Download Both PS 7 and PS 8 are due next Thursday

Both PS 7 and PS 8 are due
next Thursday
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Comments about PS6
Chymotrypsin
Elastase
Moderately Deep and Wide
Accepts Phenyl group of Phe
Shallow,
Accepts smaller apolar
residues
Gly and Ala
Trypsin
Active Site
Stabilizing
Residues
Cavity
Deep, narrow channel
Accepts Lysine
Asp 189 acts as a stabilizing
residue
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Michaelis-Menten Equation
v=
Vmax [S]
KM + [S]
Vmax the reaction rate when the enzyme is fully saturated
with substrate
KM, the Michaelis constant, is the substrate concentration
at which the reaction rate is half maximal.
.
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The turnover number
•
•
•
•
A measure of catalytic activity
kcat, the turnover number, is the number of
substrate molecules converted to product per
enzyme molecule per unit of time, when E is
saturated with substrate.
According to M-M , k2 = kcat = Vmax/Et
Values of kcat usually range from less than 1/sec
to 104/sec
Catalase is 4 x 107 /sec
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The catalytic efficiency
kcat/Km
• kcat/Km is an apparent second-order rate constant
• It measures how the enzyme performs when S is
low
• The upper limit for kcat/Km is the diffusion limit the rate at which E and S diffuse together
(~109/M for small substrates (glycerol) and 108/M
for larger substrates (nucleotides))
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Example of MM Eqn Question
triose phosphate isomerase
Glyceraldehyde-3-P ÅÆdihydroxyacetone-P
KM = 1.8 x 10-5 M
When [glyceraldehyde-3-P] = 30 µM, v = 82.5 µmol mL-1 sec-1
What is Vmax for the triose phosphate isomerase?
Assume [ET] = 3 nmol/mL, what is kcat for triose phosphate
isomerase?
What can we say about the catalytic efficiency of triose
phosphate isomerase?
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Linear Plots of the MichaelisMenten Equation
Linear plots allow Km and Vmax to be estimated by
extrapolation of lines rather than asymptotes
• Lineweaver-Burk (double reciprocal plot)
• Hanes-Woolf
– Preferred because there isn’t an overemphasis of the
data obtained at low [S]
Deviation from the linear plot implies allostery (regulation)
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Lineweaver-Burk
y =
m
x
+
b
The Lineweaver-Burk double-reciprocal plot, depicting extrapolations that allow the
determination of the x- and y-intercepts and slope.
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Hanes-Woolf
A Hanes-Woolf plot of [S]/v versus [S], another straight-line rearrangement of the MichalelisMenten equation.
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What Can Be Learned from the
Inhibition of Enzyme Activity?
• Enzymes may be inhibited reversibly or
irreversibly
• Reversible inhibitors may bind at the active
site or at some other site
• Enzymes may also be inhibited in an
irreversible manner
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Different Types of Inhibition
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Vmax
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Relative velocity
No Inhibitor
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Km
Competitive Inhibitor
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Uncompetitive Inhibitor
Inhibitor binds to same site
as substrate reversibly
Inhibitor only binds to
Enzyme/substrate complex
4
Pure Noncompetitive Inhibitor
Inhibitor binds to different
site as substrate and does not
affect the binding of substrate
Mixed NI – affects S binding
2
0
0
10
20
30
40
50
60
70
[S]
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Effect of Inhibitors on the
Michaelis-Menten Rate Equation
Inhibition Type Rate Equation
Apparent KM
Apparent Vmax
None
v = Vmax[S]/(KM+[S])
KM
Vmax
Competitive
v = Vmax[S]/ ([S]+ KM(1 + [I]/KI))
KM(1 + [I]/KI)
Vmax
Noncompetitive
v = (Vmax[S]/(1 +
[I]/KI))/(KM+[S])
KM
Vmax/(1 + [I]/KI)
Mixed
v = Vmax[S]/((KM(1 + [I]/KI)
+([S](1 + [I]/KI’)))
KM(1+[I]/KI)/
(1+[I]/KI’)
Vmax/(1 + [I]/KI’)
Uncompetitive
v = Vmax[S]/(KM+([S](1 + [I]/KI’))
KM/(1+[I]/KI’)
Vmax/(1 + [I]/KI’)
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Competitive Inhibition
Inhibitor binds to same site as substrate reversibly
As the concentration of a competitive
inhibitor increases, higher concentrations
of substrate are required to attain a
particular reaction velocity.
