  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.
