$S$-Leaping: An adaptive, accelerated stochastic simulation algorithm, bridging $\tau$-leaping and $R$-leaping

TL;DR

The paper introduces the S-leaping algorithm, which adaptively combines tau-leaping and R-leaping methods to efficiently simulate stochastic biological systems across various conditions, outperforming both methods in stiff and fast systems.

Contribution

The S-leaping algorithm innovatively merges the strengths of tau-leaping and R-leaping, maintaining efficiency across different system dynamics and improving simulation performance for stiff and fast biological systems.

Findings

S-leaping outperforms tau-leaping and R-leaping in stiff systems.

Maintains efficiency across different system conditions.

Demonstrates high accuracy on biological reaction networks.

Abstract

We propose the $S$-leaping algorithm for the acceleration of Gillespie's stochastic simulation algorithm that combines the advantages of the two main accelerated methods; the $\tau$-leaping and $R$-leaping algorithms. These algorithms are known to be efficient under different conditions; the $\tau$-leaping is efficient for non-stiff systems or systems with partial equilibrium, while the $R$-leaping performs better in stiff system thanks to an efficient sampling procedure. However, even a small change in a system's set up can critically affect the nature of the simulated system and thus reduce the efficiency of an accelerated algorithm. The proposed algorithm combines the efficient time step selection from the $\tau$-leaping with the effective sampling procedure from the $R$-leaping algorithm. The $S$-leaping is shown to maintain its efficiency under different conditions and in the case of large and stiff systems or systems with fast dynamics, the $S$-leaping outperforms both methods. We demonstrate the performance and the accuracy of the $S$-leaping in comparison with the $\tau$-leaping and $R$-leaping on a number of benchmark systems involving biological reaction networks.