There is a great need for accurate and efficient computational approachesthat can account for both the discrete and stochastic nature of chemicalinteractions as well as spatial inhomogeneities and diffusion. This isparticularly true in biology and nanoscale materials science, where the commonassumptions of deterministic dynamics and well-mixed reaction volumes oftenbreak down. In this article, we present a spatial version of thepartitioned-leaping algorithm (PLA), a multiscale accelerated-stochasticsimulation approach built upon the tau-leaping framework of Gillespie. We payspecial attention to the details of the implementation, particularly as itpertains to the time step calculation procedure. We point out conceptual errorsthat have been made in this regard in prior implementations of spatialtau-leaping and illustrate the manifestation of these errors through practicalexamples. Finally, we discuss the fundamental difficulties associated withincorporating efficient exact-stochastic techniques, such as the next-subvolumemethod, into a spatial-leaping framework and suggest possible solutions.
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