Abstraction-based segmental simulation of reaction networks using adaptive memoization

Abstract Background: Stochastic models are commonly employed in the system and synthetic biology to study the effectsof stochastic fluctuations emanating from reactions involving species with lowcopy-numbers. Many important models feature complex dynamics, involving a state-space explosion, stiffness, and multimodality, that complicate the quantitative analysis needed to understand their stochastic behavior. Direct numerical analysis of such models is typically not feasible and generating many simulation runs that adequately approximate the model’s dynamics may take a prohibitively long time. Results: We propose a new memoization technique that leverages a population\nobreakdash-based abstraction and combines previously generated parts of simulations, called \textit{segments}, to generate new simulations more efficiently while preserving the original system's dynamics and its diversity. Our algorithm adapts online to identify the most important abstract states and thus utilizes the available memory efficiently. Conclusion: We demonstrate that in combination with a novel fully automatic and adaptive hybrid simulation scheme, we can speed up the generation of trajectories significantly and correctly predict the transient behavior of complex stochastic systems.