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LECTURE No.2
Enzymes: Basic Concepts and Kinetics (Ch.8)
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Enzymes: powerful & specific catalysts
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Carbonic anhydrase: an enzyme in the blood hydrating CO2
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Peptidases hydrolysing the peptide bond in proteins
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Peptidases specificity
Leu Val Pro Arg Gly Ser
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Peptidases also hydrolysing ester bonds
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Without enzymes: still in the pre-biotic era!
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Enzymes often require cofactors
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Energy transformation(ATPase)
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The enzyme classification (EC number)
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BRENDA: online database of enzymes (www.brenda.uni-koeln.de)
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BRENDA: Searchable database
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Nucleoside monophosphate kinase in BRENDA
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Gibbs Free Energy to understand enzymatic
reactions
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Gibbs Free Energy: a fundamental thermodynamic function to describe
chemical reactions
A B + C spontaneous if G<0 (exergonic) at equilibrium if G=0 (no net change) not spontaneous if G>0 (endergonic)
G DOES NOT depend on the mechanismG DOES NOT tell about the reaction rateEnzymes DO NOT affect G
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Linking Free-Energy change with reactants & products concentrations
A + B C + D
G= G° + RT ln [C][D] / [A][B]
G° is G in standard conditions: [C]=[D]=[A]=[B]= 1M
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Equilibrium constant: K’eq= [C][D] / [A][B]
At Eq. G=0 => 0=G°’ + RT ln K’eq
=> G°’= - RT ln K’eq
=> G°’= -2.303 RT Log K’eq
=> K’eq = 10 - G°’ / 2.303 RT
=> K’eq = 10 - G°’ / 1.36
G°’ is G° for biochemical reactions: pH=7.0, T= 298K
Linking Free-Energy change with Equilibrium Constant
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Example: conversion of DHAP into GAP
K’eq = 0.0475 (pH 7.0, 25°C)
=> G°’= 1.80 kcal mol-1
G for [DHAP]=2 10-4 M ; [GAP]=3 10-6 MG= G° + RT ln [GAP]/[DHAP]G= 1.80 – 2.49 G= -0.69 kcal mol-1
Reactions not spontaneous on the G°’ criterion can be made spontaneous by adjusting concentrations
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Enzymes accelerate reactions by lowering the
transition state energy
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A fundamental property of enzymes
Enzymes DO NOT alter equilibria but enhance the rates at which they are reached
A B
K= [B]/[A] = kF/kR (=10-4/10-6=100)
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Transition state and Energy of activation
G‡ = GS‡ - GS
Enzymes facilitate formation of transition states
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Reaction speed vs Subst. Conc. : Indirect evidence for ES complexes
A BNon-catalyzed reaction
A BEnz.-catalyzed reaction
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Fluorescence spectroscopy to detect ES complex in TRP-synthetase
Pyridoxal phosphate (B6)
E + SER + Ind E-SER-Ind
TRP + H2O
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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
Substrate binding by several weak attractions
Binding specificity governed by 3D arrangement
Lysozyme
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Hydrogen bonding between substrate and active site: Ribonuclease
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Lock and Key model (E. Fisher, 1890)
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Induced-Fit model(D.E. Koshland, 1958)
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Example of induced-fit: interfacial activation in lipases
Database of Macromolecular Movements (www.molmovdb.org)
OOO
OOO
A lipid
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Many enzymes show kinetic properties explained by the
Michaelis-Menten model
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Velocity vs Substrate Concentration:The Michaelis-Menten model (1913)
Vmax: maximal velocity when all sites occupied
Km: Michaelis constant, when [S] gives Vmax/2
E + S ES E + Pk1 k2
k-1 k-2
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Enzyme-catalyzed reaction progression curves
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Basic assumptions in the Michaelis-Menten model
Formation of ES complex is necessary intermediate in catalysis
Reversion of Product to Substrate is negligible in initial stage of reaction ([P] << [S]): v = k-2[E][P] (Rate Law)
QUESTION: Mathematical expression linking catalytic velocity to substrate concentration ?
