Bacillus subtilis, a motile strain of bacteria, exhibit different colony dynamics depending on the growth conditions of the agar plates. In some cases the growth is a simple disk, while under certain conditions elaborate fractal-like patterns emerge. I intend to describe Bacillus subtilis colony dynamics physically and mathematically. I have studied the motions of bacteria in colonies and performed experiments to further my understanding of the forces controlling the growth of the colonies. From the data I have gathered, I have determined the key factors which dictate the size and shape of colonies. A simple model for the size of non-motile colonies will be presented, but the motile case will only be discussed.
To formulate a model for the growth of bacterial colonies, the pertinent facts must be identified and appropriate assumptions developed. While several key points about motile and non-motile colonies will be emphasized here, please reference the Colony Dynamics report for a more thorough discussion of the mechanisms of colony growth. Motile strains like M22(84) can, under ideal agar surface and nutrient conditions, swim towards a chemical signal, increasing colony size. Surface wetness regulates the colony expansion because a more fluid surface facilitates swimming and gliding, while nutrients provide energy for movement. Also, the cooperative whirls and jets of motile bacteria can destabilize the colony boundary, which can result in branching. The density of bacteria is not necessarily constant, especially in the branches. Non-motile strains, such as 5:7(M), cannot swim. Increase in colony size is due to the increase in total mass of bacteria cells. It is reasonable to assume that the only contribution to colony size is from the bacteria on the periphery, because interior bacteria that reproduce cannot swim to increase colony diameter. Instead, they form layers of cells. This leads to another assumption, that the bacteria density is roughly constant. This can be explained as a result of the colony density increasing (by layering) until it reaches a limit where the bacteria in upper layers cannot receive adequate nutrition. As a result, the density stops increasing and the colony has reached a maximum thickness. It is also assumed that under most non-extreme conditions, the growth of a non-motile colony is parameter independent. In both the motile and non-motile cases, the bacteria and nutrients can diffuse through soft agar.
The bacteria strains, M22(84) and 5:7(M), were obtained from Dr. Mendelson. They are maintained on standard tryptose blood agar base (TBAB) plates made from Difco medium. For growing the colonies observation, the method described in Colony Dynamics is used. The agar concentration is varied by using either six grams or ten grams with a constant amount of water. Similarly, either half or twice the standard amount of nutrients is used. The result is four different types of plates for growing colonies in the experiment. While the agar media does lose moisture, this can be limited by placing the plates in a humidity chamber and minimizing exposure to air. All of the plates were kept in the same chamber in an incubator at 24°C after inoculation. The bacteria do not exhibit much growth during the first nine hours, so measurements began nine hours after inoculation and continued for 60.5 hours. Images of the colonies were imported into a Dell computer and analyzed using Image-Pro Plus. A tool was used to measure the colony size in pixels. The size reported is the length across the widest part of the colony; this measurement is considered the diameter. A branched colony was measured the same way as a non-branched colony; the presence of branching is not indicated in the data, which was compiled in Excel spreadsheets. Further analysis using Excel included converting the sizes into centimeters, plotting the data, and plotting trendlines. The Excel workbooks are linked here for the non-motile case and the motile case.
For the non-motile case, the data leads to a simple linear model that follows the assumptions. The mathematical model, selected data, and a phase diagram can be viewed by clicking on the appropriate link.
The data for the motile case does not indicate a simple relationship between colony size and the parameters, nutrient concentration and agar concentration. A brief overview of the observations, selected data, and a phase diagram can be viewed by clicking on the appropriate link.
While bacteria reproduction is exponential in a fluid with adequate nutrients, this experiment has shown the impact of non-motility, nutrient levels, and dryness of the agar. For the non-motile case the model provides a concise and accurate description of dynamics and resulting colony morphology. While the growth rate of the motile colonies is not easily described mathematically, conclusions about the morphologies can be made from the data collected. When the agar is dry (10 g/l) the bacteria cannot swim well, and the colony size is significantly different from the non-motile case only when the nutrient concentration is high. However, when the agar concentration is relatively low, the bacteria can swim. The result is intricate branching patterns. From the data it seems that the point at which branching occurs depends on the colony size. Regardless of the nutrient concentration, branching first becomes measurable when the colony diameter is 0.3 to 0.35 cm. This suggests that branching occurs when the colony is large enough for the boundary instability to produce growth in new, asymmetric directions. Once the colony begins branching, the change in diameter is very rapid. For the low nutrient case, the branches elongated, with minor increase in branch width. When the nutrients were high, the branches would elongate and then fill in, creating a larger disk with branches. Eventually, the low agar, high nutrient condition completely covered the plate; the low nutrient condition did not do this. Comparing the phase diagram produced by this data to the phase diagram Mimura, et al. has produced, a connection is apparent. The data collected under this experiment represents three of the morphologies in the diagram, namely diffusion-limited aggregation-like (DLA), Eden-like, and dense branching morphology-like. The difference is that these morphologies occur at lower concentrations of both agar and nutrients. So, while the data for the motile case did not lead to a mathematical model, the results confirm prior understanding and assumptions about the colony dynamics.