Traveling wave solutions from microscopic to macroscopic chemotaxis models

Journal of Mathematical Biology

Volumn 61, Issue 5, 2010, Pages 739-761

  Lui, Roger ^a   Wang, Zhi An ^b  

^a WORCESTER POLYTECHNIC INSTITUTE   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Chemical kinetics; Chemotaxis; Keller Segel model; Potential functions; Traveling wave solutions; Turning rate functions

Indexed keywords

CHEMOTACTIC FACTOR;

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; CELL; CHEMOTAXIS; CYTOLOGY; DIFFUSION; KINETICS; METABOLISM; PHYSIOLOGY; SIGNAL TRANSDUCTION;

ALGORITHMS; CELLS; CHEMOTACTIC FACTORS; CHEMOTAXIS; DIFFUSION; KINETICS; MODELS, BIOLOGICAL; SIGNAL TRANSDUCTION;

EID: 77956173978     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-009-0317-0     Document Type: Article

References (22)

1. Adler J (1966) Chemotaxis in bacteria. Science 153: 708-716.
2. Alt W (1980) Biased random walk model for chemotaxis and related diffusion approximation. J Math Biol 9: 147-177.
3. Brown D, Berg H (1974) Temporal stimulation of chemotaxis in Escherichia coli. Proc Natl Acad Sci 71(4): 1388-1392.
4. Eisenbach M (2004) Chemotaxis. Imperial College Press, London.
5. Erban R, Othmer H (2004) From individual to collective behavior in bacterial chemotaxis. SIAM J Appl Math 65(2): 361-391.
6. Hillen T, Painter K (2009) A user's guide to pde models for chemotaxis. J Math Biol 58: 183-217.
7. Horstmann D (2003) From 1970 until present: the Keller-Segel model in chemotaxis and its consequences I. Jahresberichte der DMV 105(3): 103-165.
8. Horstmann D (2004) From 1970 until present: the Keller-Segel model in chemotaxis and its consequences II. Jahresberichte der DMV 106(2): 51-69.
9. Horstmann D, Stevens A (2004) A constructive approach to travelling waves in chemotaxis. J Nonlinear Sci 14: 1-25.
10. Keller EF, Segel LA (1970) Initiation of slime mold aggregation viewd as an instability. J Theor Biol 26: 399-415.
11. Keller EF, Segel LA (1971a) Model for chemotaxis. J Theor Biol 30: 225-234.
12. Keller EF, Segel LA (1971b) Traveling bands of chemotactic bacteria: a theoretical analysis. J Theor Biol 30: 235-248.
13. Kolmogorov AN, Petrovskii IG, Piskunov NS (1937) A study of the equation of diffusion with inrcease in the quantity of matter, and its application to a biological problem. Bjol Moskovskovo Gos Univ 17: 1-72.
14. Lapidus R, Schiller R (1976) Model for the chemotactic response of a bacterial population. Biophys J 16: 779-789.
15. Othmer H, Dunbar SR, Alt W (1988) Models of dispersal in biological systems. J Math Biol 26: 263-298.
16. Othmer H, Hillen T (2002) The diffusion limit of transport equations II: chemotaxis equations. SIAM J Appl Math 62(4): 1122-1250.
17. Othmer H, Stevens A (1997) Aggregation, blowup and collapse: the ABC's of taxis in reinforced random walks. SIAM J Appl Math 57: 1044-1081.
18. Parent CA (2004) Making all the right moves: chemotaxis in neutrophils and dictyostelium. Curr Opin Cell Biol 16: 4-13.
19. Patlak CS (1953) Random walk with persistence and external bias. Bull Math Biophys 15: 311-338.
20. Rosen D (1976) Existence and nature of band solutions to generic chemotactic transport equations. J Theor Biol 59: 243-246.
21. Tindall MJ, Maini PK, Porter SL, Armitage JP (2008) Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations. Bull Math Biol 70(6): 1570-1607.
22. Wang ZA (2009) Connections between microscopic and macroscopic models for chemotaxis. SIAM J Math Anal (in review).