Catherine Ott

Spring 2001

Colony Dynamics

Abstract

Bacteria grown on agar surfaces can grow into a variety of colony shapes, ranging from a basic circle to an intricate fractal-like pattern. The diversity is caused by the motility of the bacteria, which is the result of the affects of agar concentration and nutrient concentration, as well as numerous other factors. Many biologists, physicists, and mathematicians have studied the colony formations. Each group of scientists attempts to develop a model that will represent all of the possible formations. The study of these models, as well as observing bacteria and performing experiments, has lead to further understanding of the systems influencing the final shape of the colony. The observation of bacteria moving laterally (which is not a direction swimming bacteria can move) has prompted questions about the fluid dynamics of the colonies. Fluid-like motion has been observed within the colonies, and the origin of this motion must be determined for proper incorporation into the models. An experiment has been performed to make the conclusion that solely the motion of the bacteria themselves causes the fluid flow; further experiments are being developed.

Introduction

Motile strains of bacteria, such as Bacillus subtilis, swim by using flagella, which are situated around their oblong bodies. The flagella propel the cells forward only. When cells are placed on an agar surface of suitable wetness, the bacteria reproduce and form colonies of swimming cells. Through chemotaxis, oriented movement toward or away from a chemical stimulus, the cells find regions of higher nutrient concentration. Also, the cells diffuse across the agar. Diffusion is the spreading of the bacteria, or any material, down their own concentration gradient. These motions of bacteria result in diverse colony shapes, depending on parameters such as agar concentration and nutrient concentration. In softer agar, the bacteria can swim and diffuse easily. In fact, in very soft agar the bacteria actually swim inside the agar matrix. Nutrient concentration affects the strength of the cells, and their resulting ability to swim and reproduce. Scientists have tried many techniques to develop a model that accounts for diffusion and chemotaxis, and can generate each of the following forms under different initial conditions.

Figure 1. Morphological diagram of B. subtilis colony patterns. From Mimura, et al. [6]

A) diffusion-limited aggregation-like (DLA);

B) Eden-like;

C) concentric ring-like;

D) disk-like;

E) dense branching morphology-like.

The goals of my work are to understand models developed by other scientists, observe and experiment with bacteria cultures, and contribute ideas toward the development of new models.

One of the first models of bacteria movement was developed by Evelyn Keller and Lee Segel, as reported in their paper "Traveling Bands of Chemotactic Bacteria: A Theoretical Analysis." [3] Keller and Segel used partial differential equations to model bacteria swimming in a tube. The bacteria traveled in bands toward nutrients and oxygen, coined "critical substance." The model expressed the motion of bacteria through chemotaxis and diffusion, but growth was not considered. Also, the motility of the bacteria was assumed to vary with the substrate concentration, and not with the bacteria concentration. The critical substance does not diffuse a significant amount, and there is enough substance such that availability is not a limiting factor. The bacterial flux due to chemotaxis is proportional to the critical substance gradient. Traveling wave solutions of this system can be obtained. The derivation of the Keller-Segel model can be found in Michelle Cobeaga's report "Analysis of Migrating Bands of Chemotactic Bacteria." [1]

Another factor that some scientists feel is important is the excretion of a lubricating fluid by the bacteria. The reason that this could be important is that the degree of wetness of the agar is a limiting factor for the growth of a branch. In very dry agar, the expansion of the colonies is not related to motility of the bacteria; the colony spreads as a consequence of the bacteria growing and demanding more area. The secretion of a fluid would make a path of less resistance, and more cells would follow. Mendelson's "Pattern of Reporter Gene Expression in the Phase Diagram of Bacillus subtilis Colony Forms" [5] demonstrates that the breaking of a boundary of a branch is achieved by an accumulation of cells, as the surface tension of the water in the agar is too high for individual cells to overcome. So, a branch could be created by groups of cells lubricating the agar and allowing more cells to follow this path. Golding et al. reported on this in "Studies of Bacterial Branching Growth using Reaction-Diffusion Models for Colonial Development." [2] Also, the velocity of the bacteria was used to define the different colony shapes. Four of the patterns, DLA patterns, compact patterns, and dense branches and concentric rings, corresponded to three different velocities. This means that the patterns take different amounts of time to develop. Their conclusion was that the morphologies are the result of actual transitions in the way the bacteria move and the velocity of movement. One issue that Golding et al. pointed out is that two different mathematical descriptions can lead to patterns that appear similar. An example of this would be obtaining branches by including a bacteria death term, and also by having no death term but assuming the movement of the bacteria is dependent on the density of bacteria and the density of food. These are distinctly different models, but simulations show similar results.

