Petri Net Siphon Analysis and Network Centrality Measures for Identifying Combination Therapies in Signaling Pathways

Aberrant behavior of biological signaling pathways has been implicated in diseases such as cancers. Therapies have been developed to target proteins in these networks in the hope of curing the illness or bringing about remission. However, identifying targets for drug inhibition that exhibit good therapeutic index has proven to be challenging since signaling pathways have a large number of components and many interconnections such as feedback, crosstalk, and divergence. Unfortunately, some characteristics of these pathways such as redundancy, feedback, and drug resistance reduce the efficacy of single drug target therapy and necessitate the employment of more than one drug to target multiple nodes in the system. However, choosing multiple targets with high therapeutic index poses more challenges since the combinatorial search space could be huge. To cope with the complexity of these systems, computational tools such as ordinary differential equations have been used to successfully model some of these pathways. Regrettably, for building these models, experimentally-measured initial concentrations of the components and rates of reactions are needed which are difficult to obtain, and in very large networks, they may not be available at the moment. Fortunately, there exist other modeling tools, though not as powerful as ordinary differential equations, which do not need the rates and initial conditions to model signaling pathways. Petri net and graph theory are among these tools. In this thesis, we introduce a methodology based on Petri net siphon analysis and graph network centrality measures for identifying prospective targets for single and multiple drug therapies. In this methodology, first, potential targets are identified in the Petri net model of a signaling pathway using siphon analysis. Then, the graph-theoretic centrality measures are employed to prioritize the candidate targets. Also, an algorithm is developed to check whether the candidate targets are able to disable the intended outputs in the graph model of the system or not. We implement structural and dynamical models of ErbB1-Ras-MAPK pathways and use them to assess and evaluate this methodology. The identified drug-targets, single and multiple, correspond to clinically relevant drugs. Overall, the results suggest that this methodology, using siphons and centrality measures, shows promise in identifying and ranking drugs. Since this methodology only uses the structural information of the signaling pathways and does not need initial conditions and dynamical rates, it can be utilized in larger networks.

Novel Formulation and Efficient Solution Strategy for Strategic Optimization of an Industrial Chemical Supply Chain Under Demand Uncertainty

This paper is concerned with strategic optimization of a typical industrial chemical supply chain, which involves a material purchase and transportation network, several manufacturing plants with on-site material and product inventories, a product transportation network and several regional markets. In order to address large uncertainties in customer demands at the different regional markets, a novel robust scenario formulation, which has been developed by the authors recently, is tailored and applied for the strategic optimization. Case study results show that the robust scenario formulation works well for this real industrial supply chain system, and it outperforms the deterministic formulation and the classical scenario-based stochastic programming formulation by generating better expected economic performance and solutions that are guaranteed to be feasible for all uncertainty realizations. The robust scenario problem exhibits a decomposable structure that can be taken advantage of by Benders decomposition for efficient solution, so the application of Benders decomposition to the solution of the strategic optimization is also discussed. The case study results show that Benders decomposition can reduce the solution time by almost an order of magnitude when the number of scenarios in the problem is large.

ENVIRONMENTAL INFLUENCES AND EPIGENETIC MECHANISMS IN RISK FOR DEPRESSION

Genetic and environmental factors interact to influence vulnerability for internalizing psychopathology, including Major Depressive Disorder (MDD). The mechanisms that account for how environmental stress can alter biological systems are not yet well understood yet are critical to develop more accurate models of vulnerability and targeted interventions. Epigenetic influences, and more specifically, DNA methylation, may provide a mechanism by which stress could program gene expression, thereby altering key systems implicated in depression, such as frontal-limbic circuitry and its critical role in emotion regulation. This thesis investigated the role of environmental factors from infancy and throughout the lifespan affecting the serotonergic (5-HT) system in the vulnerability to and treatment of depression and anxiety and potential underlying DNA methylation processes. First, we investigated the contributions of additive genetic vs. environmental factors on an early trait phenotype for depression (negative emotionality) in infants and their stability over time in the first 2 years of life. We provided evidence of the substantial contributions of both genetic and shared environmental factors to this trait, as well as genetically- and environmentally- mediated stability and innovation. Second, we studied how childhood environmental stress is associated with peripheral DNA methylation of the serotonin transporter gene, SLC6A4, as well as long-term trajectories of internalizing behaviours. There was a relationship between childhood psychosocial adversity and SLC6A4 methylation in males, as well as between SLC6A4 methylation and internalizing trajectory in both sexes. Third, we investigated changes in emotion processing and epigenetic modification of the SLC6A4 gene in depressed adolescents before and after Mindfulness-Based Cognitive Therapy (MBCT). The alterations from pre- to post-treatment in connectivity between the ACC and other network regions and SLC6A4 methylation suggested that MBCT may work to optimize the connectivity of brain networks involved in cognitive control of emotion as well as also normalize the relationship between SLC6A4 methylation and activation patterns in frontal-limbic circuitry. Our results from these three studies strengthen the theory that environmental influences are critical in establishing early vulnerability factors for MDD, driving epigenetic processes, and altering brain processes as an individual undergoes treatment, or experiences relapse.