Active Brownian agents with concentration-dependent chemotactic sensitivity

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 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.

17 pages, 10 figures, corrected references

References in corpus (5)

• Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles
• Phase transition in the collective migration of tissue cells: experiment and model
• When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
• A continuum theory of phase separation kinetics for active Brownian particles
• Phase Transitions and superuniversality in the dynamics of a self-driven particle

Cited by in corpus (20)

• Active Brownian Particles and Run-and-Tumble Particles: a Comparative Study
• Active colloidal suspensions: Clustering and phase behavior
• Clustering and pattern formation in chemorepulsive active colloids
• Phoretic Interactions Generically Induce Dynamic Clusters and Wave Patterns in Active Colloids
• Which Interactions Dominate in Active Colloids?
• Pattern Formation in Chemically Interacting Active Rotors with Self-Propulsion
• Interactions in Active Colloids
• Non-equilibrium phase separation in mixtures of catalytically active particles: size dispersity and screening effects
• Pseudochemotaxis in inhomogeneous active Brownian systems
• Systematic extension of the Cahn-Hilliard model for motility-induced phase separation
• Dynamics of a helical swimmer crossing viscosity gradients
• Periodic patterns displace active phase separation
• Uncovering novel phase transitions in dense dry polar active fluids using a lattice Boltzmann method
• Orientational order and morphology of clusters of self-assembled Janus swimmers
• Spontaneous trail formation in populations of auto-chemotactic walkers
• Demixing of two species via reciprocally concentration-dependent diffusivity
• Coarsening dynamics of chemotactic aggregates
• Phase separation of chemokinetic active particles
• Chemotaxis-induced phase separation
• Analytical Approach for Calculating Chemotaxis Sensitivity Function