Page 101 - Color Atlas of Biochemistry

P. 101

92 Metabolism

Enzyme kinetics I enzymes whose substrate saturation curves
are shown in diagram 1, enzyme 2 has the
–1
The kinetics of enzyme-catalyzed reactions higher af nity for A [K m = 1 mmol l );
(i. e., the dependence of the reaction rate on V max , by contrast, is much lower than with
the reaction conditions) is mainly determined enzyme 1.
by the properties of the catalyst. It is therefore Since v approaches V asymptotically with
more complex than the kinetics of an uncata- increasing values of [A], it is dif cult to obtain
lyzed reaction (see p. 22). Here we discuss reliable values for V max —and thus for K m as
these issues using the example of a simple well—from diagrams plotting v against [A]. To
first-order reaction (see p. 22) get around this, the Michaelis–Menten equa-
tion can be arranged in such a way that the
measured points lie on a straight line. In the
A. Michaelis–Menten kinetics
Lineweaver–Burk plot (2),1/v is plotted
In the absence of an enzyme, the reaction rate v against 1/[A]. The intersections of the line of
is proportional to the concentration of sub- best fit with the axes then produce 1/V max
stance A (top). The constant k is the rate con- and—1/K m . This type of diagram is very clear,
stant of the uncatalyzed reaction. Like all cat- but for practical purposes it is less suitable for
alysts, the enzyme E (total concentration [E] t ) determining V max and K m . Calculation meth-
creates a new reaction pathway. Initially, A is ods using personal computers are faster and
bound to E (partial reaction 1, left). If this more objective.
reaction is in chemical equilibrium, then
with the help of the law of mass action—and
B. Isosteric and allosteric enzymes
taking into account the fact that [E] t =[E] +
[EA]—one can express the concentration [EA] Many enzymes can occur in various conforma-
of the enzyme–substrate complex as a func- tions (see p. 72), which have different catalytic
properties and whose proportion of the total
tion of [A] (left). The Michaelis constant K m
thus describes the state of equilibrium of the number of enzyme molecules is influenced by
reaction. In addition, we know that k cat >k—in substrates and other ligands (see pp.116 and
other words, enzyme-bound substrate reacts 280, for example). Allosteric enzymes of this
to B much faster than A alone (partial reaction type, which are usually present in oligomeric
2, right). k cat ,the enzyme’s turnover number, form, can be recognized by their S-shaped
corresponds to the number of substrate mol- (sigmoidal) saturation curves, which cannot
ecules converted by one enzyme molecule per be described using the Michaelis model. In
second. Like the conversion A B, the forma- thecaseofisosteric enzymes (with only one
tion of B from EA is a first-order reaction—i. e., enzyme conformation, 1), the ef ciency of
v = k [EA] applies. When this equation is substrate binding (dashed curve) declines
combined with the expression already de- constantly with increasing [A], because the
rived for EA, the result is the Michaelis– number of free binding sites is constantly
Menten equation. decreasing. In most allosteric enzymes (2),
In addition to the variables vand [A], the the binding ef ciency initially rises with in-
equation also contains two parameters that do creasing [A], because the free enzyme is
not depend on the substrate concentration present in a low-af nity conformation
[A], but describe properties of the enzyme (square symbols), which is gradually con-
itself: the product k cat [E] g is the limiting verted into a higher-af nity form (round sym-
valuefor the reaction rateata very high [A], bols) as a result of binding with A. It is only at
the maximum velocity V max of the reaction high [A] values that a lack of free binding sites
(recommended abbreviation: V). The Michae- becomes noticeable and the binding strength
lis constant K m characterizes the af nity of the decreases again. In other words, the af nity of
enzyme for a substrate. It corresponds to the allosteric enzymesisnot constant, but de-
substrate concentration at which v reaches pends on the type and concentration of the
half of V max (if v = V max /2, then [A]/(K m + ligand.
[A]) = 1/2, i. e. [A] is then = K m ). A high af nity
of theenzymefor a substrate thereforeleads
to a low K m value, and vice versa. Of the two

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