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10.4 Inhibition and Activation in Enzyme Reactions 273

reversible. Irreversible inhibitors (poisons), such as lead or cyanide, completely and
irreversibly inactivate an enzyme. Reversible inhibitors reduce enzyme activity, but al-
low enzyme activity to be restored when the inhibitor is removed. Partial reversibility
occurs when some, but not all, of the enzyme’s activity is restored on removal of the
inhibitor. If the modification of activity is irreversible, the process is known as inacti-
vation. Thus, the term “inhibition” is normally reserved for fully reversible or partially
reversible processes.
Inhibitors are usually classified according to their effect upon V,,, and Km. Com-
petitive inhibitors, such as substrate analogs, compete with the substrate for the same
binding site on the enzyme, but do not interfere with the decomposition of the enzyme-
substrate complex. Therefore, the primary effect of a competitive inhibitor is to increase
the apparent value of K,,,. The effect of a competitive inhibitor can be reduced by in-
creasing the substrate concentration relative to the concentration of the inhibitor.
Noncompetitive inhibitors, conversely, do not affect substrate binding, but produce a
ternary complex (enzyme-substrate-inhibitor) which either decomposes slowly, or fails
to decompose (i.e., is inactive). Consequently, the primary effect of a noncompetitive
inhibitor is to reduce the apparent value of V,,,,,.
The inhibition process in general may be represented by the following six-step
scheme (a similar scheme may be used for activation-see problem 10-12) in which I
is the inhibitor, EI is a binary enzyme-inhibitor complex, and EIS is a ternary enzyme-
inhibitor-substrate complex.

E + @ES
1
E + I+EI (2)
2
k3
ES + I*EIS (3)
k-x
EI + +EIS (4)
4
E&E+P (5)

EIS 5 EI + P (6)

In steps (1) and (2), S and I compete for (sites on) E to form the binary complexes ES
and ET. In steps (3) and (4) the ternary complex EIS is formed from the binary com-
plexes. In steps (5) and (6) ES and EIS form the product P; if EIS is inactive, step (6) is
ignored. Various special cases of competitive, noncompetitive, and mixed (competitive
and noncompetitive) inhibition may be deduced from this general scheme, according
to the steps allowed, and corresponding rate laws obtained.

Competitive inhibition involves (only) the substrate (S) and the inhibitor (I) competing
for one type of site on the enzyme (E), in fast, reversible steps, followed by the slow
decomposition of the complex ES to form product (P); the complex EI is assumed to be
inactive. The fact that there is only one type of binding site on the enzyme implies that a
ternary complex EIS cannot be formed.
(a) Derive the rate law for competitive inhibition.
(b) Show what effect, if any, competitive inhibition has on V,,, and Km, relative to the
uninhibited case described in Section 10.2.