Biochemistry: The Chemical Reactions of Living Cells, Volume 2 - D. Metzler 1980

Enzymes: Protein Catalysts of Cells
Fundamentals of Enzyme Kinetics
Enzyme Turnover Number

When an enzyme catalyzes The formation of product C at the maximum possible rate (V_mах), The conversion of the intermediate ES into products can be described by the equation

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Here, [E]_t is the total Enzyme Concentration, i.e., the sum of the concentrations of free enzyme E and the enzyme-substrate complex ES. Equation (6-6) holds true only under substrate saturation, i.e., under conditions where the Substrate Concentration is high enough to convert virtually all of the enzyme into the intermediate complex ES. The process under consideration is not a first-order reaction, since the depleted ES complex is continuously regenerated from the free enzyme. Nevertheless, the rate constant k can be compared to the first-order rate constants discussed in the previous section, and it serves as a measure of catalytic efficiency. If the concentration [Е]_t is expressed in moles of active sites per liter (i.e., the actual molar concentration of the enzyme multiplied by the number of active sites per enzyme molecule), the constant k is referred to as the turnover number or molecular activity [6].

The turnover number can be measured only for pure Enzymes. Partly for this reason, enzyme activity is more commonly expressed in units of activity per 1 mg of protein (specific activity). One international unit is defined as The amount of enzyme that catalyzes the formation of 1 µmol of product per minute under standard (typically optimal) conditions. Currently, the International Union of Biochemistry [7] recommends a new unit, the katal (kat), which represents the amount of enzyme that catalyzes the conversion of 1 mole of substrate into product per second.

1 kat = 6∙10⁷ international units,

1 international unit = 16.67 nkat (nanokatals).

If the enzyme is pure and saturated with substrate, and the standard conditions for activity assay are met, the turnover number can be calculated using the following relations:

Turnover number = kat/(moles of active sites) =

= (nkat/mg)∙MB∙10^-6/n =

= (international units/mg)∙MB∙10^-3 ∙ 60/n,

where MB is the Molecular Weight of the enzyme, and n is the number of active sites per molecule. Since enzyme activity depends on Temperature and pH, these parameters must be precisely specified.

Turnover numbers for enzymes typically range from ~1 to ~10⁶ s^-1. Trypsin, Chymotrypsin, and many intracellular enzymes have a turnover number of ~ 10² s^-1. Among the most rapid enzymes are catalase, which catalyzes the conversion of H₂O₂ into H₂O and O₂ (Chap. 10, Sec. B, 6), Carbonic anhydrase [8], which catalyzes the equilibrium H₂CO₃⇄H₂O+CO₂, and ∆⁵-3-Ketosteroid isomerase [9]. For these enzymes, maximum turnover numbers reach 2∙10⁵ s^-1. Compare these reaction rates with those observed in typical laboratory organic syntheses. In the latter case, accelerating the process often requires heating the reaction mixture for several hours (k<10^-3 s^-1).

Enzymatic reaction rates frequently exceed non-enzymatic rates by a factor of over 10⁶ under similar temperature and pH conditions. Because the binding of two or more substrates to specific sites (active sites) brings the reactants into close proximity, the enzymatic catalytic process proceeds at a high rate even when the reactants are present in low concentrations in the reaction mixture.