Experimental Methods for Complete Kinetic Analysis

Because of the conversion of substrate to product and the reverse, it is obviously not possible to measure directly by equilibrium methods the binding constants for substrate and product. However, the binding constants can be estimated from the ratio of the binding and dissociation rates. The methods, interpretation, and limits of such measurements will be described below. 

The net overall equilibrium constant for the reaction in solution (Kna) and the internal equilibrium constant for reaction at the active site (/fmi) can be measured most easily using radiolabeled substrates. Thus the problem becomes one of separating substrate and product chromatographically and then quantitating the ratio of /fnet = P]/[S] following incubation of the substrate with a trace of enzyme for a time sufficient for the reaction to come to equilibrium. The equilibration time can be estimated from the magnitude of kcJKm in the forward and reverse reactions. If the substrate and product concentrations are below their Km values, then the rate of approach to equilibrium can be approximated by 

The reaction will be 98% complete after six half-lives = In 2/Us- Alter- 

The concentration of enzyme added should be dictated on the one hand by the desire to minimize the time required to reach equilibrium relative to the stability of the reactants and products, and on the other hand by the requirement that the 

The internal equilibrium constant can be measured after finding conditions under which all of the substrate and product will be bound to the enzyme. This is done by working at concentrations of enzyme in 5- or 10-fold excess of the dissociation constants for each substrate. Accordingly, the ratio of [P]/[S] measured will reflect the ratio of [E-P]/[E-S] = Kim- The time required for the reaction to come to equilibrium can be approximated from the relationship /tobs itcai + kai to provide a minimum estimate of the rate of reaction at the active site. Usually the time calculated will be in the millisecond domain, but incubation for S sec is more convenient for manual mixing and usually no side products are formed on this time scale. Although in some cases it may be difficult to obtain concentrations of enzyme in excess of the dissociation constants for the substrates and products, the quantitation of the product/substrate ratio can be done quite accurately thanks to the fundamental property of enzyme catalysis that leads to an internal equilibrium constant close to unity for most enzymes (78-20). 

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