Colony formation in bacteria: experiments and modeling

Abstract

We present experimental results of colony formation in bacteria as an example of pattern formation resulting from reproduction and movement in biological populations. The bacterium Bacillus subtilis is known to exhibit at least five distinct types of colony pattern, depending on the substrate softness and nutrient concentration: diffusion-limited aggregation (DLA), compact Eden-like, dense branching morphology (DBM), concentric ring-like, and disk. We established a morphological diagram of the colony patterns, and then examined and characterized both macroscopically and microscopically how the the colonies grow. There seem to be two kinds of bacterial cells – active and inactive – and the active form drives the colony interfaces outwards. The active cells may be clearly distinguished from the inactive ones as they form the characteristic fingernail-like structure at the tips of growing branches of the DBM colony. The concentric ring-like colony is formed as a consequence of repeated alternate migration and resting of the growing interface, the cycle time for which seems to be independent of the substrate softness and nutrient concentration. So far there have been several phenomenological models proposed to qualitatively explain or reproduce the patterns observed in bacterial colonies. A few of them are reviewed here, systematically and critically, in light of our experimental results.

Self-Elongation with Sequential Folding of a Filament of Bacterial Cells

“…We represent its length by l 1 (t) [µm]. As illustrated by [1] in Fig. 4, we see the following process:…”

“…In the time interval 0 ≤ t ≤ t * , only elementary processes [1] and [2] take place. We assume that in the elongation process of a cell filament with specific growth rate α, the ratio of the frequency of elementary process [2] to that of elementary process [1] is given by β/(1 − β) with a constant 0 < β < 1.…”

“…The solution is then given by For t > t * , we take into account the following elementary processes in addition to processes [1] and [2]:…”

Statistical Features of Complex Systems –Toward Establishing Sociological Physics–

“…A typical example is colony formation in bacteria. 7) For instance, the common bacterial species Bacillus subtilis is known to exhibit various colony patterns such as diffusion-limited aggregation (DLA), Eden patterns, highly branched patterns with smooth circular envelopes, and disk-shaped, depending on the environmental conditions, namely, substrate softness and nutrient concentration. The growth behavior is strongly reminiscent of the formation of human colonies such as villages, towns, and cities.…”

“…We have established morphological diagrams of colony patterns, and then examined and characterized both macroscopically and submacroscopically how they grow. 7) The third approach may be to examine statistics, because members constituting a complex system show characteristic statistics. In this article we will discuss statistical aspects seen in complex systems from as wide viewpoint as possible.…”