Enzymes:

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Enzymes

• increase the rates of reactions
• are highly specific for their preferred substrate
• Can be regulated
• can be localized in certain organelles
• Can be organized into pathways.

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Rate Enhancement
Enzyme Non-enzymic t1/2 (yr) Rate Enhancement
OMP decarboxylase 78 000 000 1.4 X 1017
Adenosine deaminase 120 2.1 X 1012
Cytidine deaminase 69 1.2 X 1012
Carbonic anhydrase 5 sec 7.7 X 106
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The Thermodynamics of a Reaction
Reaction performed Under standard
conditions 25oC and 1 atmosphere air pressure
Free Energy (G)
Substrate (1 M)
Progress of the reaction
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The Thermodynamics of a Reaction
Reaction performed Under standard
conditions 25oC and 1 atmosphere air pressure
Free Energy (G)
Substrate (1 M)
DG0
Product (1 M)
Progress of the reaction
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The Thermodynamics of a Reaction
Reaction performed Under standard
conditions 25oC and 1 atmosphere air pressure
Free Energy (G)
A negative DG0 Makes the reaction Thermodynamicall
y favourable
Substrate (1 M)
DG0
Product (1 M)
Progress of the reaction
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The Thermodynamics of a Reaction
Reaction performed Under standard
conditions 25oC and 1 atmosphere air pressure
Free Energy (G)
The DGo is related to the Keq. The exact
relationship is as follows DGo -RTlnKeq
Substrate (1 M)
DG0
Product (1 M)
Progress of the reaction
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The Kinetics of a Reaction
Free Energy (G)
Substrate (1 M)
DG0
Product (1 M)
Progress of the reaction
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The Kinetics of a Reaction
Activation Energy DG
Free Energy (G)
Substrate (1 M)
DG0
Product (1 M)
Progress of the reaction
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The Kinetics of a Reaction
The enzyme lowers the activation energy DG
Free Energy (G)
Substrate (1 M)
DG0
Product (1 M)
Progress of the reaction
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The Kinetics of a Reaction
The enzyme lowers the activation energy DG DG
Free Energy (G)
Substrate (1 M)
DG0
Product (1 M)
Progress of the reaction
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Recapping

• Enzymes CANNOT change the thermodynamics of a
  reaction DGo or Keq
• They CANNOT change the direction of a reaction or
  the position of the equilibrium.
• They DO increase the rate of the reaction by
  lowering the activation energy.

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Reaction Rate Measurements

• The rate of a reaction is measured as the moles
  of product produced per unit time.
• The most user friendly units are mmol/min.
• The term ASSAY is used in Biochemistry to
  describe a reaction that measures something
  enzyme activity or the concentration of a
  metabolite.

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Measuring the rate of a reaction
product
Time (min)
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Measuring the rate of a reaction
The initial linear rate Is used for all enzyme
kinetics measurements
product
dP/dt
Time (min)
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Calculating Velocity

• Using the Alkaline Phosphatase Experiment,
  suppose you had a change in Absorbance per min
  (DA/min) of 0.3..
• Step 1 Convert to Dconcentration/min by dividing
  the DA/min by the extinction coefficient (e), say
  15 mM-1cm-1 giving Dconc/min 0.02 mM/min
• Step 2 Convert to nmoles/min in the assay. The
  assay is 1 mL so 0.02 mM/min 0.02 mmol/mL/min
  20 nmol/min/assay.

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The Effect of substrate
on a simple first order reaction without an enzyme
Slope k, the rate constant
Reaction rate
First order means the reaction rate is dependent
on the concentration of only one reactant.
substrate
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The Effect of substrate
on a simple first order reaction with an enzyme
All the available enzyme is saturated with
substrate
Reaction rate
substrate
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The Effect of substrate
on a simple first order reaction with an enzyme
Vmax
Reaction rate
The KM is the S at ½Vmax
substrate
KM
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The Effect of substrate
on a simple first order reaction with an enzyme
Vmax
The KM describes the shape of the curve
Reaction rate
The KM is the S at ½Vmax
substrate
KM
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Vmax What is the maximum speed the car can go at?
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KM how much petrol do you need to travel at 60
kph?
Maybe the little car is more efficient?
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The Lineweaver-Burk Plot
A double reciprocal plot used to find Vmax and KM
1/Vmax
1/v
1/S
-1/KM
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The KM
Vmax
Two different isoenzymes with different KMs for
the same substrate. Which has the higher affinity
for the substrate?
Reaction rate
KM
KM
substrate
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The KM
Vmax
Higher affinity because it takes less substrate
to attain Vmax.
Reaction rate
KM
KM
substrate
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The KM
Vmax
Higher affinity means a lower KM
Reaction rate
KM
KM
substrate
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The Progress of the Reaction in more detail.
E S
ES
EX
E P
EX
Free Energy (G)
DG
S
DG0
P E
ES
Progress of the reaction
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The KM and the Vmax
E S
ES
E P
KM
Kcat Vmax/E
Measures the affinity of the enzyme and substrate
Measures how fast the reaction can go
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The KM
In most cases
OR
Rate of dissociation
KM
Rate of association
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The Significance of KM

