Abstract
BackgroundWith recent increase in affordability and accessibility of high-performance computing (HPC), the use of large stochastic models has become increasingly popular for its ability to accurately mimic the behavior of the represented biochemical system. One important application of such models is to predict parameter configurations that yield an event of scientific significance. Due to the high computational requirements of Monte Carlo simulations and dimensionality of parameter space, brute force search is computationally infeasible for most large models.ResultsWe have developed a novel parameter estimation algorithm—Stochastic Parameter Search for Events (SParSE)—that automatically computes parameter configurations for propagating the system to produce an event of interest at a user-specified success rate and error tolerance. Our method is highly automated and parallelizable. In addition, computational complexity does not scale linearly with the number of unknown parameters; all reaction rate parameters are updated concurrently at the end of each iteration in SParSE. We apply SParSE to three systems of increasing complexity: birth-death, reversible isomerization, and Susceptible-Infectious-Recovered-Susceptible (SIRS) disease transmission. Our results demonstrate that SParSE substantially accelerates computation of the parametric solution hyperplane compared to uniform random search. We also show that the novel heuristic for handling over-perturbing parameter sets enables SParSE to compute biasing parameters for a class of rare events that is not amenable to current algorithms that are based on importance sampling.ConclusionsSParSE provides a novel, efficient, event-oriented parameter estimation method for computing parametric configurations that can be readily applied to any stochastic systems obeying chemical master equation (CME). Its usability and utility do not diminish with large systems as the algorithmic complexity for a given system is independent of the number of unknown reaction rate parameters.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-014-0126-y) contains supplementary material, which is available to authorized users.
Highlights
With recent increase in affordability and accessibility of high-performance computing (HPC), the use of large stochastic models has become increasingly popular for its ability to accurately mimic the behavior of the represented biochemical system
The number of samples generated for stochastic simulation algorithm (SSA) simulations with uniform random sampling (URS) equals the total number of Stochastic Parameter Search for Events (SParSE) ensembles computed for a specific simulation scenario, which is the sum of the following quantities: the number of intermediate event computations, the number of estimates computed for each intermediate event, and the number of estimates computed in the exponential interpolation stage
We provide four metrics on performance: the total number of SParSE estimates needed for all 30 initial parameter samples, the number of initial parameters that did not reach the solution hyperplane within 10 iterations of multilevel cross-entropy method or 3 iterations of exponential interpolation, the number of parameter sets that required interpolation in addition to the multilevel cross-entropy method, and the number of successful parameter sets generated by SSA simulations using URS for sampling reaction rates
Summary
With recent increase in affordability and accessibility of high-performance computing (HPC), the use of large stochastic models has become increasingly popular for its ability to accurately mimic the behavior of the represented biochemical system. Recent advancements in cloud computing platforms [2,3] and GPU computing [4,5,6,7] have significantly increased the affordability of computational resources This enables development and use of stochastic algorithms that would have been deemed computationally infeasible in the past. There is still a void in stochastic methods that can answer scientifically interesting questions One such application is in determining reaction rate configurations that yield an event of interest with a set success probability. Methods used to determine these reaction rate parameters include maximum likelihood ratio [8,9,10], gradient decent [11], and moment closure [12] While these algorithms are useful in its own right, scientists are often interested in knowing all parameter combinations that yield a specific event of interest. To authors’ knowledge, no algorithm has been developed in stochastic chemical kinetics setting that computes such parameter combinations
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