholar 

  43. Lo, W.-C., Lee, M.E., Narayan, M., Chou, C.-S., Pak, H.-O.: Polarization of diploid daughter cells directed by spatial cues and GTP hydrolysis of Cdc42 in budding yeast. PLoS One 8(2), 1–14 (2013)

    Google Scholar 

  44. Lo, W.-C., Park, H.-O., Chou, C.-S.: Mathematical analysis of spontaneous emergence of cell polarity. Bull. Math. Biol. 76(8), 1835–1865 (2014)

    MathSciNet  Google Scholar 

  45. Mahapatra, A., Saintillan, D., Rangamani, P.: Transport phenomena in fluid films with curvature elasticity. J. Fluid Mech. 905, A8 (2020)

    MathSciNet  Google Scholar 

  46. Marco, E., Wedlich-Soldner, R., Li, R., Altschuler, S.J., Lani, F.W.: Endocytosis optimizes the dynamic localization of membrane proteins that regulate cortical polarity. Cell 129(2), 411–422 (2007)

    Google Scholar 

  47. Maroudas-Sacks, Y., Garion, L., Shani-Zerbib, L., Livshits, A., Braun, E., Keren, K.: Topological defects in the nematic order of actin fibres as organization centres of Hydra morphogenesis. Nat. Phys. 17(2), 251–259 (2021)

    Google Scholar 

  48. McMurray, M.A., Thorner, J.: Septins: molecular partitioning and the generation of cellular asymmetry. Cell Div. 4(1), 1–14 (2009)

    Google Scholar 

  49. Mietke, A., Jülicher, F., Sbalzarini, I.F.: Self-organized shape dynamics of active surfaces. Proc. Natl. Acad. Sci. U.S.A. 116(1), 29–34 (2019)

    Google Scholar 

  50. Mori, Y., Jilkine, A., Edelstein-Keshet, L.: Wave-pinning and cell polarity from a bistable reaction-diffusion system. Biophys. J. 94(9), 3684–3697 (2008)

    Google Scholar 

  51. Murphy, L., Madzvamuse, A.: A moving grid finite element method applied to a mechanobiochemical model for 3D cell migration. Appl. Numer. Math. 158, 336–359 (2020)

    MathSciNet  Google Scholar 

  52. Noselli, S.: JNK signaling and morphogenesis in Drosophila. Trends Genet. 14(1), 33–38 (1998)

    Google Scholar 

  53. Okada, S., Leda, M., Hanna, J., Savage, N.S., Bi, E., Goryachev, A.B.: Daughter cell identity emerges from the interplay of Cdc42, septins, and exocytosis. Dev. Cell 26(2), 148–161 (2013)

    Google Scholar 

  54. Ozbudak, E.M., Becskei, A., van Oudenaarden, A.: A system of counteracting feedback loops regulates Cdc42p activity during spontaneous cell polarization. Dev. Cell 9(4), 565–571 (2005)

    Google Scholar 

  55. Pablo, M., Ramirez, S.A., Elston, T.C.: Particle-based simulations of polarity establishment reveal stochastic promotion of turing pattern formation. PLoS Comput. Biol. 14(3), 1–25 (2018)

    Google Scholar 

  56. Park, H.-O., Bi, E.: Central roles of small GTPases in the development of cell polarity in yeast and beyond. Microbiol. Mol. Biol. Rev. 71(1), 48–96 (2007)

    Google Scholar 

  57. Rätz, A., Röger, M.: Symmetry breaking in a bulk-surface reaction-diffusion model for signalling networks. Nonlinearity 27(8), 1805–1827 (2014)

    MathSciNet  Google Scholar 

  58. Rubinstein, B., Slaughter, B.D., Li, R.: Weakly nonlinear analysis of symmetry breaking in cell polarity models. Phys. Biol. 9(4), 045006 (2012)

    Google Scholar 

  59. Sarfaraz, W., Madzvamuse, A.: Classification of parameter spaces for a reaction-diffusion model on stationary domains. Chaos, Solitons and Fractals 103, 33–51 (2017)

    MathSciNet  Google Scholar 

  60. Sepúlveda-Ramírez, S.P., Toledo-Jacobo, L., Henson, J.H., Shuster, C.B.: Cdc42 controls primary mesenchyme cell morphogenesis in the sea urchin embryo. Dev. Biol. 437(2), 140–151 (2018)

