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.

Changes in the Ecology and Abundance of Smallmouth Bass in Lake Ontario: 1958-2014

Understanding the reasons for long-term population change in a species requires an evaluation of ecological variables that may account for the observed dynamics. In this study, long-term changes in indices of Smallmouth Bass condition and population levels were examined for eastern Lake Ontario and the Bay of Quinte. Smallmouth Bass are an extremely important recreational fish species native to Lake Ontario. They have experienced numerous changes in their environment through direct human impacts, climate change, predation, and habitat sharing with non-native species. Smallmouth Bass have experienced an increase in body length and weight likely due to a diet shift from crayfish to predominantly Round Gobies which has allowed them to increase their growth rate. According to existing assessment data however, this increase in body size has not been associated with an increase in abundance. Long-term data from gill net sampling shows that Smallmouth Bass populations have been declining since the late 1980s with no indication of recovery. This could be due to a variety of factors, but it is most likely due to a change in the selectivity of gill nets because of the change in body size as well as a habitat shift away from gill net sampling sites. Adjusting for gill net selectivity has revealed that sub-adult bass abundance is currently greater than it was historically, and that very large bass are likely not being retained within the gill nets that are currently used. The use of a long-term data set in this study has led to a much better understanding of Smallmouth Bass abundance and ecology.