Morphological Analysis Based on a Fractional Dynamic Model for Hyphal Growth

The development of methods capable of accurately characterising the morphology of filamentous microbes represents a significant challenge to biotechnologists. This is because the productivity of many industrial fermentation processes is heavily dependent on the morphological form adopted by an organism. It is therefore of significant value if a quantitative model and associated metric(s) for morphological forms determined by complex phenotypes can be determined non-invasively, e.g. through image analysis. Specific interest is in the quantification of the branching behaviour of an organism. This is due to the link between branching frequency, biomass and metabolite production. In this paper we present a model for three-dimensional microbial growth that is based on a fractional dynamic model involving separable coordinate geometry. This provides a focus for an approach reported in this paper where microbial growth can be quantified using a sample microscopic digital image. In particular, we study the fractal dimension of fungal mycelial structures by generating a ‘fractal signal’ based on the object boundary. In the analysis of a population of Aspergillus oryzae mycelia, both the fractal dimension and hyphal growth unit are found to increase together over time. Further, through an analysis of different populations of Penicillium chrysogenum and A. oryzae mycelia, cultivated under a variety of different conditions, we show that there is a statistically significant logarithmic correlation between the boundary fractal dimension and hyphal growth unit.