PDF《Tokyo 169, Japan》

Physica A

168 (1990) 498-506 North-Holland DIFFUSION-LIMITED GROWTH IN BACTERIAL COLONY FORMATION Mitsugu MATSUSHITA a and Hiroshi FUJIKAWA b aDepartmentof Physics, Chuo University, Kasuga, Bunkyo-ku, Tokyo 112,Japan bTokyo Metropolitan Research Laboratory of Public Health, Hyakunin-cho, Shinjuku-ku, Tokyo 169,Japan Colonies of bacterial species called Bacillus subtilis have been found to grow two- dimensionally and self-similarly on agar plates through diffusion-limited processes in a nutrient concentration field.

We obtained a fractal dimension of the colony patterns of D = 1.73--+0.02, very close to that of the two-dimensional DLA model, and confirmed the existence of the screening effect of protruding main branches against inner ones in a colony, the repulsion between two neighboring colonies and the tendency to grow toward nutrient. These effects are all characteristic of the pattern formation in a Laplacian field. This finding implies the importance of physical properties of the environment for the morphology of bacterial colonies in general. 1. Introduction The formation of random fractals and their structural properties is a problem of considerable current interest [1-3]. Among many growth models proposed so far to describe it, such as the Eden [4] and the ballistic aggregation [5, 6] models, particular attention has been paid to the diffusion-limited aggregation (DLA) model [7]. It not only generates ffactal structures with a fractal dimension D clearly less than the spatial dimension d (D ~ 1.7 and 2.5 for d =

2 and 3, respectively), but also describes the growth processes in a wide variety of physical and chemical phenomena such as electrodeposition, dielec- tric breakdown, viscous fingering, dendritic crystal growth and chemical dis- solution [8, 9]. It is now well known [8] that DLA patterns have outwardly open and randomly branched structures with no characteristic length scales except their whole size and branch thickness (aggregated particle size). Although from the physicist'

s viewpoint biological growth generally leads to the formation of too complex patterns, biology may still have great potentiality for the application of fractal concepts. In fact, there are a wide variety of biological patterns which seem to be self-similar, such as trees, bronchial trees and networks of nerves and blood vessels. This has already been confirmed by ffactal analyses for blood vessel patterns in the chicken embryo [10], the 0378-4371/90/$03.50 ? 1990-Elsevier Science Publishers B.V. (North-Holland) M. Matsushita and H. Fujikawa / Diffusion-limited bacterial colony growth

499 structure of the bronchial tree [11, 12], the cerebral surface of the normal human brain [13], the vascular heterogeneity in the heart [14, 15], the neuronal arborization [16] and the human retinal vessel [17] patterns. Unfortunately, however, they are rather static analyses to obtain the fractal dimension of snapshot patterns. One cannot fully characterize given patterns by their fractal dimensions alone. For instance, DLA and invasion percolation patterns have almost the same fractal dimensions (D ~2.5) for d = 3, but they look quite different from each other. The observation of the growth itself, i.e., the dynamical behavior, is clearly needed to characterize patterns and identify more elementary growth processes. Meakin [18] demon- strated by extensive computer simulations that when biological growth is governed by diffusion-limited processes, the growing patterns show characteris- tic features such as screening, repulsion, and so on. Conversely, the existence of these effects enables one to confirm the diffusion-limited growth in biologi- cal systems. No experiments have, however, been reported so far. In this paper, we present our recent results on the fractal growth in the formation of bacterial colonies. They clearly indicate that the growth of bacterial colonies on agar plates is governed by DLA processes of the nutrient contained in the agar plates. To the best of our knowledge this is the first unambiguous identification of fractal growth processes in biological systems. Moreover, this implies the important revelation that the formation of bacterial colonies is strongly affected by the physical conditions of the environment as well as the proliferation way of the bacteria. Only the latter aspect has so far been taken into account in the morphological study of bacterial colonies. This paper is organized as follows: Section