A hierarchical exact accelerated stochastic simulation algorithm.

A new algorithm, "HiER-leap" (hierarchical exact reaction-leaping), 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 the stochastic simulation algorithm and ER-leap on certain problems. This algorithm offers a potentially important step towards efficient in silico modeling of entire organisms.

An exact accelerated stochastic simulation algorithm.

An exact method for stochastic simulation of chemical reaction networks, which accelerates the stochastic simulation algorithm (SSA), is proposed. The present "ER-leap" algorithm is derived from analytic upper and lower bounds on the multireaction probabilities sampled by SSA, together with rejection sampling and an adaptive multiplicity for reactions. The algorithm is tested on a number of well-quantified reaction networks and is found experimentally to be very accurate on test problems including a chaotic reaction network. At the same time ER-leap offers a substantial speedup over SSA with a simulation time proportional to the 23 power of the number of reaction events in a Galton-Watson process.