• The S which gives ½ Vmax
• A measure of the affinity the enzyme has for the
  substrate
• A low KM means high affinity and vice versa a
  high KM means low affinity
• The KM is independent of the E

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What is Vmax?

• Vmax is measured in Units (U).
• 1 Unit (U) is the amount of enzyme required to
  release 1 mmole of product (P) in 1 minute under
  Vmax conditions.
• You measure the rate of the reaction over a short
  time (min).

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Vmax and E
The Vmax can be used practically to measure the
amount of active enzyme in a sample e.g. serum.
You will use this in the gene expression prac.
Vmax
enzyme
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kcat

• The number of molecules of substrate converted to
  product by 1 molecule of enzyme in 1 second.
• This is equivalent to the mmoles of product
  produced per sec per mmole of enzyme OR the
  nmoles P/sec/nmol E
• Units are seconds-1

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Calculating kcat

• Begin with the Vmax
• In the Alkaline Phosphatase experiment the Vmax
  is usually around 30 nmol/min.
• This works out to 0.5 nmoles P/sec (/60)
• Now all we need to know is how many nmoles of
  Enzyme produced this rate.
• To calculate this we need to know how much enzyme
  we added to the assay and the molecular weight of
  the enzyme.

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Calculating kcat

• In the Alkaline Phosphatase experiment you added
  20 ?L of enzyme solution containing 50 ?g/mL
  enzyme. This means we have 2050 ng 1 ?g.
• So now our Vmax rate is
• 0.5 nmoles P/sec/1 000 ng E

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Calculating kcat

• The Vmax rate is
• 0.5 nmoles P/sec/1 000 ng E
• If the molecular weight of Alkaline Phosphatase
  is 100,000 then there is 1/100 (1 000/100 000)
  of a nmole of Enzyme in the assay.

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Calculating kcat

• If 1/100 th of a nmole of Enzyme catalyses the
  formation of 0.5 nmoles of product in 1 second
  then.
• 1 nmole of enzyme will catalyse 0.5100 50
  nmoles of product in 1 second
• The Kcat 50 nmol sec-1nmol-1
• The Kcat 50 sec-1

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The Steady State Assumption

• Used to explain the shape of the hyperbola
• A level of ES, ES, is established very early in
  the reaction
• This ES level is dependent on the S
• This ES remains constant throughout the
  reaction.

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The Steady State Assumption
Product
Substrate
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The Steady State Assumption
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The Michaelis Menten Plot
Vmax
Reaction rate
The KM is the S at ½Vmax
substrate
KM
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Prac Results Alkaline Phosphatase
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Prac ResultsAlkaline Phosphatase
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The Michaelis Menten Relationship

• The equation below describes the hyperbola.
• Velocity Vmax S
• (S Km)

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Deriving the Michaelis Menten Relationship

• The steady state assumption means that the rate
  of formation of ES the rate of breakdown of ES

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Deriving the Michaelis Menten Relationship

• Mathematically the steady state assumption means
  that the rate of formation of ES the rate of
  breakdown of ES.
• Rate of formation k1ES
• Rate of breakdown k-1ES k2ES
• Therefore k1ES k-1ES k2ES

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Deriving the Michaelis Menten Relationship

• k1ES k-1ES k2ES
• Simplifying k1ES ES (k-1 k2)
• Now KM (k-1 k2)/ k1
• So ES ES KM

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Deriving the Michaelis Menten Relationship

• ES ES KM
• Now the Total amount of Enzyme ET Efree ES
• ?E Efree ET ES
• ET ES ES KM/S
• ET ES KM/S ES

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Deriving the Michaelis Menten Relationship

