From simple to detailed models for cell polarization

Philosophical Transactions of the Royal Society B: Biological Sciences

Volumn 368, Issue 1629, 2013, Pages

  Edelstein Keshet, Leah ^a   Holmes, William R ^b   Zajac, Mark ^a   Dutot, Meghan ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Cell polarization; Mathematical analysis; Pattern formation; Reaction diffusion equations

Indexed keywords

MATHEMATICAL ANALYSIS; NUMERICAL METHOD; NUMERICAL MODEL; PATTERN RECOGNITION; PERTURBATION; POLARIZATION; SIMULATION;

MONOMERIC GUANINE NUCLEOTIDE BINDING PROTEIN;

BIOLOGICAL MODEL; CELL POLARITY; CELL POLARIZATION; CELL SHAPE; COMPARATIVE STUDY; COMPUTER SIMULATION; MATHEMATICAL ANALYSIS; METABOLISM; PATTERN FORMATION; PHYSIOLOGY; REACTION-DIFFUSION EQUATIONS; REVIEW;

CELL POLARIZATION; MATHEMATICAL ANALYSIS; PATTERN FORMATION; REACTION-DIFFUSION EQUATIONS;

CELL POLARITY; CELL SHAPE; COMPUTER SIMULATION; MODELS, BIOLOGICAL; MONOMERIC GTP-BINDING PROTEINS;

EID: 84884467663     PISSN: 09628436     EISSN: 14712970     Source Type: Journal    
DOI: 10.1098/rstb.2013.0003     Document Type: Review

References (30)

