Enzymes: Basic Concepts and Kinetics

1
Enzymes Basic Concepts and Kinetics
1. Enzymes are specific catalysts 2. ?G is
useful for understanding enzymes 3. Enzymes
accelerate reactions by facilitating the
formation of the transition state 4. Michaelis
Menten model describes Kinetic properties of
many enzymes 5. Enzymes can be inhibited
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Enzymes accelerate Reactions
Carbonic anhydrase an enzyme in the blood
hydrating CO2
Transfer of CO2 from the tissue -gt blood -gt
release into air -gt one of the fastest enzymes
-gt hydrates 106 molecules/sec
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Enzymes are highly specific
-gt in reactions -gt in substrate
Proteases A -gt Trypsin B -gt Thrombin
Some proteases can also be more unspecific in
terms of -gt substrate (different peptides) -gt
reaction (cleave also esters)
DNA polymerase is highly specific -gt 1 mistake
in less than 1000 bps
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Enzymes require Cofactors
Apo enzyme cofactor -gt Holo enzyme
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Enzymes may transform Energy
ATPase Oxidation and ATP synthesis are coupled
by transmembrane H fluxes
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The enzyme classification (EC number)
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?G (Free energy) provides information about
reaction
0
positive
negative
?G
Equilibrium
Reaction cannot occurs spontaneously
Reaction occurs spontaneously
?G -gt depend on G (product ) G
(reactants) -gt independent of
path or mechanism -gt no
information about rate of reaction
(rate depends on ?G activation )
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?GO (Standard Free energy) related to
Equilibrium Konstant Keq

• A B C D
• -gt ?G ?G RT ln CD / AB
• ?G is ?G under standard conditions
• CDAB 1M

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?GO (Standard Free energy) related to
Equilibrium Konstant Keq

• Equilibrium constant Keq CD / AB
• At Eq. ?G0 gt 0?G RT ln Keq
• gt
  ?G - RT ln Keq
• gt
  ?G -2.303 RT Log Keq
• gt Keq 10 - ?G /
  2.303 RT
• ?G for biochemical reactions pH7.0, T
  298K

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Example conversion of DHAP into GAP

• The ration of GAP to DHAP at equilibrium.
• Keq 0.0475 (pH 7.0, 25C)
• gt ?G 1.80 kcal mol-1 (not
  spontaneous)
• -gt at equilibrium not spontaneous !!!
• -gt at different initial concentrations
• DHAP2 10-4 M GAP3 10-6 M
• ?G ?G RT ln GAP/DHAP
• ?G 1.80 2.49
• -gt ?G - 0.69 kcal mol-1 (spontaneous)
• Only spontaneous by adjusting concentrations !!!

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Enzymes do not alter equilibrium
Enzymes -gt alter reation rate
-gt alter NOT equilibrium -gt equilibrium is
faster reached with enzyme !!!!
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Enzymes accelerates reaction by lowering the
activation energy (?G)

• ?G GX - GS
• Enzymes facilitate formation of transition states

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Reaction speed vs Subst. Conc. Indirect
evidence for ES complexes
A ? B Non-catalyzed reaction
A ? B Enz.-catalyzed reaction
-gt Enzym catalyzed reaction have saturation
effect -gt maximum velocity !!! -gt evidence for ES
complex !!!
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X-ray crystallography to see ES complexes
Cytochrome P450
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Active sites in enzymes a number of common
features

• Active site 3D cleft with residues far apart in
  sequence
• Small proportion in volume
• Cleft or crevice with non-polar residues, little
  water (unique microenvironment)
• Substrate binding by several weak attractions
  (e.g. H-bonds)
• Binding specificity governed by 3D arrangement of
  atoms

