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Efficient Bayesian inference in stochastic chemical kinetic models using graphical processing units

A goal of systems biology is to understand the dynamics of intracellular systems. Stochastic chemical kinetic models are often utilized to accurately capture the stochastic nature of these systems due to low numbers of molecules. Collecting system data allows for estimation of stochastic chemical kinetic rate parameters. We describe a well-known, but typically impractical data augmentation Markov chain Monte Carlo algorithm for estimating these parameters. The impracticality is due to the use of rejection sampling for latent trajectories with fixed initial and final endpoints which can have diminutive acceptance probability. We show how graphical processing units can be efficiently utilized for parameter estimation in systems that hitherto were inestimable. For more complex systems, we show the efficiency gain over traditional CPU computing is on the order of 200. Finally, we show a Bayesian analysis of a system based on Michaelis-Menton kinetics.