  There is a great need for accurate and efficient computational approaches
that can account for both the discrete and stochastic nature of chemical
interactions as well as spatial inhomogeneities and diffusion. This is
particularly true in biology and nanoscale materials science, where the common
assumptions of deterministic dynamics and well-mixed reaction volumes often
break down. In this article, we present a spatial version of the
partitioned-leaping algorithm (PLA), a multiscale accelerated-stochastic
simulation approach built upon the tau-leaping framework of Gillespie. We pay
special attention to the details of the implementation, particularly as it
pertains to the time step calculation procedure. We point out conceptual errors
that have been made in this regard in prior implementations of spatial
tau-leaping and illustrate the manifestation of these errors through practical
examples. Finally, we discuss the fundamental difficulties associated with
incorporating efficient exact-stochastic techniques, such as the next-subvolume
method, into a spatial-leaping framework and suggest possible solutions.