Lysozyme
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Hydrogen bonding between substrate and active
site
Ribonuclease Forms H-bonds with uridine
component of substrate
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Lock and Key model (E. Fisher, 1890)
Binding specificity governed by 3D arrangement of
atoms
Induced-Fit model(D.E. Koshland, 1958)
Active site complementary to shape of substrate
Active site forms a complementary shape of
substrate after binding substrate
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Example of induced-fit interfacial activation in
lipasesDatabase of Macromolecular Movements
(www.molmovdb.org)
A lipid
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Michaelis-Menten Equation describes kinetic of
many enzymes
Thermodynamics does a reaction take
place? Kinetics how fast does a reaction
proceed?
Reaction rate is the change in the concentration
of a reactant or a product with time (M/s).
DA change in concentration of A over
time period Dt
DB change in concentration of B over
time period Dt
Because A decreases with time, DA is
negative.
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The Rate Law
The rate law expresses the relationship of the
rate of a reaction to the rate constant and the
concentrations of the reactants raised to some
powers.
reaction is xth order in A
reaction is yth order in B
Rate k AxBy
reaction is (x y)th order overall
rate k A
Unimolecular reaction
rate k AB
Bimolecular reaction
2nd order reaction (A B) can appear as 1st
order if -gt B in excess A is low -gt 1st
order for A -gt rate independend on B -gt
Pseudo 1st order reaction !!
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The Rate Law
Given a basic reaction
we assume that the rate of forward reaction is
linearly proportional to the concentrations of A
and B, and the back reaction is linearly
proportional to the concentration of C.
Equilibrium is reached when the net rate of
reaction is zero. Thus
or
This equilibrium constant tells us the extent of
the reaction, NOT its speed.
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Michaelis and Menten
In 1913, Michaelis and Menten proposed the
following mechanism for a saturating reaction rate
Complex.
no back reaction -gt no k-2
product
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Enzyme-catalyzed reaction progression curves
V0 -gt initial velocity -gt product formed /sec at
the beginning of the reaction (t0) -gt V0 changes
with S -gt V0 rises when S rises -gt until
saturation (Max. Velocity)
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Velocity vs Substrate ConcentrationThe
Michaelis-Menten model

• Vmax maximal velocity when all sites occupied
• Km Michaelis constant, when S gives Vmax/2

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Basic assumptions in the Michaelis-Menten model
The velocity equation is too complex to be
directly evaluated, so assumptions must be made.

• Formation of ES complex is necessary intermediate
  in catalysis
• Reversion of Product to Substrate is negligible
  in initial stage of reaction (P ltlt S) v
  k-2EP (Rate Law)

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Another basic assumption the Steady State
(Briggs Haldane, 1925)
Rapidly, ES complex reaches a constant
concentration
If S gtgt E, ES remains constant because the
large excess of S molecules rapidly fill all
enzyme active sites dES/dt 0. This holds
true until all of S is used up
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Michaelis-Menten Kinetics

• When S ltlt KM, the reaction velocity increases
  linearly with S I.e. vo (Vmax / KM ) S -gt
  pseudo 1st order reaction, Very little ES is
  formed
• When S KM, vo Vmax /2 (half maximal
  velocity) this is a definition of KM the
  concentration of substrate which gives ½ of Vmax.
  This means that low values of KM imply the enzyme
  achieves maximal catalytic efficiency at low S.
• When S gtgt Km, vo Vmax
• -gt pseudo 0 order reaction

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Michaelis-Menten Kinetics
When the enzyme is saturated with substrate, the
reaction is progressing at its maximal velocity,
Vmax. At saturation ET ES, and the
equation for reaction velocity simplies to Vmax
k2 ET Combing the steady-state assumption
(dES/dt0) with the conservation condition
(ETE ES) vo leads to the
Michaelis-Menten Equation of enzyme kinetics

where Km is

KM (k-1
k2)/k1
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Michaelis-Menten Kinetics
How do determine experimentally KM and Vmax ?
Lineweaver-Burk plot
Eadie-Hofstee plot
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Michaelis-Menten Kinetics
What is KM ?

• The concentration of substrate which gives ½ of
  Vmax. This means that low values of KM imply the
  enzyme achieves maximal catalytic efficiency at
  low S.
• KM gives an idea of the range of S at which a
  reaction will occur. When k-1gtgtk2, Kmk-1/k1 (ES
  complex dissociates faster than product is formed
  -gt no strong binding affinity)
• and KESES/ESk-1/k1 thus Km KES
  (dissociaton constant)
• -gt indicates binding strength
  (substrate affinity)
• The larger the KM, the WEAKER the binding
  affinity of enzyme for substrate.

