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J Theor Biol. 1997 Jun 21;186(4):503-26.

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

Author information

1
Department of Applied Mathematical Studies, University of Leeds, England.

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.

PMID:
11536821
DOI:
10.1006/jtbi.1997.0421
[Indexed for MEDLINE]

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