Kinetics of Substrate Binding and Catalysis

If one has a signal for the binding of S to the enzyme and follows the progress of the reaction as it goes to completion, with substrate in excess over enzyme, the time dependence of the reaction can be fit to a single exponential. If we first consider an irreversible binding reaction 

If the concentration of substrate is in sufficient excess over enzyme, then [S] can be assumed to be a constant term giving a pseudo-first-order rate constant defined by the product, k, [S]. Under these pseudo-first-order conditions the rate equation can be integrated to yield the time dependence of the reaction  

the free enzyme disappears and the enzyme-substrate complex appears with a time constant defined by the pseudo-first-order rate constant, kobs = ki [S], obtained by fitting the reaction time course to a single exponential. The half-time for the reaction can be solved according to the time required to get [E] = ifEol, which gives ty2 = In 2/ obs- 

When the concentrations of enzyme and substrate are comparable, the differ- 

We can now consider the fully reversible binding reaction. Under pseudo-first-order conditions with substrate in excess over enzyme, the rate equations can be integrated, yielding a form similar to Eq. (8)  

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