Degond, P;
Manhart, A;
Yu, H;
(2018)
An age-structured continuum model for myxobacteria.
Mathematical Models and Methods in Applied Sciences
, 28
(9)
pp. 1737-1770.
10.1142/S0218202518400043.
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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.
| Type: | Article |
|---|---|
| Title: | An age-structured continuum model for myxobacteria |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1142/S0218202518400043 |
| Publisher version: | https://doi.org/10.1142/S0218202518400043 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ |
| Keywords: | Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, Self-propelled particles, nematic alignment, hydrodynamic limit, generalized collision invariant, diffusion correction, myxobacteria, wave formation, refractory period, FRUITING BODY MORPHOGENESIS, DEVELOPMENTAL BIOLOGY, TRAVELING WAVES, CELL BEHAVIOR, ALIGNMENT, PATTERNS, LIMIT, DIFFUSION, PARTICLES |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10085923 |
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