Individual Cell Motion: A Computer Simulation Approach

Abstract

When agar is soft, cells of Bacillus subtilis can diffuse and swim into the agar matrix.  There, the cells can move individually, swimming in pockets of the agar.  The direction the cells swim is uniformly distributed, meaning that there is no preference for any direction.  Speeds follow a Maxwell distribution, and probability density for the straight run time is exponential.  This data, gathered by Michelle Cobeaga and Tim Carroll and compared with results reported in literature, has been incorporated into a computer simulation, which generates the movements of individual cells.  Ideas for further study are also presented.

Introduction

At the macroscopic level a dense bacterial colony is in constant motion in the form of cooperative whirls and jets (which can be viewed in movie Clip 2).   What causes this motion?  One way to determine how cells move in groups is to study how they move as individuals.  If the mechanisms for moving as individuals can be conjectured, and then applied to large groups of cells, the result can be compared to actual colonies.  If the movements are similar, then it is quite likely that the same general rules govern the motions of cells as individuals and as large groups.

When cells are in soft agar, they not only swim on the surface of the agar, but also inside the agar matrix.  Here, they can actively swim as individuals.  Key features to study at the level of individual cells are the directions, speeds, and length of time that a cell swims in one direction.  Kessler, et al. reported on the speed and runtime of cells in various nutrient conditions in Paths and Patterns: The Biology and Physics of Swimming Bacterial Populations. [2]  Along with another team of scientists, Kessler studied how the bacteria move depending on their position with respect to a rigid surface, and presented the information in Mutual Dynamics of Swimming Microorganisms and Their Fluid Habitat. [1]  For the purposes of this study, the bacteria will be in a nutrient rich environment.  Also, only bacteria which are surrounded by agar, and thus not touching a rigid surface, will be considered.  In addition to collecting data, it is possible to begin to make interpretations about cell-cell interactions.  The data and assumptions about interactions can be combined into a computer program which will generate trajectories for cells moving in soft agar.

Methods

The method for maintaining and growing colonies is outlined in Colony Dynamics.  Here a soft agar is used, typically made with five grams of agar per liter of water.  The nutrition is the standard amount, which provides an adequate supply of energy for growth and motion.  To view cells within the agar, a thin layer of hot agar is poured onto a microscope slide cover slip.  After the agar has solidified, it is inoculated and viewed about 24 hours later.  Usually a 40x objective is used in the microscope.  The activity of the colony is video taped and analyzed on a computer.  Then cells are tracked, noting the direction, speed, and length of movement.

The programming for the simulation was done in Java.  The codes required to run the program can be found by clicking on the appropriate links.  The code in cell.java contains the methods for generating the trajectories. CellSimulation.java uses the methods in cell.java, and sends the data points to coordinates.data. CellMain.java shows the user the moves in a Graphical User Interface (GUI). 

Formulas for the probability distributions of direction, speed, and straight run time were determined for use in the java code.  The direction follows a uniform distribution, which means that the cells have no preference for direction.  The speeds fit a Maxwell distribution with parameter 2008.83.  This means that the chosen distribution is from the Maxwell family, and the variable is assigned as 2008.83 so the distribution fits the data.  The runtimes, which correspond to the length of time during which the bacterium swims in one direction, are distributed exponentially with a mean of 0.217 seconds (the required parameter of the distribution to give the desired mean is 4.61).  A random number generator from Java's Random class was used, in conjunction with the distribution formulas, to generate the motions of individual cells.  The data points (which are equally spaced with respect to time) can either be plotted as a scatter plot in a program such as Excel, or the movements can be viewed in the GUI panel provided in CellMain.java.Then, the trajectories generated by the simulation can be compared with actual trajectories observed in the laboratory.  Possible ways to compare the trajectories include using the generated data to determine the parameters of the distributions, or simply looking at the sample trajectories to see if they are reasonably indistinguishable from the actual trajectories.

Results

The plotted trajectories look very similar to those plotted after actual bacteria.  So, the probability distributions do a good job of qualitatively modeling the motions.  Samples of the computer-generated trajectories and actual trajectories can be found here.

Discussion/Conclusion

So far, the simulation is only programmed to generate data for one cell moving.  This cell does not interact with any other cells or the agar environment.  This modeling is goal oriented, meaning that the model is formed only by considering the data, but not what is actually influencing the bacteria.  What causes the bacteria to stop moving?  How do they choose a direction to swim?  Basically what we want to know is how the bacteria interact with the environment and each other.  These ideas can be explored through the computer program.  Methods for the cells to use when they encounter other cells or irregularities in the agar could be added.  Using the new methods, we could let the program generate new trajectories to compare to the actual data.  If the plots are still similar, then this is an indication that interaction is realistic.  Once a set of reasonable rules for movement has been developed, we could see if the coordination of bacteria results in the superpatterns discussed in Colony Dynamics.   Thus, a computer simulation can provide a way to experiment with the system, and learn more about what controls the growth of a bacterial colony.

Works Cited