Overview of Mathematical Approaches Used to Model Bacterial Chemotaxis II: Bacterial Populations

Abstract

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller-Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated.

Fast, high-throughput measurement of collective behaviour in a bacterial population

“…Although chemotaxis at the single-cell level is increasingly well understood, there is a whole new layer of complexity in the macroscopic drifts and concentration imbalances at the population level [15,29]. This has been studied both theoretically [18,[29][30][31] and in simulations [32,33], typically taking a mean-field approach to modelling bacterial behaviour.…”

“…This has been studied both theoretically [18,[29][30][31] and in simulations [32,33], typically taking a mean-field approach to modelling bacterial behaviour. The Keller-Segel model (a diffusion and conservative flux equation) [29,34] is often the starting point for such work, with input parameters such as average cell velocity and binding site occupancy.…”

Large mass self-similar solutions of the parabolic–parabolic Keller–Segel model of chemotaxis

“…The Keller-Segel model is considered as a prototypical model for pattern formation in chemotaxis, and has attracted a lot of attention as a test case for more complex taxis phenomena driven by chemical substances. See [9,10,11,17,18] for further references.…”

On a parabolic–elliptic chemotactic model with coupled boundary conditions

“…There exists a large number of examples where both types of models are applied to describe different biological phenomena. Numerical simulations are used to compare the experimental data with the mathematical results and to justify these mathematical models (see, [7], [12]). In any case, the study of these systems have interest by itself (see, for instance, [13]).…”