Kinetic and Equilibrium Assays Based on the Effect of Extent of Reaction and the Uncertainty of Rate Parameters

The effect of random variations in rate constants on the precision of analysis by fixed-time kinetic methods has been treated explicitly for the case of the first-order and Mi-chaelis-Menten kinetics. The overall precision improves as time progresses. When the extent of reaction is small, the relative uncertainty in the estimated sample concentration is no better than the relative uncertainty in the rate constant. In the case of enzyme kinetics with substantial zero-order kinetics, the results can be extremely imprecise. The analytical efficiency is estimated for a first-order reaction and shown to be a minimum at kt equal to unity. Kinetic methods of analysis of the type described are less precise but more rapid than comparable equilibrium analysis systems. The approach unifies comparison of kinetic and equilibrium methods of analysis and leads to a method for estimating how closely the physical and chemical factors which affect reaction rates must be controlled.