(525d) An Accurate Multiscale Simulation Algorithm for Spatially Inhomogeneous Chemical Reaction Systems

There is a great need for accurate and efficient computational approaches that can account for the discrete and stochastic nature of chemical interactions in spatially inhomogeneous systems. 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. Towards this end, we present a spatial version of the "partitioned leaping algorithm" (PLA), a multiscale accelerated-stochastic simulation approach that seamlessly incorporates exact stochastic, τ-leaping and continuum methods into a single algorithmic framework. In developing the approach, we pay special attention to the details of the implementation within the context of a discretized grid, particularly as it pertains to the time step calculation procedure. We discuss conceptual errors that have been made in previous implementations of spatial τ-leaping and illustrate the manifestation of these errors through numerical examples. We also study the high computational cost associated with including an exact-stochastic description in the multiscale framework and consider the effects on the accuracy of the method if it is excluded. Finally, we discuss the fundamental difficulties associated with incorporating efficient exact-stochastic techniques, such as the next-subvolume method, into a spatial leaping approach and suggest possible strategies for overcoming them.