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Michaelis-Menten Kinetics
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Michaelis-Menten Kinetics
What is Vmax?

• Vmax gives an idea of how fast the reaction can
  occur under ideal circumstances.
• If Etot is known, Vmax indicates TURN-OVER
  Number
• Vmaxk2Etot or k2Vmax/Etot
• k2 is also called kcat or TURN-OVER Number

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Michaelis-Menten Kinetics
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The kcat/Km criterion a measure for catalytic
efficiency

• When SgtgtKm (enzyme saturated steady state
  conditions)
• -gt VVmax, function of kcat (turn over
  number)
• Under physiological conditions most enzymes are
  NOT saturated
• -gt 0.01 KmltSlt Km , Vltlt kcat (most sites
  are unoccopied)
• -gt Combining V0k2ES with ESES/Km
  gives
• V0(kcat/Km) SE
• -gt When Sltlt Km then EfreeEtot
• -gt kcat/Km is the rate constant for E
  and S interaction
• is measure for
  catalytic efficiency !!!
• -gt ratio kcat/Km considers -gt rate of
  catalysis (kcat) and
• -gt
  strength of enzyme/substrate interaction

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The kcat/Km criterion to probe chymotrypsin
specificity
Highest kcat/Km -gt best substrate -gt highest
efficiency for that substrate!
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Enzymes at kinetic perfection

• Ultimative limit on kcat/Km is set by k1, rate of
  formation of ES
• This rate cannot be faster than
  diffusion-controlled encounter between Enzyme and
  Product (108 to 109 s-1 M-1)

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Multiple-substrate reactions
A B ? P Q

• Sequencial displacement
• All substrates must bind to enzyme before
  product is released
• -gt ordered (substrates bind in defined
  sequence) or random
• A B E ? EAB ? E P Q

Ordered
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Multiple-substrate reactions
A B ? P Q

• Double displacement (Ping-Pong)
• One or more products are released before all
  substrates bind
• -gt a substituted enzyme intermediate exists
  
• A B E ? EA B ? E P B ? EB ? E
  Q

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Allosteric enzymes DO NOT follow Michaelis-Menten
kinetics
-gt often show sigmoidal behaviour
-gt consists of multiple subunits with multiple
active sites -gt binding of substrate to one site
alters properties for other sites in the same
enzyme -gt binding of substrate is
cooperative -gt activity altered by regulatory
molecules that bind reversible to other sites
than active site -gt Example Hemoglobin
4 subunits -gt 4 active sites
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Enzyme Inhibition -gt Reversible
Inhibitor binds to active site -gt prevents
substrate from binding -gt structural analog
Inhibitor binds only to ES complex
Inhibitor does NOT prevent substrate from
binding -gt both can bind at the same time -gt
decreases turnover number
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Competitive inhibition affects Km

• Inhibition overcome by increase in substrate
  concentration
• Km altered apparent Km value increased

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Non-Competitive inhibition affects Vmax

• -gt Inhibition cannot be overcome by increase in
  substrate concentration
• -gt Vmax altered apparent Vmax value decreased

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Un-Competitive inhibition affects Vmax and Km

• -gt Inhibition cannot be overcome by increase in
  substrate concentration
• -gt Vmax altered apparent Vmax value decreased
• -gt Km altered apparent Km value decreased

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Enzyme Inhibition -gt Irreversible

• Group-specific reagents
• -gt e.g. SN Reaction
• Esterfication
• Substrate analogs

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Enzyme Inhibition -gt Irreversible

• Suicide inhibitors
• -gt modified substrate that is
• catalytically modified by enzyme
• -gt reactive intermediate
• -gt inactivates enzyme
• Deprenyl -gt inhibits monoamine oxidase
• -gt MAO deaminates neurotransmitter
• such as dopamine and serotonin
• -gt lowering their levels in the brain
• Parkinson low level of dopamine
• Depression low level of serotonin

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Transition-state analogs the case of proline
racemase

• Pyrrole 2-carboxylic acid binds 160 times more
  tightly than L-proline