  The discrete chemical master equation (dCME) provides a general framework for
studying stochasticity in mesoscopic reaction networks. Since its direct
solution rapidly becomes intractable due to the increasing size of the state
space, truncation of the state space is necessary for solving most dCMEs. It is
therefore important to assess the consequences of state space truncations so
errors can be quantified and minimized. Here we describe a novel method for
state space truncation. By partitioning a reaction network into multiple
molecular equivalence groups (MEG), we truncate the state space by limiting the
total molecular copy numbers in each MEG. We further describe a theoretical
framework for analysis of the truncation error in the steady state probability
landscape using reflecting boundaries. By aggregating the state space based on
the usage of a MEG and constructing an aggregated Markov process, we show that
the truncation error of a MEG can be asymptotically bounded by the probability
of states on the reflecting boundary of the MEG. Furthermore, truncating states
of an arbitrary MEG will not undermine the estimated error of truncating any
other MEGs. We then provide an error estimate for networks with multiple MEGs.
To rapidly determine the appropriate size of an arbitrary MEG, we introduce an
a priori method to estimate the upper bound of its truncation error, which can
be rapidly computed from reaction rates, without costly trial solutions of the
dCME. We show results of applying our methods to four stochastic networks. We
demonstrate how truncation errors and steady state probability landscapes can
be computed using different sizes of the MEG(s) and how the results validate
out theories. Overall, the novel state space truncation and error analysis
methods developed here can be used to ensure accurate direct solutions to the
dCME for a large class of stochastic networks.
