  Models of reaction chemistry based on the stochastic simulation algorithm
(SSA) have become a crucial tool for simulating complicated biological reaction
networks due to their ability to handle extremely complicated reaction networks
and to represent noise in small-scale chemistry. These methods can, however,
become highly inefficient for stiff reaction systems, those in which different
reaction channels operate on widely varying time scales. In this paper, we
develop two methods for accelerating sampling in SSA models: an exact method
and a scheme allowing for sampling accuracy up to any arbitrary error bound.
Both methods depend on analysis of the eigenvalues of continuous time Markov
model graphs that define the behavior of the SSA. We demonstrate these methods
for the specific application of sampling breakage times for multiply-connected
bond networks, a class of stiff system important to models of self-assembly
processes. We show theoretically and empirically that our eigenvalue methods
provide substantially reduced sampling times for a wide range of network
breakage models. These techniques are also likely to have broad use in
accelerating SSA models so as to apply them to systems and parameter ranges
that are currently computationally intractable.