    Google Scholar 

  61. Shinoda, T., Ito, H., Sudo, K., Iwamoto, I., Morishita, R., Nagata, K.: Septin 14 is involved in cortical neuronal migration via interaction with septin 4. Mol. Biol. Cell 21(8), 1324–1334 (2010)

    Google Scholar 

  62. Slaughter, B.D., Das, A., Schwartz, J.W., Rubinstein, B., Li, R.: Dual modes of Cdc42 recycling fine-tune polarized morphogenesis. Dev. Cell 17(6), 823–835 (2009)

    Google Scholar 

  63. Slaughter, B.D., Smith, S.E., Li, R.: Symmetry breaking in the life cycle of the budding yeast. Cold Spring Harb. Perspect. Biol. 1(3), 18 (2009)

    Google Scholar 

  64. Stinner, B., Dedner, A., Nixon, A.: A finite element method for a fourth order surface equation with application to the onset of cell blebbing. Front. Appl. Math. Stat. 6, 21 (2020)

    Google Scholar 

  65. Takizawa, P.A., DeRisi, J.L., Wilhelm, J.E., Vale, R.D.: Plasma membrane compartmentalization in yeast by messenger RNA transport and a septin diffusion barrier. Science 290(5490), 341–344 (2000)

    Google Scholar 

  66. Tcheperegine, S.E., Gao, X.-D., Bi, E.: Regulation of cell polarity by interactions of Msb3 and Msb4 with Cdc42 and polarisome components. Mol. Cell. Biol. 25(19), 8567–8580 (2005)

    Google Scholar 

  67. Tooley, A.J., Gilden, J., Jacobelli, J., Beemiller, P., Trimble, W.S., Kinoshita, M., Krummel, M.F.: Amoeboid T lymphocytes require the septin cytoskeleton for cortical integrity and persistent motility. Nat. Cell Biol. 11(1), 17–26 (2009)

    Google Scholar 

  68. Torres-Sánchez, A., Millán, D., Arroyo, M.: Modelling fluid deformable surfaces with an emphasis on biological interfaces. J. Fluid Mech. 872, 218–271 (2019)

    MathSciNet  Google Scholar 

  69. Trogdon, M., Drawert, B., Gomez, C., Banavar, S.P., Yi, T.-M., Campàs, O., Petzold, L.R.: The effect of cell geometry on polarization in budding yeast. PLoS Comput. Biol. 14(6), 1–22 (2018)

    Google Scholar 

  70. Trong, P.K., Nicola, E.M., Goehring, N.W., Vijay Kumar, K., Grill, S.W.: Parameter-space topology of models for cell polarity. New J. Phys. 16(6), 065009 (2014)

    Google Scholar 

  71. Tsai, K., Britton, S., Nematbakhsh, A., Zandi, R., Chen, W., Alber, M.: Role of combined cell membrane and wall mechanical properties regulated by polarity signals in cell budding. Phys. Biol. 17(6), 065011 (2020)

    Google Scholar 

  72. Turing, A.M.: The chemical basis of morphogenesis. Bull. Math. Biol. 52(1), 153–197 (1990)

    Google Scholar 

  73. Walther, G.R., Marée, A.F.M., Edelstein-Keshet, L., Grieneisen, V.A.: Deterministic versus stochastic cell polarisation through wave-pinning. Bull. Math. Biol. 74(11), 2570–2599 (2012)

    MathSciNet  Google Scholar 

  74. Wu, C.-F., Lew, D.J.: Beyond symmetry-breaking: competition and negative feedback in GTPase regulation. Trends Cell Biol. 23(10), 476–483 (2013)

    Google Scholar 

  75. Zmurchok, C., Collette, J., Rajagopal, V., Holmes, W.R.: Membrane tension can enhance adaptation to maintain polarity of migrating cells. Biophys. J. 119(8), 1617–1629 (2020)

    Google Scholar 

Download references

Acknowledgements

WC benefited greatly from many stimulating discussions on cell polarization modeling with his mentor Dr. Ching-Shan Chou. The authors dedicate this paper to the memory of Dr. Chou, who had a great contribution to cell polarization modeling.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wing-Cheong Lo.

Ethics declarations

Conflict of Interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Ethical Approval

The research does not involve human participants and/or animals.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Y., Xie, J., Park, HO. et al. Mathematical Modeling of Cell Polarity Establishment of Budding Yeast. Commun. Appl. Math. Comput. 6, 218–235 (2024). https://doi.org/10.1007/s42967-022-00240-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42967-022-00240-y

Keywords

Mathematics Subject Classification

Navigation