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Journal of Physical Studies 21(3), Article 3801 [5 pages] (2017)
DOI: https://doi.org/10.30970/jps.21.3801 CHEMOTAXIS SENSITIVITY FUNCTION FOR TWO-DIMENSIONAL SYSTEM WITH RADIAL SYMMETRYD. V. Bohdanov, A. N. Vasilev
Taras Shevchenko National University of Kyiv, |
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In the paper, we consider a two-dimensional system with radial symmetry that contains bacteria and an attractant. It is known that the bacteria receptors can interact with the attractant. As a result of this interaction, the bacteria move towards the highest concentration of the attractant. The general effect is that the concentration of the bacteria increases as the attractant concentration increases. On the other hand, if the total amount of the attractant is high, then the bacteriaХs reaction to the attractant gradient is not so strong. So by changing the attractant distribution in the system one can change the bacteria distribution, and this dependence is nonlinear.
In our model, the attractant is injected into the system within its central area. We investigate the bacteria distribution due to chemotaxis under a stationary nonhomogeneous distribution of the attractant. The chemotaxis sensitivity function is used as the characteristic of the nonhomogeneity of the bacteria distribution.
We propose a methodology for calculating the chemotaxis sensitivity function for a two-dimensional system with radial symmetry. We have received an analytical expression of the chemotaxis sensitivity function, and we have also calculated how it depends on the attractant concentration at the boundary region. It has been shown that this dependence has a bell-shaped maximum, as is the case for a one-dimensional system. The position and the value of the maximum have also been found.
PACS number(s): 89.75.Fb, 87.10.+e, 87.16.Xa