Abstract
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.
Highlights
Myxobacteria are a fascinating example for how simple cell-cell interaction rules can lead to emergent, collective behavior
Continuous, age-structured macroscopic model of myxobacteria, derived systematically from an individual-based model
In excellent agreement with experimental data on myxobacteria, simulations of the full Individual Based Model (IBM) show the development of periodic waves, traveling in opposing directions and being reflected upon collision
Summary
Myxobacteria are a fascinating example for how simple cell-cell interaction rules can lead to emergent, collective behavior These single-celled organisms have the ability to move on two dimensional surfaces and form large colonies. The precise function of rippling is not known, it often serves as a prelude and overlaps with an aggregation phase: in this developmental stage bacteria aggregate into several growing mounds which eventually rise out of the plane and form large three dimensional fruiting bodies Both waves and aggregates are macroscopic structures with typical length scales of 100 μm, whereas individual bacteria are only a few microns long. To model the refractory period between two reversals of myxobacteria, we use the concept of a local time that is reset to zero after each reversal This idea is borrowed from similar ideas used in neuron dynamics
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