Mathematical modeling of filamentous microorganisms

TL;DR

This paper reviews various mathematical models of filamentous microorganisms, analyzing their ability to simulate different spatial and temporal growth patterns across multiple scales, from intracellular to colony level.

Contribution

It provides a comprehensive comparison of macroscopic, reaction-diffusion, microscopic, and cellular automata models, highlighting their strengths and limitations.

Findings

Macroscopic models capture colony growth dynamics but not morphology.

Reaction-diffusion models bridge macro and micro scales effectively.

Cellular automata simulate emergent colony behaviors.

Abstract

Growth patterns generated by filamentous organisms (e.g. actinomycetes and fungi) involve spatial and temporal dynamics at different length scales. Several mathematical models have been proposed in the last thirty years to address these specific dynamics. Phenomenological macroscopic models are able to reproduce the temporal dynamics of colony-related quantities (e.g. colony growth rate) but do not explain the development of mycelial morphologies nor the single hyphal growth. Reaction-diffusion models are a bridge between macroscopic and microscopic worlds as they produce mean-field approximations of single-cell behaviors. Microscopic models describe intracellular events, such as branching, septation and translocation. Finally, completely discrete models, cellular automata, simulate the microscopic interaction among cells to reproduce emergent cooperative behaviors of large colonies. In this comment, we review a selection of models for each of these length scales, stressing their advantages and shortcomings.