  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.

Quantitative Methods