Skip to main content
Log in

A Model for Bacterial Colonization of Sinking Aggregates

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

Sinking aggregates provide important nutrient-rich environments for marine bacteria. Quantifying the rate at which motile bacteria colonize such aggregations is important in understanding the microbial loop in the pelagic food web. In this paper, a simple analytical model is presented to predict the rate at which bacteria undergoing a random walk encounter a sinking aggregate. The model incorporates the flow field generated by the sinking aggregate, the swimming behavior of the bacteria, and the interaction of the flow with the swimming behavior. An expression for the encounter rate is computed in the limit of large Péclet number when the random walk can be approximated by a diffusion process. Comparison with an individual-based numerical simulation is also given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Acrivos, A., Goddard, J.D., 1965. Asymptotic expansions for laminar forced-convection heat and mass transfer. Part 1. Low speed flows. J. Fluid Mech. 23, 273–291.

    Article  MathSciNet  Google Scholar 

  • Alldredge, A.L., Gotschalk, C., 1988. In situ settling behavior of marine snow. Limnol. Oceanogr. 33, 339–351.

    Google Scholar 

  • Azam, F., 1998. Microbial control of oceanic carbon flux: The plot thickens. Science 280, 694–696.

    Article  Google Scholar 

  • Barbara, G.M., Mitchell, J.G., 2003. Bacterial tracking of motile algae. FEMS Microbiol. Ecol. 44, 79–87.

    Article  Google Scholar 

  • Batchelor, G.K., 1967. An introduction to fluid dynamics. Cambridge University Press, New York.

    MATH  Google Scholar 

  • Bearon, R.N., 2003. An extension of generalized Taylor dispersion in unbounded homogeneous shear flows to run-and-tumble chemotactic bacteria. Phys. Fluids 15, 1552–1563.

    Article  Google Scholar 

  • Berg, H.C., 1983. Random Walks in Biology. Princeton University Press, Englewood Cliffs, NJ.

  • Berg, H.C., Brown, D.A., 1972. Chemotaxis in Escherichia coli analysed by three-dimensional tracking. Nature 239, 500–504.

    Article  Google Scholar 

  • Blackburn, N., Fenchel, T., Mitchell, J., 1998. Microscale nutrient patches in planktonic habitats shown by chemotactic bacteria. Science 282, 2254–2256.

    Article  Google Scholar 

  • Bowen, J.D., Stolzenbach, K.D., Chisholm, S.W., 1993. Simulating bacterial clustering around phytoplankton cells in a turbulent ocean. Limnol. Oceanogr. 38, 36–51.

    Article  Google Scholar 

  • Caron, D.A., Davis, P.G., Madin, L.P., Sieburth, J.M., 1986. Enrichment of microbial populations in macroaggrgates (marine snow) from surface waters of the North Atlantic. J. Mar. Res. 44, 543–565.

    Article  Google Scholar 

  • Clift, R., Grace, J.R., Weber, M.E., 1978. Bubbles, drops and particles. Academic, New York.

    Google Scholar 

  • Frankel, I., Brenner, H., 1991. Generalized Taylor dispersion phenomena in unbounded homogeneous shear flows. J. Fluid Mech. 230, 147–181.

    Article  MATH  Google Scholar 

  • Gerritsen, J., Strickler, J.R., 1977. Encounter probabilities and community structure in zooplankton: A mathematical model. J. Fish. Res. Board Can. 34, 73–82.

    Google Scholar 

  • Grimmett, G.R., Stirzaker, D.R. 1992. Probability and Random Processes, 2nd edition. Oxford University Press, Oxford.

  • Grossart, H.-P., Riemann, L., Azam, F. 2001. Bacterial motility in the sea and its ecological implications. Aquat. Microb. Ecol. 25, 247–258.

    Google Scholar 

  • Hill, N.A., Bees, M.A., 2002. Taylor dispersion of gyrotactic swimming micro-organisms in a linear flow. Phys. Fluids 14, 2598–2605.

    Article  MathSciNet  Google Scholar 

  • Hill, N.A., Häder, D.P., 1997. A biased random walk model for the trajectories of swimming micro-organisms. J. Theor. Biol. 186, 503–526.

    Article  Google Scholar 

  • Jackson, G.A., 1989. Simulation of bacterial attraction and adhesion to falling particles in an aquatic environment. Limnol. Oceanogr. 34, 514–530.

    Article  Google Scholar 

  • Johansen, J.E., Pinhassi, J., Blackburn, N., Zweifel, U.L., Hagström, A., 2002. Variability in motility characteristics among marine bacteria. Aquat. Microb. Ecol. 28, 229–237.

    Article  Google Scholar 

  • Karp-Boss, L., Boss, E., Jumars, P.A., 1996. Nutrient fluxes to planktonic osmotrophs in the presence of fluid motion. Oceanogr. Mar. Biol. Annu. Rev. 34, 71–107.

    Google Scholar 

  • Kim, S., Karrila, S.J., 1991. Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann, London.

    Google Scholar 

  • Kiørboe, T., Grossart, H.-P., Ploug, H., Tang, K., 2002. Mechanisms and rates of bacterial colonization of sinking aggregates. Appl. Environ. Microbiol. 68, 3996–4006.

    Article  Google Scholar 

  • Kiørboe, T., Jackson, G.A., 2001. Marine snow, organic solute plumes, and optimal chemosensory behavior of bacteria. Limnol. Oceanogr. 46, 1309–1318.

    Article  Google Scholar 

  • Kiørboe, T., Ploug, H., Thygesen, U.H., 2001. Fluid motion and solute distribution around sinking aggregates. I. Small-scale fluxes and heterogeneity of nutrients in the pelagic environment. Mar. Ecol. Prog. Ser. 211, 1–13.

    Article  Google Scholar 

  • Leal, L.G., 1992. Laminar flow and convective transport processes: Scaling principles and asymptotic analysis. Butterworth-Heinemann, London.

  • Levich, V.G., 1962. Physiochemical hydrodynamics. Prentice-Hall, Englewood Cliffs, NJ.

  • Luchsinger, R.H., Bergersen, B., Mitchell, J.G., 1999. Bacterial swimming strategies and turbulence. Biophys. J. 77, 2377–2386.

    Article  Google Scholar 

  • Pedley, T.J., Kessler, J.O., 1990. A new continuum model for suspensions of gyrotactic micro-organisms. J. Fluid Mech. 212, 155–182.

    Article  MATH  MathSciNet  Google Scholar 

  • Pedley, T.J., Kessler, J.O., 1992. Hydrodynamic phenomena in suspensions of swimming microorganisms. Annu. Rev. Fluid Mech. 24, 313–358.

    Article  MathSciNet  Google Scholar 

  • Riffell, J.A., Krug, P.J., Zimmer, R.K., 2002. Fertilization in the sea. the chemical identity of an abalone sperm attractant. J. Exp. Biol. 205, 1439–1450.

    Google Scholar 

  • Vladimirov, V.A., Wu, M.S.C., Pedley, T.J., Denissenko, P.V., Zakhidova, S.G., 2004. Measurement of cell velocity distributions in populations of motile algae. J. Exp. Biol. 207, 1203–1216.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. N. Bearon.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bearon, R.N. A Model for Bacterial Colonization of Sinking Aggregates. Bull. Math. Biol. 69, 417–431 (2007). https://doi.org/10.1007/s11538-005-9038-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-005-9038-8

Keywords

Navigation