Slicing analyses for negative dependencies in reaction systems modeling gene regulatory networks

Reaction Systems (RSs) are a qualitative model inspired by biochemical processes, where the dynamics of complex systems is modelled by a collection of local reactions. Each reaction comprises a set of reactants that triggers a set of products unless hindered by the presence of some inhibitors. The use of inhibitors introduces non-monotonic behaviours that are difficult to analyze. This work focuses on the explainability of local phenomena, like the production of certain products or the reachability of certain attractors, by separating the causes responsible for reaching them from the irrelevant elements of a possibly much larger, global statespace. The main novelty of our approach is the ability to derive sufficient conditions that combine positive dependencies (e.g., requesting the presence of some entities at a certain stage, as already done in the literature) with negative ones (e.g., requesting the absence of some entities). This is achieved by combining and extending previous "static" constructions, like the transformation to Positive RSs and the minimization of RSs with "dynamic" techniques, like the process algebraic evolution of RSs, the slicing of computation and the on-the-fly generation of negative dependencies. We compare many different combinations of the above approaches, discussing their respective benefits and trade-offs in order to identify the most convenient analysis. We demonstrate our methodology on a case study involving T cell protein interactions, showing how it can reveal critical stimulus combinations and pinpoint potential drug targets by explaining phenotype emergence. Our analysis offers new insights and greater explanatory power than existing approaches.