Skip to main content
PMC home page
Biophysical Journal logoLink to Biophysical Journal
. 1998 Apr;74(4):1677–1693. doi: 10.1016/S0006-3495(98)77880-4

Physical mechanisms for chemotactic pattern formation by bacteria.

M P Brenner 1, L S Levitov 1, E O Budrene 1
PMCID: PMC1299514  PMID: 9545032

Abstract

This paper formulates a theory for chemotactic pattern formation by the bacteria Escherichia coli in the presence of excreted attractant. In a chemotactically neutral background, through chemoattractant signaling, the bacteria organize into swarm rings and aggregates. The analysis invokes only those physical processes that are both justifiable by known biochemistry and necessary and sufficient for swarm ring migration and aggregate formation. Swarm rings migrate in the absence of an external chemoattractant gradient. The ring motion is caused by the depletion of a substrate that is necessary to produce attractant. Several scaling laws are proposed and are demonstrated to be consistent with experimental data. Aggregate formation corresponds to finite time singularities in which the bacterial density diverges at a point. Instabilities of swarm rings leading to aggregate formation occur via a mechanism similar to aggregate formation itself: when the mass density of the swarm ring exceeds a threshold, the ring collapses cylindrically and then destabilizes into aggregates. This sequence of events is demonstrated both in the theoretical model and in the experiments.

Full Text

The Full Text of this article is available as a PDF (325.4 KB).

