Abstract
As mathematical models and computational tools become more sophisticated and powerful to accurately depict system dynamics, numerical methods that were previously considered computationally impractical started being utilized for large-scale simulations. Methods that characterize a rare event in biochemical systems are part of such phenomenon, as many of them are computationally expensive and require high-performance computing. In this paper, we introduce an enhanced version of the doubly weighted stochastic simulation algorithm (dwSSA) (Daigle et al. in J Chem Phys 134:044110, 2011), called dwSSA^{++}, that significantly improves the speed of convergence to the rare event of interest when the conventional multilevel cross-entropy method in dwSSA is either unable to converge or converges very slowly. This achievement is enabled by a novel polynomial leaping method that uses past data to detect slow convergence and attempts to push the system toward the rare event. We demonstrate the performance of dwSSA^{++} on two systems—a susceptible–infectious–recovered–susceptible disease dynamics model and a yeast polarization model—and compare its computational efficiency to that of dwSSA.
Highlights
When Gillespie (1976, 1977) introduced the stochastic simulation algorithm (SSA), its use was deemed purely academic as computers were not powerful enough to support SSA simulations except for toy models
In order to minimize the difference in results due to stochasticity, same random number seeds were used for the corresponding doubly weighted stochastic simulation algorithm (dwSSA) and dwSSA++ simulations
This paper describes dwSSA++ and its novel contribution in improving automatic computation of biasing parameters required to characterize a rare event probability
Summary
When Gillespie (1976, 1977) introduced the stochastic simulation algorithm (SSA), its use was deemed purely academic as computers were not powerful enough to support SSA simulations except for toy models. SSA is an exact numerical method in that its trajectories can be used to construct the chemical master equation (CME) as the number of simulations reach infinity. Roh simulated explicitly (reaction time and index) until the final simulation time is reached for each trajectory. This can be computationally infeasible for a large system or even for a small system with many reaction firings. As computer processors became more affordable and powerful, increasing number of researchers started using the SSA to model a biological system and gained useful insight from numerical simulations. The dramatic increase in the usage can be seen by the number of citations SSA received; Gillespie’s paper (1977) was cited less than 100 times annually until 2003, and the number of annual citations spiked up to over 500 after 2007 (https://scholar.google.com/citations?user=QwXwK6UAAAAJ#)
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