Microbial growth patterns described by fractal geometry

Abstract

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.

Collembolan grazing affects the growth strategy of the cord-forming fungus Hypholoma fasciculare

“…Subsequently, we obtained D B by a linear regression of the linear portion of log NðsÞ against log s. The lower limit of resolution is determined by the pixel size; according to Markx and Davey (1990); Obert et al (1990) the upper limit is usually determined by 25% of the maximum width of the image set.…”

“…(3), D B is called the mass fractal dimension D BM : For estimation of the surface fractal dimension D BS ; the boxes that contain white pixels only are omitted from calculation. The distinction between mass and surface dimension allows for the distinction between mycelia that are fractal only at their margins having plane-filled interiors ('border fractal'), and those where the interior of the system has lacunae ('mass fractal') (Obert et al, 1990). Since border boxes are not entirely filled by the mycelium, we applied a corrected formula (Eq.…”

Developmental and morphological responses of mycelial systems of Stropharia caerulea and Phanerochaete velutina to soil nutrient enrichment

“…Two fractal dimensions may be determined : the Mass fractal dimension (D BM ), which describes the space filling of the entire structure, and the Surface fractal dimension (D BS ) which describes the distribution of the perimeter and internal edges of the structure. Some structures may be fractal only at the margin (D BS 1), where the mass fractal dimension can approach plane-filling (Obert, Pfeifer & Sernetz, 1990) The box-count technique was used to estimate the fractal dimension of extra resource mycelia for each processed image by overlaying a series of grids containing boxes of varying side length (s) from 3 to 61 pixels. The number of boxes at each box size intersecting the image was counted and the fractal dimension estimated from : …”

Activated sludge morphology characterization through an image analysis procedure

“…In the present study the image analysis software estimated directly the fractal dimension of flocs applying the box counting method (Liebovitch and Toth, 1989) extensively used in literature to estimate the aggregates fractal dimension. The values for this parameter are between 1 and 2, being smaller values for objects with irregular contour and higher values for highly irregular objects (Obert et al, 1990).…”