Refinement of biomodels using Petri nets

Systems Biology is the multidisciplinary field concerned with the research of large, complex biological systems from a holistic perspective. The end goal is to understand how such systems function as a whole rather than as the sum of their composing parts. Tools and methods from disciplines such as Biology, Biochemistry, Molecular Biology, Bioinformatics, Mathematics, Physics, Systems Theory and Computer Science are used to this end. Modern Biology generates huge amounts of data, requiring computational tools and computational power to store, manage and analyze the generated data. Moreover, isolated models are not enough anymore in the quest for building comprehensive models of cells, tissues, organs or organisms. In turn, biomodeling efforts are beginning to focus on integrating existing models into larger systems. As such, efforts to reuse ready-fit models have intensified. The modeling focus is shifting from building models from scratch to refining existing models, and integrating models for the construction of large-scale models that comprise several interacting subunits that function at different resolutions. The work presented in this thesis deals with an important part of the effort of using existing models, namely model refinement. This is the process of adding details to a model in a systematic way such that the new model is more specialized and preserves the properties of the initial model. The stepwise construction (from lower to higher levels of detail) of models is a good strategy for building large models. Moreover, as a by-product it generates several models at different levels of resolution, which could consequently be organized in a comprehensive multilevel model of a system. Current modeling efforts deal with the seamless transition between different levels of detail of a model. We are concerned in this thesis with modeling methodologies for the refinement of reaction-based biomodels. As a foundation, we consider biological systems that can be modeled as sets of reactions. Namely, a number of entities (species) interact with each other and these interactions describe the behavior of the system. Reaction-based systems can be modeled and simulated using many different frameworks and techniques. We present briefly several such frameworks. We then focus on the notion of model refinement, both from a qualitative and from a quantitative point of view. We present our idea that refinements of species can propagate to refinements of their interactions when the internal composition of the species is known. We exemplify the refinement concepts on a case study of the eukaryotic heat shock response. The core of the thesis details our original contributions to refining biomodels in the framework of Petri nets. We compare two existing classes of Petri nets (standard Petri nets and colored Petri nets) with respect to their capabilities of refining models in a compact way. We show that colored Petri nets allow for compact representations of refined models, and that refinements can be modeled using different strategies. Moreover, we prove that a full structural refinement of a model can be implemented via a type refinement of a colored Petri net representation of that model. Finally, we propose a new class of Petri nets for model refinement (composition colored Petri nets), with great potential for automatizing the refinement process. The construction builds on the assumption that species are either atomic or complex (composed from several atomic species), and the internal composition of the complex species is known. This internal structure of species is explicitly modeled in the network, which makes later refinements of atomic species automatically reflect in the complex species. We conclude with a discussion on possible extensions of our formalism and an overview of the current challenges of Systems Biology