1. Jilkine A, Edelstein-Keshet L. 2011 A comparison of mathematical models for polarization of single eukaryotic cells in response to guided cues. PLoS Comput. Biol. 7, e1001121. (doi:10.1371/journal. pcbi.1001121)
2. Mori Y, Jilkine A, Edelstein-Keshet L. 2008 Wavepinning and cell polarity from a bistable reaction-diffusion system. Biophys. J. 94, 3684-3697. (doi:10.1529/biophysj.107.120824)
3. Holmes W, Carlsson A, Edelstein-Keshet L. 2012 Regimes of wave type patterning driven by refractory actin feedback: transition from static polarization to dynamic wave behaviour. Phys. Biol. 9, 046005. (doi:10.1088/1478-3975/9/4/046005)
4. Holmes W, Lin B, Levchenko A, Edelstein-Keshet L. 2012 Modelling cell polarization driven by synthetic spatially graded Rac activation. PLoS Comput. Biol. 8, e1002366. (doi:10.1371/journal.pcbi.1002366)
5. Mareé AF, Jilkine A, Dawes A, Grieneisen VA, Edelstein-Keshet L. 2006 Polarization and movement of keratocytes: a multiscale modelling approach. Bull. Math. Biol. 68, 1169-1211. (doi:10. 1007/s11538-006-9131-7)
6. Jilkine A, Marée AFM, Edelstein-Keshet L. 2007 Mathematical model for spatial segregation of the Rho-family GTPases based on inhibitory crosstalk. Bull. Math. Biol. 69, 1943-1978. (doi:10.1007/ s11538-007-9200-6)
7. Dawes A, Edelstein-Keshet L. 2007 Phosphoinositides and Rho proteins spatially regulate actin polymerization to initiate and maintain directed movement in a 1D model of a motile cell. Biophys. J. 92, 744-768. (doi:10.1529/ biophysj.106.090514)
8. Marée A, Grieneisen V, Edelstein-Keshet L. 2012 How cells integrate complex stimuli: the effect of feedback from phosphoinositides and cell shape on cell polarization and motility. PLoS Comput. Biol. 8, e1002402. (doi:10.1371/journal.pcbi.1002402)
9. Kholodenko B. 2006 Cell-signalling dynamics in time and space. Nat. Rev. Mol. Cell Biol. 7, 165-176. (doi:10.1038/nrm1838)
10. Mori Y, Jilkine A, Edelstein-Keshet L. 2011 Asymptotic and bifurcation analysis of a wave-based pattern formation mechanism in a model of cell polarization. SIAM J. Appl. Math. 71, 1401-1427. (doi:10.1137/10079118X)
11. Goehring NW, Hoege C, Grill SW, Hyman AA. 2011 PAR proteins diffuse freely across the anterior-posterior boundary in polarized C. elegans embryos. J. Cell Biol. 193, 583-594. (doi:10.1083/jcb. 201011094)
12. Goehring NW, Trong PK, Bois JS, Chowdhury D, Nicola EM, Hyman AA, Grill SW. 2011 Polarization of PAR proteins by advective triggering of a patternforming system. Sci. Signal. 334, 1137-1141. (doi:10.1126/science.1208619)
13. Wolgemuth C, Stajic J, Mogilner A. 2010 Redundant mechanisms for stable cell locomotion revealed by minimal models. Biophys. J. 98, 160a-161a. (doi:10.1016/j.bpj.2009.12.864)
14. Shao D, Levine H, Rappel W. 2012 Coupling actin flow, adhesion, and morphology in a computational cell motility model. Proc. Natl Acad. Sci. USA 109, 6851-6856. (doi:10.1073/pnas. 1203252109)
15. Walther GR, Marée AF, Edelstein-Keshet L, Grieneisen VA. 2012 Deterministic versus stochastic cell polarisation through wave-pinning. Bull. Math. Biol. 74, 2570-2599. (doi:10.1007/s11538-012-9766-5)
16. Houk AR, Jilkine A, Mejean CO, Boltyanskiy R, Dufresne ER, Angenent SB, Altschuler SJ, Wu LF, Weiner OD. 2012 Membrane tension maintains cell polarity by confining signals to the leading edge during neutrophil migration. Cell 148, 175-188. (doi:10.1016/j.cell.2011.10.050)
17. Turing A. 1952 The chemical basis of morphogenesis. Phil. Trans. R. Soc. Lond. B 237, 37-72. (doi:10.1098/rstb.1952.0012)
18. Grieneisen V. 2009 Dynamics of auxin patterning in plant morphogenesis. PhD thesis, University of Utrecht, Utrecht, The Netherlands.
19. Otsuji M, Ishihara S, Co C, Kaibuchi K, Mochizuki A, Kuroda S. 2007 A mass conserved reaction-diffusion system captures properties of cell polarity. PLoS Comput. Biol. 3, e108. (doi:10.1371/journal. pcbi.0030108)
20. Levchenko A, Iglesias P. 2002 Models of eukaryotic gradient sensing: application to chemotaxis of amoebae and neutrophils. Biophys. J. 82, 50-63. (doi:10.1016/S0006-3495(02)75373-3)
21. Goryachev A, Pokhilko A. 2008 Dynamics of Cdc42 network embodies a Turing-type mechanism of yeast cell polarity. FEBS Lett. 582, 1437-1443. (doi:10.1016/j.febslet.2008.03.029)
22. Gerisch G, Bretschneider T, Müller-Taubenberger A, Simmeth E, Ecke M, Diez S, Anderson K. 2004 Mobile actin clusters and traveling waves in cells recovering from actin depolymerization. Biophys. J. 87, 3493-3503. (doi:10.1529/biophysj.104.047589)
23. Gerisch G. 2010 Self-organizing waves that simulate phagocytic cup structures. PMC Biophys. 3, 7. (doi:10.1186/1757-5036-3-7)
24. Weiner O, Marganski W, Wu L, Altschuler S, Kirschner M. 2007 An actin-based wave generator organizes cell motility. PLoS Biol. 5, 2053-2063. (doi:10.1371/journal.pbio.0050221)
25. Machacek M et al. 2009 Coordination of rho GTPase activities during cell protrusion. Nature 461, 99-103. (doi:10.1038/nature08242)
26. Marée A, Grieneisen V, Hogeweg P. 2007 The Cellular Potts Model and biophysical properties of cells, tissues and morphogenesis. In Single-cellbased models in biology and medicine (eds ARA Anderson, MAJ Chaplain, KA Rejniak), pp. 107-136. Basel, Switzerland: Springer.
27. Lin B, Holmes WR, Wang CJ, Ueno T, Harwell A, Edelstein-Keshet L, Inoue T, Levchenko A. 2012 Synthetic spatially graded Rac activation drives cell polarization and movement. Proc. Natl Acad. Sci. USA 109, E3668-E3677. (doi:10.1073/pnas. 1210295109)
28. Osher S, Paragios N. 2003 Geometric level set methods in imaging, vision, and graphics. New York, NY: Springer.
29. Sethian J, Smereka P. 2003 Level set methods for fluid interfaces. Annu. Rev. Fluid Mech. 35, 341-372. (doi:10.1146/annurev.fluid.35. 101101.161105)
30. Wolgemuth C, Zajac M. 2010 The moving boundary node method: a level set-based, finite volume algorithm with applications to cell motility. J. Comput. Phys. 229, 7287-7308. (doi:10.1016/j. jcp.2010.06.014)