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

Hill, N.A. and Häder, D.-P. (1997) A biased random walk model for the trajectories of swimming micro-organisms. Journal of Theoretical Biology, 186(4), pp. 503-526. (doi: 10.1006/jtbi.1997.0421)

Abstract

The motion of swimming micro-organisms that have a preferred direction of travel, such as single-celled algae moving upwards (gravitaxis) or towards a light source (phototaxis), is modelled as the continuous limit of a correlated and biased random walk as the time step tends to zero. This model leads to a Fokker–Planck equation for the probability distribution function of the orientation of the cells, from which macroscopic parameters such as the mean cell swimming direction and the diffusion coefficient due to cell swimming can be calculated. The model is tested on experimental data for gravitaxis and phototaxis and used to derive values for the macroscopic parameters for future use in theories of bioconvection, for example.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Hill, Professor Nicholas
• Authors: Hill, N.A., and Häder, D.-P.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Theoretical Biology
• ISSN: 0022-5193
• ISSN (Online): 1095-8541