Analytical Approach for Calculating the Chemotaxis Sensitivity Function

Authors

  • A. N. Vasilev Taras Shevchenko National University of Kyiv, Department of Theoretical Physics, Physics Faculty

DOI:

https://doi.org/10.15407/ujpe63.3.255

Abstract

We consider the chemotaxis problem for a one-dimensional system. To analyze the interaction of bacteria and an attractant, we use a modified Keller–Segel model, which accounts for the attractant absorption. To describe the system, we use the chemotaxis sensitivity function, which characterizes the nonuniformity of the bacteria distribution. In particular, we investigate how the chemotaxis sensitivity function depends on the concentration of an attractant at the boundary of the system. It is known that, in the system without absorption, the chemotaxis sensitivity function has a bell shape maximum. Here, we show that the attractant absorption and special boundary conditions for bacteria can cause the appearance of an additional maximum in the chemotaxis sensitivity function. The value of this maximum is determined by the intensity of absorption.

References

<ol>
<li>J.D. Murray. Mathematical Biology: I. An Introduction (Springer, 2007).
</li>
<li>H.C. Berg. E. coli in Motion (Springer, 2004).
<a href="https://doi.org/10.1007/b97370">https://doi.org/10.1007/b97370</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>R.M. Macnab, D.E. Koshland. The gradient-sensing mechanism in bacterial chemotaxis. Proc. Natl. Acad. Sci. USA 69, 2509 (1972).
<a href="https://doi.org/10.1073/pnas.69.9.2509">https://doi.org/10.1073/pnas.69.9.2509</a>
</li>
<li>H.C. Berg, D.A. Brown. Chemotaxis in Escherichia 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>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>B.A. Camley, J. Zimmermann, H. Levine, W.-J. Rappel. Emergent collective chemotaxis without single-cell gradient sensing. Phys. Rev. Lett. 116, 098101 (2016).
<a href="https://doi.org/10.1103/PhysRevLett.116.098101">https://doi.org/10.1103/PhysRevLett.116.098101</a>
</li>
<li>A. Geiseler, P. H?anggi, F. Marchesoni, C. Mulhern, S. Savel'ev. Chemotaxis of artificial microswimmers in active density waves. Phys. Rev. E 94, 012613 (2016).
<a href="https://doi.org/10.1103/PhysRevE.94.012613">https://doi.org/10.1103/PhysRevE.94.012613</a>
</li>
<li>S. Dev, S. Chatterjee. Optimal search in E. coli chemotaxis. Phys. Rev. E 91, 042714 (2015).
<a href="https://doi.org/10.1103/PhysRevE.91.042714">https://doi.org/10.1103/PhysRevE.91.042714</a>
</li>
<li> P. Romanczuk, G. Salbreux. Optimal chemotaxis in intermittent migration of animal cells. Phys. Rev. E 91, 042720 (2015).
<a href="https://doi.org/10.1103/PhysRevE.91.042720">https://doi.org/10.1103/PhysRevE.91.042720</a>
</li>
<li> M. Ebrahimian, M. Yekehzare, M.R. Ejtehadi. Low-Reynolds-number predator. Phys. Rev. E 92, 063035 (2015).
<a href="https://doi.org/10.1103/PhysRevE.92.063035">https://doi.org/10.1103/PhysRevE.92.063035</a>
</li>
<li> M. Leoni, P. Sens. Polarization of cells and soft objects driven by mechanical interactions: Consequences for migration and chemotaxis. Phys. Rev. E 91, 022720 (2015).
<a href="https://doi.org/10.1103/PhysRevE.91.022720">https://doi.org/10.1103/PhysRevE.91.022720</a>
</li>
<li> M. Meyer, L. Schimansky-Geier. Active Brownian agents with concentration-dependent chemotactic sensitivity. Phys. Rev. E 89, 022711 (2014).
<a href="https://doi.org/10.1103/PhysRevE.89.022711">https://doi.org/10.1103/PhysRevE.89.022711</a>
</li>
<li> J. Zhuang, G. Wei, R.W. Carlsen, M.R. Edwards, R. Marculescu, P. Bogdan, M. Sitti. Analytical modeling and experimental characterization of chemotaxis in Serratia marcescens. Phys. Rev. E 89, 052704 (2014).
<a href="https://doi.org/10.1103/PhysRevE.89.052704">https://doi.org/10.1103/PhysRevE.89.052704</a>
</li>
<li> T. Sagawa, Y. Kikuchi, Y. Inoue, H. Takahashi, T. Muraoka, K. Kinbara, A. Ishijima, H. Fukuoka. Single-cell E.coli response to an instantaneously applied chemotactic signal. Biophys. J. 10, 730 (2014).
<a href="https://doi.org/10.1016/j.bpj.2014.06.017">https://doi.org/10.1016/j.bpj.2014.06.017</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> D.A. Clark, L.C. Grant. The bacterial chemotactic response rejects a compromise between transient and steady-state behavior. Proc. Natl. Acad. Sci. USA 102, 9150 (2005).
