Related papers: Macroscopic limits of pathway-based kinetic models…
Chemotaxis of the bacterium Escherichia coli is well understood in shallow chemical gradients, but its swimming behavior remains difficult to interpret in steep gradients. By focusing on single-cell trajectories from simulations, we…
In this work we upscale a prototypical kinetic transport equation which models a cell population moving in a fibrous environment with a chemo- or haptotactic signal influencing both the direction and the magnitude of the cell velocity. The…
Bacterial chemotaxis for E.coli is controlled by methylation of chemoreceptors, which in a biochemical pathway regulates the concentration of the CheY-P protein that finally controls the tumbling rate. As a consequence, the tumbling rate…
In this paper, we propose a numerical scheme to solve the kinetic model for chemotaxis phenomena. Formally, this scheme is shown to be uniformly stable with respect to the small parameter, consistent with the fluid-diffusion limit…
We study an anomalous behavior observed in interacting E. coli populations. When two populations of E. coli are placed on opposite ends of a long channel with a supply of nutrient between them, they will travel as pulses toward one another…
This manuscript deals with the three-dimensional version of a flux-limited Keller-Segel system coupled to the incompressible Stokes equations through transport and buoyancy. The main goal consists in verifying that within a certain…
A connection is established between discrete stochastic model describing microscopic motion of fluctuating cells, and macroscopic equations describing dynamics of cellular density. Cells move towards chemical gradient (process called…
Chemotaxis is the physical phenomenon that bacteria adjust their motions according to chemical stimulus. A classical model for this phenomenon is a kinetic equation that describes the velocity jump process whose tumbling/transition kernel…
In this paper, we propose a kinetic model describing the collective motion by chemotaxis of two species in interaction emitting the same chemoattractant. Such model can be seen as a generalisation to several species of the Othmer-Dunbar-Alt…
Originally motivated by the morphogenesis of bacterial microcolonies, the aim of this article is to explore models through different scales for a spatial population of interacting, growing and dividing particles. We start from a microscopic…
The bacterium Escherichia coli (E. coli) moves in its natural environment in a series of straight runs, interrupted by tumbles which cause change of direction. It performs chemotaxis towards chemo-attractants by extending the duration of…
Mathematical modelling of biological population dynamics often involves proposing high fidelity discrete agent-based models that capture stochasticity and individual-level processes. These models are often considered in conjunction with an…
Chemotaxis systems of Keller--Segel type constitute one of the central mathematical frameworks for understanding aggregation phenomena in biological and ecological systems. Over the past decades, the theory has evolved from the classical…
We study the derivation of macroscopic traffic models out of optimal speed and follow-the-leader particle dynamics as hydrodynamic limits of non-local Povzner-type kinetic equations. As a first step, we show that optimal speed vehicle…
Chemotaxis is a fundamental mechanism of cells and organisms, which is responsible for attracting microbes to food, embryonic cells into developing tissues, or immune cells to infection sites. Mathematically chemotaxis is described by the…
A novel trait-structured Keller-Segel model that explores the dynamics of a migrating cell population guided by chemotaxis in response to an external ligand concentration is derived and analysed. Unlike traditional Keller-Segel models, this…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
This paper deals with the micro-macro derivation of virus models coupled with a reaction diffusion models that generates the dynamics in space of the virus particles. The first part of the presentation focuses, starting from [5, 6] on a…
While the role of local interactions in nonequilibrium phase transitions is well studied, a fundamental understanding of the effects of long-range interactions is lacking. We study the critical dynamics of reproducing agents subject to…
We consider an initial-boundary value problem describing the formation of colony patterns of bacteria Escherichia coli. This model consists of reaction-diffusion equations coupled with the Keller-Segel system from the chemotaxis theory in a…