Emerging patterns in a hyperbolic model for locally interacting cell systems

Journal of Nonlinear Science

Volumn 12, Issue 6, 2003, Pages 619-640

  Lutscher, F ^b   Stevens, A ^a  

^a MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Hyperbolic system; Myxobacteria; Rippling; Traveling wavetrains

Indexed keywords

EID: 0042848804     PISSN: 09388974     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00332-002-0510-4     Document Type: Article

References (29)

1. B. D. Blackhard and D. R. Zusman. "Frizzy" genes of Myxococcus xanthus are involved in control of frequency of reversal of gliding motility. Proc. Natl. Acad. Sci. USA, 82:8767-8770, 1995.
2. U. Börner, A. Deutsch, H. Reichenbach, and M. Bär. Rippling patterns in aggregates of myxobacteria arising from cell-cell collisions. Phys. Rev. Lett., 89:078101, 2002.
3. 1 PhD thesis, Universität Bonn, 1999.
4. E.Geigant K. Ladizhansky, and A. Mogilner. An integro-differential model for orientational distributions of F-actin in cells. SIAM J. Appl. Math., 59:787-809, 1999.
5. K. P. Hadeler. Reaction telegraph equations and random walk systems. In S. J. v. Strien and S. M. Verduyn Lunel, editors, Stochastic and Spatial Structures of Dynamical Systems. Kon. Nederlandse Akad. Weteusch. Verhandl., Afd. Naturkunde, 1. Serie, North-Holland, 133-161, 1996, Amsterdam.
6. K. P. Hadeler Reaction transport systems in biological modelling. In V. Capasso and O. Diekmann, editors, Mathematics Inspired by Biology, Lect. Notes Math. 1714, pages 95-150. Springer-Verlag, Heidelberg, 1999.
7. T. Hillen. A Turing model with correlated random walk. J. Math. Biol., 35:49-72, 1996.
8. T. Hillen. Invariance principles for hyperbolic random walk systems. J. Math. Anal. Appl., 210:360-374, 1997.
9. T. Hillen, C. Rohde, and F. Lutscher. Existence of weak solutions for a hyperbolic model for chemosensitive movement. J. Math. Anal. Appl., 260:173-199, 2001.
10. T. Hillen and A. Stevens. Hyperbolic models for chemotaxis in 1-D. Nonlinear Analysis: Real World Applications, 1:409-433, 2000.
11. O. Igoshin, A. Mogilner, R. Welch, D. Kaiser, and G. Oster. Pattern formation and traveling waves in myxobacteria: Theory and modeling. Proc. Natl. Acad. Sci. USA, 98:14913-14938, 2001.
12. M. Kac. A stochastic model related to the telegrapher's equation. Rocky Mountain J. Math., 4:497-509, 1956.
13. D. Kaiser and L. Kroos. Intercellular signaling. In M. Dworkin and D. Kaiser, editors, Myxobacteria II. American Society for Microbiology, Washington, DC, 1993.
14. R. LeVeque. Numerical Methods for Conservation Laws. Birkhäuser, Basel, 1992.
15. F. Lutscher. Modeling moving polarized groups of animals and cells. PhD thesis, Universität Tübingen, 2000. http://w210.ub.uni-tuebingen.de/dbt/volltexte/ 2000/203.
16. F. Lutscher. Modeling alignment and movement of animals and cells. J. Math. Biol., to appear.
17. M. J. McBride, P. Hartzell, and D. R. Zusman. Motility and tactic behavior of Myxococcus xanthus. In M. Dworkin and D. Kaiser, editors, Myxobacteria II. American Society for Microbiology, Washington, DC, 1993.
18. B. Pfistner. A one-dimensional model for the swarming behavior of Myxobaktena. In W. Alt and G. Hoffmann, editors, Biological Motion. Lect. Notes on Biomath., 89, Springer-Verlag, Berlin, Heidelberg, 1990.
19. H. Reichenbach. Myxococcus spp. (Myxobacteriales). Schwarmentwicklung und Bildung von Protocysten. Publikationen zu wissenschaftlichen Filmen, Vol. 1A, 557-578. Göttingen, Germany, 1966.
20. B. Sager and D. Kaiser. Intercellular C-signaling and the traveling waves of Myxococcus. Genes & Development, 8:2793-2804, 1994.
21. L. Shimkets and D. Kaiser. Murein components rescue developmental sporulation of Myxococcus xanthus. J. Bacteriol., 152:451-461, 1982.
22. A. Stevens. Simulations of the gliding behavior and aggregation of myxobacteria. In W. Alt and G. Hoffmann, editors, Biological Motion, pages 548-555. Lect. Notes on Biomath., 89, Springer-Verlag, Berlin, Heidelberg, 1990.
23. A. Stevens. Trail following and aggregation of myxobacteria. J. Biol. Systems, 3(4): 1059-1068, 1995.
24. A. Stevens. The derivation of chemotaxis-equations as limit dynamics of moderately interacting stochastic many particle systems. SIAM J. Appl. Math., 61(1): 183-212, 2000.
25. A. Stevens. A stochastic cellular automaton, modeling gliding and aggregation of myxobacteria. SIAM J. Appl. Math., 61(1):172-182, 2000.
26. J. Strickwerda. Finite difference schemes and partial differential equations. Chapman & Hall, New York, 1989.
27. M. E. Taylor. Partial Differential Equations III. Springer-Verlag, New York, 1996.
28. R. Welch and D. Kaiser. Cell behavior in traveling wave patterns of myxobacteria. Proc Natl. Acad. Sci. USA, 98:14907-14912, 2001.
29. D. White. Myxospore and fruiting body morphogenesis. In M. Dworkin and D. Kaiser, editors, Myxobacteria II. American Society for Microbiology, Washington, DC, 1993.