  We introduce an alternative formulation of the exact stochastic simulation
algorithm (SSA) for sampling trajectories of the chemical master equation for a
well-stirred system of coupled chemical reactions. Our formulation is based on
factored-out, partial reaction propensities. This novel exact SSA, called the
partial propensity direct method (PDM), is highly efficient and has a
computational cost that scales at most linearly with the number of chemical
species, irrespective of the degree of coupling of the reaction network. In
addition, we propose a sorting variant, SPDM, which is especially efficient for
multiscale reaction networks.
