Journal article
Fundamental theoretical aspects of bacterial chemotaxis
Journal of theoretical biology, v 41(2), pp 201-208
1973
PMID: 4584509
Abstract
From the parabolic partial differential equation for the diffusion and chemotactic transport of a spatial distribution of bacteria, there follow associated Fokker-Planck and Langevin equations for the stochastic motion of individual bacteria cells. It is pointed out that the Fokker-Planck equation is applicable on a macroscopic time-scale which makes the mean time for flagella reorientations a small quantity, while the Langevin equation must be used directly for a finer description of the time-development of the density of chemotactic bacteria cells. It is shown that the Langevin equation is appropriate for the low Reynolds number motion of a bacterium if and only if the total flagellar propulsive force takes a specific form. The average of the latter quantity is derived from a potential energy which has the same form as the Gibbs free energy for
N molecules of the chemotactic agent in a solution of varying concentration. The conjecture that
N molecules of the chemotactic agent are adsorbed at the surface of a bacterium cell membrane, and that changes in the potential energy equal the negative of changes in the Gibbs free energy, produces a formula for the chemotactic flux coefficient which yields a magnitude consonant with experiment for
N of the order 10
5. Finally, it is observed that the Fokker-Planck equation governing bacterial chemotaxis on a macroscopic time-scale can be transformed to an equivalent Schrödinger-Block equation, and thus particular solutions known from quantum statistical mechanics can be evoked to provide immediate solutions to initial-value problems in bacterial chemotaxis, as shown by example.
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Details
- Title
- Fundamental theoretical aspects of bacterial chemotaxis
- Creators
- Gerald Rosen - Drexel University
- Publication Details
- Journal of theoretical biology, v 41(2), pp 201-208
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Physics
- Web of Science ID
- WOS:A1973Q722400001
- Scopus ID
- 2-s2.0-0015857696
- Other Identifier
- 991019173962304721