Asymptotic and bifurcation analysis of wave-pinning in a reaction-diffusion model for cell polarization

SIAM Journal on Applied Mathematics

Volumn 71, Issue 4, 2011, Pages 1401-1427

  Mori, Yoichiro ^a   Jilkine, Alexandra ^b   Edelstein Keshet, Leah ^c  

^a UNIVERSITY OF MINNESOTA   (United States)

^b UNIVERSITY OF TEXAS AT DALLAS   (United States)

^c UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Bistable reaction diffusion system; Cell polarization; Mass conservation; Rho GTPases; Stationary front; Wave pinning

Indexed keywords

BISTABLE REACTION-DIFFUSION SYSTEM; CELL POLARIZATION; MASS CONSERVATION; RHO GTPASES; STATIONARY FRONT; WAVE-PINNING;

ACTIVATION ANALYSIS; ASSOCIATION REACTIONS; ASYMPTOTIC ANALYSIS; BIFURCATION (MATHEMATICS); DIFFUSION IN LIQUIDS; POLARIZATION;

REACTION KINETICS;

EID: 80052734197     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/10079118X     Document Type: Article

References (44)

1. S. ALTSCHULER, S. ANGENENT, Y. WANG, and L. WU, On the spontaneous emergence of cell polarity, Nature, 454(2008), pp. 886-889.
2. T. BRETSCHNEIDER, K. ANDERSON, M. ECKE, A. MÜLLER-TAUBENBERGER, B. SCHROTH-DIEZ, H. C. ISHIKAWA-ANKERHOLD, and G. GERISCH, The three-dimensional dynamics of actin waves, a model of cytoskeletal self-organization, Biophys. J., 96(2009), pp. 2888-2900.
3. A. DAWES and L. EDELSTEIN-KESHET, 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(2007), pp. 1-25.
4. C. DERMARDIROSSIAN, G. ROCKLIN, J.-Y. SEO, and G. M. BOKOCH, Phosphorylation of RhoGDI by Src regulates Rho GTPase binding and cytosol-membrane cycling, Mol. Biol. Cell, 17(2006), pp. 4760-4768. (Pubitemid 44665745)
5. G. FUSCO and J. HALE, Slow-motion manifolds, dormant instability, and singular perturbations, J. Dynam. Differential Equations, 1(1989), pp. 75-94.
6. A. B. GORYACHEV and A. V. POKHILKO, Dynamics of cdc42 network embodies a Turing-type mechanism of yeast cell polarity, FEBS Lett., 582(2008), pp. 1437-1443.
7. P. GRINDROD, The Theory and Applications of Reaction-Diffusion Equations: Patterns and Waves, 2nd ed., Oxford University Press, New York, 1996.
8. J. HALE and K. SAKAMOTO, Shadow systems and attractors in reaction-diffusion equations, Appl. Anal., 32(1989), pp. 287-303.
9. A. S. HOWELL, N. S. SAVAGE, S. A. JOHNSON, I. BOSE, A. W. WAGNER, T. R. ZYLA, H. F. NIJHOUT, M. C. REED, A. B. GORYACHEV, and D. J. LEW, Singularity in polarization: Rewiring yeast cells to make two buds, Cell, 139(2009), pp. 731-743.
10. J. IRAZOQUI, A. GLADFELTER, and D. LEW, Scaffold-mediated symmetry breaking by cdc42p, Nature Cell Biol., 5(2003), pp. 1062-1070. (Pubitemid 37509112)
11. A. JILKINE, A Wave-Pinning Mechanism for Eukaryotic Cell Polarization Based on Rho GTP-ase Dynamics, Ph. D. thesis, University of British Columbia, Vancouver, BC, Canada, 2010.
12. A. JILKINE, A. F. M. MARÉE, and L. EDELSTEIN-KESHET, Mathematical model for spatial segregation of the Rho-family GTPases based on inhibitory crosstalk, Bull. Math. Biol., 69(2007), pp. 1943-1978. (Pubitemid 47222246)
13. J. KEENER, Principles of Applied Mathematics, Perseus Books, Cambridge, MA, 2000.
14. J. KEENER and J. SNEYD, Mathematical Physiology, Springer, New York, 1998.
15. V. KRAYNOV, C. CHAMBERLAIN, G. BOKOCH, M. SCHWARTZ, S. SLABAUGH, and K. HAHN, Localized Rac activation dynamics visualized in living cells, Science, 290(2000), pp. 333-337.
16. Y. KUZNETSOV, Elements of Applied Bifurcation Theory, Springer, New York, 2004.
17. A. LEVCHENKO and P. IGLESIAS, Models of eukaryotic gradient sensing: Application to chemotaxis of amoebae and neutrophils, Biophys. J., 82(2002), pp. 50-63. (Pubitemid 34289781)
18. A. MARÉE, V. GRIENEISEN, and L. EDELSTEIN-KESHET, How cells untangle complex stimuli: The effect of feedback from phosphoinositides and cell shape on cell polarization and motility, submitted.
19. A. MARÉE, A. JILKINE, A. DAWES, V. GRIENEISEN, and L. EDELSTEIN-KESHET, Polarisation and movement of keratocytes: A multiscale modelling approach, Bull. Math. Biol., 68(2006), pp. 1169-1211. (Pubitemid 44195545)
