Modeling of Bacterial Chemotaxis in a Medium with a Repellent

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.

Функція Чутливості Хемотаксису Для Системи Зі Сферичною Геометрією

“…where the dependence 𝑎(𝜃) is given by relation (13), and the constant 𝐵 0 can be found from condition (12):…”

“…For practical applications, it is convenient to use the phenomenological model based on a system of nonlinear differential equations of the diffusion type. This model has certain restrictions, but it was used to study various chemotaxis systems and proved itself well [10][11][12][13][14]. The model is based on an approach with a rather long and successful history [15][16][17][18][19][20][21].…”

“…For the flux of bacteria j 𝑏 (r, 𝑡) at the point r at the time 𝑡, the following expression was proposed in the framework of the model [10][11][12][13][14]:…”