Chemistry 340 Exam 2 Lectures 3-5 |
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Enzyme Kinetics
Major concepts:
1. What observation led to derivation of the Michaelis-Menton equation as a description of
enzyme behavior? What type of curve is described by the Michaelis-Menton equation?
2. What are the simplifications and assumptions made during derivation of the equation,
and why are they important?
3. Why is kcat /KM: important?
4. Which enzyme characteristic–KM and/or Vmax–does each type of reversible inhibitor
affect, and what is the effect?
5. For each type of reversible inhibition, what is the appearance of a Lineweaver-Burk plot,
and why?
Core knowledge:
1. What is the Michaelis-Menton equation, and what does each term in the equation mean?
2. How is KM determined? How is Vmax determined?
3. What is the Lineweaver-Burk plot, and why is it significant?
4. What is kcat (how is it defined)?
5. What are the different types of reversible enzyme inhibitors, and to what part of E or ES
does each bind?
6. What are the classes of bi-substrate enzymes, and how are they different from each other?
What is the appearance of a Lineweaver-Burk plot for each class?
Observation of changes in rate v0 as [S] increase: a hyperbolic curve Fig. 6-11
v0 = initial (early) rate, before P → S
Measured, typically, by observing appearance of a colored product over a short period
of time (1 min), repeatedly, with [E] constant and increasing [S].
Mathematical equation: v0 is related to [S]/(K + [S])
Michaelis-Menton equation derived by Michaelis and Menton considers this situation:
Simplifications:
A. 1 S and 1 P.
B. [S] >>> [E]
Assumptions:
A. [P] is small, so k-2 can be ignored.
B. [ES] is constant and is equivalent to [Et] = the steady-state assumption.
Definitions:
KM = (k2 + k-1)/k1, an overall rate constant, the Michaelis constant
Vmax = rate at which the enzyme is saturated = k2 [Et]
Equation: 
KNOW the equation. Fig. 6-12
Significance and limitations of KM
1. KM = [S] when v0 = 1/2 Vmax .
2. When k2 is rate-limiting, KM = k-1 /k1 = Kd for ES complex.
Under these conditions, KM is a measure of E's affinity for S.
3. When other steps are rate-limiting, KM is more complicated.
When the reaction involves several steps, KM is more complicated.
4. KM varies from one enzyme to another.
KM varies from one substrate to another for the same enzyme. Table 6-6
5. KM for many enzymes is approximately cellular [S].
Significance and limitations of Vmax
1. Measuring Vmax requires high [S]
classically Vmax is approached but not attained.
Since KM was classically determined by determining 1/2 Vmax , this was a problem.
One reason for transforming the Michaelis-Menton equation to a straight-line plot.
2. Vmax varies from one enzyme to another.
3. Vmax in the classic Michaelis-Menton is a function of k2.
For enzymes with additional steps, Vmax may be a function of a different k.
Lineweaver-Burk Equation and Plot:
Equation: 
Figure 1 in Box 6-1
y-intercept = 1/Vmax and x-intercept = – 1/KM
kcat = a more general rate constant = Vmax /[Et]
Characteristics and significance of kcat
1. Measuring kcat : calculate Vmax (units = M s-1) and divide by [Et] (units = M)
kcat units = s-1 = first-order rate constant
2. kcat = turnover number, a measure of an individual enzyme molecule's efficiency,
although that's only at saturating [S].
kcat /KM = the specificity constant
Characteristics and significance of kcat /KM
1. Allows comparison of enzymes with the same Vmax but different KM's
and comparison of different substrates for the same enzyme.
2. At very low [S] (much lower than KM ), v0 = (kcat /KM ) [Et] [S],
so kcat /KM = apparent second order rate constant.
3. A true measure of an enzyme's efficiency because [S] can be less than saturating.
4. The upper limit of kcat /KM is 108 – 109 M-1 s-1 = limit imposed by diffusion.
Enzymes with this value catalyze the reaction at each encounter with substrate.
Defines catalytic perfection.
