Analytical Approach for Calculating the Chemotaxis Sensitivity Function

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.K e y w o r d s: chemotaxis, attractant, bacteria, absorption.

Peculiarities of Bacterial Chemotaxis in a Cylindrical Pore

“…The dependence ( ) is dome-shaped (like those obtained for one-and two-dimensional systems [6,[19][20][21]). The dependence of this type can be explained as follows.…”

“…The presence of a denominator in this term is explained by the experimental fact (see, e.g., work [6]) that the growth of the attractant concentration results in the saturation of the bacterial receptor sensitivity, so that the attractant gradient effect decreases. As was shown in works [19,21], the choice of the term associated with chemotaxis in the presented form [see Eq. (1)] makes it possible to correctly describe the chemotaxis effect not only at the qualitative level, but also at the quantitative one.…”

“…which characterizes the deviation of the ratio between the average bacterial concentrations at the left end and throughout the system from unity. Expression (11) defines the chemotaxis sensitivity function , which numerically characterizes the non-uniformity in the bacterial distribution [6,[19][20][21]. The case = 0 means that the average concentration of bacteria at the left end of the system is equal to the average concentration over the whole system.…”

“…In this work, we propose a mathematical model that describes specific features in the behavior of bacteria located in a system with the geometry of a cylindrical pore. This research is methodologically based on a series of our previous studies [19][20][21] carried out for one-and twodimensional systems and is their continuation. But, unlike the cited works, we consider a spatially confined three-dimensional system: a cylinder that is finite along its main axis.…”

Modeling of Bacterial Chemotaxis in a Medium with a Repellent

“…To elucidate the character and specific features of the bacterial distribution in the system (and their dependences on the repellent distribution), a mathematical model is proposed, which is based on a nonlinear differential equation. The models of this type were used earlier to study the bacterial behavior in a medium with an attractant [22][23][24]. A similar approach is used in this work, but now, when developing the model, we take into account that the repellent is dealt with.…”