Drug Metabolism in Drug Design and Development Basic Concepts and Practice

linear metabolite production of up to 45 min of incubation.

Nevertheless, the concentrations of the compounds and microsomal

proteins can largely govern the suitable incubation time, as well as the

overall metabolic rates.

Michaelis–Menten (M–M) hyperbolic kinetics (Eq. 13.7) is often

assumed and directly applied in rate determination, particularly in early

discovery when the enzyme kinetic behavior is usually unknown:

V¼VmaxS=ðSþKmÞð 13 : 7 Þ

IfSKm; V¼VmaxS=Km¼CL

0

intS; or

CL

0

int¼V=S: ð^13 :^8 Þ

Equation 13.8 provides one of several means for estimatingCL

0

int.

Again, this approach is valid only when the initial substrate concentra-

tion is much lower than the anticipatedKm, that is,S<Km/5 (Soars et

al., 2002). HereVis reaction rate,Vmaxis the maximal rate, andKmis the

substrate concentration at half maximum rate, andS is substrate

concentration.

Alternatively, reaction rates can be expressed as follows (Zhang and

Wong, 2005):

V¼ðkcat=KmÞES ð 13 : 9 Þ

wherekcatis the maximal catalytic rate constant, andkcat/Kmis defined as

catalytic efficiency.

The rate is thus a first-order function of the substrate and enzyme

concentrations (Eq. 13.9). Although governed by two variables, enzyme

concentrations in the steady state are pseudoconstant during a normal

incubation period, that is, 15 or 30 min, while the substrate concentra-

tions are continuously reduced as a consequence of the formation of

metabolites.

If the substrate concentration (Ct) is reduced to 60% of the initial

concentration (C 0 ) during a given reaction period (t), the rate at the end

of that period (Vt) will theoretically be 60% of the initial rate (V 0 )

(Eq. 13.9). Therefore, the initial rates are apparently underestimated

when Equation 13.6 is used; instead, this equation determines the

average rates during the reaction period. To minimize such a potential

bias, the substrate concentration during the reaction periods should be

pseudoconstant or, at most, reduced by 20%; such reduction can often

be achieved by reducing enzyme quantities and/or incubation time.

Besides the possible inaccuracy of the calculation, the determination

of rate can be further complicated by potential atypical enzyme kinetics

424 DETERMINATION OF METABOLIC RATES AND ENZYME KINETICS