Nonlinear concentration patterns and bands in autochemotactic suspensions

Abstract

In suspensions of microorganisms, pattern formation can arise from the interplay of chemotaxis and the fluid flows collectively-generated by the organisms themselves. Here we investigate the resulting pattern formation in square and elongated domains in the context of two distinct models of locomotion in which the chemo-attractant dynamics is fully coupled to the fluid flows and swimmer motion. Analyses for both models reveal an aggregative instability due to chemotaxis, independent of swimmer shape and type, and a hydrodynamic instability for "pusher" swimmers. We discuss the similarities and differences between the models. Simulations reveal a critical length scale of the swimmer aggregates and this feature e can be utilized to stabilize swimmer concentration patterns into quasi-one-dimensional bands by varying the domain size. These concentration bands transition to traveling pulses under an external chemo-attractant gradient, as observed in experiments with chemotactic bacteria.

Multi-fractal characterization of bacterial swimming dynamics: a case study on real and simulatedSerratia marcescens

“…For the interactions among cells, we consider volume exclusion effects and also autochemotaxis (chemical interaction) between the bacteria inside the swarm in all of our simulations. Autochemotaxis happens when bacteria excrete the converted substrate succinate molecules in the environment into chemoattractant aspartate molecules [ 26 , 46 – 48 ]. Once the succinate gets depleted, bacteria start consuming the chemoattractant aspartate excreted by themselves and they may detect each other's presence through this process [ 24 ].…”

Hydrochemical interactions in dilute phoretic suspensions: From individual particle properties to collective organization

“…Having understood and fully characterized the behavior and chemohydrodynamic footprints of individual particles, we now turn to the description of a dilute suspension of autophoretic Janus swimmers. The approach followed here considers that the suspension dynamics are studied on a length scale much larger than the particle radius, and instead of characterizing each particle's state individually the probability to find a particle in a given small volume of fluid with a set orientation is fully described by the probability distribution function (x, p, t ) of the particle position, x, and director, p [32,42,44]. The evolution of the suspension then classically follows a Smoluchowski 104203-6 equation:…”

“…Due to the fully deterministic modeling of the chemically induced rotation, which is well suited for phoretic particles, this approach is sometimes referred to as the turning-particle model. For other systems such as swimming bacteria, other models have been proposed, e.g., run-and-tumble [44]. The mean pressure and velocity fields in the suspension, q and u, satisfy the incompressible Stokes equations, forced by the hydrodynamic stresses generated by each JP individually:…”

“…To this end, we model suspensions of chemically active Janus particles using a kinetic model, extending to that purpose a recent and popular framework initially proposed to study the emergence 104203-2 of hydrodynamic instabilities within bacterial suspension [42] and later extended to analyze the detailed rheology of active suspensions [43] or chemotaxis [32,44]. The fundamental idea of such modeling is to describe the evolution in time of a probability density to find a particle at a given location and with a particular orientation in terms of ambient mean chemical and hydrodynamic fields, which are in turn forced by the distribution and action of the particles.…”

Onset of nonlinearity in a stochastic model for auto-chemotactic advancing epithelia

“…Auto-chemotaxis can be considered as a mechanism for neighbour cell communication, which by transforming biochemical signaling into mechanical stresses induce collective migration 13 . This process has also been investigated in the dynamical aggregation of dense micro-swimmer colonies 14 . It is worth stressing that, even in extremely well controlled experiments, it appears difficult to distinguish between chemotaxis and mechanotaxis 10 13 15 (including all forces and stresses that a cell can feel in a moving epithelium).…”