Abstract
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 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 the analysis of the eigenvalues of continuous time Markov models that define the behavior of the SSA. We show how each can be applied to accelerate sampling within known Markov models or to subgraphs discovered automatically during execution. We demonstrate these methods for two applications of sampling in stiff SSAs that are important for modeling self-assembly reactions: sampling breakage times for multiply connected bond networks and sampling assembly times for multisubunit nucleation reactions. We show theoretically and empirically that our eigenvalue methods provide substantially reduced sampling times for a large class of models used in simulating self-assembly. These techniques are also likely to have broader use in accelerating SSA models so as to apply them to systems and parameter ranges that are currently computationally intractable.
Highlights
Stochastic simulation methods have become increasingly widespread as a means of simulating and analyzing biochemical reaction kinetics[1]
We have investigated the problem of efficiently simulating stochastic reaction models and introduced two methods for accelerating sampling on problems characterized by multiple time scales
We have applied these methods in the present work to two special cases of these models that are important to simulations of molecular self-assembly: sampling times to break multiply-connected bond networks and simulating growth in nucleation-limited assembly systems
Summary
Stochastic simulation methods have become increasingly widespread as a means of simulating and analyzing biochemical reaction kinetics[1]. Nucleation events can be orders of magnitude slower than individual binding reactions In these stiff systems, an SSA model can become “trapped” for many steps in a small subset of the state space, resulting in negligible simulation progress for long periods of time. To overcome the presence of traps or landscape irregularity, we propose two non-local simulation algorithms that rely on the spectral decomposition of the Kolmogorov matrix (for a CTMM) or the transition matrix (for the Embedded Markov Chain (EMC)) These eigenvalues and their associated eigenvectors describe global modes of relaxation of the full graph or any of its sub-graphs. This technique allows efficient implementation of spectral methods for large state spaces by isolating regions repeatedly visited by a given random trajectory and using spectral sampling to escape any such subgraph.
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