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An age-structured continuum model for myxobacteria

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Title: An age-structured continuum model for myxobacteria
Authors: Degond, PAA
Manhart, A
Yu, H
Item Type: Journal Article
Abstract: Myxobacteria are social bacteria, that can glide in 2D 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 SOH (Self- Organized Hydrodynamics) 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 equa- tions, 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.
Issue Date: 4-Jul-2018
Date of Acceptance: 1-Apr-2018
URI: http://hdl.handle.net/10044/1/58834
DOI: https://dx.doi.org/10.1142/S0218202518400043
ISSN: 1793-6314
Publisher: World Scientific Publishing
Start Page: 1737
End Page: 1770
Journal / Book Title: Mathematical Models and Methods in Applied Sciences
Volume: 28
Issue: 09
Copyright Statement: © The Author(s). This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited.
Sponsor/Funder: The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: WM130048
EP/M006883/1
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
SELF-PROPELLED PARTICLES
DEVELOPMENTAL BIOLOGY
MYXOCOCCUS-XANTHUS
TRAVELING WAVES
CELL BEHAVIOR
ALIGNMENT
PATTERNS
LIMIT
DIFFUSION
q-bio.CB
math.AP
physics.bio-ph
35L60, 35K55, 35Q70, 82C05, 82C22, 82C70, 92D50, 92C15, 92C17
0102 Applied Mathematics
Applied Mathematics
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences