VALIDITY OF THE QUASI STEADY STATE ASSUMPTION FOR ENZYME-CATALYSED REACTIONS WITH COMPETITIVE INHIBITION AND SUBSTRATE INPUT

Abstract

Enzyme-catalysed reactions are chemical reactions within cells in which the rate of the reaction is significantly increased through the action of enzymes. They are usually part of large and complex bio¬chemical networks, which form the central processing units of the living cell. Enzymatic reactions often operate on multiple time scales, which can be characterized as being either fast or slow. The quasi steady¬state approximation (QSSA) utilizes time scale separation to pro ject these complex models onto lower-dimensional slow manifolds. In this paper, we investigate the validity of a quasi steady-state assumption for enzyme-catalysed biochemical reactions with competitive inhibition that are subject to a constant substrate input. Necessary and sufficient conditions for the validity of these assumptions were derived and were shown to be dependent, among others, on the substrate input. The validity conditions are numerically verified using the classical Runge- Kutta method.