20. B. MEERSON and P. SASOROV, Domain stability, competition, growth and selection in globally constrained bistable systems, Phys. Rev. E (3), 53(1996), pp. 3491-3494. (Pubitemid 126584034)
21. H. MEINHARDT, Orientation of chemotactic cells and growth cones: Models and mechanisms, J. Cell Sci., 112(1999), pp. 2867-2874. (Pubitemid 29430032)
22. Y. MORI, A. JILKINE, and L. EDELSTEIN-KESHET, Wave-pinning and cell polarity from a bistable reaction-diffusion system, Biophys. J., 94(2008), pp. 3684-3697.
23. J. MURRAY, Mathematical Biology, 2nd ed., Springer, Berlin, 1993.
24. P. NALBANT, L. HODGSON, V. KRAYNOV, A. TOUTCHKINE, and K. HAHN, Activation of endogenous Cdc42 visualized in living cells, Science, 305(2004), pp. 1615-1619. (Pubitemid 39296355)
25. A. NARANG, Spontaneous polarization in eukaryotic gradient sensing: A mathematical model based on mutual inhibition of frontness and backness pathways, J. Theoret. Biol., 240(2006), pp. 538-553. (Pubitemid 43765934)
26. Y. NISHIURA, Global structure of bifurcating solutions of some reaction-diffusion systems, SIAM J. Math. Anal., 13(1982), pp. 555-593.
27. M. OTSUJI, S. ISHIHARA, C. CO, K. KAIBUCHI, A. MOCHIZUKI, and S. KURODA, A mass conserved reaction-diffusion system captures properties of cell polarity, PLoS Comput. Biol., 3(2007), e108.
28. M. POSTMA, L. BOSGRAAF, H. LOOVERS, and P. VAN HAASTERT, Chemotaxis: Signalling modules join hands at front and tail, Embo Rep., 5(2004), pp. 35-40. (Pubitemid 38228525)
29. L. REYNA and M. WARD, Metastable internal layer dynamics for the viscous Cahn-Hilliard equation, Methods Appl. Anal., 2(1995), pp. 285-306. (Pubitemid 126030554)
30. J. RUBINSTEIN and P. STERNBERG, Nonlocal reaction-diffusion equations and nucleation, IMA J. Appl. Math., 48(1992), pp. 249-264.
31. B. SCHROTH-DIEZ, S. GERWIG, M. ECKE, R. HEGERL, S. DIEZ, and G. GERISCH, Propagating waves separate two states of actin organization in living cells, HFSP J., 3(2009), pp. 412-427.
32. J.-A. SEPULCHRE and V. I. KRINSKY, Bistable reaction-diffusion systems can have robust zerovelocity fronts, Chaos, 10(2000), pp. 826-833.
33. B. D. SLAUGHTER, A. DAS, J. W. SCHWARTZ, B. RUBINSTEIN, and R. LI, Dual modes of cdc42 recycling fine-tune polarized morphogenesis, Dev. Cell, 17(2009), pp. 823-835.
34. J. SMOLLER and A. WASSERMAN, Global bifurcation of steady state solutions, J. Differential Equations, 39(1981), pp. 269-290.
35. J. SNEYD and A. ATRI, Curvature dependence of a model for calcium wave propagation, Phys. D, 65(1993), pp. 365-372.
36. K. SUBRAMANIAN and A. NARANG, A mechanistic model for eukaryotic gradient sensing: Spontaneous and induced phosphoinositide polarization, J. Theoret. Biol., 231(2004), pp. 49-67. (Pubitemid 39201036)
37. X. SUN and M. WARD, Dynamics and coarsening of interfaces for the viscous Cahn-Hilliard equation in one spatial dimension, Stud. Appl. Math., 105(2000), pp. 203-234. (Pubitemid 33321661)
38. J. TYSON, K. CHEN, and B. NOVAK, Sniffers, buzzers, toggles and blinkers: Dynamics of regulatory and signaling pathways in the cell, Curr. Opin. Cell Biol., 15(2003), pp. 221-231. (Pubitemid 36332198)
39. B. VANDERLEI, J. FENG, and L. EDELSTEIN-KESHET, A computational model of cell polarization and motility coupling mechanics and biochemistry, submitted.
40. A. B. VERKHOVSKY, T. M. SVITKINA, and G. G. BORISY, Self-polarization and directional motility of cytoplasm, Curr. Biol., 9(1999), pp. 11-20. (Pubitemid 29045790)
41. M. J. WARD, Metastable bubble solutions for the Allen-Cahn equation with mass conservation, SIAM J. Appl. Math., 56(1996), pp. 1247-1279. (Pubitemid 126554159)
42. O. WEINER, W. MARGANSKI, L. WU, S. ALTSCHULER, and M. KIRSCHNER, An actin-based wave generator organizes cell motility, PLoS Biol., 5(2007), e221.
43. J. J. WYLIE and R. M. MIURA, Traveling waves in coupled reaction-diffusion models with degenerate sources, Phys. Rev. E (3), 74(2006), 021909.
44. J. XU, F. WANG, A. VAN KEYMEULEN, P. HERZMARK, A. STRAIGHT, K. KELLY, Y. TAKUWA, N. SUGIMOTO, T. MITCHISON, and H. BOURNE, Divergent signals and cytoskeletal assemblies regulate self-organizing polarity in neutrophils, Cell, 114(2003), pp. 201-214. (Pubitemid 36936914)