Quantifying and comparing causal patterns in stochastic chemical reaction networks

Chemical reaction networks (CRNs) are broadly used to study biological systems via simulations. Gillespie's Stochastic Simulation Algorithm (SSA) is commonly used to perform stochastic simulations with CRNs. Comparing two CRNs in such a setting relies on ad hoc signals obtained from the time series, which the simulations output by discarding causal patterns. To this end, we introduce a general method and its implementation for quantitatively comparing CRNs' dynamic behaviour based on causal dependencies in stochastic simulations. Our method detects causal patterns, as in Petri nets, as resource dependencies between reactions during simulation. We present our method within a conservative extension of SSA that tracks and logs these dependencies in simulations as weighted directed graphs. These graphs provide discrete structures that quantify the CRNs' stochastic dynamic behaviour, complementing the simulations' time series output. We use these graphs to compare the behaviour of any two CRNs for the resource dependencies of their components for any time interval. We measure the similarity of the two CRNs via a distance metric. We illustrate different use cases of our method on models of various molecular mechanisms, including gene regulation and drug metabolism.