The reaction pathway suggests how
sufficiently high concentrations of
substrate can completely relieve
competitive inhibition.
KI = k-3/k3
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Competitive Inhibition
KI = [E][I]/[EI] = k-3/k3
Lineweaver-Burk plot of competitive inhibition, showing lines for no I, [I], and 2[I].
Note that when [S] is infinitely large (1/[S] = 0), Vmax is the same, whether I is
-1
present of not. In the presence of I, the
x-intercept =
[I] ⎞
⎛
Km ⎜1 +
⎟
KI ⎠
⎝
Derivation on page 423
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An example of a competitive inhibitor
Structures of succinate, the substrate of succinate dehydrogenase (SDH), and malonate,
the competitive inhibitor. Fumarate (the product of SDH action on succinate) is also shown.
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Pure Noncompetitive Inhibition
Inhibitor binds to different site as substrate
and does not affect the binding of substrate
KI = KI’
KI’
The reaction pathway shows that the
inhibitor binds both to free enzyme and
to enzyme complex.
Consequently, Vmax cannot be attained,
even at high substrate concentrations.
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Pure Noncompetitive Inhibition
KI = KI’
Lineweaver-Burk plot of pure noncompetitive inhibition. Note that I does not alter Km but
that it decreases Vmax. In the presence of I, the y-intercept is equal to (1/Vmax)(1 + I/KI).
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Mixed Noncompetitive Inhibition
Inhibitor binds to different site as substrate and affects the binding of substrate
KI ≠ KI’
KI’
Lineweaver-Burk plot of mixed noncompetitive inhibition. Note that both intercepts and the
slope change in the presence of I. (a) When KI is less than KI'; (b) when KI is greater than
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KI'.
Pure Uncompetitive Inhibition
Inhibitor only binds to enzyme/substrate complex
Lineweaver-Burk plot of pure uncompetitive inhibition. Note that both intercepts
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change, but the slope (KM/Vmax) remains constant in the presence of I.
Which of the following graphs shows the results of reaction rate vs substrate
concentration for an non-allosteric enzyme in the absence and presence of a noncompetitive inhibitor (non-competitive inhibitors bind to an enzyme at a site
different than the active site)?
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What Is the Kinetic Behavior of
Enzymes Catalyzing Bimolecular
Reactions?
• Enzymes often use two (or more) substrates
• Reactions may be sequential or singledisplacement reactions
• And they can be random or ordered
enzyme
A + B ÅÆP + Q
E + A + B ÆAEBÆPEQÆE + P + Q
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Creatine kinase acts by a random, single-displacement mechanism
The structures of creatine and creatine
phosphate, guanidinium compounds
that are important in muscle energy
metabolism.
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Single-displacement bisubstrate mechanism
Single-displacement bisubstrate mechanism. Double-reciprocal plots of the rates observed
with different fixed concentrations of one substrate (B here) are graphed versus a series of
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concentrations of A. Note that, in these Lineweaver-Burk plots for single-displacement
bisubstrate mechanisms, the lines intersect to the left of the 1/v axis.
Random, single-displacement bisubstrate mechanism
Random, single-displacement bisubstrate mechanisms where A does not affect B binding, and
vice versa. Note that the lines intersect at the 1/[A] axis. (If [B] were varied in an experiment
with several fixed concentrations of A, the lines would intersect at the 1/[B] axis in a 1/v versus
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1/[B] plot.)
Ping-pong bisubstrate mechanism of glutamate aspartate aminotransferase
Glutamate:aspartate
aminotransferase is a pyridoxal
phosphate-dependent enzyme.
The pyridoxal serves as the NH2 acceptor from glutamate to
form pyridoxamine.
Pyridoxamine is then the amino
donor to oxaloacetate to form
aspartate and regenerate the
pyridoxal coenzyme form. (The
pyridoxamine: enzyme is the E'
form.)
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Ping-pong bisubstrate mechanism
Double-displacement (ping-pong) bisubstrate mechanisms are characterized by LineweaverBurk plots of parallel lines when double-reciprocal plots of the rates observed with different
fixed concentrations of the second substrate, B, are graphed versus a series of
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concentrations of A.