[A model for the formation of ring-shaped structures in colonies of mycelial fungi]

Mathematical model of the development of the pattern of colonies is considered. The model represents the systems of differential equations of the first order. It includes non-dimensional parameters characterizing the following features: concentration of substrate, concentration of metabolic products--growth inhibitor, mycelium and spores, radial and specific rate of mycelium growth, rate of substrate consumption and production of metabolic products, coefficients of diffusion of substrate and metabolic products, initial concentration of mycelium and substrate, time of delay of mycelium reaction on metabolic products and spore formation, threshold concentration of metabolic products. The model is adequate to the experiments with cultivation of Penicillium chrysogenum. It was shown that necessary condition for the formation of the circle periodical structures (zoning) in the colonies is an ability for the production of growth inhibitors (antibiotics, etc.). It was proved that formation of colonies of "continuous lawn" type is caused by restrictions on growth because of mycelium satiation or exhaustion of substrate. Such growth scenario is realized in experiments either on reach substrate or on hungry agar. For the appearance of regulating of "zone structure" type limitation on critical level of metabolic product concentration is very important. The number of periodical zone structures and their widths are determined by the above parameters.