The global turning probability density function for motile bacteria and its applications.

The angular turning probability density distribution for motile bacteria is usually measured in local coordinates and is therefore inconvenient for global analyses of the chemotactic bacterial migration. In this paper we present analytical derivations that convert the local angular turning probability density distribution into a global one. The explicit expression of a reduced global turning probability density function for motile bacteria was derived and its relevant properties were investigated. Depending on the angle variable being intergrated and the integration range, three types of cosine moments were separately defined and studied. Some statistical indices and parameters such as the directional persistence, persistence number, and one-dimensional reversal probability were found to be embedded in the various moments of the reduced global turning probability density function. Applications of the reduced global turning probability and its integrated moments to a three-dimensional cell balance equation in an axisymmetric system were also discussed.

[1]  R. M. Ford,et al.  CELLULAR DYNAMICS SIMULATIONS OF BACTERIAL CHEMOTAXIS , 1993 .

[2]  G. Weiss,et al.  A descriptive theory of cell migration on surfaces. , 1974, Journal of theoretical biology.

[3]  Nicholas I. Fisher,et al.  Statistical Analysis of Spherical Data. , 1987 .

[4]  H. Berg,et al.  Chemotaxis in Escherichia coli analysed by Three-dimensional Tracking , 1972, Nature.

[5]  K. Papadopoulos,et al.  Unidirectional motility of Escherichia coli in restrictive capillaries , 1995, Applied and environmental microbiology.

[6]  H. Othmer,et al.  Models of dispersal in biological systems , 1988, Journal of mathematical biology.

[7]  Random walks in biology: Howard C. Berg (New, expanded edition), Princeton Press, 152 pages, 1993 , 1994 .

[8]  H. Berg,et al.  Adaptation kinetics in bacterial chemotaxis , 1983, Journal of bacteriology.

[9]  R. M. Ford,et al.  Random walk calculations for bacterial migration in porous media. , 1995, Biophysical journal.

[10]  Daniel W. Stroock,et al.  Some stochastic processes which arise from a model of the motion of a bacterium , 1974 .

[11]  Peter T. Cummings,et al.  Perturbation Expansion of Alt's Cell Balance Equations Reduces to Segel's One-Dimensional Equations for Shallow Chemoattractant Gradients , 1998, SIAM J. Appl. Math..

[12]  R. Macnab,et al.  Persistence as a concept in the motility of chemotactic bacteria. , 1973, Journal of mechanochemistry & cell motility.

[13]  F. Dahlquist,et al.  Statistical measures of bacterial motility and chemotaxis. , 1975, Journal of theoretical biology.

[14]  J. A. Quinn,et al.  Random motility of swimming bacteria: Single cells compared to cell populations , 1994 .

[15]  H. Berg,et al.  Transient response to chemotactic stimuli in Escherichia coli. , 1975, Proceedings of the National Academy of Sciences of the United States of America.

[16]  C. Patlak.  Random walk with persistence and external bias , 1953 .

[17]  Douglas A. Lauffenburger,et al.  Transport models for chemotactic cell populations based on individual cell behavior , 1989 .

[18]  E. Hobson.  The Theory of Spherical and Ellipsoidal Harmonics , 1955 .

[19]  R. Macnab,et al.  The gradient-sensing mechanism in bacterial chemotaxis. , 1972, Proceedings of the National Academy of Sciences of the United States of America.

[20]  Lee A. Segel,et al.  A Theoretical Study of Receptor Mechanisms in Bacterial Chemotaxis , 1977 .

[21]  Peter T. Cummings,et al.  On the relationship between cell balance equations for chemotactic cell populations , 1992 .

[22]  M. Schnitzer,et al.  Theory of continuum random walks and application to chemotaxis. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  R. M. Ford,et al.  Turn angle and run time distributions characterize swimming behavior for Pseudomonas putida , 1997, Journal of bacteriology.

[24]  L. Segel,et al.  Incorporation of receptor kinetics into a model for bacterial chemotaxis. , 1976, Journal of theoretical biology.