equals its rate of breakdown, and steady-state kinetics
2. Only initial velocities are measured. Hence, during
the period of measurement, [S] is not significantly
depleted as [P] increases.
[ES] is constant during the period of measurement,
which means that (a) enough time has elapsed since
mixing E and S for [ES] to build up; (b) not enough
time has passed for the rate of formation of ES
to decrease owing to substrate depletion; and
k2 < k -
, so that [ES] can build up. If
ES breaks down as rapidly as it is formed, and a
steady-state can never be established.
These expressions can both be solved for
ÏË d '
_ Vmax or
[ES] “ [ET] OI ^max
Substituting the latter equation for [ES]/[ET] in Equa-
tion (6.3), we obtain
~ ~ ~
-f [S ]).
Rate of formation of ES
i [E] [S]
([E T] - [ES]) [ S ] .
Rearranging and solving for v,
Rate of breakdown of ES
= k_! [ES] +
= (*_j +
Under steady-state conditions, the rate of formation of
ES equals its rate of breakdown, so that
([Et] - [ES]) [S] = (*_,+
Rearranging the above Equation yields
([E T] - [ES]) [S] = * _ i
+ k 2
rium constant but a ratio of rate constants.
Equation (6.2) can be rearranged in the following ways:
[S][ET] - [S][ES] =
[S][ET] = [ES](/fm + [S])
It is usually difficult to measure [ES] in a reaction mixture.
Consequently, Equation (6.3) is not useful experimentally.
On the other hand, the velocity (v) and the maximum
are readily determined by a variety of
As indicated in Figure 6-4, Vmax is the limiting value that
v approaches as [S] -* oo. In that situation, all enzyme
molecules have substrate bound to them, and so [E ] = 0
and [ET] = [ES], Thus, v = k
[ES], and Vmax = k
Equation (6.4) is known as the
and the following points should be noted.
is a constant for a particular enzyme and
substrate and is independent of enzyme and
. Vmax depends on enzyme concentration, and at
saturating substrate concentration, it is independent
of substrate concentration.
and Vmax may be influenced by pH, temperature,
and other factors.
4. A plot of v versus [S] fits a rectangular hyperbolic
function (Figure 6-4).
5. If an enzyme binds more than one substrate, the
values for the various substrates can be used as a
relative measure of the affinity of the enzyme for
each substrate (the smaller the value of
higher the affinity of the enzyme for that substrate).
. In a metabolic pathway,
values for enzymes that
catalyze the sequential reactions may indicate the
rate-limiting step for the pathway (the highest
corresponds roughly to the slowest step).
[ES] is assumed to be at
equilibrium with [E] and [S], ES is dissociating
more often to yield E and S than to yield product.
Under this condition,
the dissociation constant of the
for this equilibrium
(ES ^ E + S) is
[E] [S] = U