Can Be Determined by DoubleReciprocal Plots

free energy of activation
active site
induced fit
K M (the Michaelis constant)
V max
Michaelis-Menten equation
turnover number
k cat/K M
sequential displacement reaction
double-displacement (Ping-Pong) reaction
allosteric enzyme
competitive inhibition
noncompetitive inhibition
group-specific reagent
affinity label
mechanism-based (suicide) inhibition
transition-state analog
catalytic antibody (abzyme)
vitamin
I. The Molecular Design of Life
8. Enzymes: Basic Concepts and Kinetics
Appendix: V max and K M Can Be Determined by Double-Reciprocal Plots
Before the availability of computers, the determination of K M and V max values required algebraic manipulation of the
basic Michaelis-Menten equation. Because V max is approached asymptotically (see Figure 8.11), it is impossible to
obtain a definitive value from a typical Michaelis-Menten plot. Because K M is the concentration of substrate at V max/2,
it is likewise impossible to determine an accurate value of K M. However, V max can be accurately determined if the
Michaelis-Menten equation is transformed into one that gives a straight-line plot. Taking the reciprocal of both sides of
equation 23 gives
A plot of 1/V 0 versus 1/[S], called a Lineweaver-Burk or double-reciprocal plot, yields a straight line with an intercept
of 1/V max and a slope of K M/V max (Figure 8.36). The intercept on the x-axis is -1/K M.
Double-reciprocal plots are especially useful for distinguishing between competitive and noncompetitive inhibitors. In
competitive inhibition, the intercept on the y-axis of the plot of 1/V 0 versus 1/[S] is the same in the presence and in the
absence of inhibitor, although the slope is increased (Figure 8.37). That the intercept is unchanged is because a
competitive inhibitor does not alter V max. At a sufficiently high concentration, virtually all the active sites are filled by
substrate, and the enzyme is fully operative. The increase in the slope of the 1/V 0 versus 1/[S] plot indicates the strength
of binding of competitive inhibitor. In the presence of a competitive inhibitor, equation 31 is replaced by
in which [I] is the concentration of inhibitor and K i is the dissociation constant of the enzyme-inhibitor complex.
In other words, the slope of the plot is increased by the factor (1 + [I]/K i) in the presence of a competitive inhibitor.
Consider an enzyme with a K M of 10-4 M. In the absence of inhibitor, V 0 = V max/2 when [S] = 10-4 M. In the presence
of 2 × 10-3 M competitive inhibitor that is bound to the enzyme with a K i of 10-3 M, the apparent K M (K app M ) will be
equal to K M × (1 + [I]/K i), or 3 × 10-4 M. Substitution of these values into equation 23 gives V 0 = V max/4, when [S] =
10-4 M. The presence of the competitive inhibitor thus cuts the reaction rate in half at this substrate concentration.
In noncompetitive inhibition (Figure 8.38), the inhibitor can combine with either the enzyme or the enzyme-substrate
complex. In pure noncompetitive inhibition, the values of the dissociation constants of the inhibitor and enzyme and of
the inhibitor and enzyme-substrate complex are equal (Section 8.5.1). The value of V max is decreased to a new value
called V app max, and so the intercept on the vertical axis is increased. The new slope, which is equal to K M/V app max, is
larger by the same factor. In contrast with V max, K M is not affected by pure noncompetitive inhibition. The maximal
velocity in the presence of a pure noncompetitive inhibitor, V i max, is given by
I. The Molecular Design of Life
8. Enzymes: Basic Concepts and Kinetics
Appendix: V max and K M Can Be Determined by Double-Reciprocal Plots
Figure 8.36. A Double-Reciprocal or Lineweaver-Burk Plot. A double-reciprocal plot of enzyme kinetics is generated
by plotting 1/V 0 as a function 1/[S]. The slope is the K M/V max, the intercept on the vertical axis is 1/V max, and the
intercept on the horizontal axis is -1/K M.
I. The Molecular Design of Life
8. Enzymes: Basic Concepts and Kinetics
Appendix: V max and K M Can Be Determined by Double-Reciprocal Plots
Figure 8.37. Competitive Inhibition Illustrated on a Double-Reciprocal Plot. A double-reciprocal plot of enzyme
kinetics in the presence (
) and absence (
) of a competitive inhibitor illustrates that the inhibitor has no effect
on V max but increases K M.
I. The Molecular Design of Life
8. Enzymes: Basic Concepts and Kinetics
Appendix: V max and K M Can Be Determined by Double-Reciprocal Plots
Figure 8.38. Noncompetitive Inhibition Illustrated on a Double-Reciprocal Plot. A double-reciprocal plot of enzyme
kinetics in the presence (
) and absence (
) of a noncompetitive inhibitor shows that K M is unaltered and V max
is decreased.