Modelling the growth of soil-borne fungi in response to carbon and nitrogen

Growth of soil-borne fungi is poorly described and understood, largely because non-destructive observations on hyphae in soil are difficult to make. Mathematical modelling can help in the understanding of fungal growth. Except for a model by Paustian & Schnürer (1987a), fungal growth models do not consider carbon and nitrogen contents of the supplied substrate, although these nutrients have considerable effects on hyphal extension in soil. We introduce a fungal growth model in relation to soil organic matter decomposition dealing with the detailed dynamics of carbon and nitrogen. Substrate with a certain carbon : nitrogen ratio is supplied at a constant rate, broken down and then taken up by fungal mycelium. The nutrients are first stored internally in metabolic pools and then incorporated into structural fungal biomass. Standard mathematical procedures were used to obtain overall-steady states of the variables (implicitly from a cubic equation) and the conditions for existence. Numerical computations for a wide range of parameter combinations show that at most one solution for the steady state is biologically meaningful, specified by the conditions for existence. These conditions specify a constraint, namely that the 'energy' (in terms of carbon) invested in breakdown of substrate should be less than the 'energy' resulting from breakdown of substrate, leading to a positive carbon balance. The biological interpretation of the conditions for existence is that for growth the 'energy' necessary for production of structural fungal biomass and for maintenance should be less than the mentioned positive carbon balance in the situation where all substrate is colonized. In summary, the analysis of this complicated fungal growth model gave results with a clear biological interpretation.