enzyme catalysis ?
Enzyme catalysis
catalyst is a substance that accelerates a reaction but
undergoes no net chemical change.
Physical Chemistry. P. Atkins & de Paula
catalyst is a substance that makes available a reaction path with a
lower free energy of activation than is available in its absence.
Chemical Kinetics. K. A. Connors
catalyst is a substance that accelerates a chemical reaction but is
not consumed in the reaction and does not affect its equilibrium.
Vicent Moliner
Catalytic Chemistry. B. C. Gates
Departament de Química Física i Analítica, Universitat Jaume I, Castelló
Universidad Autónoma de Madrid, 21 Setembre, 2007
catalysis ?
catalysis
catalysts decrease
∆G‡
of the reaction
TSuncat
a substance is a catalyst for a chemical reaction if its concentration
appears at the rate equation with an exponential factor greater than the
expected
TS-C
catalysis is the acceleration of a chemical reaction by means of a substance,
called a catalyst, which is itself not consumed by the overall reaction…
free energy
Bell 1930s
TS’-C
∆G‡ uncatalyzed
I’-C
Wikipedia.org
I-C
∆G
P +C
a catalyst provides an alternative route of reaction where the
activation energy is lower than in the original chemical reaction.
Wikipedia.org
principle of the
microscopic reversibility
∆G‡ catalyzed
S+ C
reaction coordinate
catalyst is not consumed
(in general)
enzyme catalysis
?
enzyme ?
enzymes are biological catalysts that allow
organisms to carry out biological reactions
with time scales compatible with life
enzymes are fundamental for life
Almost all reactions in living organisims are catalized by enzymes
We will see its application!
hydrolysis of glycosidic bonds of cellulose would require
several million years to reach its half-time
enzyme catalysis
enzyme catalysis
Historical:
rate enhancement by selected enzymes
1783
First observation of an enzyme activity
liquid
meat
solid
meat
Lazaro Spallanzani
gastric juice
of hawks
1833
First isolation of an enzyme
enzymes are able to speed up chemical reactions
in an order of magnitude of 106 to 1020
amylase
starch
soluble sugar
A. Payen
J. F. Persoz
enzyme catalysis
enzyme catalysis
1926
first enzyme recognized as a protein
urease
(NH2)2CO2 + H2O
are enzymes always proteins?
always?
CO2 + 2NH3
J. B. Sumner
1960
first to sequence an enzyme
Ribonuclease A
What is a protein?
most enzymes consist primarily of proteins, but nucleic acids
can also be biological catalysts:
ribozymes
- their own cleavege
- cleavage of other RNAs,
- aminotransferase activity
- their own synthesis (RNA polymerase) .
deoxyribozymes
- gene replication
Nobel Prize 1972
and relate it with biologically
conformation
W. H. Stein
S. Moore C. B. Anfinsen
enzyme catalysis
proteins are large polimer whose monomers, amino acids,
arranged in a linear chain and joined together by peptide bonds.
The sequence of amino acids in a protein is defined by a gene
and encoded in the genetic code
representation of the 3D structure of myoglobin,
showing coloured alpha helices.
This protein was the first to have its structure solved
By X-ray crystallography.
enzyme catalysis
there are 20 common
amino acids found
in proteins
How do they bond?
enzyme catalysis
enzyme catalysis
the different
combinations of
aminoacids
structure of protein
structure of protein
(A) primary structure, its amino acid sequence;
(B) secondary structure, polypeptide coiling or folding;
(C) tertiary structure, the overall shape of the polypeptide.
function
enzyme catalysis
E. coli
Chorismate Mutase
enzyme catalysis
substrate
COMT
substrate
molecule/s
suffering chemical
transformation
active
site
active
site
where the
chemical reaction
takes place
Cofactor
EC 2.1.1.6 Vidgren, et al.. (1994) Nature 368, 354-358
S-Adenosin Methyonine
enzyme catalysis
enzyme catalysis
two copper
11 Å
CuM :
“chemistry” site
CuH :
“electron store”
Oxidized PHM with substrate (PDB entry : 1OPM)
enzyme catalysis ?
enzyme catalysis
catalyst is a substance that accelerates a reaction but
undergoes no net chemical change.
Physical Chemistry. P. Atkins & de Paula
catalyst is a substance that makes available a reaction path with a
lower free energy of activation than is available in its absence.
