Mathematical description of bacterial traveling pulses

PLoS Computational Biology

Volumn 6, Issue 8, 2010, Pages

  Saragosti, Jonathan ^a   Calvez, Vincent ^b,c   Bournaveas, Nikolaos ^d   Buguin, Axel ^a   Silberzan, Pascal ^a   Perthame, Benoît ^e,f  

^a INSTITUT CURIE   (France)

^b UNIVERSITÉ DE LYON   (France)

^c INRIA RHÔNE ALPES   (France)

^d UNIVERSITY OF EDINBURGH   (United Kingdom)

^e UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^f INSTITUT UNIVERSITAIRE DE FRANCE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

'CURRENT; COLLECTIVE MOTIONS; E. COLI; KELLER-SEGEL; KINETIC DESCRIPTION; MACROSCOPIC SCALE; MATHEMATICAL DESCRIPTIONS; MESOSCOPICS; MODELING TASK; TRAVELING PULSE;

ESCHERICHIA COLI;

ARTICLE; BACTERIAL KINETICS; CHEMOTAXIS; CONTROLLED STUDY; ESCHERICHIA COLI; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; NONHUMAN; POPULATION DENSITY; POPULATION DISPERSION; QUALITATIVE ANALYSIS; QUANTITATIVE ANALYSIS;

BACTERIA (MICROORGANISMS); ESCHERICHIA COLI;

EID: 78049435271     PISSN: 1553734X     EISSN: 15537358     Source Type: Journal    
DOI: 10.1371/journal.pcbi.1000890     Document Type: Article

References (47)

