  "Leaping" methods show great promise for significantly accelerating
stochastic simulations of complex biochemical reaction networks. However, few
practical applications of leaping have appeared in the literature to date.
Here, we address this issue using the "partitioned leaping algorithm" (PLA)
[L.A. Harris and P. Clancy, J. Chem. Phys. 125, 144107 (2006)], a
recently-introduced multiscale leaping approach. We use the PLA to investigate
stochastic effects in two model biochemical reaction networks. The networks
that we consider are simple enough so as to be accessible to our intuition but
sufficiently complex so as to be generally representative of real biological
systems. We demonstrate how the PLA allows us to quantify subtle effects of
stochasticity in these systems that would be difficult to ascertain otherwise
as well as not-so-subtle behaviors that would strain commonly-used "exact"
stochastic methods. We also illustrate bottlenecks that can hinder the approach
and exemplify and discuss possible strategies for overcoming them. Overall, our
aim is to aid and motivate future applications of leaping by providing stark
illustrations of the benefits of the method while at the same time elucidating
obstacles that are often encountered in practice.
