Abstract
When a suspension of bacterial cells of the speciesBacillus subtilis is placed in a chamber with its upper surface open to the atmosphere complex bioconvection patterns are observed. These arise because the cells: (1) are denser than water; and (2) usually swim upwards, so that the density of an initially uniform suspension becomes greater at the top than the bottom. When the vertical density gradient becomes large enough, an overturning instability occurs which ultimately evolves into the observed patterns. The reason that the cells swim upwards is that they are aerotactic, i.e. they swim up gradients of oxygen, and they consume oxygen. These properties are incorporated in conservation equations for the cell (N) and oxygen (C) concentrations, and these are solved in the pre-instability phase of development whenN andC depend only on the vertical coordinate and time. Numerical results are obtained for both shallow- and deep-layer chambers, which are intrinsically different and require different mathematical and numerical treatments. It is found that, for both shallow and deep chambers, a thin boundary layer, densely packed with cells, forms near the surface. Beneath this layer the suspension becomes severely depleted of cells. Furthermore, in the deep chamber cases, a discontinuity in the cell concentration arises between this cell-depleted region and a cell-rich region further below, where no significant oxygen concentration gradients develop before the oxygen is fully consumed. The results obtained from the model are in good qualitative agreement with the experimental observations.
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Literature
Berg, H. C. 1975. Bacterial behaviour.Nature 254, 389–392.
Berg, H. C. 1983.Random Walks in Biology. Princeton: Princeton University Press.
Dew, P. M. and J. E. Walsh. 1981 A set of library routines for solving parabolic equations in one space variable.ACM Transactions on Mathematical Software 7, 295–314.
Fletcher, C. A. 1991.Computational Techniques for Fluid Dynamicists. Berlin: Springer-Verlag.
Gear, C. W. 1971.Numerical Initial Value Problems in Ordinary Differential Equations. Englewood Cliffs, NJ: Prentice-Hall.
Keller, E. F. and L. A. Segel. 1971. Model for chemotaxis.J. theor. Biol.,30, 235–248.
Keller, H. U., P. C. Wilkinson, M. Abercrombie, E. L. Becker, J. G. Hirsch, M. E. Miller, W. Scott Ramsey and Sally H. Zigmond. 1977. A proposal for the definition of terms related to the locomotion of leukocytes and other cells.Clin. Expl Immunol. 27, 377–380.
Kessler, J. O. 1989. Path and pattern—the mutual dynamics of swimming cells and their environment.Comments theor. Biol. 1, 85–108.
Pedley, T. J. and J. O. Kessler. 1990. A new continuum model for suspensions of gyrotactic micro-organisms.J. Fluid Mech. 212, 155–182.
Pedley, T. J. and J. O. Kessler. 1992. Hydrodynamic phenomena in suspensions of swimming micro-organisms.Ann. Rev. Fluid Mech. 24, 313–358.
Platt, J. R. 1961. “Bioconvection patterns’ in cultures of free swimming organisms,Science 133, 1766–1767.
Schnitzer, M. J., S. M. Block, H. C. Berg and E. M. Purcell. 1990. InBiology of the Chemotactic Response, J. P. Armitage and J. M. Lackie (Eds) pp. 15–34 Cambridge, U.K.: Cambridge University Press.
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Hillesdon, A.J., Pedley, T.J. & Kessler, J.O. The development of concentration gradients in a suspension of chemotactic bacteria. Bltn Mathcal Biology 57, 299–344 (1995). https://doi.org/10.1007/BF02460620
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DOI: https://doi.org/10.1007/BF02460620