A biased random walk model for the trajectories of swimming micro-organisms

Journal of Theoretical Biology

Volumn 186, Issue 4, 1997, Pages 503-526

  Hill, N A ^a   Hader D P ^b  

^a UNIVERSITY OF LEEDS   (United Kingdom)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

GRAVITAXIS; MICROALGAE; MICROORGANISM; MICROORGANISMS; ORIENTATION BEHAVIOUR; PHOTOTAXIS; RANDOM WALK MODEL; SWIMMING;

ARTICLE; CELL MOTILITY; DIFFUSION COEFFICIENT; GRAVITY; MICROORGANISM; MODEL; NONHUMAN; PHOTOTAXIS; PRIORITY JOURNAL; PROBABILITY; SWIMMING;

ALGAE;

EID: 0031582488     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.1997.0421     Document Type: Article

References (21)

1. ALT, W. & HOFFMANN, G. (1990). Biological Motion. Berlin: Springer-Verlag. Lecture Notes in Biomathematics 89.
2. BATSCHELET, E. (1981). Circular Statistics in Biology. London: Academic Press.
3. BERG, H. C. & BROWN, D. A. (1972). Chemotaxis in Escherichia coli analysed by three-dimensional tracking. Nature 239, 500-504.
4. BOLD, H. C. & WYNNE, M. J. (1978). Introduction to the Algae. Structure and Reproduction. New Jersey: Prentice Hall.
5. BOVET, P. & BENHAMOU, S. (1988). Spatial analysis of animals' movement using a correlated random walk model. J. theor. Biol. 131, 419-433.
6. CHILDRESS, S., LEVANDOWSKY, M. & SPIEGEL, E. A. (1975). Pattern formation in a suspension of swimming micro-organisms: equations and stability theory. J. Fluid Mech. 63, 591-613.
7. COX, D. R. & MILLER, H. D. (1965). The Theory of Stochastic Processes. New York: John Wiley and Sons Inc.
8. FISHER, N. I., LEWIS, T. & EMBLETON, B. J. J. (1987). Statistical Analysis of Spherical Data. Cambridge University Press.
9. HÄDER, D. P. & LEBERT, M. (1985). Real time computer-controlled tracking of micro-organisms. Photochem. Photobiol. 42, 509-514.
10. HILL, N. A., PEDLEY, T. J. & KESSLER, J. O. (1989). Growth of bioconvection patterns in a suspension of gyrotactic microorganisms in a layer of finite depth. J. Fluid Mech. 208, 509-543.
11. HILL, N. A. & VINCENT, R. V. V. (1993). A simple model and strategies for orientation in phototactic microorganisms. J. theor. Biol. 163, 223-235.
12. KESSLER, J. O. (1986). Individual and collective fluid dynamics of swimming cells. J. Fluid Mech. 73, 191-205.
13. KESSLER, J. O., HILL, N. A. & HÄDER, D.-P. (1992). Orientation of swimming flagellates by simultaneously acting external factors. J. Phycology 28, 816-822.
14. LEBERT, M. & HÄDER, D.-P. (1996). How Euglena tells up from down. Nature 379, 590.
15. LINDSTRÖM, K. (1982). Environment requirement of the dinoflagellate peridinium cinetum fa. westii. Acta Universitatis Upsaliensis. Abstracts of Uppsala Dissertations from the Faculty of Science 646.
16. LOVELY, P. S. & DAHLQUIST, F. W. (1975). Statistical measures of bacterial motility and chemotaxis. J. Theor. Biol. 50, 477-496.
17. MARDIA, K. V. (1972). Statistics of Directional Data. London: Academic Press.
18. PEDLEY, T. J., HILL, N. A. & KESSLER, J. O. (1988). The growth of bioconvection patterns in a uniform suspension of gyrotactic micro-organisms. J. Fluid Mech. 195, 223-237.
19. PEDLEY, T. J. & KESSLER, J. O. (1990). A new continuum model for suspensions of gyrotactic micro-organisms. J. Fluid Mech. 212, 155-182.
20. RISKEN, H. (1989). The Fokker-Planck Equation. 2nd Edn. Berlin: Springer-Verlag.
21. VINCENT, R. V. V. & HILL, N. A. (1996). Bioconvection in a suspension of phototactic algae. J. Fluid Mech. 327, 343-371.