Subgraph Epimorphisms: Theory and Application to Model Reductions in Systems Biology

Abstract : This thesis develops a framework of graph morphisms and applies it to model reduction in systems biology. We are interested in the following problem: the collection of systems biology models is growing, but there is no formal relation between models in this collection. Thus, the task of organizing the existing models, essential for model refinement and coupling, is left to the modeler. In mathematical biology, model reduction techniques have been studied for a long time, however these techniques are far too restrictive to be applied on the scales required by systems biology. We propose a model reduction framework based solely on graphs, allowing to organize models in a partial order. Systems biology models will be represented by their reaction graphs. To capture the process of reduction itself, we study a particular kind of graph morphisms: subgraph epimorphisms, which allow both vertex merging and deletion. We first analyze the partial order emerging from the merge/delete graph operations, then develop tools to solve computational problems raised by this framework, and finally show both the computational feasibility of the approach and the accuracy of the reaction graphs/subgraph epimorphisms framework on a large repository of systems biology models.
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Submitted on : Tuesday, December 1, 2015 - 3:24:01 PM
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Steven Gay. Subgraph Epimorphisms: Theory and Application to Model Reductions in Systems Biology. Programming Languages [cs.PL]. Université Paris Diderot, 2015. English. ⟨tel-01236291⟩

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