  A new algorithm, "HiER-leap", is derived which improves on the computational
properties of the ER-leap algorithm for exact accelerated simulation of
stochastic chemical kinetics. Unlike ER-leap, HiER-leap utilizes a hierarchical
or divide-and-conquer organization of reaction channels into tightly coupled
"blocks" and is thereby able to speed up systems with many reaction channels.
Like ER-leap, HiER-leap is based on the use of upper and lower bounds on the
reaction propensities to define a rejection sampling algorithm with inexpensive
early rejection and acceptance steps. But in HiER-leap, large portions of
intra-block sampling may be done in parallel. An accept/reject step is used to
synchronize across blocks. This method scales well when many reaction channels
are present and has desirable asymptotic properties. The algorithm is exact,
parallelizable and achieves a significant speedup over SSA and ER-leap on
certain problems. This algorithm offers a potentially important step towards
efficient in silico modeling of entire organisms.
