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

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 solved numerically by generating enough traces of random reaction events. The resulting event-time series can be evaluated statistically to identify, for example, the reaction clusters, rare reaction events, and the periods of increased or steady-state activity. The aim of this paper is to newly exploit the empirical statistics of the reaction events in order to obtain causally and anti-causally related sub-sequences of reactions. This allows discovering some of the causal dynamics of the reaction networks as well as uncovering their more deterministic behaviors. In particular, it is proposed that the reaction sub-sequences that are conditionally nearly certain or nearly uncertain can be considered as being causally related or unrelated, respectively. Moreover, since time-ordering of reactions is locally irrelevant, the reaction sub-sequences can be transformed into the reaction event sets or multi-sets. The appropriately defined distance metrics can be then used to define equivalences between the reaction sub-sequences. The proposed framework for identifying causally associated reaction sub-sequences has been implemented as a computationally efficient query-response mechanism. The framework was evaluated assuming five selected models of genetic reaction networks in seven defined numerical experiments. The models were simulated in BioNetGen using NFsim, which had to be modified to allow recording of the traces of reaction events. The generated event time-series were analyzed by Python and Matlab scripts. The whole process of data generation, analysis and visualization has been nearly fully automated using shell scripts.Comment: 7 figures and supplementary file include