Active Brownian agents with concentration-dependent chemotactic sensitivity
Authored by Marcel Meyer, Lutz Schimansky-Geier, Pawel Romanczuk
Date Published: 2014
DOI: 10.1103/physreve.89.022711
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Abstract
We study a biologically motivated model of overdamped, autochemotactic
Brownian agents with concentration-dependent chemotactic sensitivity.
The agents in our model move stochastically and produce a chemical
ligand at their current position. The ligand concentration obeys a
reaction-diffusion equation and acts as a chemoattractant for the
agents, which bias their motion towards higher concentrations of the
dynamically altered chemical field. We explore the impact of
concentration-dependent response to chemoattractant gradients on
large-scale pattern formation, by deriving a coarse-grained macroscopic
description of the individual-based model, and compare the conditions
for emergence of inhomogeneous solutions for different variants of the
chemotactic sensitivity. We focus primarily on the so-called
receptor-law sensitivity, which models a nonlinear decrease of
chemotactic sensitivity with increasing ligand concentration. Our
results reveal qualitative differences between the receptor law, the
constant chemotactic response, and the so-called log law, with respect
to stability of the homogeneous solution, as well as the emergence of
different patterns (labyrinthine structures, clusters, and bubbles) via
spinodal decomposition or nucleation. We discuss two limiting cases, where the model can be reduced to the dynamics of single species: (I)
the agent density governed by a density-dependent effective diffusion
coefficient and (II) the ligand field with an effective bistable, time-dependent reaction rate. In the end, we turn to single clusters of
agents, studying domain growth and determining mean characteristics of
the stationary inhomogeneous state. Analytical results are confirmed and
extended by large-scale GPU simulations of the individual based model.
Tags
population
Bacterial chemotaxis
Aggregation
growth
Cells
Escherichia-coli
Mathematical-models
Pattern-formation
Phase-separation
Diffusion gradient chamber