E + S ES E + Pk1 k2
k-1 k-2
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The rate law
Consider the simple reaction : A P (conversion of P back to A negligible)
Velocity or Rate of reaction or
Proportionality between Velocity and reactant concentration
k
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Another basic assumption: the Steady State (Briggs & Haldane, 1925)
E + S ES E + Pk1 k2
k-1
Rapidly, ES complex reaches a constant concentration
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Linking substrate and enzymes concentrations to rate constants
ES formation rate is: vf = k1([Etot] - [ES])[S] with [E] = [Etot] - [ES]
ES disappearance rate is: vd = k-1[ES] + k2[ES] = (k-1 + k2)[ES]
At steady state: d[ES]/dt = 0 => vf = vd
So: k1([Etot] - [ES])[S] = (k-1 + k2)[ES]
Rearranging: ([Etot] - [ES])[S] / [ES] = (k-1 + k2) / k1
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The Michaelis-Menten constant Km
From: ([Etot] - [ES])[S] / [ES] = (k-1 + k2) / k1
The M-M constant is defined as Km = (k-1 + k2) / k1
So: ([Etot] - [ES])[S] / [ES] = Km
Which rearranges into: [ES] = ([Etot] - [S]) / (Km + [S])
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Linking the rate of product formation to Km : Michaelis-Menten equation
Rate of product formation: V=dP/dt =k2[ES]
In [ES] = ([Etot] - [S]) / (Km + [S]) gives:
V= k2[Etot][S] / (Km + [S])
The term k2[Etot] is equal to Vmax, when [ES]=[Etot]
So: V= Vmax[S] / (Km + [S])
Note: When [S]= Km then V=Vmax/2
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Back to the Velocity vs Substrate Concentration plot
V= Vmax[S] / (Km + [S])
When [S]<< Km , V~Vmax
[S]/Km
When [S]>> Km, V~Vmax
When [S]=Km: V=Vmax/2
E + S ES E + Pk1 k2
k-1
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A double reciprocal plot: the Lineweaver-Burk plot
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Km values vary widely
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Km and Vmax provide valuable information about biochemical processes
When k-1>>k2, Km=k-1/k2
and KES=[E][S]/[ES]=k-1/k2 thus Km= KES
indicates binding strength (substrate affinity)
If [Etot] is known, Vmax indicates TURN-OVER Number
Vmax=k2[Etot] or k2=Vmax/[Etot]
k2 is also called kcat or TURN-OVER Number
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The kcat/Km criterion
In physiological conditions: 0.01 Km<[S]< Km
Combining V0=k2[ES] with [ES]=[E][S]/Km gives
V0=(kcat/Km) [S][E]
When [S]<< Km then [E]=[Etot]
kcat/Km is the rate constant for E and S interaction
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Application of kcat/Km criterion to probe chymotrypsin ”specificity”
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The kinetic perfection
Attained when kcat/Km reaches k1, rate of formation of ES
Cannot be faster than diffusion-controlled encounter between Enzyme and Product (108 to 109 s-1 M-1)
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SOD an example of ”kinetically perfect” enzyme
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Sequencial displacement, ordered or random A + B + E EAB E + P + Q
Double displacement (Ping-Pong) A + B + E EA + B E + P + B EB E +
Q
Multiple-substrate reactions
A + B P + Q
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Example of sequencial, ordered reaction
Lactate dehydrogenase
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Example of sequencial, random reaction
Creatine kinase (energy in the muscle tissue)
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Example of Ping-Pong reaction:Aspartate amino-transferase
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Allosteric enzymes DO NOT follow Michaelis-Menten kinetics
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Inhibitors reveal intimate catalytic mechanisms and
modulate enzyme activity in vivo
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Competitive vs Non-Competitive inhibition
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THF cofactor for DHF reductase (nucleotide bases synthesis)
Anti-cancer drug
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Competitive inhibition affects Km
Inhibition overcome by increase in substrate concentration
Km altered: apparent Km value increased
Kmapp=Km(1+[I]/Ki)
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Non-Competitive inhibition affects Vmax
Inhibition cannot be overcome by increase in substrate concentration
Vmax altered: apparent Vmax value decreased
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Irreversible inhibitors to identify/map active-site residues
Group-specific reagents
Substrate analogs
Suicide inhibitors
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Example of Group-Specific inhibitor
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Example of Affinity-labeling
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Example of mechanism-based inhibition: mono-amine oxidase
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Transition-state analogs: the case of proline racemase
Pyrrole 2-carboxylic acid binds 160 as tightly as L-proline
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Penicillin an irreversible inhibitor of bacterial transpeptidase
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Schematic diagram of bacterial cell-wall peptidoglycans
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Reaction catalysed by trans-peptidase
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Reaction mechanism
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Penicillin as substrate analogue: case of affinity labeling
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Blocking of the SER active-site residue of trans-peptidase
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Vitamins as precursors of co-enzymes
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NEXT LECTURE
Catalytic strategies (Ch.9)
Regulatory strategies (Ch.10)
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Notes after lecture
2h15 of lecture approx: too long Main message: see summary from Stryer Ch.01 +
Organization of Euk/Prok cell: importance of membranes/structure, subcellular compartments in Euk, diverse biochemical reactions in compartments.
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