Semi-Quantitative Abstraction and Analysis of Chemical Reaction Networks

Abstract

Analysis of large continuous-time stochastic systems is a computationally intensive task. In this work we focus on population models arising from chemical reaction networks (CRNs), which play a fundamental role in analysis and design of biochemical systems. Many relevant CRNs are particularly challenging for existing techniques due to complex dynamics including stochasticity, stiffness or multimodal population distributions. We propose a novel approach allowing not only to predict, but also to explain both the transient and steady-state behaviour. It focuses on qualitative description of the behaviour and aims at quantitative precision only in orders of magnitude. Firstly, we abstract the CRN into a compact model preserving rough timing information, distinguishing only signifcinatly different populations, but capturing relevant sequences of behaviour. Secondly, we approximately analyse the most probable temporal behaviours of the model through most probable transitions. As demonstrated on complex CRNs from literature, our approach reproduces the known results, but in contrast to the state-of-the-art methods, it runs with virtually no computational cost and thus offers unprecedented~scalability.