Quasi-steady-state approximation in the mathematical modeling of biochemical reaction networks

Abstract

In the mathematical modeling of biochemical reaction networks the application of the quasi-steady-state approximation permits a reduction of the number of dynamic variables as well as of the number of parameters. It is shown that the quasi-steady-state approximation represents the zeroth approximate solution of the perturbation problem dX dt = RV(X)+ 1 μ S W ̃ (X) with μ ⪡ 1. The perturbation equation develops by subdivision of the flux rates of the model into the rates w i(X) = (1/μ) w ̃ i(X) of fast reactions and the rates v j ( X) of slow reactions. The matrix C=( R⋮ S) denotes the stochiometric matrix of the reaction network. The analysis of this perturbation problem provides conditions for the applicability of the quasi-steady-state approximation in a given network. The paper presents a practical guide for the construction of the approximate solution.