l16 enzyme kinetics (ch14)
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Chapter 14Rates of Enzymatic Reactions
Reading:
V&V pp. 472-487
Chymotrypsin with bound substrate
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Enzyme Kinetics
Several terms to know:
• rate or velocity
• rate constant
• rate law
• order of a reaction
• molecularity of a reaction
• Enzymes accelerate reactions by lowering thefree energy of activation
• Enzymes do this by binding the transition state
of the reaction better than the substrate
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The Michaelis-Menten Equation
• Louis Michaelis and Maude Menten's theory
• It assumes the formation of an enzyme-substrate complex
• It assumes that the ES complex is in rapidequilibrium with free enzyme
• Breakdown of ES to form products is assumed
to be slower than(1) formation of ES and
(2) breakdown of ES to re-form E and S
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The dual nature of the Michaelis-Menten equation
Combination of zero-order and 1st-order kinetics
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E + S ES E + P
k1
k-1
k2
Vo = k2 [ES]
Rate of ES formation = k1 [E][S] = k1 ([Etotal] - [ES]) [S]
Rate of ES breakdown = k-1 [ES] + k2 [ES]
k1 ([Etotal] - [ES]) [S] = k-1 [ES] + k2 [ES](steady state assumption)
(k-2 is insignificant early in rxn)
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k1 [Etotal][S] - k1[ES][S] = ( k-1 + k2 )[ES]
k1 [Etotal][S] = (k1[S] + k-1 + k2 )[ES]
[ES] =[Etotal][S]
________________________
[S] + (k2 + k-1 ) ___________
k1
=[Etotal][S]
____________
KM + [S]
Vo = k2 [ES] Vo =k2 [Etotal][S] ____________
KM + [S]
Vo = Vmax when [Etotal] = [ES](at saturation)
Therefore Vmax = k2 [Etotal]
Vo =Vmax[S]
____________
KM + [S]
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The dual nature of the
Michaelis-Menten equation
Combinat ion o f zero-order and f i rs t -order kinet ics
• When [S] is low, the equation for rate is first order in [S]
• When [S] is high, the equation for rate is zero-order in [S]
• The Michaelis-Menten equation describes a rectangular hyperbolic
dependence of Vo on [S]
Vo = Vmax[S] _________
Km + [S]
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Vmax[S]Vo = ____________
KM + [S]
KM = [S]
when Vo
= Vmax _____
2
Enzyme Kinetics: Michaelis-Menton Equation
From LehningerPrinciples of Biochemistry
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The following data were obtained in a study of an enzyme known to follow
Michaelis Menten kinetics:
V 0
Substrate added
(mmol/min) (mmol/L)
—————————————
216 0.9
323 2
435 4
489 6647 2,000
—————————————
Calculate the K m for this enzyme.
Without graphing
Vmax = 647
Vmax /2 = 647 / 2 = 323.5
Km = 2 mmol/L
Km is the substrate
concentration that
corresponds to Vmax
2
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Understanding Km
• Km is a constant • Km is a constant derived from rate constants
• Km is, under true Michaelis-Menten conditions,
an estimate of the dissociation constant of Efrom S
• Small Km means tight binding; high Km means
weak binding
Enzyme Substrate Km (mM)Glutamate dehydrogenase NH4
+ 57
Glutamate 0.12
Carbonic anhydrase CO2 12
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Understanding Vmax
The theoretical maximal velocity
• Vmax is a constant
• Vmax is the theoretical maximal rate of thereaction - but it is NEVER achieved in reality
• To reach Vmax would require that ALLenzyme molecules are tightly bound with
substrate• Vmax is asymptotically approached assubstrate is increased
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The turnover number (also known as the molecular activity of the enzyme)
A measure of its maximal 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.• If the M-M model fits, k2 = kcat
kcat = Vmax/Et
• Values of kcat range from less than 1/sec to many millions per sec
Turnover number comparison
Catalase 40,000,000 sec-1
Lysozyme 0.5 sec-1
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Catalytic efficiency of an enzymeName for k cat /K m
• An estimate of "how perfect" the enzyme is • kcat/Km is an apparent second-order rate constant
• It measures how the enzyme performs when S islow
• Catalytic efficiency cannot exceed the diffusionlimit - the rate at which E and S diffuse together
• WT and a mutant protein k cat /K m comparision
WT sulfite oxidase 1.1
Mutant R160K 0.015
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Double-Reciprocal or Lineweaver-Burk Plot
1 KM
1 ______ = _______ + ______
Vo Vmax[S] Vmax
From LehningerPrinciples of Biochemistry
Use linear plot and intercepts to
determine Km and Vmax
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pH must be specified!
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Enzyme Inhibitors
Reversible versus Irreversible
• Reversible inhibitors interact with an
enzyme via noncovalent associations
• Irreversible inhibitors interact with an
enzyme via covalent associations
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Classes of Inhibition
Two real, one hypothetical
• Competitive inhibition - inhibitor (I) binds
only to E, not to ES
• Uncompetitive inhibition - inhibitor (I) binds
only to ES, not to E. This is a hypotheticalcase that has never been documented for a
real enzyme, but which makes a useful
contrast to competitive inhibition• Noncompetitive (mixed) inhibition - inhibitor
(I) binds to E and to ES
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Inhibitor (I) binds only to E, not to ES
Inhibitor (I) binds only to ES, not to E.
This is a hypothetical case that hasnever been documented for a realenzyme, but which makes a usefulcontrast to competitive inhibition
Inhibitor (I) binds to E and to ES. Enzyme Inhibition
From LehningerPrinciples of Biochemistry
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Competitive Uncompetitive NoncompetitiveInhibition Inhibition (Mixed) Inhibition
Kmchangeswhile Vmax does not
Km and Vmax both change
Km and Vmax both change
From LehningerPrinciples of Biochemistry
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Succinate dehydrogenase is a classic example of competitive inhibition
From LehningerPrinciples of Biochemistry
Malonate is a strong
competitive inhibitor of
succinate dehydrogenase
C titi I hibiti
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1/[S]
1/V
+ I
No I
-1 / Km
-1 / Kmapp
Competitive Inhibition
Km
changes whileVmax does not
Where Kmapp = a Km a = 1 + [I]
KI
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1/[S]
1/V+ I
No I
-a’ / Km
-1 / Km
a‘ = 1 + [I]
KI
Uncompetitive inhibition
a’/Vmax
1/Vmax
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Type of inhibition Vmaxapp KM
app
No inhibitor Vmax KM
Competitive Vmax aKM
Uncompetitive Vmax/a’ KM/a’
Noncompetitive (Mixed) Vmax/a’ aKM/a’
a = 1 + [I] a’ = 1 + [I]
KI KI’
Effects of Inhibitors on the parameters of Michaelis-Menten Equation
R l ti f ti ti it
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Regulation of enzymatic activity
Two ways that this may occur:
1) Control of enzyme availability
Depends on rate of enzyme synthesis & degradation
2) Control of enzyme activityEnzyme-substrate binding affinity may vary with
binding of small molecules called allosteric effectors(ex: BPG for Hb)
Allosteric mechanisms can cause large changes in
enzymatic activity
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Regulatory Enzymes
important in controlling flux through metabolic pathways
2. Regulation by covalent modification
1. Allosteric enzymes
From LehningerPrinciples of Biochemistry
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Conversion of L-threonine toL-isoleucine catalyzed by asequence five enzymes, E1-E5
L-isoleucine is an inhibitoryallosteric modulator of E1
Regulation by Feedback Inhibition
From Lehninger