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the maximum rate (Fig. 15.3) and has units of molarity. Values ofKmare usually in

the range 10^2 to 10^5 M and are important because they enable the concentration of

substraterequiredtosaturatealloftheactivesitesoftheenzymeinanenzymeassayto

be calculated. When [S] »Km,equation 15.1 reduces to 0 Vmax,butasimplecalculation

reveals that when [S]¼ 10 Vmax,n 0 is only 90%Vmaxand that when [S]¼ 100 Km,

 0 ¼99%Vmax. Appreciation of this relationship is vital in enzyme assays.

As previously stated, enzyme-catalysed reactions proceed via the formation of an

enzyme substrate complex in which the substrate (S) is non-covalently bound to the

active site of the enzyme (E). The formation of this complex for the majority of

enzymes is rapid and reversible and is characterised by the dissociation constant,Ks,

of the complex:

EþS^ !

kþ 1

k 1

ES

wherekþ 1 andk 1 are the rate constants for the forward and reverse reactions.

At equilibrium, the rates of the forward and reverse reactions are equal and the Law of

Mass Action can be applied to the reversible process:

kþ 1 ½EŠ½SŠ¼k 1 ½ESŠð 15 : 2 Þ

hence:

Ks¼

½EŠ½SŠ

½ESŠ

¼

k 1

kþ 1

¼

1

Ka

whereKais theassociation(oraffinity)constant.

Initial rate,

v^0

Km Substrate concentration, [S]

Vmax

Vmax

Vmax

1 unit of enzyme

2 units of enzyme

4 units of enzyme

Fig. 15.3The effect of substrate concentration on the initial rate of an enzyme-catalysed reaction in the

presence of three different concentrations of enzyme. Doubling the enzyme concentration doubles

the maximum initial rate,Vmax, but has no effect onKm.

586 Enzymes