  We consider stochastic descriptions of chemical reaction networks in which
there are both fast and slow reactions, and for which the time scales are
widely separated. We develop a computational algorithm that produces the
generator of the full chemical master equation for arbitrary systems, and show
how to obtain a reduced equation that governs the evolution on the slow time
scale. This is done by applying a state space decomposition to the full
equation that leads to the reduced dynamics in terms of certain projections and
the invariant distributions of the fast system. The rates or propensities of
the reduced system are shown to be the rates of the slow reactions conditioned
on the expectations of fast steps. We also show that the generator of the
reduced system is a Markov generator, and we present an efficient stochastic
simulation algorithm for the slow time scale dynamics. We illustrate the
numerical accuracy of the approximation by simulating several examples.
Graph-theoretic techniques are used throughout to describe the structure of the
reaction network and the state-space transitions accessible under the dynamics.

Dynamical Systems