Irreversible inhibitors react with and covalently modify enzymes.
Example: aspirin modifies an enzyme required for prostaglandin synthesis
Suicide inhibitors = irreversible inhibitors
Reversible inhibitors form a complex with the enzyme that prevents activity:
E + I ↔ EI if I binds only to E. Neither E nor I is changed (reacts).
Complex formation is characterized by KI = ([E] [I])/ [EI]
If KI is small, [I] << [EI]. If KI is large, most I is free (not bound to E).
We can define a term α = 1 + [I]/KI .
If KI is large, α may not be much greater than 1, but if KI is small, α is more significant.
Types of reversible inhibition: Fig. 6-15
A. Competitive inhibition can occur for enzymes with either one or more than one S.
1. Part of the enzyme to which the inhibitor (I) binds: active site
I resembles S and binds the active site but can't be converted to product
2. Example is inhibition of succinate dehydrogenase which catalyzes this reaction:
Malonate is a competitive inhibitor of succinate dehydrogenase.
FAD is a prosthetic coenzyme that was originally thought to be a co-substrate.
3. Effect on kinetics:
a. KM increases, because [S] must be higher for v0 = 1/2 Vmax .
apparent KM = α KM
b. At high [S] (with constant [I]), Vmax remains the same.
c. In general, v0 is reduced: 
B. Uncompetitive inhibition occurs only with enzymes that have more than one S.
1. Part of the enzyme to which the inhibitor binds is not the active site, but in some way
binding by I impedes catalysis.
I binds only to the ES complex, so terms related to binding by I must be changed:
I + ES ↔ ESI; K′I = ([I] [ES])/[ESI]; α′ = 1 + [I]/K′I .
2. Example: I could not find an example in any text I had available, but
an uncompetitive inhibitor of liver alcohol dehydrogenase is better for treatment
of methanol poisoning because it can be effective even when [methanol] is high.
3. Effect on kinetics (the main reason for including uncompetitive inhibition):
a. KM decreases, but this is because Vmax decreases.
apparent KM = KM /α′
b. At high [S] with constant [I], Vmax is reduced; apparent Vmax = Vmax /α′.
c. v0 is reduced: 
C. Mixed inhibition also occurs only with enzymes that have more than one S.
1. Part of the enzyme to which the inhibitor binds is not the active site.
I binds either E or ES, which means that both α and α′ must be considered.
Again, in some way, binding I reduces enzyme activity.
2. No example.
3. Effect on kinetics:
a. KM is changed. The change depends on whether α or α′ is larger.
apparent KM = α KM /α′.
b. Vmax is reduced. Apparent Vmax = Vmax /α'.
c. v0 is reduced: 
These different types of inhibition can be distinguished from each other most easily with Lineweaver-Burk plots of v0 without I, v0 with I, and v0 with n [I].
A. Competitive inhibitors: all plots have the same y-intercept because Vmax is unchanged.
Because KM changes, the slope and x-intercept are changed.
B. Uncompetitive: plots are parallel, with both Vmax and KM changing but a constant slope.
C. Mixed: plots intersect, but not at the y-axis, because both Vmax and KM change, in different
ways.
See Box 6-2, Figures 1-3.
Having gone through all of that, let's return to the study of enzymes that are not inhibited, that have more than one substrate = bi-substrate enzymes.
Reaction: A + B ↔ P + Q
A. Enzymes that form a ternary complex = enzymes that catalyze single displacement
(sequential) reactions.
1. Reaction: A + B + E ↔ ABE ↔ PQE ↔ P + Q + E
2. Types: either ordered (A binds first and P is released first) or
random (A or B can bind first, and P or Q can be released first)
3. If [A] is held constant and [B] is varied, the Lineweaver-Burk graph shows
intersecting plots.
Changing [B} changes Vmax and KM to different degrees.
4. Example (ordered single displacement/ternary complex) is lactate dehydrogenase:
The coenzyme must bind first, and then the substrate binds.
The modified coenzyme is released first.
