**A semantic equivalence motivated by time-scale differences**

**V.C. Galpin**

**SICSA Workshop on Multi-scale Modelling for Biological Systems, University of Stirling, July 2010**

**Abstract**

The stochastic process algebra Bio-PEPA, developed specifically for modelling biological systems, permits concentrations to be discretised and molecular counts to be stratified, effectively reducing the number of states and hence offering access to transition-system-based analysis techniques such as those based on continuous-time Markov chains. This allows for the definition of semantic equivalences in the process algebra tradition. For a model where there are time-scale differences, namely that some reactions are fast and others are much slower, the Quasi-Steady-State Assumption allows the modelling of a system at a more abstract level where the concentration of intermediate species are assumed to be constant. In the case of the substrate-enzyme example, this leads to Michaelis-Menten kinetics.

Using this approach as motivation, a new qualitative equivalence called fast-slow bisimilarity will be presented. It has similarities to weak bisimilarity but is not identical. Its use will demonstrated via a competitive inhibition example, together with a proof technique to simplify showing that a relation is a fast-slow bisimulation. Congruence will be shown for the cooperation operator and quantitative aspects will be discussed.

This is joint work with Jane Hillston and Federica Ciocchetta.

Slides - PDF