Stochastic Reaction-Diffusion Methods for Modeling Gene Expression and Spatially Distributed Chemical Kinetics

Dedicated to my family. Their help and support has been greatly appreciated. iii Acknowledgments Foremost, I would like to thank my adviser Charles S. Peskin. Working with Charlie the past five years has been a wonderful experience. His enthusiasm was always uplifting, and his insight was a joy to see first hand. I’ve learned a great deal from my conversations with him and watching his thought process. I would also like to thank my family. My father has always been there when I needed someone to discuss an idea with, and has given me many helpful suggestions over the years. I’ve had a great time learning from him throughout my entire life. My mother deserves thanks for all the hard work she has put in helping me with various annoying and unpleasant tasks the past several years. I had a great time living with my brother Will the past year. It was fun having the chance to hang out with him again. I’d also like to thank my brothe