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

Efficient stochastic sampling of first-passage times with applications to self-assembly simulations