Abstraction-based segmental simulation of reaction networks using adaptive memoization

Background

Stochastic models are commonly employed in the system and synthetic biology to
study the effects of stochastic fluctuations emanating from reactions involving
species with low copy-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-based
abstraction and combines previously generated parts of simulations,
called 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.