1. Enzyme Kinetics Velocity (V) = k [S]
[Substrate] affects rate and it changes during reaction
Can measure just initial rate, Vo, when [S]>>[E]
E + S ES E + P k1 k2
k-1
k-2
Slow step
Rate-limiting
maximum velocity
Velocity (V) = k [S]

2. Enzyme Kinetics Michaelis-Menten Michaelis-Menten equation Derive:
E + S ES E + P
k-1
k-2
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]
k1[Et][S]
[ES] =
(k1[S] + k-1 + k2)

3. Enzyme Kinetics Michaelis-Menten [ES] = (k1[S] + k-1 + k2) [Et][S]
Km = (k-1 + k2) / k1
[ES] =
[S] + (k-1 + k2) / k1
Km = Michaelis constant
[Et][S]
Remember
V0 = k2[ES]
[ES] =
[S] + Km
k2 [Et][S]
Vmax occurs when [ES] = [Et]
Vmax = k2[Et]
V0 =
[S] + Km
Vmax[S]
V0 =
Michaelis-Menten equation!!
Rate equation for 1 substrate, enzyme-catalyzed reaction
Km has units of concentration
[S] + Km

4. Enzyme Kinetics Michaelis-Menten Km = [S] Vmax[S] V0 = [S] + Km
When V0 = 1/2 Vmax
Vmax[S]
[S]
Vmax / 2 =
1 / 2 =
[S] + Km
[S] + Km
Km = [S]
Vmax[S] Km
V0 =
Low [S], Km >> [S]
High [S], [S] >> Km
Vmax
V0 =

5. Transform Michaelis-Menten Equation
Enzyme Kinetics
Transform Michaelis-Menten Equation
Vmax[S] Km 1 1
V0 = +
V0 =
Vmax[S]
[S] + Km
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

6. Enzyme Kinetics Km and kcat
k2 + k-1
Km = 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

7. Enzymes can be Inhibited
Competitive inhibitor competes with substrate for active site
Noncompetitive inhibitor binds elsewhere, influencing binding at active site

8. 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

9. 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

10. Enzymes can be Inhibited
Competitive Inhibition
Competitive inhibitor
Apparent Km will increase
No effect on Vmax
Increasing concentration of inhibitor
-1/aKm

11. 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

12. Enzymes can be Inhibited
Noncompetitive Inhibition
+Noncompetitive
inhibitor
1/V
No inhibitor
-1/Km
1/[S]
Noncompetitive inhibitor
Apparent Km not affected
Lowering of Vmax

13. 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

14. 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)