The role and consequences of stochastic noise in biological systems continues to be a subject of great interest within theoretical biology and biophysics. In cellular systems, probabilistic interactions between components present in small numbers, such as genes, mRNAs and proteins, result in noisy intracellular dynamics and have been implicated as the source of non-genetic variability in clonal cell populations. From a computational standpoint, such effects can lead to dynamical behaviors that deviate from predictions based on deterministic ordinary differential equations (ODEs). This fact has motivated the use of stochastic simulation methods for studying the dynamics of biochemical reaction networks; Gillespie's "stochastic simulation algorithm" (SSA), in particular, has found widespread use in recent years. Stochastic methods such as the SSA are known to be limited to relatively small system sizes and short time courses, however, thus limiting their utility for studying realistic biological processes. As a result, great effort has been expended recently in developing accelerated stochastic simulation methods, of which so-called "leaping" approaches are particularly popular. Despite their popularity, however, very few biologically relevant applications of leaping have been reported in the literature. This is a curious fact that has yet to be fully explored or explained.

Here, we use our recent contribution, the "partitioned leaping algorithm" (PLA), to investigate stochastic-to-deterministic transitions in two simple, yet biologically relevant, reaction networks. We probe stochastic effects arising in these systems, uncovering subtleties associated with their dynamics and garnering insight as to why leaping methods have not yet found widespread use in computational systems biology. Specifically, reactions with small populations and large rate constants, which are common in biological systems, cause the method to "bog down" by limiting the number of reaction firings possible at each simulation step and minimizing any gains due to leaping. We show how model reduction can be used to help attenuate this problem and demonstrate its use in conjunction with leaping. Overall, our results lend insight into questions regarding the appropriateness of deterministic descriptions for modeling biochemical systems dynamics, the feasibility of using exact-stochastic methods and the role played by model reduction.