Dimension Reduction of Large AND-NOT Network Models

Boolean networks have been used successfully in modeling biological networks and provide a good framework for theoretical analysis. However, the analysis of large networks is not trivial. In order to simplify the analysis of such networks, several model reduction algorithms have been proposed; however, it is not clear if such algorithms scale well with respect to the number of nodes. The goal of this paper is to propose and implement an algorithm for the reduction of AND-NOT network models for the purpose of steady state computation. Our method of network reduction is the use of "steady state approximations" that do not change the number of steady states. Our algorithm is designed to work at the wiring diagram level without the need to evaluate or simplify Boolean functions. Also, our implementation of the algorithm takes advantage of the sparsity typical of discrete models of biological systems. The main features of our algorithm are that it works at the wiring diagram level, it runs in polynomial time, and it preserves the number of steady states. We used our results to study AND-NOT network models of gene networks and showed that our algorithm greatly simplifies steady state analysis. Furthermore, our algorithm can handle sparse AND-NOT networks with up to 1000000 nodes

Unraveling the Complex Regulatory Relationships between Metabolism and Signal Transduction in Breast Cancer.

Almost all cancer cells exhibit a metabolic phenotype characterized by high rates of glucose uptake known as the Warburg effect. Metabolic changes that are representative of distinct stages of breast cancer may suggest dependence by cancer cells on certain metabolic processes that are not relevant to normal cells. Importantly, these differences may help identify therapeutic targets that are non-lethal to normal cells. In this thesis, I present a set of models and methodologies developed using both experimental and theoretical approaches to investigate the complex intracellular signaling and metabolic networks associated with distinct stages of breast cancer. First, a detailed literature search was used to construct a logic network model of the PI3K signaling pathway, which is known to play an important regulatory role in glucose metabolism. Comparisons of experimental and simulated results suggest that the network model is well constructed but some regulatory crosstalk with MAPK requires additional refinement. Targeted therapeutic inhibitors frequently induce off-target effects. This thesis also explored the role of retroactivity in generating off-target effects in signaling networks using a computational model. The simulation results suggest that the kinetics governing covalently modified cycles in a cascade are more important for propagating an upstream off-target effect via retroactivity than the binding affinity of a drug to a targeted protein, which is a commonly optimized property in drug development. Finally, 13C tracer experiments were used to infer relative glucose and glutamine derived flux in cell lines representing distinct stages of breast cancer. Steady state metabolic flux analysis was also used to computationally fit the absolute TCA cycle flux in these cell lines. Variations in acetyl-CoA, citrate, pyruvate, and alpha-ketoglutarate flux were identified. A particularly important finding was a large reductive carboxylation flux from alpha-ketoglutarate to citrate in SUM-149 cells. Together, the models presented in this thesis provide a framework for identifying mechanistic drivers of the Warburg effect, which may represent important therapeutic targets for modulating cancer proliferation and progression.PHDBioinformaticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/98062/1/mlwynn_1.pd