Modeling paradigms for Systems Biology plays an important role in investigating the orchestrated function of various biological systems. Additionally, they permit one to study a system in-silico in order to gain mechanistic insights from the trajectories resulting from the model. A common battle to derive an ideal representation for a system process is the descriptive trade-off between the simplicity and accuracy. On one hand, too simple models are prone to reproduce only a priori knowledge. On the other hand, too descriptive models result in behaviors too difficult to parse, or even yet compute. In both cases, gaining new insights is hampered. Thus, it is arguably important in generating tools to measure the impact model selection has in capturing biological phenomena, especially those which can be verified.
In this manuscript, we report a formal framework to automatically derive discrete models of biological systems from stochastic reaction networks. To do so, we utilize techniques offered by Abstract Interpretation to assess the behaviors resulting from logical models, a popular Systems Biology modeling tool. Albeit the success of logical models in recapitulating experimental observations and predicting local system properties, their underlying modeling assumptions are often kept implicit. Instead, the coarse-grain models that we obtain deal with all the behaviors of the stochastic semantics of the initial reaction networks, which is explicitly defined. More precisely, the state space of the reaction network is split into abstract regions and non-deterministic transitions between abstract regions are derived conservatively. Also, we recover the probabilities of transitions from the reference reaction network, so that bounds to the probability of unlikely behaviors can be computed. Importantly, we emphasize how one can use this framework to assess, via the formally derived model, the behaviors of the accompanying logical model of each reaction system. Namely, the work established in this thesis bares an avenue to assess those models which are naturally discrete, while also paving a path towards establishing more efficient model reduction techniques for stochastic, combinatorial systems.
