# An age-structured continuum model for myxobacteria

## TL;DR

This paper introduces a novel age-structured macroscopic model for myxobacteria movement, derived from microscopic rules, highlighting the importance of a diffusion term for accurate wave behavior and analyzing the role of refractory periods.

## Contribution

It presents a new continuum model based on microscopic interactions, incorporating age structure and emphasizing the need for a diffusion term for realistic wave dynamics.

## Key findings

- The macroscopic model aligns well with biological observations after adding diffusion.
- Refractory periods are not essential for wave formation but are crucial for synchronization.
- Higher order approximations are necessary to include diffusion in the model.

## 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 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.