Symmetric branching model for the kinetics of mycelial growth

A mathematical model, linking microscopic to macroscopic parameters of the kinetics of mycelial growth is presented. The model consists of two parts: (a) a microscopic description, based on the assumption that growth of a mycelium can be represented approximately by the growth of a symmetric binary tree, where the branching level (microscopic state variable) is logarithmically related to the number of tips and segments; and (b) a macroscopic description which makes use of the microscopic description in order to define the parameters related to the evolution of biomass (macroscopic state variable) as a function of time. The latter uses a distribution of arrested tips in a population of mycelia, in order to estimate the fraction of non-growing biomass in terms of a power law function with coefficient, n, of the biomass concentration. The microscopic description explains the fact that the germ tube specific growth rate of Aspergillus nidulans measured in a growth chamber, is about the double the specific growth rate of this organism, when measured in shake flasks. It predicts that the length of the hyphal growth unit of the mycelium of Geotrichum candidum would be approximately the double the germ tube length measured at the time just before the first branching event. It also allows the derivation of useful expressions for predicting macroscopic parameters, such as the maximal specific growth rate, the initial amount of biomass, and the amount of biomass before the branching process starts. Those estimates are done in terms of microscopic quantities, i.e., the amount of germinated spores, the diameters of the spores and hyphae, the average rate of tip extension, and the average internodal segment length. Estimation of coefficient n by fitting the macroscopic description to a growth curve of A. niger gives an indication on the degree of skewness of the distribution of arrested mycelia. Estimated macroscopic parameters are in relative good agreement with measured average segment length.