Modeling of Bacterial Chemotaxis in a Medium with a Repellent

Authors

  • O. M. Vasilev Taras Shevchenko National University of Kyiv, Faculty of Physics, Chair of Theoretical Physics
  • V. O. Karpenko Taras Shevchenko National University of Kyiv, Faculty of Physics, Chair of Theoretical Physics

DOI:

https://doi.org/10.15407/ujpe63.9.802

Keywords:

bacterium, chemotaxis, repellent, attractant, tumbling

Abstract

The bacterial chemotaxis in a one-dimensional system with a repellent has been considered. The process of bacterial redistribution in the system is analyzed, and a corresponding phenomenological model is proposed, which makes allowance for the diffusion of bacteria and their motion caused by the repellent gradient. The repellent injection into the system is governed by boundary conditions. In the framework of this model, the chemotaxis sensitivity function, a numerical characteristic, which describes the nonuniformity in the bacterial distribution, is calculated. A dependence of the chemotaxis sensitivity function on the repellent concentration at the system boundaries is obtained. A relation between the bacterial distribution and the parameters of repellent distribution is found.

References

<ol>
<li>J.D. Murray. Mathematical Biology: I. An Introduction (Springer, 2007).
</li>
<li>T. Namba, M. Nishikawa, T. Shibata. The relation of signal transduction to the sensitivity and dynamic range of bacterial chemotaxis. Biophys. J. 103, 1390 (2012).
<a href="https://doi.org/10.1016/j.bpj.2012.08.034">https://doi.org/10.1016/j.bpj.2012.08.034</a>
</li>
<li>J. Adler. Chemotaxis in bacteria. Science 153, 708 (1966).
<a href="https://doi.org/10.1126/science.153.3737.708">https://doi.org/10.1126/science.153.3737.708</a>
</li>
<li>H.C. Berg, D.A. Brown. Chemotaxis in E. coli analysed by three-dimensional tracking. Nature 239, 500 (1972).
<a href="https://doi.org/10.1038/239500a0">https://doi.org/10.1038/239500a0</a>
</li>
<li>J. Adler. The sensing of chemicals by bacteria. Sci. Am. 234, No. 4, 40 (1976).
<a href="https://doi.org/10.1038/scientificamerican0476-40">https://doi.org/10.1038/scientificamerican0476-40</a>
</li>
<li>C. Zhang, R. He, R. Zhang, J. Yuan. Motor adaptive remodeling speeds up bacterial chemotactic adaptation. Biophys. J. 114, 1225 (2018).
<a href="https://doi.org/10.1016/j.bpj.2018.01.018">https://doi.org/10.1016/j.bpj.2018.01.018</a>
</li>
<li>A.J. Waite, N.W. Frankel, T. Emonet. Behavioral variability and phenotypic diversity in bacterial chemotaxis. Annu. Rev. Biophys. 47, 27 (2018).
<a href="https://doi.org/10.1146/annurev-biophys-062215-010954">https://doi.org/10.1146/annurev-biophys-062215-010954</a>
</li>
<li>J. Wong-Ng, A. Celani, M. Vergassola. Exploring the function of bacterial chemotaxis. Curr. Opin. Microbiol. 45, 16 (2018).
<a href="https://doi.org/10.1016/j.mib.2018.01.010">https://doi.org/10.1016/j.mib.2018.01.010</a>
</li>
<li>Z. Long, B. Quaife, H. Salman, Z.N. Oltvai. Cell-cell communication enhances bacterial chemotaxis toward external attractants. Sci. Rep. 7, 12855 (2017).
<a href="https://doi.org/10.1038/s41598-017-13183-9">https://doi.org/10.1038/s41598-017-13183-9</a>
</li>
<li> G. Si, T.Wu, Q. Ouyang, Y. Tu. Pathway-based mean-field model for Escherichia coli chemotaxis. Phys. Rev. Lett. 109, 048101 (2012).
<a href="https://doi.org/10.1103/PhysRevLett.109.048101">https://doi.org/10.1103/PhysRevLett.109.048101</a>
</li>
