Narrow Results

Myxobacteria are social bacteria, that can glide in two dimensions and form counter-propagating, interacting waves. Here, we present a novel age-structured, continuous macroscopic model for the movement of myxobacteria. The derivation is based on microscopic interaction rules that can be formulated as a particle-based model and set within the Self-Organized Hydrodynamics (SOH) framework. The strength of this combined approach is that microscopic knowledge or data can be incorporated easily into the particle model, whilst the continuous model allows for easy numerical analysis of the different effects. However, we found that the derived macroscopic model lacks a diffusion term in the density equations, which is necessary to control the number of waves, indicating that a higher order approximation during the derivation is crucial. Upon ad hoc addition of the diffusion term, we found very good agreement between the age-structured model and the biology. In particular, we analyzed the influence of a refractory (insensitivity) period following a reversal of movement. Our analysis reveals that the refractory period is not necessary for wave formation, but essential to wave synchronization, indicating separate molecular mechanisms.

Myxobacteria have a high level of intercellular coordination. Their swarms show “streets” and “whirls” of parallel gliding cells as well as wave-like moving cell density fields, so called “rippling”. The dependence from two phenomenological parameters, gliding velocity and turning frequency, has turned out to be characteristic for cell behavior at the swarm edge. As cells at the swarm edge are mostly gliding parallel in one dimension, the behavior of single cells can be comprised in a one-dimensional model describing interactions between cells of the same species in a homogenous environment, where turning frequency determines the cell density distribution via a hyperbolic differential integral equation. After specifying the parameter functions appearing in the integral, it is examined how these parameters influence the turning behavior and therefore the edge development of swarms over time.

Numerical simulations of this model are performed both for the stationary and the time dependent case. For the time dependent model a front tracking method is applied using a Lagrange interpolation at the swarm edge. The simulations show that perception of different gliding directions is significant for the dynamics of swarm expansion and retraction.

This paper reviews recent progress in modeling collective behaviors in myxobacteria using lattice gas cellular automata approach (LGCA). Myxobacteria are social bacteria that swarm, glide on surfaces and feed cooperatively. When starved, tens of thousands of cells change their movement pattern from outward spreading to inward concentration; they form aggregates that become fruiting bodies. Cells inside fruiting bodies differentiate into round, nonmotile, environmentally resistant spores. Traditionally, cell aggregation has been considered to imply chemotaxis, a long-range cell interaction. However, myxobacteria aggregation is the consequence of direct cell-contact interactions, not chemotaxis. In this paper, we review biological LGCA models based on local cell–cell contact signaling that have reproduced the rippling, streaming, aggregating and sporulation stages of the fruiting body formation in myxobacteria.