Proton coupled electron transfer
in cell respiration oxygen reduction and
proton pumping
Margareta Blomberg
Leiden, March 2011
Coworker: Per Siegbahn
Stockholm University
Quantum chemical studies of
enzyme mechanisms
involving proton and electron transfer
to or from outside a membrane
2H2O --> O2 + 4e- + 4H+
Photosynthesis
O2 + 4H+ + 4e- --> 2H2O
Respiration
Methods and models
Hybrid DFT (B3LYP or B3LYP*) calculations on large
cluster models of the enzyme active site from X-ray,
empirical dispersion (Grimme)
The rest of the protein is treated as a dielectric
medium (ε=4) , large models  small solvent effects
Geometry optimization of stationary points (min and
TS), a few atoms fixed to the X-ray structure
Estimated accuracy in the calculations: 3-5 kcal/mol,
from bench mark calculations on bond energies of small
molecules
Binding of O2, NO and CO to heme-Fe
- effect of dispersion
7-10 kcal/mol
(Kcal/mol)
O2
CO
NO
10.1
22.8
19.5
B3LYP
1.1
7.6
10.9
B3LYP-D
8.1
16.9
20.6
exp
Dispersion effects on homolytic Co-C
bond strength in methyl cobalamine (B12)
11 kcal/mol
(Kcal/mol)
Co-C
exp
37±3
B3LYP
16.2
B3LYP-D
27.5
B3LYP*-D
32.0
Dispersion effects on water binding
in proteins
0-7 kcal/mol
(Kcal/mol)
W1
B3LYP*
B3LYP*-D
W2
W3
W4
16.0 13.0
13.0
11.9
16.3 18.8
18.8
19.0
Exp: > 14 kcal/mol (present in X-ray)
Water molecules important
e.g. for proton transport
Methods and models
Hybrid DFT (B3LYP or B3LYP*) calculations on large
cluster models of the enzyme active site from X-ray,
empirical dispersion (Grimme)
The rest of the protein is treated as a dielectric
medium (ε=4), large models  small solvent effects
Geometry optimization of stationary points (min and
TS), a few atoms fixed to the X-ray structure
Estimated accuracy in the calculations: 3-5 kcal/mol,
from bench mark calculations on bond energies of small
molecules
Respiration - electron transport chain
Cytochrome c oxidase (CcO)
O2 + 4H+ + 4e-  2H2O + ΔE
cyt.
c
P-side
e-
CuA
H+
membrane
CuB
heme a
heme a3
O2
(BNC)
O2 + 8HN+ + 4eP- ---> 2H2O + 4HP+
N-side
H+
O2 + 8H+n + 4e-cytc  2H2O + 4H+p
Fe
Cu
BNC
Mechanisms for
proton pumping
against the gradient?
Energetics of the
catalytic cycle?
O2 + 8H+n + 4e-cytc  2H2O + 4H+p
Fe
Cu
BNC
Relative energies
of intermediates
What is the “cost”
of e- and H+?
a.) Calculated relative values for EA and PA for the
different intermediates - reliable: same active site,
same surrounding
b.) Calculated EA and PA for the donors of the
electron (cytc) and the proton (H+ in bulk H2O)
– NOT reliable: different systems and different
surroundings
Alternative procedure to b.): Parametrize cost of e- and H+
to reproduce experiment
ΔG
0
O2 + 4H+bulk + 4e-cytc
Experiment:
E0(cytc) = 0.25 V
E0(O2) = 0.80 V
H
ΔE = 4x0.55 V = 51 kcal/mol
E
H
R
One fixed parameter:
e- + H + = H
PM
H
F
H
-51
2H2O + ΔE
No cost for
proton pumping
without gradient
Second, adjustable,
parameter  e- and H+
Assume linear gradient
across the membrane
(max 200 mV)
eT and PT barriers
not included
Mechanism for
proton pumping
against gradient?
Remaining problem:
energy gain in each step
should be more similar
to maintain pumping at
full gradient
(BNC models: 100-200
atoms)
“standard mechanism”
cyt.
c
P-side
e-
H+
membrane
H+
PL
heme a
PL = Pump
Loading site
eH+
BNC
Push effect:
electrostatic
repulsion
N-side
P-side
The push effect does not work,
no directionality
membrane
H+ PL
10 kcal/mol
heme a
e5 kcal/mol
H+
PL = Pump
Loading site
BNC
H+
Gating mechanism
needed
N-side
cyt.
c
P-side
e-
Kinetic gating
H+
H+
X
PL
TSP
membrane
PL = Pump
Loading site
heme a
X
Two transition
states: TSG and TSP
N-side
X
TSG
BNC
Energy diagram
GluH, pKa>9
Reaction scheme.
Experiment: one
single reduction step
Belevich I et al. PNAS 2007;104:2685-2690
©2007 by National Academy of Sciences
Transition state theory
Fairly high PT barriers: essential!
Forbidden paths, no pumping
cyt.
c
H+
P-side
TSP
e-
H+
H+
LOW
N-side
TSG
Positively
charged
GluH…H3O+
PL
X
e-
heme a
HIGH
membrane
TSG
BNC
Conventional:
charge
separation
Glu-…H3O+
cyt.
c
P-side
TSP
membrane
TSG
Positively
charged
GluH…H3O+
H+ PL
heme a
14.2 Å
13.6 Å
BNC
TSG
ε=3.3
(deduced from exp)
N-side
Positively charged TSG : GluH-H3O+
Allowed path
Experiment: TST
Forbidden path
Estimate: Coulombs law
Model for DFT - calculations
X-ray
Model, 250 atoms
Effect of the electron on TSG - DFT
ΔG# : PLH+  TSG independent of e-
The DFT model
H+
Model, 250 atoms
Model, 390 atoms
ΔG#: PLH+  TSG
16.0 kcal/mol
H+
Smaller model:
15-16 kcal/mol
Some difficulties in
the model still remain
(boundery effects)
Conventional mechanism: Glu- - H3O+
Can not prevent back leakage
to the N-side
DFT:
Intermediate Glu- + PLH+
too high: +8.5 kcal/mol
Forward barrier much too high:
> 30 kcal/mol
Stability of results with choice of ε
(kcal/mol)
ε=4
ε=10
GluH-H+
Glu- -H+
380 atoms
16.4
20.3
15.9
13.6
GluH-H+
Glu- -H+
16.0
8.5
13.0
7.8
250 atoms
Binding of “extra” water molecules
Five added water molecules,
necessary for proton transfer
Binding energy in bulk: 14 kcal/mol
(kcal/mol)
GluH Glu-
B3LYP
9.8
13.6
B3LYP-D
13.7
18.0
Dispersion effect: ≈ 4 kcal/mol
On-going work: the chemical proton
P-side
membrane
H+ PL
heme a
e-
H+
N-side
BNC
Model: 340 atoms
BNC, Rred-state:
Cu(I)-OH
Fe(II)-OH2
TyrOH
GluOH
Concluding remarks
Complex problems, such as mechanisms for proton gating,
can be studied with QM-models, in combination with
experimental results and simpler theories (TST, Coloumb)
Methodological aspects in studies of enzyme mechanisms:
Large cluster models possible, aim at small solvent effects
Empirical dispersion should be used together with DFT
Proton and electron uptake (release) can be handled with
reasonable accuracy in calculated energetics