Modeling of fungal mycelium growth by fourth-class continuous stochastic cellular automaton with continuously defined growth conditions

The aim of this work was to simulate the growth and spatial structure of the fungal mycelium using a cellular automaton based on the synthesis of various model approaches. The spatial structure of the mycelium is described in the structural submodel of the cellular automaton, which determines the growth rate in the direction of larger resource amount and the number of branches of the mycelium per area unit. The amount of available substrate determines the probability of unidirectional apical growth. Another, biochemical part of the model allows us to describe the rate of transport of resources into the cell, their transport within the mycelium, and also their excretion, and is intended to describe the vertical and horizontal migration in the soil of two nutrients. The proposed model makes it possible to quantitatively describe such a feature of fungal colony growth as more active absorption of resources by external cells, compared to central ones due to separation of transport resources into active and passive resources. The active transport was described using the Michaelis-Menten kinetics. We were able to simulate the stockpiling of surplus resources and their redistribution over the mycelium after the exhaustion of reserves in the external environment, and also to simulate typical growth patterns of mycelial colonies that were observed in experiments published in the literature.