  At the cellular scale, biochemical processes are governed by random
interactions between reactant molecules with small copy counts, leading to
behavior that is inherently stochastic. Such systems are often modeled as
continuous-time Markov jump processes that can be described by the Chemical
Master Equation. Gillespie's Stochastic Simulation Algorithm (SSA) generates
exact trajectories of these systems. The amount of computational work required
for each step of the original SSA is proportional to the number of reaction
channels, leading to computational complexity that scales linearly as the
problem size increases. The original SSA is therefore inefficient for large
problems, which has prompted the development of several alternative
formulations with improved scaling properties. We describe an exact SSA that
uses a table data structure with event time binning to achieve constant
computational complexity. Optimal algorithm parameters and binning strategies
are discussed. We compare the computational efficiency of the algorithm to
existing methods and demonstrate excellent scaling for large problems. This
method is well suited for generating exact trajectories of large models that
can be described by the Reaction-Diffusion Master Equation arising from
spatially discretized reaction-diffusion processes.