A paper by Mimura et al., entitled "Reaction-Diffusion Modeling of Bacterial Colony Patterns" [6] begins by asking a question: "Is the diversity of such colony patterns caused by different effects or governed by the same underlying principles?" To answer this question, the authors first critiqued a variety of models developed by other scientists. The models are based on reaction-diffusion (RD) concepts, in which "spatial and temporal change of bacteria are described by using their average densities." The models discussed included Kessler and Levine's cutoff mechanism in the growth term, which allowed the development of branching patterns. Kawasaki et al. assumed that the diffusion coefficient of bacteria depends on their own density, the density of the nutrients, and a stochastic term to introduce frontal instability. These ideas led to a nonlinear diffusion model. Finally, Kitsunezaki developed a density-dependent model with an interesting term that separated bacteria into groups with different motility properties. The bacteria are divided into those that are active, and bacteria that are inactive; this idea is very similar to Golding et al.'s death term. This model also produces frontal instability that results in branching patterns. Mimura et al. proposed an improved model, which accounts for the motility rate of the active bacteria, the diffusion rate of nutrients, the growth rate of the bacteria, and the rate of conversion of active bacteria into inactive bacteria. The primary difference from the previous models is in the death term. Mimura et al. use a piecewise function that is dependent on the bacterial and nutrient concentrations to model the death of bacteria. This model can produce four different types of patterns by changing the motility of bacteria (dependent on the concentration of agar) and the nutrient concentration. The Eden-like patterns (shown in Figure 1.1) can be reproduced from a proposed nonlinear diffusion model.

While these models have shown an accurate description of the end result of a colony shape, the process of achieving that shape is much more detailed. Cells have three main levels of organization, as described by Mendelson, et al. in "Organized Cell Swimming Motions in Bacillus subtilis Colonies: Patterns of Short-Lived Whirls and Jets." [4] The first level is that of individual cell motion. Secondly, groups of cells form whirls and jets. What is most interesting is that after an opposing jet disorganizes a whirl, the whirl reorganizes into a whirl in the opposite direction of what it started. To show that this is actually a function of bacteria motion, marker beads were added to the colony’s advancing finger. While the markers did participate in whirls and jets, they did not reverse direction not retrace an earlier route. The third level of organization occurs when the whirls and jets organize into a superpattern. This superpattern withstands the individual pattern elements reorganizing. Ultimately, this interconnectedness is what forms extensive colony morphology. When the whirls and jets strike a boundary, some cells are left at the edge and push it outward; this is colony expansion. What should be determined is what causes the swimming patterns. Could it be that the path is the result of the physics of swimming, or is this chemotactic response towards a self-emitted attractant?

