Parallel implementations of random time algorithm for chemical network stochastic simulations

In this study, we have developed a parallel version of the random time simulation algorithm. Firstly, we gave a rigorous basis of the random time description of the stochastic process of chemical reaction network time evolution. And then we reviewed the random time simulation algorithm and gave the implementations for the parallel version of next reaction random time algorithm. The discussion of computational complexity suggested a factor of $M$ (which is the connection number of the network) folds time consuming reduction for random time simulation algorithm as compared to other exact stochastic simulation algorithms, such as the Gillespie algorithm. For large-scale system, such like the protein-protein interaction network, $M$ is on order of $10^8$. We further demonstrate the power of random time simulation with a GPGPU parallel implementation which achieved roughly 100 folds acceleration as compared with CPU implementations. Therefore the stochastic simulation method we developed here can be of great application value for simulating time evolution process of large-scale network.