• ET ES KM/S ES
• Now Vmax ETk2 and velocity (v) ESk2
• So multiplying both sides by k2
• ET k2 ES k2(KM/S 1)
• Vmax v (KM/S 1)

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Deriving the Michaelis Menten Relationship

• Vmax v (KMS)/S )
• Cross multiplying 1/v (KM S)
• Inverting V Vmax S
• (KMS)

VmaxS
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kcat/KM

• This measurement reflects the efficiency of the
  enzyme.
• What we really want to know is how often ES goes
  to E P.
• An efficient enzyme will send all the ES to E
  P.
• An inefficient enzyme will send some back to E
  S

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kcat/KM

• Kcat is k2 and KM (k-1 k2)/k1
• So kcat/KM k2 k1 / (k-1 k2)
• Now if the enzyme is really efficient k-1 will be
  really small (very little ES going back to E S)
• kcat/KM approaches k1. This is limited by the
  rate of diffusion.

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Inhibitors

• Inhibitors can be irreversible or reversible.
• Irreversible inhibitors usually covalently bind
  to the enzyme they are often slower to act (time
  dependent inhibition) and present as
  non-competitive inhibition. They cannot be
  dialysed out or diluted out.
• Reversible inhibitors competitive,
  non-competitive, mixed, uncompetitive

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The Competitive Inhibitor

• The inhibitor binds to the same site on the
  enzyme as the substrate
• Thus it competes with the substrate
• It eventually reaches Vmax
• It needs more substrate to do it ? Km increases

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The Effect of a Competitive Inhibitor
Vmax
The competitive Inhibitor Is in yellow
Reaction rate
substrate
KM
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The Competitive Inhibitor
1/v
A Competitive Inhibitor
No Inhibitor
1/Vmax
1/S
-1/KM
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The Competitive Inhibitor
Vmax unchanged Km increases -1/Km increases
1/v
A Competitive Inhibitor
No Inhibitor
1/Vmax
1/S
-1/KM
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The Non-Competitive Inhibitor

• The inhibitor binds to a site other than the
  substrate binding site
• Both I and S can bind to the enzyme
  simultaneously
• It never reaches Vmax
• The Km does not change
• It is like adding less enzyme to an assay

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The Effect of a Non-competitive Inhibitor
Vmax
Reaction rate
The non-competitive Inhibitor Is in yellow
substrate
KM
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The Non-competitive Inhibitor
A Non-competitive Inhibitor
1/v
No Inhibitor
1/Vmax
1/S
-1/KM
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The Non-competitive Inhibitor

• Vmax decreases
• 1/Vmax increases
• Km unchanged

A Non-competitive Inhibitor
1/v
No Inhibitor
1/Vmax
1/S
-1/KM
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The mixed Non-Competitive Inhibitor

• The inhibitor binds to a site other than the
  substrate binding site
• But the binding of the substrate to the enzyme
  alters the affinity of the inhibitor for the
  enzyme
• Both Km and Vmax change
• The most common type of inhibition

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Ki ? Ki
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The mixed non-competitive Inhibitor
A mixed non-competitive Inhibitor
1/v
No Inhibitor
1/Vmax
1/S
-1/KM
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The Uncompetitive Inhibitor

• The inhibitor binds to the ES complex only
• Both Km and Vmax decrease
• Vmax/Km unchanged

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The Uncompetitive Inhibitor

• Vmax decreases
• Km decreases
• Vmax/Km unchanged

An uncompetitive Inhibitor
1/v
No Inhibitor
1/Vmax
1/S
-1/KM
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Regulatory Enzymes

• Allosteric regulation the binding of a small
  molecule (ligand) distant from the active site,
• Covalent modification, often phosphorylation of
  serine, threonine or tyrosine residues,

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Regulatory Enzymes

• Changes in the amount of enzyme either by changes
  in gene expression, (often at the level of
  transcription) or protein turnover,
• Substrate availability,
• Inhibition (competitive etc),
• Activation of zymogens or pro-enzymes.

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Allosteric Regulation
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Allosteric Enzymes
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Allosteric Regulation
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Covalent Modification

• Usually phosphorylation
• Residues serine, threonine or tyrosine
• The example of glycogen synthase
• Often used in cell signalling
• Insulin signalling

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Zymogen Activation

• Often used with proteases
• To prevent random destruction of the cell
• Produced as an inactive form
• A small portion cleaved off to activate
• Chymotrypsinogen ? chymotrypsin
• Trypsinogen ? trypsin