Enzyme Kinetics

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Chapter 12

• Enzyme Kinetics

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Enzyme Kinetics

• Study of Enzymatic Reaction Rates
• Start with Chemical Kinetics
• REACTION ORDER
• dependent upon the of substrates in a reaction

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Enzyme Kinetics

• Describing the simple reaction
• A?P
• Each elementary reaction may be characterized by
  a mechanistic description that includes
  intermediates
• A?I1? I2 ?P

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REACTION RATES

• At constant temperature, the rate of an
  elementary reaction is proportional to the
  frequency with which the reacting molecules come
  together.
• Thus, for A?P, the appearance of P or
  disappearance of A can be expressed as a function
  of a rate constant, k, by determining the
  INSTANTANEOUS VELOCITY which is governed by the
  REACTION ORDER

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REACTION ORDER
The REACTION ORDER of an elementary reaction
corresponds to the molecularity of the reaction
the number of molecules that must simultaneously
collide First Order Reaction Unimolecular
Reaction where k has units of sec-1
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Reaction Velocity
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REACTION ORDER
Second Order Reaction Bimolecular Reaction
where k has units of M-1sec-1 Examples 2 A
? P or A B ? P A bimolecular reaction
that is first order in A and first order in B
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REACTION ORDER

• Unimolecular and Bimolecular Reactions are Common
• Termolecular (third order) and higher reactions
  an unusual because of the extremely low
  probability of the simultaneous collision of
  three molecules thus, rate equations do not
  become overly complex!

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RATE EQUATION

• Velocity describes the progress of a reaction as
  a function of time thus, the rate equation can
  be derived from the instantaneous velocity
  equation
• Taking into account the change of A with time

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1st ORDER RATE EQUATION
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1st ORDER RATE EQUATION
Taking the antilog of both sides,
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1st ORDER RATE EQUATION
y b mx
lnA0
lnA
Slope -k
time
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1st ORDER RATE EQUATION
Half-life t1/2 is a constant independent of
A0
lnA0
lnA
Slope -k
time
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RADIOACTIVE DECAY IS 1st ORDER
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Problem 12.1
If there are 10 ?mol of 32P at t 0, how much
will remain at 7 days?
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2nd ORDER RATE EQUATION
Taking t1/2 depends on A
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2nd ORDER RATE EQUATION
To avoid complex calculations, 2nd order
reactions are often made into Pseudo-first-order
reactions by making one reactant significantly
higher than the other. EXAMPLE for A B ? P,
if AgtgtB then the reaction is 1st order with
respect to B
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Problem 12.2
Determine if the following are 1st or 2nd Order
determine K
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Problem 12.2
Time versus ln A (1st order) for Reaction A and
Reaction B
Reaction A
Reaction B
lnA
lnA
Time
Time
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Enzyme Kinetics

• Enzymes use 6 different mechanisms, yet all can
  be analyzed so that reaction rates and
  efficiencies can be quantified
• Example ?-fructofuranosidase
• Sucrose H2O ? Glucose Fructose
• If SucrosegtgtEnzyme rate becomes 0 order
  with respect to sucrose (rate is independent of
  Sucrose), and

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Enzyme Kinetics

• Sucrose H2O ? Glucose Fructose
• E S ES P E
• Assume When S is very high the second step
  is the rate-limiting reaction and is irreversible

k1
k2
k-1
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Michaelis-Menten Equation

• Sucrose H2O ? Glucose Fructose
• E S ES P E

k1
k2
k-1
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Michaelis-Menten Equation

• Simplification of this equation requires an
  assumption
• 1. Equilibrium Assumption of Michaelis and
  Menten k-1gtgtk2 so that

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Michaelis-Menten Equation

• Simplification of this equation requires an
  assumption
• 2. Steady State Assumption of Briggs and Haldane
  when SgtgtE, the ES is constant after the
  first milliseconds, i.e.,
• Figure 12.2

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Michaelis-Menten Equation

• These two assumptions allow substitutions in the
  original rate equations to yield the
  Michaelis-Menten Equation for kinetics
• Where

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Michaelis-Menten Equation

• Sucrose H2O ? Glucose Fructose
• E S ES P E
• Assumes k2 is small with respect to k-1, and that
  k2is irreversible

k2
k1
k-1
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Michaelis-Menten Equation

• Importance of the M-M Equation
• Where SKm, v0Vmax/2 or
• Km S where the reaction velocity is ½ max

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Michaelis-Menten Equation

• Km is a function of the enzyme, substrate,
  temperature and pH
• Km is also a measure of the substrates affinity
  for the enzyme if k2ltltk-1 (Equilibrium
  Assumption)
• Km k-1/k1 k2/k1 Ks k2/k1
• As Km or Ks decrease, S affinity increases

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Michaelis-Menten Equation

• The double-reciprocal of the M-M equation yields
  a linear relationship that is often shown as as a
  Lineweaver-Burk Plot

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Michaelis-Menten Equation

• The double-reciprocal of the M-M equation yields
  a linear relationship that is often shown as as a
  Lineweaver-Burk Plot
• Problem 12.6

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Michaelis-Menten Equation

• Catalytic Constant or Kcat (Turn over number per
  unit time) ?k2 in the M-M model
• Table 12-1

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Michaelis-Menten Equation

• Catalytic Constant or Kcat is limited by k1 ES
  can go to E P no faster than E S come
  together
• Kcat/Km represents the catalytic efficiency of
  the enzyme and is limited by the rate of
  diffusion (108 to 109 M-1 s-1)
• Such enzymes do exist and virtually catalyze a
  reaction every time they come in contact with a
  substrate molecule

