Catherine Ott
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. 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]
ForSpring 2002
Individual Cell Motion: A Computer Simulation Approach
Abstract
Introduction
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.
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.
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.
1.
Kessler,
J. O., G. D. Burnett, and K. E. Remick. 1998.
Mutual Dynamics of Swimming Microorganisms and Their Fluid
Habitat. Nonlinear Science at the
Dawn of the 21st Century.
P. L. Christiansen and M. P. Sorensen, Eds. Springer-Verlag
Lecture Notes in Physics. 2.
Kessler,
J. O., R. P. Strittmatter, D. L. Swartz, D. A. Wiseley, and M. F. Wojciechowski. 1995.
Paths and Patterns: The
Biology and Physics of Swimming Bacterial Populations. The Society for Experimental
Biology. 1995: 91-107.
Works Cited
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