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Michaelis-Menten Kinetics

Sometimes the relationship between the rate of an enzyme-catalysed reaction and the substrate concentration takes the form

........ (10)

where V and K _mA are constants at a given temperature and a given enzyme concentration. The reaction is then said to display Michaelis-Menten kinetics. (The term hyperbolic kinetics is also sometimes used because a plot of v against [A] has the form ot a rectangular hyperbola through the origin with asymptotes v = V and [A] = - K _mA. This term, and others that imply the use of particular kinds of plot. should be used with care to avoid ambiguity, as they can be misleading if used out of context.) The constant V is the limiting rate, with the same meaning as in Section 4.1. The second constant K _mA is known as the Michaelis constant for A; the alternative name Michaelis concentration may also be used and has the advantage of emphasizing that the quantity concerned has the dimensions of a concentration and is not, in general, an equilibrium constant. When only one substrate is being considered the qualifier A may be omitted, so that the symbol becomes K _m. When the qualifier is included its location is a matter of typographical convenience; no particular significance attaches to such variants as or K _mA. The Michaelis constant (or Michaelis concentration) is the substrate concentration at which v = 0.5 V, and its usual unit is mol dm^-3, which may be written as mol L^-1 or M. The term Michaelis constant and the symbol K _m should not be used when Michaelis-Menten kinetics are not obeyed (see Section 4.3).

For a reaction obeying Michaelis-Menten kinetics the rate in the limit of very low substrate concentrations is v = V [A]/ K _mA, and comparison with Eqn (8) shows that V / K _mA = k _A [E]₀. In the limit of very high substrate concentrations v = V, and comparison with Eqn (9) gives V = k ₀ [E]₀. The Michaelis constant K _mA is therefore k ₀/ k _A, and Eqn (10) can be written as

........ (11)

An indefinitely large number of mechanisms generate Michaelis-Menten kinetics, and still more generate limiting behaviour of the kind described in Section 4.1. Consequently there is no general definition of any of the kinetic parameters k _A, k ₀, V and K _mA in terms of the rate constants for the elementary steps of a particular mechanism.

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