Mathematical Methods for studying DNA and Protein Interactions

Deoxyribnucleic Acid (DNA) damage can lead to health related issues such as developmental disorders, aging, and cancer. It has been estimated that damage rates may be as high as 100,000 per cell per day. Because of the devastating effects that DNA damage can have, DNA repair mechanisms are of great interest yet are not completely understood. To gain a better understanding of possible DNA repair mechanisms, my dissertation focused on mathematical methods for understanding the interactions between DNA and proteins. I developed a damaged DNA model to estimate the probabilities of damaged DNA being located at specific positions. Experiments were then performed that suggested that the damaged DNA may be repositioned. These experimental results were consistent with the model's prediction that damaged DNA has preferred locations. To study how proteins might be moving along the DNA, I studied the use of the uniform motion “n-step” model. The n-step model has been used to determine the kinetics parameters (e.g. rates at which a protein moves along the DNA, how much energy is required to move a protein along a specified amount of DNA, etc.) of proteins moving along the DNA. Monte Carlo methods were used to simulate proteins moving with different types of non-uniform motion (e.g. backward, jumping, etc.) along the DNA. Estimates for the kinetics parameters in the n-step model were found by fitting of the Monte Carlo simulation data. Analysis indicated that non-uniform motion of the protein may lead to over or underestimation of the kinetic parameters of this n-step model