A 3-variable PDE model for predicting fungal growth derived from microscopic mechanisms

Area of Science:

• Mycology
• Mathematical Biology
• Computational Science

Background:

• Fungal growth, particularly brown rot fungus (Postia placenta), is complex and challenging to model.
• Existing discrete models, while biologically grounded, are computationally intensive.
• Accurate simulation of fungal spread is crucial for understanding ecological impact and developing control strategies.

Purpose of the Study:

• To develop a novel, computationally efficient partial differential equation (PDE) model for Postia placenta growth.
• To validate the PDE model against experimental data and a discrete model.
• To provide a tool for correlating local biological mechanisms with global biomass distribution.

Main Methods:

• Formulation of a new reaction-diffusion model based on tip concentration, branch density, and hyphal density.
• Numerical solution using an efficient exponential Euler method with Krylov subspace approximation.
• Validation against experimental data and comparison with a discrete model.

Main Results:

• The PDE model accurately reproduces averaged radial tip/hyphal densities.
• Simulations of 104-day growth are completed in 3.5 seconds, a significant speedup compared to the discrete model's 8 hours.
• The model demonstrates reduced RAM and computing time, enabling upscaled simulations.

Conclusions:

• The novel PDE system offers a computationally efficient and accurate method for modeling fungal spatial colonization via diffusion.
• The model successfully correlates biological mechanisms with biomass distribution, aiding in the analysis of experimental data.
• This approach provides mutual insights between micro-level biological processes and macro-level fungal spread.