  We introduce expandable partial propensity direct method (EPDM) - a new exact
stochastic simulation algorithm suitable for systems involving many interacting
molecular species. The algorithm is especially efficient for sparsely populated
systems, where the number of species that may potentially be generated is much
greater than the number of species actually present in the system at any given
time. The number of operations per reaction scales linearly with the number of
species, but only those which have one or more molecules. To achieve this kind
of performance we are employing a data structure which allows to add and remove
species and their interactions on the fly. When a new specie is added, its
interactions with every other specie are generated dynamically by a set of
user-defined rules. By removing the records involving the species with zero
molecules, we keep the number of species as low as possible. This enables
simulations of systems for which listing all species is not practical. The
algorithm is based on partial propensities direct method (PDM) by Ramaswamy et
al. for sampling trajectories of the chemical master equation.
