×

Traveling bands of chemotactic bacteria in the context of population growth. (English) Zbl 0525.92018


MSC:

92D25 Population dynamics (general)
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
92Cxx Physiological, cellular and medical topics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Adler, J. and M. Dahl. 1967. ”Method for Measuring the Motility of Bacteria and Comparing Random and Nonrandom Motility.”J. gen. Microbiol. 46, 161–173. · doi:10.1099/00221287-46-2-161
[2] Barrachini, O. and J. C. Sherris. 1959. ”Chemotactic Effect of Oxygen on Bacteria.”J. Path. Bact. 77, 565–574. · doi:10.1002/path.1700770228
[3] Chapman, P. 1973. ”Chemotaxis in Bacteria.” PhD Thesis, University of Minnesota.
[4] Chet, I. and R. Mitchell. 1976. ”Ecological Aspects of Microbial Chemotactic Behavior.”Ann. Rev. Microbiol. 30, 221–239. · doi:10.1146/annurev.mi.30.100176.001253
[5] Holz, M. and S.-H. Chen. 1978. ”Quasi-elastic Light Scattering from Migrating Chemotactic Bands ofEscherichia coli.”Biophys. J. 23, 15–31. · doi:10.1016/S0006-3495(78)85429-0
[6] Keller, E. F. 1980. ”Assessing the Keller-Segel Model: How Has It Fared?.”Lect. Notes Biomath. 38, 379–387. · Zbl 0437.92003 · doi:10.1007/978-3-642-61850-5_34
[7] Keller, E. F. and G. Odell. 1975. ”Necessary and Sufficient Conditions for Chemotactic Bands.”Math. Biosci. 27, 309–317. · Zbl 0346.92009 · doi:10.1016/0025-5564(75)90109-1
[8] – and L. A. Segel. 1971a. ”Model for Chemotaxis.”J. theor. Biol. 30, 225–234. · Zbl 1170.92307 · doi:10.1016/0022-5193(71)90050-6
[9] –. 1971b. ”Traveling Bands of Chemotactic Bacteria: a Theoretical Analysis.”J. theor. Biol. 30, 235–248. · Zbl 1170.92308 · doi:10.1016/0022-5193(71)90051-8
[10] Kennedy, C. R. and R. Aris. 1980. ”Traveling Waves in a Simple Population Model Involving Growth and Death.”Bull. math. Biol. 42, 397–429. · Zbl 0431.92021 · doi:10.1007/BF02460793
[11] Lapidus, I. R. and R. Schiller. 1976. ”Model for the Chemotactic Response of a Bacterial Populations.”Biophys. J. 16, 779–789. · doi:10.1016/S0006-3495(76)85728-1
[12] –. 1978. ”A Model for Traveling Bands of Chemotactic Bacteria.”Biophys. J. 22, 1–13. · doi:10.1016/S0006-3495(78)85466-6
[13] Lauffenburger, D., R. Aris and K. H. Keller. 1981. ”Effects of Random Motility on Growth of Bacterial Populations.”Microb. Ecol. 7, 207–227. · doi:10.1007/BF02010304
[14] —- and K. H. Keller. 1982. ”Effects of Cell Motility and Chemotaxis on Microbial Population Growth.”Biophys. J. 40, 209–219. · doi:10.1016/S0006-3495(82)84476-7
[15] Mesibov, R., G. W. Ordal and J. Adler. 1973. ”The Range of Attractant Concentrations for Bacterial Chemotaxis and the Threshold and Size of Response over the Range.”J. gen. Physiol. 62, 203–223. · doi:10.1085/jgp.62.2.203
[16] Nossal, R. 1972a. ”Growth and Movement of Rings of Chemotactic Bacteria.”Exp. Cell Res. 75, 138–142. · Zbl 0337.92017 · doi:10.1016/0014-4827(72)90529-0
[17] –. 1972b. ”Boundary Movement of Chemotactic Bacterial Populations.”Math. Biosci. 13, 397–406. · Zbl 0337.92017 · doi:10.1016/0025-5564(72)90058-2
[18] Odell, G. and E. F. Keller. 1976. ”Traveling Bands of Chemotactic Bacteria Revisited.”J. Theor. Biol. 56, 243–247. · doi:10.1016/S0022-5193(76)80055-0
[19] Rosen, G. 1974. ”On the Propagation Theory for Bands of Chemotactic Bacteria.”Math. Biosci. 20, 185–189. · Zbl 0281.92006 · doi:10.1016/0025-5564(74)90078-9
[20] –. 1975. ”Analytical Solution to the Initial Value Problem for Traveling Bands of Chemotactic Bacteria.”J. theor. Biol. 49, 311–32. · doi:10.1016/0022-5193(75)90174-5
[21] –. 1976. ”Existence and Nature of Band Solutions to Generic Chemotactic Transport Equations.”J. theor. Biol. 59, 243–246. · doi:10.1016/S0022-5193(76)80038-0
[22] – and S. Baloga. 1975. ”On the Stability of Steadily Propagating Bands of Chemotactic Bacteria.”Math. Biosci. 24, 273–279. · Zbl 0307.92013 · doi:10.1016/0025-5564(75)90080-2
[23] – and S. Baloga. 1976. ”On the Structure of Steadily Propagating Rings of Chemotactic Bacteria.”J. Mech. Cell Motil. 3, 225–228.
[24] Scribner, T., L. A. Segel and E. H. Rogers. 1974. ”Numerical Study of Formation and Propagation of Traveling Bands of Chemotactic Bacteria.”J. theor. Biol. 46, 189–219. · doi:10.1016/0022-5193(74)90147-7
[25] Segel, L. A. 1983. ”Taxes in Cellular Ecology.” (Proceedings of Meeting on Mathematics in Ecology, Trieste, Italy, 1982) (In press).Lect. Notes Biomath.
[26] –, I. Chet and Y. Henis. 1977. ”A Simple Quantitative Assay for Bacterial Motility.”J. gen. Microbiol. 98, 329–337. · doi:10.1099/00221287-98-2-329
[27] Seymour, F. W. K. and R. N. Doetsch. 1973. ”Chemotactic by Motile Bacteria.”J. gen. Microbiol. 78, 287–296. · doi:10.1099/00221287-78-2-287
[28] Sinclair, C. G. and H. H. Topiwala. 1970. ”Model for Continuous Culture which Considers the Viability Concept.”Biotech. Bioeng. 12, 1069–1079. · doi:10.1002/bit.260120612
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.