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Adler J. Chemoreceptors in bacteria. Science. 1969 Dec 26;166(3913):1588–1597. doi: 10.1126/science.166.3913.1588. [DOI] [PubMed] [Google Scholar]
  2. Adler J. Chemotaxis in bacteria. Science. 1966 Aug 12;153(3737):708–716. doi: 10.1126/science.153.3737.708. [DOI] [PubMed] [Google Scholar]
  3. Adler J., Templeton B. The effect of environmental conditions on the motility of Escherichia coli. J Gen Microbiol. 1967 Feb;46(2):175–184. doi: 10.1099/00221287-46-2-175. [DOI] [PubMed] [Google Scholar]
  4. Amsler C. D., Cho M., Matsumura P. Multiple factors underlying the maximum motility of Escherichia coli as cultures enter post-exponential growth. J Bacteriol. 1993 Oct;175(19):6238–6244. doi: 10.1128/jb.175.19.6238-6244.1993. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Andersen K. B., von Meyenburg K. Are growth rates of Escherichia coli in batch cultures limited by respiration? J Bacteriol. 1980 Oct;144(1):114–123. doi: 10.1128/jb.144.1.114-123.1980. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Ben-Jacob E., Cohen I., Shochet O., Aranson I., Levine H., Tsimring L. Complex bacterial patterns. Nature. 1995 Feb 16;373(6515):566–567. doi: 10.1038/373566a0. [DOI] [PubMed] [Google Scholar]
  7. Berg H. C. A physicist looks at bacterial chemotaxis. Cold Spring Harb Symp Quant Biol. 1988;53(Pt 1):1–9. doi: 10.1101/sqb.1988.053.01.003. [DOI] [PubMed] [Google Scholar]
  8. Berg H. C., Brown D. A. Chemotaxis in Escherichia coli analysed by three-dimensional tracking. Nature. 1972 Oct 27;239(5374):500–504. doi: 10.1038/239500a0. [DOI] [PubMed] [Google Scholar]
  9. Berg H. C., Turner L. Chemotaxis of bacteria in glass capillary arrays. Escherichia coli, motility, microchannel plate, and light scattering. Biophys J. 1990 Oct;58(4):919–930. doi: 10.1016/S0006-3495(90)82436-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Blair D. F., Berg H. C. Restoration of torque in defective flagellar motors. Science. 1988 Dec 23;242(4886):1678–1681. doi: 10.1126/science.2849208. [DOI] [PubMed] [Google Scholar]
  11. Block S. M., Berg H. C. Successive incorporation of force-generating units in the bacterial rotary motor. 1984 May 31-Jun 6Nature. 309(5967):470–472. doi: 10.1038/309470a0. [DOI] [PubMed] [Google Scholar]
  12. Budrene E. O., Berg H. C. Complex patterns formed by motile cells of Escherichia coli. Nature. 1991 Feb 14;349(6310):630–633. doi: 10.1038/349630a0. [DOI] [PubMed] [Google Scholar]
  13. Budrene E. O., Berg H. C. Dynamics of formation of symmetrical patterns by chemotactic bacteria. Nature. 1995 Jul 6;376(6535):49–53. doi: 10.1038/376049a0. [DOI] [PubMed] [Google Scholar]
  14. Dahlquist F. W., Lovely P., Koshland D. E., Jr Quantitative analysis of bacterial migration in chemotaxis. Nat New Biol. 1972 Mar 29;236(65):120–123. doi: 10.1038/newbio236120a0. [DOI] [PubMed] [Google Scholar]
  15. Keller E. F., Segel L. A. Initiation of slime mold aggregation viewed as an instability. J Theor Biol. 1970 Mar;26(3):399–415. doi: 10.1016/0022-5193(70)90092-5. [DOI] [PubMed] [Google Scholar]
  16. Kessler DA, Levine H. Pattern formation in Dictyostelium via the dynamics of cooperative biological entities. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1993 Dec;48(6):4801–4804. doi: 10.1103/physreve.48.4801. [DOI] [PubMed] [Google Scholar]
  17. Khan S., Macnab R. M. Proton chemical potential, proton electrical potential and bacterial motility. J Mol Biol. 1980 Apr 15;138(3):599–614. doi: 10.1016/s0022-2836(80)80019-2. [DOI] [PubMed] [Google Scholar]
  18. Lee KJ, Cox EC, Goldstein RE. Competing patterns of signaling activity in dictyostelium discoideum. Phys Rev Lett. 1996 Feb 12;76(7):1174–1177. doi: 10.1103/PhysRevLett.76.1174. [DOI] [PubMed] [Google Scholar]
  19. Nanjundiah V. Chemotaxis, signal relaying and aggregation morphology. J Theor Biol. 1973 Nov 5;42(1):63–105. doi: 10.1016/0022-5193(73)90149-5. [DOI] [PubMed] [Google Scholar]
  20. Oster G. F., Murray J. D. Pattern formation models and developmental constraints. J Exp Zool. 1989 Aug;251(2):186–202. doi: 10.1002/jez.1402510207. [DOI] [PubMed] [Google Scholar]
  21. Rascle M., Ziti C. Finite time blow-up in some models of chemotaxis. J Math Biol. 1995;33(4):388–414. doi: 10.1007/BF00176379. [DOI] [PubMed] [Google Scholar]
  22. Schnitzer MJ. Theory of continuum random walks and application to chemotaxis. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1993 Oct;48(4):2553–2568. doi: 10.1103/physreve.48.2553. [DOI] [PubMed] [Google Scholar]
  23. Segall J. E., Block S. M., Berg H. C. Temporal comparisons in bacterial chemotaxis. Proc Natl Acad Sci U S A. 1986 Dec;83(23):8987–8991. doi: 10.1073/pnas.83.23.8987. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Tsimring L, Levine H, Aranson I, I, Ben-Jacob E, Cohen I, I, Shochet O, Reynolds WN. Aggregation Patterns in Stressed Bacteria. Phys Rev Lett. 1995 Aug 28;75(9):1859–1862. doi: 10.1103/PhysRevLett.75.1859. [DOI] [PubMed] [Google Scholar]
  25. Vasiev BN, Hogeweg P, Panfilov AV. Simulation of dictyostelium discoideum aggregation via reaction-diffusion model. Phys Rev Lett. 1994 Dec 5;73(23):3173–3176. doi: 10.1103/PhysRevLett.73.3173. [DOI] [PubMed] [Google Scholar]
  26. Wolfe A. J., Berg H. C. Migration of bacteria in semisolid agar. Proc Natl Acad Sci U S A. 1989 Sep;86(18):6973–6977. doi: 10.1073/pnas.86.18.6973. [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. Woodward D. E., Tyson R., Myerscough M. R., Murray J. D., Budrene E. O., Berg H. C. Spatio-temporal patterns generated by Salmonella typhimurium. Biophys J. 1995 May;68(5):2181–2189. doi: 10.1016/S0006-3495(95)80400-5. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES