  We apply the "weighted ensemble" (WE) simulation strategy, previously
employed in the context of molecular dynamics simulations, to a series of
systems-biology models that range in complexity from one-dimensional to a
system with 354 species and 3680 reactions. WE is relatively easy to implement,
does not require extensive hand-tuning of parameters, does not depend on the
details of the simulation algorithm, and can facilitate the simulation of
extremely rare events.
  For the coupled stochastic reaction systems we study, WE is able to produce
accurate and efficient approximations of the joint probability distribution for
all chemical species for all time t. WE is also able to efficiently extract
mean first passage times for the systems, via the construction of a
steady-state condition with feedback. In all cases studied here, WE results
agree with independent calculations, but significantly enhance the precision
with which rare or slow processes can be characterized. Speedups over
"brute-force" in sampling rare events via the Gillespie direct Stochastic
Simulation Algorithm range from ~10^12 to ~10^20 for rare states in a
distribution, and ~10^2 to ~10^4 for finding mean first passage times.
