Current models that describe the extension of fungal hyphae and development of a mycelium either do not describe the role of vesicles in hyphal extension or do not correctly describe the experimentally observed profile for distribution of vesicles along the hypha. The present work uses the n-tanks-in-series approach to develop a model for hyphal extension that describes the intracellular transport of nutrient to a sub-apical zone where vesicles are formed and then transported to the tip, where tip extension occurs. The model was calibrated using experimental data from the literature for the extension of reproductive aerial hyphae of three different fungi, and was able to describe different profiles involving acceleration and deceleration of the extension rate. A sensitivity analysis showed that the supply of nutrient to the sub-apical vesicle-producing zone is a key factor influencing the rate of extension of the hypha. Although this model was used to describe the extension of a single reproductive aerial hypha, the use of the n-tanks-in-series approach to representing the hypha means that the model has the flexibility to be extended to describe the growth of other types of hyphae and the branching of hyphae to form a complete mycelium.

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Solid-state fermentation (SSF) with filamentous fungi is a promising technique for the production of a range of biotechnological products and has the potential to play an important role in future biorefineries. The performance of such processes is intimately linked with the mycelial mode of growth of these fungi: Not only is the production of extracellular enzymes related to morphological characteristics, but also the mycelium can affect bed properties and, consequently, the efficiency of heat and mass transfer within the bed. A mathematical model that describes the development of the fungal mycelium in SSF systems at the particle scale would be a useful tool for investigating these phenomena, but, as yet, a sufficiently complete model has not been proposed. This review presents the biological and mass transfer phenomena that should be included in such a model and then evaluates how these phenomena have been modeled previously in the SSF and related literature. We conclude that a discrete lattice-based model that uses differential equations to describe the mass balances of the components within the system would be most appropriate and that mathematical expressions for describing the individual phenomena are available in the literature. It remains for these phenomena to be integrated into a complete model describing the development of fungal mycelia in SSF systems.

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