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whereVmaxis the limiting value of the initial rate when all the active sites are occupied,

Kmis theMichaelis constantand [S] is the substrate concentration. At low substrate

concentrations the occupancy of the active sites on the enzyme molecules is low and the

reaction rate is directly related to the number of sites occupied. This approximates to

first-order kineticsin that the rate is proportional to substrate concentration. At high

substrate concentrations effectively all of the active sites are occupied and the reaction

becomes independent of the substrate concentration since no more enzyme–substrate

complex can be formed andzero-orderorsaturation kineticsare observed. Under these

conditions the reaction rate is only dependent upon the conversion of the enzyme–

substrate complex, ES, to products and the diffusion of the products from the enzyme.

It can be seen from equation 15.1 that when 0 ¼0.5Vmax,Km¼[S]. ThusKmis

numerically equal to the substrate concentration at which the initial rate is one-half of

V 0

Concentration

Time

[P]

V 0

[S]

Fig. 15.2Calculation of initial rate ( 0 ) from the time-dependent change in the concentration of substrate (S)

and product (P) of an enzyme-catalysed reaction.

E

Concentration

t Time

Pre-steady-state

kinetics

Steady-state

kinetics

ES

P

Fig. 15.1Pre-steady-state progress curve for the interaction of an enzyme (E) with its substrate (S).

P, product;t, induction time.

585 15.2 Enzyme steady-state kinetics