[Paper Review] Mathematical modeling of filamentous microorganisms

Michele Bezzi, Andrea Ciliberto|ArXiv.org|Feb 3, 2004

Gene Regulatory Network Analysis47 references3 citations

TL;DR

This paper reviews mathematical models of filamentous microorganisms—such as fungi and actinomycetes—across multiple scales, from single hyphae to entire colonies. It evaluates macroscopic, reaction-diffusion, microscopic, and cellular automata models, highlighting their ability to simulate hyphal growth, branching, septation, and emergent colony morphologies, while identifying limitations in parameter estimation, computational cost, and lack of integration with molecular genetic data.

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.

Motivation & Objective

• To provide a comprehensive review of mathematical modeling approaches for filamentous microorganisms across different biological scales.
• To identify the strengths and limitations of macroscopic, reaction-diffusion, microscopic, and cellular automata models in simulating hyphal dynamics and colony morphology.
• To highlight the gap in integrating modern genetic data with growth and pattern formation models in filamentous organisms.
• To emphasize the need for multiscale modeling that bridges single-cell behaviors with emergent macroscopic colony patterns.
• To advocate for the development of molecular-scale models based on gene networks to predict and control filamentous growth.

Proposed method

• Classifying models by length scale: macroscopic (colony-level), reaction-diffusion (mean-field approximation), microscopic (single hyphae), and cellular automata (discrete, agent-based simulation).
• Analyzing reaction-diffusion models that use partial differential equations to describe local hyphal density and growth factor concentrations.
• Evaluating cellular automata models that simulate radial growth using a one-dimensional base space with increasing radius to preserve circular symmetry.
• Comparing phenomenological macroscopic models that reproduce colony growth rates without resolving morphological details.
• Assessing microscopic models that simulate tip growth, branching, septation, and translocation at the single-hypha level.
• Using case studies such as Neurospora crassa and Streptomyces rutgersensis to validate model predictions against experimental morphologies.

Experimental results

Research questions

• RQ1 How do different modeling approaches (macroscopic, reaction-diffusion, microscopic, cellular automata) compare in simulating filamentous microorganism growth and morphology?
• RQ2 To what extent can reaction-diffusion models bridge the gap between single-cell dynamics and macroscopic colony patterns?
• RQ3 Why do purely microscopic models fail to scale efficiently despite their biological fidelity?
• RQ4 What are the limitations of current models in capturing emergent behaviors like interference patterns in colonies?
• RQ5 Why is there a lack of models integrating recent genetic data on gene networks with growth and morphogenesis in filamentous organisms?

Key findings

• Macroscopic models effectively reproduce temporal dynamics of colony growth rates but fail to explain spatial mycelial morphology or single-hyphal behaviors.
• Reaction-diffusion models provide a mean-field approximation of microscopic dynamics, enabling simulation of spatial patterns while losing individual cell variability.
• Microscopic models accurately simulate tip growth, branching, and septation but are computationally intractable due to high nonlinearity and large parameter sets.
• Cellular automata models successfully reproduce radial colony patterns of Neurospora crassa by using a one-dimensional base space with increasing radius, preserving radial symmetry.
• The model based on radial cellular automata cannot simulate interference patterns seen in species like Streptomyces rutgersensis, indicating limitations in modeling complex colony interactions.
• Despite advances in genetic analysis of filamentous organisms, no models currently integrate gene networks with growth kinetics or pattern formation, representing a critical research gap.