A semi-quantitative equivalence for abstracting from fast reactions

TL;DR

This paper introduces a semi-quantitative bisimilarity for stochastic process algebra in biological modeling, enabling abstraction from fast reactions under the Quasi-Steady-State Assumption, with proven congruence properties.

Contribution

It defines a novel fast-slow bisimilarity for Bio-PEPA that captures fast reaction abstraction and establishes conditions for congruence, extending the modeling toolkit for biological systems.

Findings

Fast-slow bisimilarity is congruent under specific conditions.

The equivalence simplifies biological models by ignoring fast reactions.

Illustrated with models of competitive inhibition.

Abstract

Semantic equivalences are used in process algebra to capture the notion of similar behaviour, and this paper proposes a semi-quantitative equivalence for a stochastic process algebra developed for biological modelling. We consider abstracting away from fast reactions as suggested by the Quasi-Steady-State Assumption. We define a fast-slow bisimilarity based on this idea. We also show congruence under an appropriate condition for the cooperation operator of Bio-PEPA. The condition requires that there is no synchronisation over fast actions, and this distinguishes fast-slow bisimilarity from weak bisimilarity. We also show congruence for an operator which extends the reactions available for a species. We characterise models for which it is only necessary to consider the matching of slow transitions and we illustrate the equivalence on two models of competitive inhibition.