Layered decomposition for the model order reduction of timescale separated biochemical reaction networks

Abstract

Biochemical reaction networks tend to exhibit behaviour on more than one timescale and they are inevitably modelled by stiff systems of ordinary differential equations. Singular perturbation is a well-established method for approximating stiff systems at a given timescale. Standard applications of singular perturbation partition the state variable into fast and slow modules and assume a quasi-steady state behaviour in the fast module. In biochemical reaction networks, many reactants may take part in both fast and slow reactions; it is not necessarily the case that the reactants themselves are fast or slow. Transformations of the state space are often required in order to create fast and slow modules, which thus no longer model the original species concentrations. This paper introduces a layered decomposition, which is a natural choice when reaction speeds are separated in scale. The new framework ensures that model reduction can be carried out without seeking state space transformations, and that the effect of the fast dynamics on the slow timescale can be described directly in terms of the original species.