Cofactors often
derived from
vitamins
Chemical Kinetics. K. A. Connors
catalyst is a substance that accelerates a chemical reaction but is
not consumed in the reaction and does not affect its equilibrium.
Catalytic Chemistry. B. C. Gates
catalysis is the acceleration of a chemical reaction by means of a substance,
called a catalyst, which is itself not consumed by the overall reaction…
Wikipedia.org
a catalyst provides an alternative route of reaction where the
activation energy is lower than in the original chemical reaction.
Catechol Methyl-transferase
when tightly
bound to
enzyme,
cofactor =
prosthetic group
enzyme catalysis
enzyme catalysis
are enzymes homogenous or heterogeneous catalysts?
enzymes can be thought of as a mixture of a
homogenous and heterogeneous catalyst;
the enzyme is in solution itself,
but the reaction takes place on the enzyme surface.
enzymes are also specific
substrate specificity
A) Trypsin cleavage site
(digestive enzyme)
B) Thrombin cleavage site
(blood clotting enzyme)
(we will compare reaction profiles later on)
C) Subtilisin will cleave any
peptide bond
enzyme catalysis
enzyme catalysis
there are six major classes of enzyme
enzymes are also specific
The specificity of an enzyme is due to the precise
substrate-enzyme interactions. This is a result of
the intricate three-dimensional structure of the
enzyme protein.
substrate
active site
substrate
schematic model
of an enzyme
active site
schematic model
of an enzyme
1964, classification & nomenclature of enzymes developed
by the Enzyme Commission (EC)
eg. Nucleoside monophosphate (NMP) kinase = EC 2.7.4.4
2 = class, 7 = phosphoryl group, 4 = phosphate acceptor, 4 = precise acceptor (NMP)
enzyme kinetics & thermodynamics
enzyme kinetics & thermodynamics
∆G = ∆Hsystem - T∆Ssystem
∆G tells us if the reaction can occur spontaneously:
1. If ∆G is negative, reaction spontaneous, exergonic
2. If ∆G is zero, no net change, system at equilibrium
3. If ∆G is positive, free energy input required, endergonic
An enzyme cannot alter the equilibrium of a chemical reaction.
This means, an enzyme accelerates the forward and reverse
reactions by precisely the same factor.
Enzymes accelerate the attainment of equilibria but do not shift
their positions.
∆G of a reaction depends only on free-energy of products minus
free-energy of reactants.
1. ∆G of a reaction is independent of path (or molecular
mechanism) of the transformation
2. ∆G provides no information about the rate of a reaction
enzyme kinetics & thermodynamics
The equilibrium position is a function only of ∆G between
reactants and products
enzyme kinetics & thermodynamics
TSuncat
TSuncat
TS-C
TS’-C
∆G‡ uncatalyzed
∆G‡ catalyzed
S+ C
I’-C
I-C
∆G
TScat
∆G‡ uncatalyzed
∆G‡ catalyzed
S+ C
∆GMCbind
enzyme vs solution
P-C
MC
∆G
Michaelis Complex
P +C
P +C
reactants chemical products
binding reaction release
(we will compare reaction profiles later on)
enzyme catalysis
enzyme kinetics & thermodynamics
TSuncat
enzyme vs solution
Reaction profile of a heterogeneous catalyzed process
E
R
∆G‡ uncatalyzed
TScat
1. difussion
2. adsorption
3. chemical reaction on surface
4. desorption
5. difussioón
∆GMCbind
P
P-C
∆G
MC
P +C
R
R´
∆G‡ catalyzed
S+ C
reactants chemical products
binding reaction release
P
P´
k1
E+S
go to F. Illasc.r.
