Mathematical model for apical growth, septation, and branching of mycelial microorganisms

Abstract

A mathematical model for apical growth, septation, and branching of mycelial microorganisms is presented. The model consists of two parts: the deterministic part of the model is based on fundamental cellular and physical mechanisms; it represents the kinetics for growth of hyphal tips and septation of apical as well as intercalary compartments. In regard to random occurrences of hyphal growth and branching, the stochastic part deals with branching processes, tip growth directions, and outgrowth orientations of branches. The model can explain the morphological development of mycelia up to the formation of pellets. The results, as predicted by the model, correspond very closely to those observed in experiments. In addition, some unmeasured states can be ascertained, such as the distribution functions of hyphal length (biomass) and tips along pellet radii.

Hyphal growth and fragmentation of Penicillium chrysogenum in submerged cultures

“…Equation (24) is a much more reasonable expression for the rate of fragmentation than (19), because with (24) fragmentation does not occur for hyphal elements smaller than le,eq.…”

On-line study of fungal morphology during submerged growth in a small flow-through cell

“…Growth, i.e., incorporation of cell wall components in the tip, must therefore be supported by the germ tube itself, and the rate of supply of wall materials will become relatively smaller, which results in a decrease in the specific growth rate. Trinci (1971) and Yang et al (1992) described this process by three distinct growth phases-an exponential growth phase, an intermediate growth phase, and a linear growth phase. These three growth phases can be combined into an empirical expression, Eq.…”

“…Applied in model work and observed for submerged growth in flow-through cell Yang et al (1992) Trichoderma reesei Applied in model work for submerged-batch experiments Lejeune et al (1995) Table IV. The maximum tip extension rate and the saturation constant for the individual branches appearing on the primary hypha at time t i after the first appearance of the germ tube ‫ס‬ the primary hypha.…”

Soil‐borne fungal pathogens: scaling‐up from hyphal to colony behaviour and the probability of disease transmission

“…Thus during early colony growth the patterns of biomass distribution fail to conform to a Gaussian shape, and the analytical approximation fails to predict the colony-scale parameters. A stochastic model, such as that developed by Yang et al (1992), may be more appropriate for investigating and predicting the properties of the colony under these circumstances. In this paper, we focus primarily on the later growth of the colony and the consequences of that growth for transmission of disease; we therefore do not consider the early growth in depth here.…”

“…The model introduced here allows the derivation of colony-scale parameters that control these variables in terms of microscopic hyphal-scale parameters that control growth, death and branching of individual hyphae. There is already a considerable amount of literature on the modelling of fungal growth, ranging from the microscopic scale (Trinci & Saunders, 1977) through the hyphal scale ( Yang et al , 1992) to the colony (Edelstein &Segel, 1983 andDavidson et al , 1996) and the epidemic scales (Kleczkowski et al , 1996). Although the literature provides plausible mechanisms for qualitative fungal behaviour at the various scales, such as the formation of density bands (Edelstein-Keshet & Ermentrout, 1989), the shape of the hyphal tip (BartnickiGarcia et al , 1989) and patterns of interaction between colonies (Davidson et al , 1996), relatively little attention has been given to determining quantitatively how hyphal parameters map onto colony-scale parameters.…”