2 Enzymes

2005-9-23

The Hill equation describes the behavior of enzymes that exhibit cooperative binding of substrate1. some enzymes bind their substrates in a cooperative

fashion analogous to the binding of oxygen by hemoglobin.

2. Cooperative behavior may be encountered for multimeric enzymes that bind substrate at multiple sites. 3. For enzymes that display positive cooperativity in

binding substrate, the shape of the curve that relates changes in vi to changes in [S] is sig

moidal (fig 8-6).

8-6

4. Enzymologists employ a graphic representation of

the Hill equation originally derived to describe

the cooperative binding of O2 by hemoglobin.

5. Equation (43) represents the Hill equation, where

K’ is a complex constant. Equation (43) states that

when [S] is low relative to k’, the initial reaction

velocity increases as the nth power of [S].

Explaining

1. A graph of log vi/(Vmax – vi) versus log[S] give a

straight line (fig. 8-7), where the slope of the

line n is the Hill coefficient, an empirical para

meter whose value is a function of the number, kind,

and strength of the interactions of the multiple subst

rate-binding sites on the enzyme.

2. When n = 1, all binding sites behave independ

ently, and simple Michaelis-Menten kinetic behavio

r is observed.

3. If n is greater than 1, the enzyme is said to exhibit positive cooperativity. Binding of first substrate molecule then enhances the affinity of the enzyme for binding additional substrate. The greater the value for n, the higher the degree of cooperativity and the more sigmoidal will be the plot of vi versus [S]. 4. a perpendicular dropped from the point where the y term log vi/(Vmax – vi) is zero intersects the x axis at a substrate concentration termed S50, the substrate

concentration that results in half-maximal velocity. S

50 thus is a analogous to the P50 for oxygen binding t

o hemoglobin.

8-7

Kinetic analysis distinguishes competitive from

noncompetitive inhibition

1. Inhibitors can be classified based upon their site of

action on the enzyme

2. Kinetically, we distinguish two classes of

inhibitors based upon whether raising the

substrate concentration does or does not

overcome inhibition.

Competitive inhibitors typically resemble substrates1. can be overcome by raising the concentration of

the substrate. 2. binds to the substrate-binding portion of the active

site and blocks access by the substrate. 3. Example: Succinate dehydrogenase catalyzes the

removal of one hydrogen atom from each of the two methylene carbons of succinate (fig. 8-8)

both succinate and its structural analog malonate (-OOC-CH2-COO-) can bind to the active site of succinate dehydrogenase, forming an ES or an EI complex.

8-8

However, since malonate contains only one methylene carbon, it cannot undergo dehydrogenation. The formation and dissociation of the EI complex is a dynamic process described by

In effect, a competitive inhibitor acts by decreasing th

e number of free enzyme molecules available to bind s

ubstrate, ie, to form ES, and thus eventually to form pr

oduct, as described below:

Double reciprocal plots facilitate the evaluation of inhibitors1. Double reciprocal plots distinguish between competitive and noncompetitive inhibitors and simplify evaluation of inhibition constants Ki. 2. vi is determined at several substrate concentrations

both in the presence and in the absence of inhibitor. 3. For classic competitive inhibition, the lines that

connect the experimental data points meet at the y axis (fig. 8-9).

8-9

4. Since the y intercept is equal to 1/Vmax, this pattern indicates that when 1/[S] approaches 0; vi is independent of the presence of inhibitor. 5. Note, however, that the intercept on the x axis does vary with inhibitor concentration- and that since -1/Km’ is smaller than -1/Km, Km’ (the “apparent Km”) becomes larger in the presence of increasing concentrations of inhibitor. Thus, a competitive inhibitor has no effect on Vmax but raises K’m, the apparent Km for the substrate.

For simple competitive inhibition, the intercept on the x axis is

Once Km has been determined in the absence of inhibitor, Ki can be calculated from equation (47). Ki values are used to compare different inhibitors of the same enzyme. The lower the value for Ki, the more effective the the inhibitor. For example, the statin drugs that act as competitive inhibitors of HMG-CoA reductase have Ki values several orders of magnitude lower than the Km for the substrate HMG-CoA.

Simple noncompetitive inhibitors lower Vmax bu

t do not affect Km

1. binding of the inhibitor does not affect binding of

substrate.

2. Formation of both EI and EIS complexes is th

erefore possible.

3. However, while the enzyme-inhibitor complex ca

n still bind substrate, its efficiency at transforming

substrate to product, reflected by Vmax is decreased.

4. For simple noncompetitive inhibition, E and EI

possess identical affinity for substrate, and the

EIS complex generates product at a negligible

rate (fig. 8-10).

5. More complex noncompetitive inhibition occurs

when binding of the inhibitor does affect the

apparent affinity of the enzyme for substrate,

causing the lines to intercept in either the third

or fourth quadrants of a double reciprocal plot

(not shown).

8-10

Irreversible inhibitors “poison” enzymes

1. involve making or breaking covalent bonds with

aminoacyl residues essential for substrate bind

ing, catalysis, or maintenance of the enzyme’s funct

ional conformation.

2. Since these covalent changes are relatively stable,

an enzyme that has been “poisoned” by an irre

versible inhibitor remains inhibited even after rem

oval of the remaining inhibitor form the surroundi

ng medium.

FINE

2005-9-23