The catalytic efficiency of enzymes
The turnover frequency, or catalytic constant, of an enzyme, kcat, is the number of catalytic cycles (turnovers) performed by the active site in a given interval divided by the duration of the interval. This quantity has units of a first-order rate constant and, in terms of the Michaelis–Menten mechanism, is numerically equivalent to kb, the rate constant for release of product from the enzyme–substrate complex. It follows from the identification of kcat with kb and from eqn 23.20b that
kcat = kb =
The catalytic efficiency, ε (epsilon), of an enzyme is the ratio kcat/KM. The higher the value of ε, the more efficient is the enzyme. We can think of the catalytic activity as the effective rate constant of the enzymatic reaction. From KM = (k′ a + kb)/ka and eqn 23.23, it follows that
ε =
The efficiency reaches its maximum value of ka when kb >> k′ a. Because ka is the rate constant for the formation of a complex from two species that are diffusing freely in solution, the maximum efficiency is related to the maximum rate of diffusion of E and S in solution. This limit (which is discussed further in Section 24.2) leads to rate constants of about 108–109 dm3 mol−1s−1 for molecules as large as enzymes at room temperature. The enzyme catalase has ε = 4.0 × 108 dm3 mol−1s−1 and is said to have attained ‘catalytic perfection’, in the sense that the rate of the reaction it catalyses is controlled only by diffusion: it acts as soon as a substrate makes contact.
Fig. 23.12The Lineweaver–Burk plot of the data for Example 23.3.
