A novel two-dimensional lattice-free mathematical model of fungal mycelia and its dynamic simulation

Filamentous fungi represent a diverse group of microorganisms, encompassing industrially significant species such as Aspergillus oryzae and Aspergillus niger, as well as biologically active, edible, and medicinal fungi such as Ganoderma lucidum (G. lucidum) and Auricularia auricula. The morphology of filamentous fungal mycelia is crucial for species development, natural product synthesis, and environmental adaptation. Therefore, accurate qualitative and quantitative assessment of mycelial morphology is imperative. Mathematical modeling is a useful tool for investigating microbial morphology, aiding in experimental research on mycelial development. However, owing to the inherent complexity of mycelial development, it cannot be fully captured by existing models. This paper presents a two-dimensional, lattice-free mathematical model using MATLAB (R2023b). The model incorporates hyphal tip extension, branching, anastomosis, and energy translocation, while introducing continuous growth, range anastomosis, and variable growth length behaviors. These enhancements allow more accurate simulation of real mycelial growth patterns. The model was used to simulate and optimize G. lucidum growth, and its accuracy was verified. Our findings indicate that the proposed model effectively simulates filamentous fungi mycelial growth and provides a generalized framework for describing the morphology of other filamentous fungi.