  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 non-linear 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 an 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.
