Culture analysis and external interaction models of mycelial growth
This paper reports on a joint project by biologists and mathematicians to describe and model morphogenetic aspects of mycelial growth mechanisms. The life cycle of a fungus starts with the germination of a spore leading to a mycelium. The mycelium has a tendency to form a circular growth front, which enables it to uniformly explore its medium. Certain questions arise concerning the underlying mechanisms of this behavior: (1) How does circularization happen? (2) Do different fungal species follow different circularization stragegies? (3) Do different culture conditions change circularization behavior? (4) Can the branching patterns and circularization behaviors be linked to known physiological and cytological observations, such as the relations between the growth rates of leading hyphae and secondary and tertiary hyphae; the occurrence of physiological delimiters within the mycelial cells, such as sealed cross walls, or large vacuoles? We study the morphogenesis of young developing mycelia through direct observation of growth patterns and through their mathematical models. We describe observations of the zygomycete Mucor spinosus (which was chosen for its easy handling) that show how the young mycelium occupies the surface of its culture medium. In particular we introduce parameters to quantify the efficiency of territory occupation. These parameters measure circularization, branching rate, growth rates of primary, secondary and tertiary hyphae, and the choice of growth direction. We present a growth model without interaction with the medium that yields closed form expressions for several quantities of interest as function of the model parameters and finally we report simulation models based on interactions between hyphae exclusively through the surrounding medium via secretion, diffusion and detection of some inhibitory substance. Although it is very likely that branching of the hyphae is affected by certain internal messages traveling within the mycelium, we first propose to study hyphal growth by simplifying branching rules to random decisions, subject to external regulatory influences. We study the behavior of these models with respect to circularization, growth efficiency and other measures. These models are able to reproduce some of the observed phenomena as will be shown by comparing simulation runs with experimental observations on living fungi.
discrete models of two-dimensional filamental branching growth
scientific article; zbMATH DE number 682046