Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30302
On a Negative Relation between Bacterial Taxis and Turing Pattern Formation

Authors: A. Elragig, S. Townley, H. Dreiwi

Abstract:

In this paper we introduce a bacteria-leukocyte model with bacteria chemotaxsis. We assume that bacteria develop a tactic defence mechanism as a response to Leukocyte phagocytosis. We explore the effect of this tactic motion on Turing space in two parameter spaces. A fine tuning of bacterial chemotaxis shows a significant effect on developing a non-uniform steady state.

Keywords: chemotaxis-diffusion driven instability, bacterial chemotaxis

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1094283

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1392

References:


[1] T. P. Stossel, "Phagocytosis”, the department of defence, N. E. J. Med, 286 (1972) 776-777.
[2] P. Parham, The immune system, Garland science, 3rd edition , 2009.
[3] P, C, Wilkinson,Chemotaxis and inflammation, Churchil-Livingston, 1974.
[4] D. Lauffenburger, C. R. Kennedy, "Analysis of a Lumped model for tissue inflammation dynamics”, Mathematical Biosciences, 53 (1981) 189-221.
[5] D. Lauffenburger, C. R. Kennedy, "Localised bacterial infection in a distributed model for tissue inflamation”, Mathematical biology, 16 (1983) 141-163.
[6] S. Mergenhagen, R. Snyderman, "Peridical disease: a model for the study of inflammation”, J. Inf. Dis, 123 (1971) 676-677.
[7] D. Lauffenburger, K. H. Keeler, "Effects of leukocytes random motility and chemotaxis in tissue inflammatory response”, Journal of theoretical biology, 81 (1979) 475-503.
[8] M. J. Tindall, P. K. Maini, S. L. Porter, J. P. Armitage, "Overview of mathematical approaches used to model bacterial chemotaxis II : Bacterial population”, Bulletin of mathematical biology, 70 (2008)1570-1607.
[9] J. D. Murray, Mathematical Biology II : Spatial models and biomedical applications, Springer, Berlin, 2008, ch. 3.
[10] A. Edelstein-Keshet, Mathematical Models in Biology, McGraw-Hill Companies, 1988, ch. 11.
[11] K. J. Painter, P. K. Maini, H. G. Othmer, "Development and applications of a model for cellular response to multiple chemotactic cues”, J. Mathematical Biology, 41(2000) 285-314.
[12] M. Zhu, J. Murray," Parameter domains for generating spatial pattern: a comparison of reaction-diffusion and cell chemotaxis models”, Int. J. Bifurc. Chaos. 5 (1995) 1503-1524.
[13] D. Lauffenburger, Personal communication, Murch 2012.
[14] J. Adler, W. Tso, ”Decision-making in bacteria: Chemotaxis response of Escherichia coli conflicting stimuli”, Science, 184 (1974) 1292-1294.
[15] A. M. Turing, "The chemical basis of Morphogenesis”, Phil. Trans. Roy. Soc. London B.237 (1952) 37-72.