---Pattern Formation and Growth Competition
Shane Stafford
Yan
Li
Introduction:
Bacterial colonies exhibit
complex growth patterns in starvation conditions, which are reminiscent
of those observed in non-equilibrium growth processes found in non-living
systems, such as dielectric breakdown, liquid-crystal solidification, etc
[1].
It was found that these growth patterns and their fractal dimensions depend
both on the available food (nutrient concentration) and on the roughness
of the surface (agar concentration). At high peptone concentration, the
bacteria form compact patterns with dimension close to 2. As the peptone
concentration decreases, the bacterial colonies branch and form ramified
patterns, so that they can reach out for limited food in the most efficient
way, as shown in Figure 1. At extremely low peptone levels (Figure1
(4)) the patterns become dense again, as could be explained by chemotactic
signaling [2], which is not dealt with in our project.
Figure 1. Observed patterns of bacterial colonies with
peptone concentration: 5,2,0.5,0.25 g l -1 [2]. It
was revealed that bacteria perform a random walk like movement on the substrate,
confined within a well-defined envelope. It was proposed that the envelope
is possibly formed by chemicals excreted and/or fluid drawn by the bacteria.
The envelope acts as a lubricating liquid and propagates slowly, pushed
by the bacteria colliding with it.The
higher the concentration of the agar, the rougher the substrate surface
and the more the effort needed to push the envelope. Thus, at
the same peptone level, the bacterial colonies form more branched patterns
at high agar concentration, as observed in experiments [2].
We use an active walker model to reproduce the experimentally
observed fractal patterns of bacterial colonies and study their dependence
on food level and roughness of the substrate surfaces. The structures of
the patterns are characterized by analyzing the fractal dimension, angular
mass distribution, and growth velocity.We
also look at the interaction between individual colonies, the strength
of which is determined by the separation between the inoculation points.
Interesting phenomena are observed when we bring the two colonies close
enough, where the two colonies expel each other, resembling repulsion between
two like charges.
