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The stochastic kinetics of BRN are described by a chemical master equation(CME) and the underlying laws of mass action. The CME must be usually solvednumerically by generating enough traces of random reaction events. Theresulting event-time series can be evaluated statistically to identify, forexample, the reaction clusters, rare reaction events, and the periods ofincreased or steady-state activity. The aim of this paper is to newly exploitthe empirical statistics of the reaction events in order to obtain causally andanti-causally related sub-sequences of reactions. This allows discovering someof the causal dynamics of the reaction networks as well as uncovering theirmore deterministic behaviors. In particular, it is proposed that the reactionsub-sequences that are conditionally nearly certain or nearly uncertain can beconsidered as being causally related or unrelated, respectively. Moreover,since time-ordering of reactions is locally irrelevant, the reactionsub-sequences can be transformed into the reaction event sets or multi-sets.The appropriately defined distance metrics can be then used to defineequivalences between the reaction sub-sequences. The proposed framework foridentifying causally associated reaction sub-sequences has been implemented asa computationally efficient query-response mechanism. The framework wasevaluated assuming five selected models of genetic reaction networks in sevendefined numerical experiments. The models were simulated in BioNetGen usingNFsim, which had to be modified to allow recording of the traces of reactionevents. The generated event time-series were analyzed by Python and Matlabscripts. The whole process of data generation, analysis and visualization hasbeen nearly fully automated using shell scripts.

A Query-Response Causal Analysis of Reaction Events in Biochemical Reaction Networks