In January of 2001 I began working on a project that would combine mathematics and biology. My study of the application of mathematics to bacterial colonies has led me through a process of data gathering through laboratory work, reading technical papers, mathematical modeling, and computer programming.
I began my project by learning about Bacillus subtilis through experimentation and reading. Dr. Joceline Lega, of the Department of Mathematics, chose papers written by mathematicians and biologists concerning modeling bacterial colony growth. The authors of many of the papers developed equations to describe the methods of growth into different classifications of morphologies. Others focused on observations of colony dynamics. From the reading, I developed an understanding of the process for modeling this type of biological system, and I was able to make conclusions about what I feel are the most important factors in the growth of the colonies. While reading introduced me to the current research in the field, working in the laboratory of Dr. Neil Mendelson, of the Department of Molecular and Cellular Biology, gave me the opportunity to make my own observations and run experiments. For example, I wanted to determine if all motion in the colony is due to the controlled movements of the bacteria. I used formaldehyde to poison a colony, and quickly all motion ceased, which reinforced my hypothesis. These activities were performed over the course of one semester and one month of summer work.
Next, in the fall semester of 2001, I specified my research to the study of bacterial colony growth rates under particular conditions. By reviewing a phase diagram created by Mendelson and B. Salhi, published in Patterns of reporter gene expression in the phase diagram of Bacillus subtilis colony forms, I chose four regions to study. With the help of Tim Carroll, I grew non-motile and motile colonies on agar plates that fit the specified conditions. I measured the size of the colonies as they grew over approximately sixty hours. From the data and my knowledge of colony growth mechanisms, I was able to derive a differential equation to model the linear expansion of the non-motile colonies. The motile growth was much more complicated. While I was unable to determine an equation to model the growth, I arrived at important conclusions about how the conditions control the growth of the colonies. I presented a poster covering the highlights of this work at the annual meeting of the American Mathematics Society and the Mathematical Association of America in an undergraduate poster session.
During the spring semester of 2002, I used probability models and Java to create a simulation of the motion of bacteria in wet conditions. In such conditions, the bacteria can actually swim inside the agar. I used probability distributions of speed, direction, and length of straight run time. The distributions are based on data collected by Michelle Cobeaga, who worked in Mendelson's lab, as well as on data reported in literature. The simulation is a Java program which displays bacteria moving as determined by the model. Kevan Holdaway and Tareq Hossain, computer science students, have shared examples of Java code they have written for simulations, and also advised me on writing programs to create realistic results. Motions for single cells have been generated by the simulation. Also, I present ideas for further developing the simulation.
This project has allowed me to explore the applications of mathematics to biology. Working on both sides of the project gave me the opportunity to understand the interplay necessary between fields to produce the most accurate, efficient, and useful results.