Methods

The bacteria strains, M8, M22(81), and M22(84), were obtained from Mendelson. They were maintained on standard tryptose blood agar base (TBAB) plates made from Difco medium. For growing colonies of the morphologies described above, a softer version was made, which contained only 0.6% agar, instead of 1.5%. The method for making this media [4] is to dissolve 10 grams (g) of tryptose, 3 g of beef extract, and 5 g of NaCl in 1.0 liters of deionized water. Six grams of agar was added. To sterilize, the mixture was autoclaved at 121° C for 20 minutes. The solution was cooled to 48° C and maintained at this temperature for one hour. Then, the plates were poured and the agar was allowed to solidify at 23° C in a 50% relative humidity chamber. For clearer resolution on a microscope, this media could be melted and dropped onto a cover slip. Then, to keep the media from drying out, the cover slips were placed on a specimen slide, and this was set on a bent glass rod, in a petri dish with a small amount of water. These plates were stored in an incubator at 24° C. For viewing, the cover slip would be taken off the slide and placed under the microscope. This ensures a minimum amount of glass and agar between the microscope and the bacteria. Cultures were inoculated using sterile toothpicks. The colonies were viewed with a Nikon-inverted phase-contrast microscope with a 20x or 40x objective. Using a Cohu camera fitted directly to the microscope, the images were transferred to VHS tape on a JVC or GYYR tape deck, and recorded on a standard cassette. Then, the films were transferred into a Dell computer and the images were analyzed using Matrox Inspector, Image-Pro Plus, and Adobe Photoshop. Also, some frames were printed onto transparencies using a Tektronix Phaser II SDX. An experiment using formaldehyde to kill the bacteria was performed. In this experiment, cultures were grown on cover slips in the standard way. Then, the cover slips were placed under the microscope with a petri dish lid over them. A strip of paper towel wet with water was taped to the inside of the lid, to keep the cultures moist and active. Another lid was set up in the same way, but the paper towel was moistened with formaldehyde instead of water. Fumes were allowed to build up inside the lid, and then the lids were switched. The bacteria were almost immediately engulfed in formaldehyde fumes.

Results

The observations and experiments serve to reinforce the previous observations described by Mendelson et al., and also lead to a new observation. I saw the whirls and jets I had read about, and noticed the patterns of disorganization and reorganization. By varying the agar concentration, I witnessed the bacteria trapped within the agar, bouncing between the walls of the pockets. I was also able to capture clear images of the whirls depositing cells at the edge of the colony, and the colony expansion that results. Performing the formaldehyde experiment described above, as devised by Mendelson, showed the motion of the bacteria ceased within seconds of introducing the formaldehyde into the system. The most exciting observation, noticed by Mendelson, is of the parallel alignment of cells while in whirls and jets, in which groups of cells are carried perpendicular to the direction of movement cells are capable of through their own swimming. This lateral motion, and resulting compression of the bacteria, is the result of a force other than that of the bacteria exhibiting the motion. So, either the bacteria create a fluid flow which pushes the bacteria, or there is an external force creating the flow.

Discussion/Conclusion

Most of the observations and experiments only served to reinforce previous knowledge, and give me first hand experience with the techniques and observations made by others. I witnessed the advancement of the colony edge by depositing cells, and how the wetness of the agar is a factor in growth. The rate of edge growth can be compared to the rate of movement of the individual cells caught inside the agar. This will give an indication of affect of the agar concentration on movement. The formaldehyde experiment proves that only the force of the bacteria causes the flow of the fluid and the resulting lateral movement of the groups of cells; one group of cells is able to push another group of cells. Also, the rate of the compression of the cells is in the process of being analyzed. These ideas will increase the understanding of the dynamics of colony growth.

Reading the discussions of various models and observing the colonies myself has led me to a few conclusions about the current models. Golding et al. [2] expressed that including terms for "diffusion, food consumption, reproduction, and inactivation" do not sufficiently describe the phenomena, and they propose to include chemotactic signaling. While this is an improvement, I do not feel that this will adequately describe the dynamics within the colonies. The models I have read about focus on what happens at the edges to determine the colony shape. My observations of the colonies have shown me that the rest of the colony is important as well. Mendelson et al. [4] describe the levels of organization of bacteria movement and resulting colony development, and I feel that the interconnectedness of the movements can play an important role in developing a comprehensive model.

Works Cited