(14th Sept) or P. Sautet (24th Sept)
your attention, please!
chemical reaction is not always
the rate determining step
∆GMCbind
E+P
enzyme kinetics & thermodynamics
Michaelis-Menten mechanism
k1
E+S
MC
k2
E+P
monitoring the initial rate
of products formation
at [E]↓↓
k-1
TSbind TScat TSp.rel
TScat
cat
k2
k-1
enzyme kinetics & thermodynamics
∆G‡ catalyzed
S+ C
MC
[S ] >> K m
∆∆GG‡ ‡catalyzed
catalyzed
P-C
P-C
MC
MC P-C
v=
P +C
d [P ]
= k 2 [MC ] = k 2 [E ][S ]
dt
[S ] + K m
Km =
reactants chemical products
binding reaction release
k1
E+S
MC
k-1
k2
E+P
k −1
k1
[S ] << K m
Transition State Theory
V = k 2 [E ] = Vmax
V=
Vmax [S ]
[S ] + K m
V=
k2
[E ][S ]
Km
V=
(
k BT
‡
exp ∆Gcat
h
) [E ]
enzyme kinetics & thermodynamics
Vmax
 K
1
1
=
+  m
V
Vmax  Vmax
V=
V
enzyme kinetics & thermodynamics
Lineweaver-Burk plots
 1

 [S ]
Vmax
1 + K m [S ]
V=
 K
1
1
=
+  m
V
Vmax  Vmax
 1

 [S ]
1
V
Vmax [S ]
[S ] + K m
1
Vmax
[S ]0
−
enzyme kinetics & thermodynamics
Inhibitors:
a substance that decreases the rate of product formation
by binding to:
competitive inhibition
a) to E
uncompetitive inhibition
b) to ES
c) to E and ES simultaneusly
non-competitive inhibition
uncompetitive inhibition
competitive inhibition
E+S
+
I
ES
EI
E+P
E+S
ES
KM
KM
KI =
KI
k2
[E ][I ]
[EI ]
k2
ESI
Inhibitors:
a substance that decreases the rate of product formation
by binding to:
competitive inhibition
a) to E
uncompetitive inhibition
b) to ES
c) to E and ES simultaneusly
non-competitive inhibition
Non-competitive inhibition
E+S
+
I
K I' =
K’I
enzyme kinetics & thermodynamics
E+P
+
I
[ES ][I ]
[ESI ]
[S1]0
[S ]0
1
K max
KI
ES
KM
k2
E+P
general equation
V=
+
I
K’I
EI
ESI
α = 1+
Vmax
αK m
α/ +
[S ]0
[I ]
KI
α / = 1+
[I ]
K I/
enzyme kinetics & thermodynamics
uncompetitive inhibition
k2
competitive inhibition
k2
E+S
ES
E+P
E+S
[E ][I ]
[EI ]
KI =
KI
EI
ES
KM
+
I
KI
+
I
K I' =
ESI
[ES ][I ]
[ESI ]
True or false ?
α
α’
for an uninhibited enzyme process
0
0
for an uninhibited enzyme process
1
1
for a competitive enzyme process
>1
1
for a uncompetitive enzyme process
1
>1
>1
>1
for a non-competitive enzyme process
E+P
the lower the values of
KI and KI’, the more efficient
the inhibitor is
+
I
K’I
EI
which are the values of α and α’ for…
E+P
K’I
Non-competitive inhibition
k2
E+S
ES
KM
KM
+
I
enzyme kinetics & thermodynamics
V=
Vmax
αK m
α/ +
[S ]0
α = 1+
[I ]
KI
α / = 1+
[I ]
K I/
ESI
enzyme kinetics & thermodynamics
How do enzymes work?
uninhibited
 K
1
1
=
+  m
V
Vmax  Vmax
1
V
 1

 [S ]
inhibited
V=
1
Vmax
−
1
K max
competitive
α >1
α / =1
1
α /  αK m  1

=
+
V
Vmax  Vmax  [S ]
1
[S ]0
uncompetitive
α =1
Vmax
αK m
α/ +
[S ]0
α / >1
noncompetitive
α =1
α / >1
evidences
1. Enzymes accelerate reactions by decreasing ∆G‡,
the activation energy
2. The combination of substrate and enzyme creates a new
reaction pathway, with a lowered transition-state energy
3. More molecules have the required energy to reach the
transition state (analogous to lowering the height of a
high-jump bar)
4. The essence of catalysis is specific binding of the transition
state
How do enzymes work?
How do enzymes work?
M. Polany (1921)
J.B.S Haldane (’20s - ‘30’s)
L. Pauling (’30s - ‘40s)
enzyme
Koshland’s Induced-fit model
M. Polany (1921)
J.B.S Haldane (’20s-‘30’s)
L. Pauling (’30s- ‘40s)
TS
R
P
“any catalyst can enhance the rate of a reaction
only to the extent that it binds the substrate more tightly
in the transition state than in the ground state”
Transition State theory
reaction coordinate
enzyme
How do enzymes work?
