Modelling fungal growth with fractional transport models

Due to the network-shaped colony formed by the filamentous fungi, fractional operators are likely to capture the time-evolution of their biomass distribution. In this paper, a generalised fractional transport model is developed to simulate the colony growth of a wood-rot fungus, Postia placenta. The colony is described by two variables, active and inactive biomass. The active biomass corresponds to the tips and the “active points”, responsible for biomass formation, while the inactive component represents the remaining biomass, which is assumed immobile. The fractional in time and space derivatives are applied to the active biomass to represent the spatial colonisation (i.e., tip movement). The proliferation of biomass (local densification of the network due to branching) is driven by a source term, while a portion of active biomass becomes inactive over time. The model is solved using an extended finite volume discretisation scheme and the accuracy is confirmed by comparison to an analytic solution obtained for the case where the source term is assumed linear. Next, the model parameters are identified for an optimized solution of the model that matches experimental observations well, indicating the suitability of the fractional operators for modelling biomass diffusion in a fungal colony. An interesting finding is that the best results are obtained when only anomalous diffusion in space (not time) is considered, which is probably related to the fractal dimension of mycelia. The spatial fractional-order derivative provides a unique ability to capture the non-local biomass diffusion of the fungal colony. We postulate that the fractional indices may provide a form of biological marker for the growth characteristics of different fungal species.