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1st ORDER RATE EQUATION
Taking the antilog of both sides,
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2nd ORDER RATE EQUATION
Taking t1/2 depends on A
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Problem 12.2
Determine if the following are 1st or 2nd Order
determine K
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Problem 12.2
Time versus lnA (1st order) for Reaction A and
Reaction B
Reaction A
Reaction B
lnA
lnA
Time
Time
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Problem 12.2
Time versus 1/A (2nd order) for Reaction A
Reaction A
1/A
Time
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Michaelis-Menten Equation

• Importance of the M-M Equation
• Where SKm, v0Vmax/2 or
• Km S where the reaction velocity is ½ max

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Michaelis-Menten Equation

• The double-reciprocal of the M-M equation yields
  a linear relationship that is often shown as as a
  Lineweaver-Burk Plot

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Michaelis-Menten Equation

• The double-reciprocal of the M-M equation yields
  a linear relationship that is often shown as a
  Lineweaver-Burk Plot
• Problem 12.6
• Vmax 1.20 mM/s
• Km 0.25 ?M

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Bisubstrate Reactions

• 2 substrate 2 product reactions 60 of
  biochemical reactions
• A B ? P Q
• P-X B ? P B-X
• Examples Transfer Rxns Peptide hydrolysis
  with water
• Redox Rxns Alcohol dehydrogenase hydride
  transfer

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Bisubstrate Reactions

• Classifications
• Binding Order Rxns in which all substrates
  bind before any are released are termed
  Sequential or Single-displacement Reactions
• Single-displacement reactions involve a single
  group transfer from A to B
• These Rxns may be ORDERED or RANDOM
• Notation developed by Cleland demonstrate these
  mechanisms

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Bisubstrate Reactions
A
B
P
Q
E
EA
EAB?EPQ
EQ
E
Ordered
A
B
P
Q
EA
EQ
E
E
EAB?EPQ
EB
EP
B
Random
A
P
Q
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Bisubstrate Reactions

• Rxns in which some products are released before
  others bind are termed Ping Pong Reactions
• These reactions may still involve a single group
  transfer from A to B but are termed
  double-displacement reactions substrates A and
  B never meet on the enzyme surface

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Bisubstrate Reactions
Double-Displacement/Ping Pong Reactions
A
B
P
Q
E
EA?FP
FB?EQ
E
F
Example Trypsin / Serine Proteases (Fig. 11-26,
p.313)
Peptide
ILT
H2O
VAK
Trypsin (His57-Ser195 H-bond)
Trypsin (His57-Ser195 H-bond)
TrypsinPeptideVAKILT ?TrypsinH--VAK-ILT
TrypsinH--VAK
TrypsinH--VAK-H2O ?Trypsin VAK
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Bisubstrate Reactions

• Rate equations beyond this course
• Steady State measurements can, however,
  distinguish between mechanisms
• Stop-flow techniques of biochemistry become
  necessary for measuring rates of ES formation

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Enzyme Inhibition

• Basis for much of pharmacology AZTreverse
  transcriptase inhibitor peptidometicsviral
  protease inhibitor
• Side Effects
• Bioavailability
• Developed Resistance
• Can be enzyme-specific issues

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Enzyme Inhibition

• Modes of Inhibition
• Competitive
• Uncompetitive
• Mixed or Noncompetitive
• All can be diagnosed by M-M kinetics using
  Lineweaver-Burk plots

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Competitive Enzyme Inhibition

• Competitive Inhibition
• I directly competes with S for E-binding
  site, but will not react like substrate
• e.g. Succinate Dehydrogenase

COO-
COO-
COO-
CH
CH2
CH2
CH
CH2
COO-
COO-
COO-
Succinate S
Fumarate P
Malonate I
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Competitive Enzyme Inhibition
E S ? ES ? P E I ? EI S ?
NO REACTION Km appears larger because more S
is needed to outcompete I, but ultimately the
same Vmax may be achieved
X
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Competitive Enzyme Inhibition
Vmax
I2
I1
I0
Slope?Km/Vmax
-1/?Km (Apparent Km)
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Uncompetitive Enzyme Inhibition

• Uncompetitive Inhibition
• Inhibitor binds to ES (Michaelis) Complex, but
  not to free enzyme
• Inhibitor affects the catalytic function but not
  substrate binding
• Rare in single-substrate enzymes

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Uncompetitive Enzyme Inhibition
E S ? ES ? P E
I ?
EIS ? NO REACTION Km and Vmax both
decrease (increasing S cannot overcome
I)
X
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Uncompetitive Enzyme Inhibition
Apparent Vmax
I1
I2
I0
Y intercept?/Vmax
Apparent -1/Km
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Mixed Enzyme Inhibition
E S ? ES ? P E I
I ? ? EI
EIS ? NO REACTION Vmax decreases Km may
increase or decrease
X
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Mixed Enzyme Inhibition
Apparent Vmax
I1
I2
I0
Slope?Km/Vmax
Y intercept?/Vmax
Apparent -1/Km
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Mixed Enzyme Inhibition

• Mixed or NONcompetitive Inhibition
• Inhibitor binds both to free enzyme to block
  substrate binding and to ES (Michaelis) Complex
• Most common in multi-substrate reaction
• Irreversible inactivation (inactivators) will
  resemble noncompetitive inhibition by reducing
  the effective level of ET, producing with an
  intersection on the x-axis (1/S)

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Regulation of Enzyme Activity

• Enzme Availability
• Enzyme Synthesis Degradation
• Activity
• Covalent Modification (Phosphorelation)
• Allosteric Effectors
• Sigmoidal Kinetics
• Symmetrical, Multisubunit
• Communication via quaternary shifts

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QUIZ 5

• TRY PROBLEM 12.11