How do enzymes work?
at least 21 different hipothesis for how enzymes catalyze reactions
have been proposed !!
Transition State Theory
20
TS
∆G (kcal mol-1)
free energy
Fisher’s Lock-and-key model
10
∆G‡cat
k TST =
0
kBT −( ∆G
e
h
-20
−2
k = γ(T ) k TST
γ(T ) = κ(T ) ⋅ Γ(T ) ⋅ g(T )
MC
-10
/ RT )
2 c.r.
0
kexp
TS
problems:
hypothesis:
|
∆ GMCS
=
a)
R
b)
substrate
c)
classical description
of movement along rc
TS
P
environment
|
∆ Guncat
- κ(T) dynamic effects (recrossings)
- g(T) non equilibrium effects
- Γ(T) tunneling
TS
∆ GBind
=
E·TS
MCS
MCS
∆ GR
E+S
MCS
∆ GBind
MC
∆ GBind
MC
|
∆ GE
=
|
∆ Gcat
=
E+P
How do enzymes work?
How do enzymes work?
TS
TS
∆G TS
Bind
‡
∆Guncat
TS-theories
E ·TS
MC-theories
MCS
∼
∆G MC
Bind
‡
∆G cat
E+P
aqueous solution
enzyme
MC
‡
TS
MC
= ∆Gcat − ∆GBind
∆Guncat−∆GBind
−
=
MCS
∆G Bind
∆G MC
Bind
RC
‡
∆G cat
MC
E+P
aqueous solution
enzyme
A. Warshel et al. : the transition state stabilisation is basically due
to the electrostatic environment provided by the active site of the enzyme
‡
−
∆G MCS
assoc
E+S
RC
∼
∆G MCS
assoc
MCS
∆G Bind
TS-theories
E ·TS
MC-theories
MCS
E+S
∆G TS
Bind
‡
∆Guncat
>0
catalytic
power
How do enzymes work?
Page and Jencks: entropic trap. The MC formation implies the loss of
translational and rotational degrees of freedom rendering a loss of entropy
that is, a priori, always a non-favourable term
Kollman et al. centred the attention on the free energy needed to preorganize
the reactants in solution, by comparison with enzymes: cratic energy
How do enzymes work?
TS
∆G TS
Bind
‡
∆Guncat
TS-theories
E ·TS
MC-theories
Truhlar and Gao.: chemical catalyzed reactions are strongly coupled to the
relative motions of the enzyme. Importance of tunneling
MCS
∆G MCS
assoc
RC
∼
E+S
MCS
∆G Bind
∆G MC
Bind
MC
‡
∆G cat
E+P
aqueous solution
enzyme
Bruice et al.: Near Attack Conformation (NAC) concept as those ground
state conformers that closely resemble the TS
Menger et al.: the spatial-temporal hypothesis have previously used
closely related arguments
Hammes-Schiffer, Klinman, Kohen….: tunneling can increase the rate of an
enzymatic reaction substantially
Scrutton….: dynamics aspects of catalysis, protein motions, help the reaction
to proceeds
Houk….: most enzymes and cofactors speed up reactions via covalent bonding
to the substrate
How do enzymes work?
Theoretical modeling of enzyme catalysis
…if we know the TS of
a chemical reaction…
let’s use Computational Chemistry
to “obtain” the TS of the
enzyme
TSA
chemical reaction
energy
TSuncat
∆G‡ uncatalyzed
TScat
∆G‡ catalyzed
S+ C
∆GMCbind
enzyme vs solution
P-C
MC
∆G
P +C
reaction coordinate ?
synthesis of
inhibitor
synthesis of
biocatalists
Theoretical modeling of enzyme catalysis
Theoretical modeling of enzyme catalysis
reaction coordinate
a) distance O———C
b) distance C———Cl
c) angle O——C——H
d) d(O———C) – d(C———Cl)
r.c.
e) others
TS
P
rbc
R
rab
reaction coordinate ≠ distinguished reaction coodinate
Ha + Hb- Hc
Hessian
Ha- Hb + Hc
Theoretical modeling of enzyme catalysis
Theoretical modeling of enzyme catalysis
gas phase Potential Energy Surface
TS
products
catalysis
d1
/Å
/
d2
reactants
Theoretical modeling of enzyme catalysis
Å
R
P
Theoretical modeling of enzyme catalysis
optimizing…
MC
?
