pSpatiocyte: A Parallel Stochastic Method for Particle   Reaction-Diffusion Systems
  Computational systems biology has provided plenty of insights into cell biology. Early on, the focus was on reaction networks between molecular species. Spatial distribution only began to be considered mostly within the last decade. However, calculations were restricted to small systems because of tremendously high computational workloads. To date, application to the cell of typical size with molecular resolution is still far from realization. In this article, we present a new parallel stochastic method for particle reaction-diffusion systems. The program called pSpatiocyte was created bearing in mind reaction networks in biological cells operating in crowded intracellular environments as the primary simulation target. pSpatiocyte employs unique discretization and parallelization algorithms based on a hexagonal close-packed lattice for efficient execution particularly on large distributed memory parallel computers. For two-level parallelization, we introduced isolated subdomain and tri-stage lockstep communication for process-level, and voxel-locking techniques for thread-level. We performed a series of parallel runs on RIKEN's K computer. For a fine lattice that had relatively low occupancy, pSpatiocyte achieved 7686 times speedup with 663552 cores relative to 64 cores from the viewpoint of strong scaling and exhibited 74\% parallel efficiency. As for weak scaling, efficiencies at least 60% were observed up to 663552 cores. In addition to computational performance, diffusion and reaction rates were validated by theory and another well-validated program and had good agreement. Lastly, as a preliminary example of real-world applications, we present a calculation of the MAPK model, a typical reaction network motif in cell signaling pathways. 
Atsushi Miyauchi, Kazunari Iwamoto, Satya Nanda Vel Arjunan, Koichi   Takahashi
q-bio.QM