Enzyme Kinetics
[Substrate] affects rate and it changes during reaction
Can measure just initial rate, Vo, when [S]>>[E]
k2
k1
E + S
ES
k-1
E + P
k-2
Slow step
Rate-limiting
maximum velocity
Velocity (V) = k [S]
Enzyme Kinetics
Michaelis-Menten
Michaelis-Menten equation
k2
k1
E + S
ES
E + P
k-2
k-1
Derive:
Assume that [P] low at start and that k-2 is very small
V0 = k2[ES]
[ES] hard to measure, so [Et] used
[Et] = [E] + [ES], [E] = [Et] - [ES]
[ES] small because [S] so large, [Et] = [E]
Formation of ES = k1([Et] - [ES])[S]
Breakdown of ES = k-1[ES] + k2[ES]
Assume steady state [ES] ~ constant, so
k1([Et] - [ES])[S] = k-1[ES] + k2[ES]
Rearrange:
k1[Et][S] = (k1[S] + k-1 + k2) [ES]
[ES] =
k1[Et][S]
(k1[S] + k-1 + k2)
Enzyme Kinetics
Michaelis-Menten
[ES] =
[ES] =
[ES] =
V0 =
V0 =
k1[Et][S]
(k1[S] + k-1 + k2)
[Et][S]
[S] + (k-1 + k2) / k1
[Et][S]
[S] + Km
k2 [Et][S]
[S] + Km
Vmax[S]
[S] + Km
Km = (k-1 + k2) / k1
Km = Michaelis constant
Remember
V0 = k2[ES]
Vmax occurs when [ES] = [Et]
Vmax = k2[Et]
Michaelis-Menten equation!!
Rate equation for 1 substrate,
enzyme-catalyzed reaction
Km has units of concentration
Enzyme Kinetics
Michaelis-Menten
Michaelis-Menten
Vmax[S]
V0 =
[S] + Km
When V0 = 1/2 Vmax
Vmax / 2 =
Vmax[S]
[S]
1/2=
[S] + Km
[S] + Km
Km = [S]
Low [S], Km >> [S]
V0 =
High [S], [S] >> Km
V0 =
Vmax[S]
Km
Vmax
Enzyme Kinetics
Transform Michaelis-Menten Equation
V0 =
Vmax[S]
[S] + Km
Km
1
1
+
V0 = Vmax[S]
Vmax
Double reciprocal or Lineweaver-Burk plot
plot 1/V vs. 1/[S]
Straight line --> slope, y-intercept, x-intercept
More accurate determination of Vmax
Enzyme Kinetics
Km and kcat
Km =
k2 + k-1
k1
Km measurement --> affinity of enzyme for its substrate
kcat = Vmax/[E]T
kcat is catalytic constant or turnover number
(first order rate constant, s-1)
CATALYTIC EFFICIENCY
Enzymes can be Inhibited
Competitive inhibitor competes with substrate for active site
Noncompetitive inhibitor binds elsewhere, influencing binding at active site
Enzymes can be Inhibited
Competitive Inhibition
Active
site of
enzyme
Substrate
Inhibitor
Substrate and Inhibitor can bind to active site
Inhibitor prevents binding of substrate
Enzymes can be Inhibited
Noncompetitive Inhibition
Active
site of
enzyme
Substrate
Inhibitor
Inhibitor site
Substrate can bind to
active site
product forms
Inhibitor binding
distorts active site
Inhibitor and
substrate can
bind
simultaneously,
rate slowed
Enzymes can be Inhibited
Competitive Inhibition
Competitive inhibitor
Apparent Km will increase
No effect on Vmax
Increasing
concentration of
inhibitor
-1/aKm
Enzymes can be Inhibited
Competitive Inhibition
Ingestion of methanol (gas-line antifreeze)
In liver, alcohol dehydrogenase converts methanol to formaldehyde
(BAD)
Ethanol competes effectively with methanol for binding to alcohol
dehydrogenase
Therapy for methanol poisoning is IV with ethanol, formaldehyde
not formed as readily, little tissue damage, kidneys excrete methanol
Enzymes can be Inhibited
Noncompetitive Inhibition
+Noncompetitive
inhibitor
1/V
No inhibitor
-1/Km
0
1/[S]
Noncompetitive inhibitor
Apparent Km not affected
Lowering of Vmax
Enzymes can be Inhibited
Noncompetitive Inhibition
Also called allosteric inhibition
Example of noncompetitive inhibitor = aspirin
Aspirin inhibits a cyclo-oxygenase so that prostaglandins may not be
synthesized, thereby reducing pain, fever, inflammation, blood
clotting, etc.
Aspirin does not bind to the active site of cyclo-oxygenase but to a
separate/allosteric site
Enzymes can be Inhibited
Irreversible Inhibition - Inhibitor
binds covalently to or destroys
essential functional group on enzyme
Suicide inactivators undergoes first few steps of
rxn and then converts to a
reactive compound that
combines irreversiby with
enzyme (high specificity)
INHIBITS ornithine
decarboxylase (cure for
African sleeping sickness)