Chapter 14 Rates of Enzymatic Reactions

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Chapter 14Rates of Enzymatic Reactions

• Reading
• VV pp. 472-487

Chymotrypsin with bound substrate
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Enzyme Kinetics

• Enzymes accelerate reactions by lowering the free
  energy of activation
• Enzymes do this by binding the transition state
  of the reaction better than the substrate

• Several terms to know
• rate or velocity
• rate constant
• rate law
• order of a reaction
• molecularity of a reaction

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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 rapid
  equilibrium 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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k2
(k-2 is insignificant early in rxn)
Vo k2 ES
Rate of ES formation k1 ES 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)
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The dual nature of the Michaelis-Menten equation

• Combination of zero-order and first-order
  kinetics
• 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

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Enzyme Kinetics Michaelis-Menton Equation
VmaxS Vo ____________
KM S


KM S when Vo Vmax
_____
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From Lehninger Principles of Biochemistry
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The following data were obtained in a study of an
enzyme known to follow Michaelis Menten
kinetics V0 Substrate
added (mmol/min) (mmol/L)
216 0.9
323 2
435 4 489 6 647
2,000 Calculate the Km for
this enzyme.
Km is the substrate concentration that
corresponds to Vmax
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Without graphing Vmax 647 Vmax /2 647 / 2
323.5 Km 2 mmol/L
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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 E from S
  
• Small Km means tight binding high Km means weak
  binding

Enzyme Substrate Km (mM) Glutamate
dehydrogenase NH4 57 Glutamate 0.12 Carbo
nic anhydrase CO2 12
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Understanding Vmax

• The theoretical maximal velocity
• Vmax is a constant
• Vmax is the theoretical maximal rate of the
  reaction - but it is NEVER achieved in reality
• To reach Vmax would require that ALL enzyme
  molecules are tightly bound with substrate
• Vmax is asymptotically approached as substrate
  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 enzyme

• Name for kcat/Km
• 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 is low
  
• Catalytic efficiency cannot exceed the diffusion
  limit - the rate at which E and S diffuse
  together
• WT and a mutant protein kcat/Km comparision
• WT sulfite oxidase 1.1
• Mutant R160K 0.015

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Use linear plot and intercepts to determine Km
and Vmax
1 KM 1 ______
_______ ______ Vo VmaxS
Vmax
Double-Reciprocal or Lineweaver-Burk Plot
From Lehninger Principles of Biochemistry
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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 hypothetical case
  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 has never been
documented for a real enzyme, but which makes a
useful contrast to competitive inhibition
Enzyme Inhibition
Inhibitor (I) binds to E and to ES.
From Lehninger Principles of Biochemistry
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Competitive Uncompetitive
Noncompetitive Inhibition
Inhibition (Mixed) Inhibition
Kmchanges while Vmax does not
Km and Vmax both change
Km and Vmax both change
From Lehninger Principles of Biochemistry
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Succinate dehydrogenase is a classic example of
competitive inhibition
Malonate is a strong competitive inhibitor of
succinate dehydrogenase
From Lehninger Principles of Biochemistry
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Competitive Inhibition
Kmchanges while Vmax does not
1/S
I
1/V
No I
-1 / Km
-1 / Kmapp
Where Kmapp a Km
a 1 I KI
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Uncompetitive inhibition
1/S
I
a/Vmax
1/V
No I
-a / Km
1/Vmax
-1 / Km
a 1 I KI
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Effects of Inhibitors on the parameters of
Michaelis-Menten Equation
Type of inhibition Vmaxapp KMapp No
inhibitor Vmax KM Competitive Vmax aKM U
ncompetitive Vmax/a KM/a Noncompetitive
(Mixed) Vmax/a aKM/a a 1 I a
1 I KI KI
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• Regulation of enzymatic activity
• Two ways that this may occur
• Control of enzyme availability
• Depends on rate of enzyme synthesis
  degradation
• Control of enzyme activity
• Enzyme-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
From Lehninger Principles of Biochemistry
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Regulation by Feedback Inhibition
Conversion of L-threonine to L-isoleucine
catalyzed by a sequence five enzymes,
E1-E5 L-isoleucine is an inhibitory allosteric
modulator of E1
From Lehninger Principles of Biochemistry