Perturbation expansion of Alt`s cell balance equations reduces to Segel`s one-dimensional equations for shallow chemoattractant gradients

Journal Article · Tue Sep 01 04:00:00 EDT 1998 · SIAM Journal of Applied Mathematics

DOI:https://doi.org/10.1137/S0036139996301283· OSTI ID:343618

Chen, K C ^[1]; Ford, R M ^[2]; Cummings, P T ^[3]

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1. New York Univ. Medical Center, NY (United States). Dept. of Physiology and Neuroscience
2. Univ. of Virginia, Charlottesville, VA (United States). Dept. of Chemical Engineering
3. Univ. of Tennessee, Knoxville, TN (United States). Dept. of Chemical Engineering

The cell balance equations of Alt are rigorously studied and perturbatively expanded into forms similar to Segel`s new-dimensional phenomenological cell balance equations by considering the simplifying case of bacterial density possessing symmetry in the x and y directions responding to an attractant gradient present only in the z direction. The authors prove that for shallow attractant gradients the lumped integrals involving the tumbling probability frequency distribution and bacterial density distribution in the {theta} direction can be explicitly expressed as a product of three quantities: the mean tumbling frequency, the bacterial subpopulation density, and a reversal probability. The authors also derive expressions for the bacterial net flux in the Fickian form from which two macroscopic transport parameters, the random motility coefficient and the chemotactic velocity, are explicitly related to individual cell properties and chemical gradients.

• OSTI ID: 343618
• Journal Information: SIAM Journal of Applied Mathematics, Journal Name: SIAM Journal of Applied Mathematics Journal Issue: 1 Vol. 59; ISSN SMJMAP; ISSN 0036-1399
• Country of Publication: United States
• Language: English

Related Subjects

54 ENVIRONMENTAL SCIENCES
55 BIOLOGY AND MEDICINE
BASIC STUDIES
BACTERIA
BIODEGRADATION
ENVIRONMENTAL TRANSPORT
MOTION
PERTURBATION THEORY
REMEDIAL ACTION