4.3.1 Meanings ofKm,Vmaxand Their Clinical Relevance
The kinetic parametersKmandVmaxare estimated from the Michaelis–Menten
equation and provide quantitative information regarding enzyme function.Km
or the Michaelis constant is operationally defined as the concentration of
substrate at which half-maximal velocity of the reaction is achieved (Fig. 4.1).
With respect to the single substrate reaction scheme (Scheme 4.1), it should
be realized thatKmis equal to (k 1 +k 2 )/k 1 and thus is the amalgamation of
several rate constants. With respect to affinity, unfortunately,Kmis frequently
(and incorrectly) used interchangeably with KS, which is the substrate
dissociation constant. ThoughKmmay sometimes approximateKS, the two
do not have to be equal and numerous examples exist where these parameter
values vary dramatically.
Vmaxis an estimation of the maximum velocity of the reaction (Fig. 4.1) and
is the product ofkcatande 0 , wherekcatis the capacity of the enzyme–substrate
complex to form product and e 0 is the enzyme concentration. The kcat
parameter is also known as thecatalytic constantor theturnover numberand
refers to the number of catalytic cycles or the number of molecules of substrate
that one molecule of enzyme can convert to product per unit time. As stated
above,Vmaxis only an ‘‘estimation’’ of the maximum velocity of the reaction,
since the true maximum velocity is never reached at a finite substrate
concentration.
Apart from simply obtaining kinetic parameters and understanding reaction
rates, the estimation ofKmandVmaxhas several important applications in the
drug discovery and development processes. Typically, it is assumed thatin vivo,
enzymatic reactions take place when substrate concentrations are much lower
FIGURE 4.1 Representative hyperbolic plot indicative of a reaction following
Michaelis–Menten kinetics.Km¼substrate concentration necessary to achieve one-
half maximum velocity.Vmax¼maximum velocity.
MICHAELIS–MENTEN KINETICS 91