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Theoretical significance of the condition δ=2μ in bacterial chemotaxis

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Abstract

First-order spatial gradients are reliquished in the Schrödinger-Bloch equation for bacterial chemotaxis if and only if the flux coefficient-motility ratio equals 2, the precise value measured in recent experiments onEscherichia coli attracted by oxygen. Moreover, for δ/μ=2 the Schrödinger-Bloch function Ψ is simply equal to the number of bacteria cells per unit volume divided by the chemoattractant concentration.

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Literature

  • Ames, W. F. 1972.Nonlinear Partial Differential Equations in Engineering, Vol. II, pp. 96–100. New York: Academic Press.

    MATH  Google Scholar 

  • Goel, N. C., S. C. Maitra and E. W. Montroll. 1971. “On the Volterra and Other Nonlinear Models of Interacting Populations”.Rev. mod. phys. 43, 231–276.

    Article  MathSciNet  Google Scholar 

  • Holz, M. and S. H. Chen. 1979. “Spatio-temporal Structure of Migrating Chemotactic Band ofEscherichia coli”.Biophys. J. 26, 243–261.

    Article  Google Scholar 

  • Keller, E. F. and L. A. Segel. 1971. “Traveling Bands of Chemotactic Bacteria: A Theoretical Analysis”.J. theor. Biol. 30, 235–248.

    Article  Google Scholar 

  • Lapidus, R. I. 1981. “Analysis of Bacterial Chemotaxis in Flowing Water”.Math. Biosci. 54, 79–90.

    Article  MATH  Google Scholar 

  • McCabe, M. and T. V. Laurent. 1975. “Diffusion of Oxygen, Nitrogen and Water in Hyaluronate Solutions”.Biochim. biophys. Acta 399, 131–137.

    Google Scholar 

  • Montroll, E. W. 1972. “Some Statistical Aspects of the Theory of Interacting Species”. InSome Mathematical Problems in Biology III, pp. 101–143. Providence, RI: American Math. Soc.

    Google Scholar 

  • Rosen, G. 1973. “Fundamental Theoretical Aspects of Bacterial Chemotaxis”.J. theor. Biol. 41, 201–208.

    Article  Google Scholar 

  • — 1975. “Analytical Solution to the Initial-value Problem for Traveling Bands of Chemotactic Bacteria”.J. theor. Biol. 49, 311–321.

    Article  Google Scholar 

  • — 1976. “Existence and Nature of Band Solutions to Generic Chemotactic Transport Equations”.J. theor. Biol. 59, 243–246.

    Article  Google Scholar 

  • — 1978. “Steady-state Distribution of Bacteria Chemotactic Toward Oxygen”.Bull. math. Biol. 40, 671–674.

    Article  MATH  MathSciNet  Google Scholar 

  • Segel, L. A. and J. L. Jackson. 1973. “Theoretical Analysis of Chemotactic Movement in Bacteria”.J. mechanochem. Cell. Motil. 2, 25–34.

    Google Scholar 

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  1. Department of Physics, Drexel University, 19104, Philadelphia, PA, USA

    Gerald Rosen

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  1. Gerald Rosen
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Rosen, G. Theoretical significance of the condition δ=2μ in bacterial chemotaxis. Bltn Mathcal Biology 45, 151–153 (1983). https://doi.org/10.1007/BF02462353

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  • DOI: https://doi.org/10.1007/BF02462353

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