Mycelial response to spatiotemporal nutrient heterogeneity: a velocity-jump mathematical model

The processes underpinning mycelial growth and function operate over a vast range of scales that can lead to inherent difficulties when investigated using experimental means alone. However, mathematical modelling provides a structured framework that combines scales and instead focuses on the fundamental processes. In this paper a new mathematical model of the growth of a mycelium is described where a velocity-jump process simulates apical extension. Explicit unconstrained planar networks were produced incorporating sub-apical branching, anastomosis, nutrient uptake and its subsequent translocation. The model was used to simulate the outgrowth of a fungus into an environment where nutrient resources are made available and the resultant biomass response was highly dependent on the position and distribution of such resources. Furthermore, specific channels for the movement of internally-located material arose through an initially stochastic but then self-reinforcing mechanism which is suggested to be a potential precursor to cord formation in fungi.