<li> Y.S. Dufour, X. Fu, L. Hernandez-Nunez, T. Emonet. Limits of feedback control in bacterial chemotaxis. PLoS Comput. Biol. 10, e1003694 (2014).
<a href="https://doi.org/10.1371/journal.pcbi.1003694">https://doi.org/10.1371/journal.pcbi.1003694</a>
</li>
<li> Y. Tu, T.S. Shimizu, H.C. Berg. Modeling the chemotactic response of Escherichia coli to time-varying stimuli. Proc. Natl. Acad. Sci. USA 105, 14855 (2008).
<a href="https://doi.org/10.1073/pnas.0807569105">https://doi.org/10.1073/pnas.0807569105</a>
</li>
<li> M.J. Schnitzer. Theory of continuum random walks and application to chemotaxis. Phys. Rev. E 48, 2553 (1993).
<a href="https://doi.org/10.1103/PhysRevE.48.2553">https://doi.org/10.1103/PhysRevE.48.2553</a>
</li>
<li> S. Asakura, H. Honda. Two-state model for bacterial chemo-receptor proteins. The role of multiple methylation. J. Mol. Biol. 176, 349 (1984).
<a href="https://doi.org/10.1016/0022-2836(84)90494-7">https://doi.org/10.1016/0022-2836(84)90494-7</a>
</li>
<li> V. Sourjik, H.C. Berg. Functional interactions between receptors in bacterial chemotaxis. Nature 428, 437 (2004).
<a href="https://doi.org/10.1038/nature02406">https://doi.org/10.1038/nature02406</a>
</li>
<li> D. Bray, M.D. Levin, C.J. Morton-Firth. Receptor clustering as a cellular mechanism to control sensitivity. Nature 393, 85 (1998).
<a href="https://doi.org/10.1038/30018">https://doi.org/10.1038/30018</a>
</li>
<li> B.A. Mello, Y. Tu. An allosteric model for heterogeneous receptor complexes: understanding bacterial chemotaxis responses to multiple stimuli. Proc. Natl. Acad. Sci. USA 102, 17354 (2005).
<a href="https://doi.org/10.1073/pnas.0506961102">https://doi.org/10.1073/pnas.0506961102</a>
</li>
<li> Y. Miyanaga, S. Matsuoka, T. Yanagida, M. Ueda. Stochastic signal inputs for chemotactic response in Dictyostelium cells revealed by single molecule imaging techniques. Biosystems 88, No. 3, 251 (2007).
<a href="https://doi.org/10.1016/j.biosystems.2006.07.011">https://doi.org/10.1016/j.biosystems.2006.07.011</a>
</li>
<li> P.G. de Gennes. Chemotaxis: the role of internal delays. Eur. Biophys. J. 33, 691 (2004).
<a href="https://doi.org/10.1007/s00249-004-0426-z">https://doi.org/10.1007/s00249-004-0426-z</a>
</li>
<li> E. Keller, L. Segel. Model for chemotaxis. J. Theor. Biol. 30, 225 (1971).
<a href="https://doi.org/10.1016/0022-5193(71)90050-6">https://doi.org/10.1016/0022-5193(71)90050-6</a>
</li>
<li> G.R. Ivanitskii, A.B. Medvinskii, M.A. Tsyganov. From disorder to ordering – on an example of microorganism motion. Usp. Fiz. Nauk 161, 13 (1991) (in Russian).
<a href="https://doi.org/10.3367/UFNr.0161.199104b.0013">https://doi.org/10.3367/UFNr.0161.199104b.0013</a>
</li>
<li> O.M. Vasilev, D.E. Sakovich, Modeling of bacterial chemotaxis in a one-dimensional system. Zh. Fiz. Dosl. 19, 1801 (2015) (in Ukrainian).
</li>
<li> D.V. Bogdanov, O.M. Vasilev. Chemotaxis sensitivity function for a two-dimensional system with a radial symmetry. Zh. Fiz. Dosl. 21, 3801 (2017) (in Ukrainian).
</li>
<li> A.N. Vasilev. Analytical approach for calculating the chemotaxis sensitivity function. Ukr. J. Phys. 63, 255 (2018).
<a href="https://doi.org/10.15407/ujpe63.3.255">https://doi.org/10.15407/ujpe63.3.255</a>
</li>
</ol>

Published

2018-09-24

How to Cite

Vasilev, O. M., & Karpenko, V. O. (2018). Modeling of Bacterial Chemotaxis in a Medium with a Repellent. Ukrainian Journal of Physics, 63(9), 802. https://doi.org/10.15407/ujpe63.9.802

Issue

Section

Physics of liquids and liquid systems, biophysics and medical physics