Derivation of Kcat or Turnover Number

The highest rate obtainable is when the enzyme is saturated with substrate, i.e. at high [S]. Then [ES] = []

for this reason, , which is also called when the enzyme is saturated, is referred to as the turnover number, and

Equation 1

When [S] is low, [E] []

Therefore, at low [S], from Equation 1 and the Michaelis-Menten equation, since

Consider the situation where we have an enzyme and two different substrates A and B. If the concentration of the enzyme is the same in both reactions it can be shown that

Therefore, / is a measure of how rapidly an enzyme works at low [S] and is referred to as the specificity constant. It is a means of comparing substrates, i.e. studying the specificity of and enzyme. For chymotrypsin with N-acetyl amino acid methyl esters as the substrates the values for Gly and Phe vary by about 1 million, explaining the specificity of this enzyme. Note that the upper limit of / is about , which is enzymatic perfection. Substrate cannot diffuse to the enzyme any faster.

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