Lamour A, Van den Bosch F, Termorshuizen A J, Jeger M J
Laboratory of Phytopathology, Wageningen Agricultural University, The Netherlands.
IMA J Math Appl Med Biol. 2000 Dec;17(4):329-46.
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 & Sch urer (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.
土壤传播真菌的生长情况鲜为人知且理解有限，主要是因为对土壤中菌丝进行非破坏性观察很困难。数学建模有助于理解真菌生长。除了保斯廷和舒勒（1987a）的一个模型外，真菌生长模型并未考虑所提供底物的碳和氮含量，尽管这些养分对土壤中菌丝的延伸有相当大的影响。我们引入了一个与土壤有机质分解相关的真菌生长模型，该模型涉及碳和氮的详细动态变化。以恒定速率供应具有一定碳氮比的底物，底物被分解，然后被真菌菌丝体吸收。养分首先在代谢池中内部储存，然后并入真菌的结构生物量中。使用标准数学程序来获得变量的整体稳态（隐含地从一个三次方程中获得）以及存在条件。对广泛参数组合的数值计算表明，对于稳态，最多只有一个解在生物学上是有意义的，这由存在条件指定。这些条件规定了一个约束，即投入底物分解的“能量”（以碳计）应小于底物分解产生的“能量”，从而导致正的碳平衡。存在条件的生物学解释是，对于生长而言，在所有底物都被定殖的情况下，产生真菌结构生物量和维持所需的“能量”应小于上述正的碳平衡。总之，对这个复杂的真菌生长模型的分析得出了具有清晰生物学解释的结果。
