Accurate implementation of leaping in space: The spatial partitioned-leaping algorithm

TL;DR

This paper introduces a spatial version of the partitioned-leaping algorithm for stochastic chemical simulations, addressing implementation details, correcting prior errors, and discussing integration challenges with exact methods.

Contribution

It provides a detailed implementation of spatial leaping, identifies conceptual errors in previous methods, and discusses solutions for combining it with exact stochastic techniques.

Findings

Identified and corrected errors in prior spatial tau-leaping implementations.

Presented a detailed procedure for time step calculation in spatial leaping.

Discussed challenges and potential solutions for integrating exact stochastic methods.

Abstract

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.