1. Adler J (1966) Chemotaxis in bacteria. Science 153: 708-716.
2. Budrene E, Berg H (1995) Dynamics of formation of symmetrical patterns by chemotactic bacteria. Nature 376: 49-53.
3. Park S, Wolanin P, Yuzbashyan E, Lin H, Darnton N, et al. (2003) Influence of topology on bacterial social interaction. Proc Natl Acad Sci USA 100: 13910-15.
4. Berg H (2004) E. coli in motion Springer.
5. Alt W (1980) Biased random walk models for chemotaxis and related diffusion approximations. J Math Biol 9: 147-177.
6. Othmer H, Dunbar S, Alt W (1988) Models of dispersal in biological systems. J Math Biol 26: 263-298.
7. Gregor T, Fujimoto K, Masaki N, Sawai S (2010) The onset of collective behavior in social amoebae. Science (in press).
8. Holmes A, Kalvala S, Whitworth D (2010) Spatial simulations of myxobacterial development. PLoS Comput Biol 6: doi:10.1371/journal.pcbi.1000686.
9. Perthame B (2007) Transport Equations in Biology. Frontiers in Mathematics. Birkhäuser Verlag.
10. Hillen T, Painter K (2009) A user's guide to PDE models for chemotaxis. J Math Biol 58: 183-217.
11. Mazzag B, Zhulin I, Mogilner A (2003) Model of bacterial band formation in aerotaxis. Biophys J 85: 3558-74.
12. Murray J (2002) Mathematical biology, volume 2, Springer, 3rd edition.
13. Keller E, Segel L (1970) Initiation of slime mold aggregation viewed as an instability. J Theor Biol 26: 399-415.
14. Höfer T, Sherratt J, Maini P (1995) Dictyostelium discoideum: Cellular selforganisation in an excitable medium. Proc Roy Soc Lond B 259: 249-257.
15. Khonsari H, Calvez V (2007) The origins of concentric demyelination: selforganization in the human brain. Plos ONE;doi:10.1371/journal.pone.0000150.
16. Keller E, Segel L (1971) Traveling bands of chemotactic bacteria: A theoretical analysis. J Theor Biol 30: 235-248.
17. Nagai T, Ikeda T (1991) Traveling waves in a chemotactic model. J Math Biol 30: 169-184.
18. Horstmann D, Stevens A (2004) A constructive approach to traveling waves in chemotaxis. J Nonlinear Sci 14: 1-25.
19. Li T, Wang Z (2009) Nonlinear stability of traveling waves to a hyperbolicparabolic system modeling chemotaxis. SIAM J Appl Math 70: 1522-1541.
20. Tindall M, Maini P, Porter S, Armitage J (2008) Overview of mathematical approaches used to model bacterial chemotaxis ii: bacterial populations. Bull Math Biol 70: 1570-1607.
21. Landman KA, Simpson MJ, Slater JL, Newgreen DF (2005) Diffusive and chemotactic cellular migration: smooth and discontinuous traveling wave solutions. SIAM J Appl Math 65: 1420.
22. Funaki M, Mimura M, Tsujikawa T (2006) Traveling front solutions arising in the chemotaxis-growth model. Interfaces Free Bound 8.
23. Nadin G, Perthame B, Ryzhik L (2008) Traveling waves for the Keller-Segel system with Fisher birth terms. Interfaces Free Bound 10: 517-538.
24. Brenner M, Levitov L, Budrene E (1998) Physical mechanisms for chemotactic pattern formation by bacteria. Biophys J 74: 1677-93.
25. Salman H, Zilman A, Loverdo C, Jeffroy M, Libchaber A (2006) Solitary modes of bacterial culture in a temperature gradient. Phys Rev Lett 97: 118101.
26. Rivero MA, Tranquillo RT, Buettner HM, Lauffenburger DA (1989) Transport models for chemotactic cell populations based on individual cell behavior. Chem Eng Sci 44: 2881-2897.
27. Hillen T, Othmer H (2000) The diffusion limit of transport equations derived from velocity-jump processes. SIAM J Appl Math 61: 751-775.
28. Chalub F, Markowich P, Perthame B, Schmeiser C (2004) Kinetic models for chemotaxis and their drift-diffusion limits. Monatsh Math 142: 123-141.
29. Filbet F, Laurençot P, Perthame B (2005) Derivation of hyperbolic models for chemosensitive movement. J Math Biol 50: 189-207.
30. Erban R, Othmer H (2004) From individual to collective behavior in bacterial chemotaxis. SIAM J Appl Math 65: 361-391.
31. Dolak Y, Schmeiser C (2006) Kinetic models for chemotaxis: hydrodynamic limits and spatio-temporal mechanisms. J Math Biol 51: 595-615.
32. Chalub F, Dolak-Struss Y, Markowich P, Oelz D, Schmeiser C, et al. (2006) Model hierarchies for cell aggregation by chemotaxis. Math Models Methods Appl Sci 16: 1173-97.
33. Erban R, Othmer H (2007) Taxis equations for amoeboid cells. J Math Biol 54: 847-885.
34. Xue C, Hwang H, Painter K, Erban R (2010) Travelling waves in hyperbolic chemotaxis equations. Preprint.
35. After submission of their manuscript, the authors have been aware of a similar work by Xue et al. they obtain analogous results based on an alternative approach.
36. Brown D, Berg H (1974) Temporal stimulation of chemotaxis in Escherichia coli. Proc Natl Acad Sci USA 71.
37. Segall J, Block S, Berg H (1986) Temporal comparisons in bacterial chemotaxis. Proc Natl Acad Sci USA 83: 8987-91.
38. Mittal N, Budrene E, Brenner M, Oudenaarden AV (2003) Motility of Escherichia coli cells in clusters formed by chemotactic aggregation. Proc Natl Acad Sci USA 100: 13259-63.
39. Inoue M, Kaneko K (2008) Conditions for self-consistent aggregation by chemotactic particles. Phys Rev E 77: 041916.
40. Fisher R (1937) The advance of advantageous genes. Ann Eugenics 7: 335-369.
41. Spiro P, Parkinson J, Othmer H (1997) A model of excitation and adaptation in bacterial chemotaxis. Proc Natl Acad Sci USA 94: 7263-68.
42. Bournaveas N, Calvez V (2008) Global existence for the kinetic chemotaxis model without pointwise memory effects, and including internal variables. Kinet Relat Models 1: 29-48.
43. Keymer J, Endres R, Skoge M, Meir Y, Wingreen N (2006) Chemosensing in Escherichia coli: two regimes of two-state receptors. Proc Natl Acad Sci USA 103: 1786-91.
44. Xia Y, Whitesides G (1998) Soft lithography. Annu Rev Mat Sci 28: 153-184.
45. Hwang H, Kang K, Stevens A (2005) Global solutions of nonlinear transport equations for chemosensitive movement. SIAM J Math Anal 36.
46. Bournaveas N, Calvez V, Gutiérrez S, Perthame B (2008) Global existence for a kinetic model of chemotaxis via dispersion and Strichartz estimates. Comm Partial Differential Equations 33: 79-95.
47. Berg H (1993) Random walks in biology Princeton University Press, 2nd edition.