Analytical solutions for distributions of chemotactic bacteria |
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Authors: | Gerald Rosen |
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Institution: | (1) Department of Physics, Drexel University, 19104 Philadelphia, PA, U.S.A. |
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Abstract: | This paper reports general and specialized results on analytical solutions to the governing phenomenological equations for
chemotactic redistribution and population growth of motile bacteria. It is shown that the number of bacteria cells per unit
volume,b, is proportional to a certain prescribed function ofs, the concentration of the critical substrate chemotactic agent, for steady-state solutions through an arbitrary spatial region
with a boundary that is impermeable to bacteria cell transport. Moreover, it is demonstrated that the steady-state solution
forb ands is unique for a prescribed total number of bacteria cells in the spatial region and a generic Robin boundary condition ons. The latter solution can be approximated to desired accuracy in terms of the Poisson-Green's function associated with the
spatial region. Also, as shown by example, closed-form exact steady-state solutions are obtainable for certain consumption
rate functions and geometrically symmetric spatial regions. A solutional procedure is formulated for the initialvalue problem
in cases for which significant population growth is present and bacteria cell redistribution due to motility and chemotactic
flow proceeds slowly relative to the diffusion of the chemoattractant substrate. Finally, a remarkably simple exact analytical
solution is reported for a stradily propagating plane-wave which features motility, chemotactic motion and bacteria population
growth regulated by substrate diffusion. |
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