A Technique to Accelerate Stochastic Markov Chain Monte Carlo Simulations of Calcium-Induced Calcium Release in Cardiac Myocytes

Abstract

Considerable insight into intracellular calcium (Ca) responses has been obtained through the development of whole cell models that are based on molecular mechanisms, e.g., the kinetics of intracellular Ca channels and the feedback of Ca upon these channels. However, a limitation of most deterministic whole cell models to date is the assumption that channels are globally coupled by a “common pool” of [Ca], when in fact channels experience localized “domain” [Ca]. More realistic stochastic Monte Carlo simulations are capable of capturing the influence of local [Ca] on channel gating. Unfortunately, such local control models of calcium-induced calcium release (CICR) are computationally expensive due to the explicit representation of 10,000 to 20,000 release sites, each containing 50 to 300 stochastically gating Ca channels. Here, we present a novel technique called vectorized gating that optimizes the solution time of Markov chain Monte Carlo (MCMC) simulations. Additionally, as this technique leverages vector and matrix algebra it can benefit from the use of the advanced NVIDIA TESLA graphics processing unit (GPU) to further accelerate MCMC models. NVIDIA TESLA cards utilize the parallel nature of the NVIDIA CUDA architecture and are powered by up to 960 parallel processing cores. Benchmark simulations indicate that the GPU-enhanced vectorized gating technique is significantly faster than CPU-only driven calculations. The vectorized gating technique also lends itself to the direct calculation of an adaptive time step which optimizes speed while maintaining numerical stability. These computational enhancements are utilized to facilitate study of sarcoplasmic reticulum (SR) leak from clusters of ryanodine receptor (RyR) Ca channels in cardiac myocytes.