Mathematical modeling of signaling and synthetic networks in single cells /

Recent advances in quantification methods of regulatory and signaling gene networks has lead to an increasing amount of data that has opened the door for improved understanding of cell behavior. The key to that understanding is through the use of mathematical models that can explain existing data as well as help generate new hypotheses through prediction. Refinement of these models with new experimental data creates a feedback loop, where modeling drives experiments while newly generated data constrain the model. Mathematical principles underlying various models can then give us insight into basic biological principles that describe network dynamics. In this thesis, several different applications of mathematical modeling are used to help further our understanding of signaling and synthetic gene networks. First, mathematical modeling is used to explain the underlying mechanisms in coupling of two synthetic gene oscillators to each other as well as to the host environment, which leads to the observed non-trivial biological behavior. Second, focusing on a specific signaling protein network, characterized by transcription factor nuclear factor kappa B (NF-[kappa]B), mathematical modeling is used to understand how the underlying the cell -to-cell variability leads to variability in the response of the system to gradually increasing levels of the network-activating tumor necrosis factor alpha (TNF[alpha]). Finally, information-theoretic approach is applied to three different signaling networks to help gain insight into the role that various sources of noise and various forms of network responses play in signal transductio