copyright (c) by w. h. freeman and company lecture no.2 enzymes: basic concepts and kinetics (ch.8)

Copyright (c) by W. H. Freeman and Company

LECTURE No.2

Enzymes: Basic Concepts and Kinetics (Ch.8)

Enzymes: powerful & specific catalysts

Carbonic anhydrase: an enzyme in the blood hydrating CO2

Peptidases hydrolysing the peptide bond in proteins

Peptidases specificity

Leu Val Pro Arg Gly Ser

Peptidases also hydrolysing ester bonds

Without enzymes: still in the pre-biotic era!

Enzymes often require cofactors

Energy transformation(ATPase)

The enzyme classification (EC number)

BRENDA: online database of enzymes (www.brenda.uni-koeln.de)

BRENDA: Searchable database

Nucleoside monophosphate kinase in BRENDA

Gibbs Free Energy to understand enzymatic

reactions

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

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

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

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

Enzymes accelerate reactions by lowering the

transition state energy

A fundamental property of enzymes

Enzymes DO NOT alter equilibria but enhance the rates at which they are reached

K= [B]/[A] = kF/kR (=10-4/10-6=100)

Transition state and Energy of activation

G‡ = GS‡ - GS

Enzymes facilitate formation of transition states

Reaction speed vs Subst. Conc. : Indirect evidence for ES complexes

A BNon-catalyzed reaction

A BEnz.-catalyzed reaction

Fluorescence spectroscopy to detect ES complex in TRP-synthetase

Pyridoxal phosphate (B6)

E + SER + Ind E-SER-Ind

TRP + H2O

X-ray crystallography to ”see” ES complexes

Cytochrome P450

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

Hydrogen bonding between substrate and active site: Ribonuclease

Lock and Key model (E. Fisher, 1890)

Induced-Fit model(D.E. Koshland, 1958)

Example of induced-fit: interfacial activation in lipases

Database of Macromolecular Movements (www.molmovdb.org)

A lipid

Many enzymes show kinetic properties explained by the

Michaelis-Menten model

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

Enzyme-catalyzed reaction progression curves

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

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

Another basic assumption: the Steady State (Briggs & Haldane, 1925)

E + S ES E + Pk1 k2

Rapidly, ES complex reaches a constant concentration

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

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])

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

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

A double reciprocal plot: the Lineweaver-Burk plot

Km values vary widely

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

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

Application of kcat/Km criterion to probe chymotrypsin ”specificity”

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)

SOD an example of ”kinetically perfect” enzyme

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 +

Multiple-substrate reactions

A + B P + Q

Example of sequencial, ordered reaction

Lactate dehydrogenase

Example of sequencial, random reaction

Creatine kinase (energy in the muscle tissue)

Example of Ping-Pong reaction:Aspartate amino-transferase

Allosteric enzymes DO NOT follow Michaelis-Menten kinetics

Inhibitors reveal intimate catalytic mechanisms and

modulate enzyme activity in vivo

Competitive vs Non-Competitive inhibition

THF cofactor for DHF reductase (nucleotide bases synthesis)

Anti-cancer drug

Competitive inhibition affects Km

Inhibition overcome by increase in substrate concentration

Km altered: apparent Km value increased

Kmapp=Km(1+[I]/Ki)

Non-Competitive inhibition affects Vmax

Inhibition cannot be overcome by increase in substrate concentration

Vmax altered: apparent Vmax value decreased

Irreversible inhibitors to identify/map active-site residues

Group-specific reagents

Substrate analogs

Suicide inhibitors

Example of Group-Specific inhibitor

Example of Affinity-labeling

Example of mechanism-based inhibition: mono-amine oxidase

Transition-state analogs: the case of proline racemase

Pyrrole 2-carboxylic acid binds 160 as tightly as L-proline

Penicillin an irreversible inhibitor of bacterial transpeptidase

Schematic diagram of bacterial cell-wall peptidoglycans

Reaction catalysed by trans-peptidase

Reaction mechanism

Penicillin as substrate analogue: case of affinity labeling

Blocking of the SER active-site residue of trans-peptidase

Vitamins as precursors of co-enzymes

NEXT LECTURE

Catalytic strategies (Ch.9)

Regulatory strategies (Ch.10)

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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