Fractal scaling of microbial colonies affects growth

The growth dynamics of filamentary microbial colonies is investigated. Fractality of the fungal or actinomycetes colonies is shown both theoretically and in numerical experiments to play an important role. The growth observed in real colonies is described by the assumption of time-dependent fractality related to the different ages of various parts of the colony. The theoretical results are compared to a simulation based on branching random walks.

Figure 1

(a) Part of a Streptomyces Coelicolor $A3\left(2\right)$ colony. Picture taken in the Arizona Research Lab is courtesy of Alain Goriely and Michael Tabor. (b) Number $N\left(\epsilon \right)$ of boxes of linear size $\epsilon$ covering filaments in picture (a) scales as $N\sim {\epsilon }^{-D}$, where $D=1.73\pm 0.03$ is the fractal dimension of this part of the colony. The horizontal axis is rescaled by the linear size $L$ of image (a). For large boxes, $\epsilon$ reaches the size of image (a) (right side, with tangent $-2$).

Figure 2

(Color online) Nutrients are consumed from a narrow stripe of width $\Delta \sigma$ along the hyphae of radius $r$ during time $\Delta t$.

Figure 3

(a) Part of the simulated colony. Applied parameters are in the text. (b) Comparison of the measured total hyphal length (solid line) in the course of time with that obtained from Eq. (11) (dashed line). Units used for length are converted to the dimensionless units of the simulation; thus total length is measured and computed inside region $A_0$ with hyphal diameter 0.04 (see main text).