The Chemotaxis Sensitivity Function for a System with a Spherical Geometry
Keywords:chemotaxis, bacteria, attractant, concentration, distribution
The problem of determining the chemotaxis sensitivity function, which is used to characterize the heterogeneity of a distribution of bacteria in the system with an attractant, has been solved for a system with spherical geometry. In the presence of an attractant, bacteria are distributed according to the attractant distribution in the system. At the same time, the important role is played by the system geometry, boundary conditions, the attractant injection regime, and the control over the number of bacteria in the system. In particular, a system, where bacteria are distributed over the surface of a sphere, is considered. The attractant concentration in the system is controlled by its fixation at the sphere’s poles using a thin capillary. The number of bacteria in the system is considered constant. For such a system, an analytic expression for the chemotaxis sensitivity function is obtained. The obtained results can be useful when predicting the behavior of bacteria in real systems with a complicated geometry and when processing experimental data.
J. Adler. Chemotaxis in bacteria. Science 153, 708 (1966).
J. Adler. Chemoreceptors in bacteria. Science 166, 1588 (1969).
H.C. Berg, D.A. Brown. Chemotaxis in Escherichia coli analysed by three-dimensional tracking. Nature 239, 500 (1972).
J. Adler, G.L. Hazelbauer, M.M. Dahl. Chemotaxis toward sugars in Escherichia coli. J. Bacteriol. 115, 824 (1973).
H.C. Berg. E. Coli in Motion (Springer, 2004).
J.D. Murray. Mathematical Biology: I. An Introduction (Springer, 2007).
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).
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).
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).
O.M. Vasyliev, D.E. Sakovych. Simulation of bacterial chemotaxis in a one-dimensional system. J. Phys. Stud. 19, 1801 (2015) (in Ukrainian).
D.V. Bogdanov, O.M. Vasyliev. Chemotaxis sensitivity function for a two-dimensional system with a radial symmetry Zh. Fiz. Dosl. 21, 3801 (2017) (in Ukrainian).
A.N. Vasilev. Analytical approach for calculating the chemotaxis sensitivity function. Ukr. J. Phys. 63, 255 (2018).
O.M. Vasilev, V.O. Karpenko. Modeling of bacterial chemotaxis in a medium with a repellent. Ukr. J. Phys. 63, 802, (2018).
A.N. Vasilev. Peculiarities of bacterial chemotaxis in a cylindrical pore. Ukr. J. Phys. 64, 137, (2018).
E.F. Keller, L.A. Segel. Travelling bands of chemotactic bacteria: A theoretical analysis. J. Theor. Biol. 30, 235 (1971).
E. Keller, L. Segel. Model for chemotaxis. J. Theor. Biol. 30, 225 (1971).
R. Lapidus, R. Schiller, Model for the chemotactic response of a bacterial population. Biophys. J. 16, 779 (1976).
R. Lapidus, R. Schiller, Bacterial chemotaxis in a fixed attractant gradient. J. Theor. Biol. 53, 215 (1975).
R. Lapidus, R. Schiller, A mathematical model for bacterial chemotaxis. Biophys. J. 14, 825 (1974).
M. Widman, D. Emerson, C. Chiu, R. Worden, Modelling microbial chemotaxis in a diffusion gradient chamber. Biotech. Bioeng. 55, 191 (1997).
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).
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