PC
substrate, cofactor and reactive aminoacids
are not free to move in the enzyme active site
substrate, cofactor and reactive aminoacids
are not free to move in the enzyme active site
Theoretical modeling of enzyme catalysis
optimizing…
enzymes
are big
Theoretical modeling of enzyme catalysis
A Computational Strategy Based on:
1) QM/MM Hybrid Techniques
MC
?
2) flexyble models and algorithms
PC
enzymes
are
A) do we optimize the
systemflexible
in gas phase?
B) do we anchor the position of any aminoacid
to optimize the system in gas phase?
Theoretical modeling of enzyme catalysis
Lactate
dehydrogenase
(LDH)
QM region: 78 atoms
Covalent bond at the
boundary: GHO method.1
Theoretical modeling of enzyme catalysis
O
H
micro/macro
iterations
go to I. Tuñón
(25th Sept)
Rib
MM region:
22139 atoms
1
H
C
HO
H
HO
N
eff
=H
QM
+H
MM
+ H elec
+ H vdW
QM / MM
QM / MM
Gao,
Gao, J. et al. J.Phys.Chem.
J.Phys.Chem. A 1998, 102, 4714.
O
N
H
H
NH 2
H
/
H
H
N
Arg-109
C
C
H +N
O
N
H
H
H
H
CH 3
N
C O
C
C
H
H C
O
H
Thr-246
O
QM
O
H
H
O
C
N
H
//
N
C
(79)
(39)
(52)
N
H
H
N
N
C
C
O
H
His-195
H
O
C
H
H
H
+
N
H
+
H
H
H
C
H
core
(147)
H
H C
H
H
C
O
H
C
N
H
H
CH 3
MM :15191 fixed atoms
Lactate
dehydrogenase
(LDH)
Asn-140
NADH
O
-
C
C
H
Arg-171
H
H
N
C
C
H
H
Asp-168
C
O
different models can render different results!!
Theoretical modeling of enzyme catalysis
Condensed media PES
Theoretical modeling of enzyme catalysis
A Computational Strategy Based on:
Energy
TS
1) QM/MM Hybrid Techniques
Products
Energy
ξj
∆E2‡ ∆E ‡
1
2) flexyble models and algorithms
∆E2
∆E1
3) MD or MC Simulation Methods
Reactants
RC
ξj
An energy profile for large systems
is not a single line !
statistical simulations
Free energies
go to I. Tuñón
(25th Sept)
Kinetic Isotope Effects (KIE)
K, k, k/k’
Kinetic Isotope Effects (KIE)
∆E0‡
1H
2H
∆E0‡
TS
2H
kH
>1
kD
R
c.r.
kH
kD
(k T / h)KH = KH = (MMI)(ZPE)(EXC)
= B
(kBT / h)KD KD
‡
‡
‡
‡
∆E0‡
Energía
Energía
1H
1H
kH
<1
‡
0
KIEs are ∆E
one
of the few magnitudes
that
kD
2H
TS
1H
2H
provide direct experimental informtion of the
R
TS
c.r.
kH
kD
(k T / h)KH = KH = (MMI)(ZPE)(EXC)
= B
(kBT / h)KD KD
‡
‡
‡
‡
Chorismate Mutase
Chorismate Mutase
water
EPot = EMM + EQM + EQM/MM + EBound
vs
enzyme
No Covalent Bonds QM-MM
Environment reorganization /
EMM
=
Environment reorganization
EQM/MM = ESOLUTE/SOLVENT , ESUBSTRATE/ENZYME
(kcal—
kcal—mol-1)
∆E‡QM
Enzyme
Water
42.1
40.4
Theoretical insights in enzyme catalysis
Interaction energy
∆E‡MM
∆E‡Int
∆E ‡
1.2
1.4
-16.2
-2.8
27.1
39.0
COMT
Rare event trajectories from TS
TS
Energy
-V
trajectories from
selected TS structures
time
reac
tion
c
V
oord
inate
long molecular dynamics
constrained on TS region
RP:
RR:
PP:
reactives
non-reactives
non-reactives
Theoretical Insights in Enzyme Catalysis
● development of enzyme Inhibitors
● development of new biological catalysts