<a href="https://doi.org/10.1073/pnas.0407659102">https://doi.org/10.1073/pnas.0407659102</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> R. Tyson, S.R. Lubkin, J.D. Murray. A minimal mechanism of bacterial pattern formation. Proc. Roy. Soc. Lond. B 266, 299 (1999).
<a href="https://doi.org/10.1098/rspb.1999.0637">https://doi.org/10.1098/rspb.1999.0637</a>
</li>
<li> E.O. Budrene, H. Berg. Complex patterns formed by motile cells of Escherichia coli. Nature 376, 49 (1995).
<a href="https://doi.org/10.1038/376049a0">https://doi.org/10.1038/376049a0</a>
</li>
<li> E. Ben-Jacob, O. Schochet, A. Tenenbaum, I. Cohen, A. Czirok, T. Vicsek. Generic modelling of cooperative growth patterns in bacterial colonies. Nature 368, 46 (1994).
<a href="https://doi.org/10.1038/368046a0">https://doi.org/10.1038/368046a0</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> E.F. Keller, L.A. Segel. Travelling bands of chemotactic bacteria: A theoretical analysis. J. Theor. Biol. 30, 235 (1971).
<a href="https://doi.org/10.1016/0022-5193(71)90051-8">https://doi.org/10.1016/0022-5193(71)90051-8</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> E. Keller, L. Segel. Initiation of slime mold aggregation viewed as an instability. J. Theor. Biol. 26, 399 (1970).
<a href="https://doi.org/10.1016/0022-5193(70)90092-5">https://doi.org/10.1016/0022-5193(70)90092-5</a>
</li>
<li> M.J. Tindall, S.K. Porter, P.K. Maini, G. Gaglia, J.P. Armitage. Overview of mathematical approaches used to model bacterial chemotaxis. II: Bacterial populations. Bull. Math. Biol. 70, 1570 (2008).
<a href="https://doi.org/10.1007/s11538-008-9322-5">https://doi.org/10.1007/s11538-008-9322-5</a>
</li>
<li> F.J. Peaudecerf, R.E. Goldstein. Feeding ducks, bacterial chemotaxis, and the Gini index. Phys. Rev. E 92, 022701 (2015).
<a href="https://doi.org/10.1103/PhysRevE.92.022701">https://doi.org/10.1103/PhysRevE.92.022701</a>
</li>
<li> M. Hilpert. Lattice-Boltzmann model for bacterial chemotaxis. J. Math. Biol. 51, 302 (2005).
<a href="https://doi.org/10.1007/s00285-005-0318-6">https://doi.org/10.1007/s00285-005-0318-6</a>
</li>
<li> C. Chiu, F. Hoppensteadt. Mathematical models and simulations of bacterial growth and chemotaxis in a diffusion gradient chamber. J. Math. Biol. 42, 120 (2001).
<a href="https://doi.org/10.1007/s002850000069">https://doi.org/10.1007/s002850000069</a>
</li>
<li> K. Chen, R. Ford, P. Cummings. Mathematical models for motile bacterial transport in cylindrical tubes. J. Theor. Biol. 195, 481 (1998).
<a href="https://doi.org/10.1006/jtbi.1998.0808">https://doi.org/10.1006/jtbi.1998.0808</a>
</li>
<li> M. Widman, D. Emerson, C. Chiu, R. Worden. Modelling microbial chemotaxis in a diffusion gradient chamber. Biotech. Bioeng. 55, 191 (1997).
<a href="https://doi.org/10.1002/(SICI)1097-0290(19970705)55:1<191::AID-BIT20>3.0.CO;2-O">https://doi.org/10.1002/(SICI)1097-0290(19970705)55:1<191::AID-BIT20>3.0.CO;2-O</a>
</li>
<li> R. Lapidus, R. Schiller. Model for the chemotactic response of a bacterial population. Biophys. J. 16, 779 (1976).
<a href="https://doi.org/10.1016/S0006-3495(76)85728-1">https://doi.org/10.1016/S0006-3495(76)85728-1</a>
</li>
<li> R. Lapidus, R. Schiller. Bacterial chemotaxis in a fixed attractant gradient. J. Theor. Biol. 53, 215 (1975).
<a href="https://doi.org/10.1016/0022-5193(75)90112-5">https://doi.org/10.1016/0022-5193(75)90112-5</a>
</li>
<li> R. Lapidus, R. Schiller. A mathematical model for bacterial chemotaxis. Biophys. J. 14, 825 (1974).
<a href="https://doi.org/10.1016/S0006-3495(74)85952-7">https://doi.org/10.1016/S0006-3495(74)85952-7</a>
</li></ol>

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Published

2018-04-20

How to Cite

Vasilev, A. N. (2018). Analytical Approach for Calculating the Chemotaxis Sensitivity Function. Ukrainian Journal of Physics, 63(3), 255. https://doi.org/10.15407/ujpe63.3.255

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Section

Physics of liquids and liquid systems, biophysics and medical physics