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a substrate to product as a function of the reaction coordinate that measures the time-

related progress of the reaction. The number ofenergy barriersintheprofilewilldepend

upon the number of kineticallyimportant stages in the reactions. For the majority of

enzyme-catalysed reactions the major energy barrier, which dictates the activation

energy for the overall reaction and hence its rate, is the formation of one or more

intermediates in which covalent bonds are being made and broken and which cannot be

isolated. However, for a few enzymes, notably ATP synthase, the energy-requiring step is

the initial binding of the substrate(s) and the subsequent release of the product(s).

The thermodynamic constantsG^0 ,H^0 andS^0 for the binding of substrate to

the enzyme can be calculated from a knowledge of the binding constant,Ka(¼1/Ks).

G^0 can be obtained from the equation:

G^0 ¼RTlnKa ð 15 : 15 Þ

IfKais measured at two or more temperatures, a plot of lnKaversus 1/T, known as the

van’t Hoff plot,will give a straight line slopeH^0 /Rwith intercept on theyaxis of

S^0 /R, the relevant equation being:

lnKa¼

S^0

R



H^0

RT

ð 15 : 16 Þ

A small number of enzymes appear to operate by a mechanism that does not rely on

the formation of a transition state. Studies with the enzyme methylamine dehydro-

genase, which promotes the cleavage of a C–H bond, have shown that the reaction

is independent of temperature and hence is inconsistent with transition state theory.

Energy

Transition

state

Transition

state

E + S

ES

EP

Eact

Eact

(non-enzymatic)

(enzymatic)

Transition state

–E + P

Reaction coordinate

ΔG^0

Fig. 15.7Energy profile of a simple enzyme-catalysed reaction. The formation of ES and EP and the subsequent

release of EþP proceeds via several transition states. The activation energy for the overall reaction is

dictated by the initial free energy of E and S and the highest energy transition state. The non-enzyme-catalysed

reaction proceeds via a higher energy transition state and hence the reaction has a higher activation energy

than the enzyme-catalysed reaction.

597 15.2 Enzyme steady-state kinetics