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Description
Gene regulatory networks capture interaction patterns and mechanics of how gene expression is regulated based on signals and components that are internal or external to the organism. Together with metabolic networks and signal networks, they provide a functional description of cell processes. There is a need to model and analyze such processes in an integrated fashion. In particular, the long-term steady-state analysis of such an integrated network provides insight into the system and its properties. This thesis presents an extension to the pseudo-stoichiometric matrix framework for the steady-state analysis of gene regulatory networks. The focus here lies in the ability to integrate Boolean networks into the matrix approach and to use this generalized matrix approach to calculate the steady states. Hereby, Boolean rules can be transformed into reactions and metabolites. A modified pathway analysis algorithm determines steady states for the given Boolean network. By adding further parameters, the dynamics can be analyzed as well. Minimal bistable chemical networks can be used to express regulatory rules. This concept gives the ability to add dynamics to the model and perform a steady-state analysis as well. Steady states for the pseudo-stoichiometric matrix can be calculated by Extreme Pathway Analysis (EPA). This is demonstrated in a commonly used signal network given as Boolean rules. This work shows how different steady state problems can be formulated in a stoichiometric approach without losing the ability to determine relevant steady states. A future outlook shows how dynamic parts can be taken into account in a more detailed model and how the long-term behavior can be analyzed through simulations.
