Microbial growth patterns described by fractal geometry.
Fractal geometry has made important contributions to understanding the growth of inorganic systems in such processes as aggregation, cluster formation, and dendritic growth. In biology, fractal geometry was previously applied to describe, for instance, the branching system in the lung airways and the backbone structure of proteins as well as their surface irregularity. This investigation applies the fractal concept to the growth patterns of two microbial species, Streptomyces griseus and Ashbya gossypii. It is a first example showing fractal aggregates in biological systems, with a cell as the smallest aggregating unit and the colony as an aggregate. We find that the global structure of sufficiently branched mycelia can be described by a fractal dimension, D, which increases during growth up to 1.5. D is therefore a new growth parameter. Two different box-counting methods (one applied to the whole mass of the mycelium and the other applied to the surface of the system) enable us to evaluate fractal dimensions for the aggregates in this analysis in the region of D = 1.3 to 2. Comparison of both box-counting methods shows that the mycelial structure changes during growth from a mass fractal to a surface fractal.
Obert
M
M
Institut für Biochemie und Endokrinologie, Justus-Liebig-Universität Giessen, Federal Republic of Germany.
Pfeifer
P
P
Sernetz
M
M
D005658:Fungi / Q000254:growth & development*; D008433:Mathematics; D008962:Models, Theoretical; D013305:Streptomyces griseus / Q000254:growth & development*