An age-structured continuum model for myxobacteria

Pierre Degond Imperial College London Angelika Manhart New York University Hui Yu Tsinghua University

Fluid Dynamics and Shock Waves Data Analysis, Bio-Statistics, Bio-Mathematics mathscidoc:1906.14001

Mathematical Models and Methods in Applied Sciences, 28, (9), 1737–1770, 2018
Myxobacteria are social bacteria, that can glide in two dimensions and form counterpropagating, 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.
Self-propelled particles; nematic alignment; hydrodynamic limit; generalized collision invariant; diffusion correction; myxobacteria; wave formation; refractory period.
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  title={An age-structured continuum model for myxobacteria},
  author={Pierre Degond, Angelika Manhart, and Hui Yu},
  booktitle={Mathematical Models and Methods in Applied Sciences},
Pierre Degond, Angelika Manhart, and Hui Yu. An age-structured continuum model for myxobacteria. 2018. Vol. 28. In Mathematical Models and Methods in Applied Sciences. pp.1737–1770.
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