Introduction to Enzyme and Coenzyme Chemistry - E-Library Home

56 Chapter 4
The two kinetic constants in the Michaelis–Menten rate equation have special
signiWcance. The k cat parameter is the turnover number mentioned above: it is a
unimolecular rate constant whose units are s 1 (or min 1 if it is a very slow
enzyme!), and it represents the number of mmoles of substrate converted per
mmole of enzyme per second. Alternatively, in molecular terms it represents the
number of molecules turned over by one molecule of enzyme per second, which
gives a good feel for how quickly the enzyme is operating. Typically values are
in the range 0:1--100 s 1 .
The K M parameter is known as the Michaelis constant for the enzyme: its
units are mol l
1 or m. In practice, the K M is the concentration of substrate at
which half-maximal rate is observed. It can be taken as a rough indication of
how tightly the enzyme binds its substrate, so a substrate bound weakly by an
enzyme will have a large K M value, and a substrate bound tightly will have a
small K M . However, it must be stressed that K M is not a true dissociation
constant for the substrate, since it also depends on the rate constant k 2 . Values
of K M are typically in the range 1 mm–1 mm.
Values of k cat and K M can be measured for a particular enzyme by measuring
the rate of the enzymatic reaction at a range of diVerent substrate concentrations.
At high substrate concentrations ([S] >> K M ) the rate equation
reduces to v ¼ k cat [E 0 ], so a maximum rate is observed however high the
substrate concentration. Under these conditions the enzyme is fully saturated
with substrate, and no free enzyme is present. So as soon as an enzyme molecule
releases a molecule of product it immediately picks up another molecule of
substrate. In other words the enzyme is working Xat out: the observed rate of
reaction is limited only by the rate of catalysis.
Under low substrate concentrations the rate equation reduces to
v ¼ ðk cat =K M Þ[E][S], so the observed rate is proportional to substrate concentration,
and the reaction has eVectively become a bimolecular reaction between
free enzyme, E, and free substrate, S. Under these conditions the majority of
enzyme is free enzyme, and the observed rate of reaction depends on how
eYciently the enzyme can bind the substrate at that concentration. The bimolecular
rate constant under these conditions k cat =K M is known as the catalytic
eYciency of the enzyme, since it represents how eYciently free enzyme will react
with free substrate.
A schematic representation of the energetic proWles at high and low substrate
concentrations is given in Figure 4.4. At high substrate concentrations
the enzyme is fully saturated with substrate, so the activation energy for the
enzymatic reaction is the free energy diVerence between the ES complex and the
transition state. At [S] ¼ K M the enzyme is half-saturated with substrate. At
low substrate concentrations the majority of the enzyme is free of substrate, so
the activation energy for the reaction is the free energy diVerence between free
enzyme þ substrate and the transition state.