4.2 Enzyme Catalysis
The catalysis by enzymes involved in oxidative drug metabolism reactions (e.g.,
the cytochromes P450) typically follow the kinetic scheme as outlined in
Scheme 4.1. In this case, in theory all reactions are reversible and an enzyme–
substrate complex [E-S] must be formed before product formation and
subsequent release can occur. In this case,kcat, which is the capacity of the
enzyme–substrate complex to generate product, is equal tok 2. For clarification,
it should be noted that the Michaelis constant (Km, see below) is derived from
the microscopic rate constants in Scheme 4.1 (Km=(k 1 +k 2 )/k 1 ) using the
steady state assumption.
Though not depicted kinetically here, the reader should be aware that conjug-
ation enzyme reactions (such as the glucuronosyl transferases) are terreactant
systems that involve an enzyme and two cosubstrates and are generally more
complicated kinetically but can readily be described in the same fashion.
4.3 Michaelis–Menten Kinetics
The fundamental cornerstone of the kinetic characterization of enzymatic
reactions has been and remains the Michaelis–Menten equation (Eq. 4.1).
n¼
Vmax½S
Kmþ½Sð 4 : 1 ÞIn this case, n is the velocity of the reaction, [S] is the substrate
concentration,Vmax(also known asVorVm) is the maximum velocity of the
reaction, andKmis the Michaelis constant. From this equation quantitative
descriptions of enzyme-catalyzed reactions, in terms of rate and concentration,
can be made. As can be surmised by the form of the equation, data that is
described by the Michaelis–Menten equation takes the shape of a hyperbola
when plotted in two-dimensional fashion with velocity as the y-axis and
substrate concentration as thex-axis (Fig. 4.1). Use of the Michaelis–Menten
equation is based on the assumption that the enzyme reaction is operating
under both steady state and rapid equilibrium conditions (i.e., that the
concentration of all of the enzyme–substrate intermediates (see Scheme 4.1)
become constant soon after initiation of the reaction). The assumption is also
made that the active site of the enzyme contains only one binding site at which
catalysis occurs and that only one substrate molecule at a time is interacting
with the binding site. As will be discussed below, this latter assumption is not
always valid when considering the kinetics of drug metabolizing enzymes.
SCHEME 4.1 Kinetics of catalysis.90 ENZYME KINETICS