Electron Transfer in Proteins: Structural and Energetic Control
of the Electronic Coupling
Jose ´ -Maria Lopez-Castillo, Abdelali Filali-Mouhim,
†
E Ä lise Nguyen Van Binh-Otten, and Jean-Paul Jay-Gerin*
Contribution from the Groupe du Conseil de Recherches Me ´ dicales du Canada en Sciences des
Radiations, De ´ partement de Me ´ decine Nucle ´ aire et de Radiobiologie, Faculte ´ de Me ´ decine,
UniVersite ´ de Sherbrooke, Sherbrooke (Que ´ bec) J1H 5N4, Canada
ReceiVed June 12, 1996
X
Abstract: The available experimental data on the electron donor (D)-acceptor (A) coupling (H
DA
) for electron-
transfer (ET) reactions in proteins are re-examined. In spite of their structural and energetic similarities, the
photosynthetic reaction center and other ET protein systems exhibit a marked difference of the exponential decay of
H
DA
with the distance separating D and A. A numerical study shows that this difference is explained in terms of
very small variations of the energetics between these two classes of proteins.
Since the proposal of Dutton and co-workers
1
of a “universal”
relationship between the electron donor (D)-acceptor (A)
coupling (H
DA
) and the distance (d) separating D and A in
electron-transfer (ET) proteins, a number of experiments have
shown important departures from such a simple picture.
2
The
situation has come to a tendency toward a classification of ET
proteins into two groups, according to their ability to fit or not
to fit the “universal” law.
3,4
Proteins of the “universal” type
seem to conform to a one-dimensional square-barrier (1DSB)
model, for which Gamow’s formula gives an exponential
dependence of H
DA
on d, with a decay constant
1DSB
) (2mE/
p
2
)
1/2
, where m is the electron mass, p is Planck’s constant
divided by 2π, and E is the energy of the tunneling electron.
Dutton’s compilation
1
gives
1DSB
) 0.7 Å
-1
from the average
exponential decay of the maximum ET rate constant k
max
(s
-1
)
) 10
13
e
-1.4(d-3.6)
Versus d (Å). Other ET proteins do not show
such a simple correlation of H
DA
with d. Instead, there seems
to be a more pronounced correlation of H
DA
with the length of
some specific pathways from D to A, along the protein bonds.
Onuchic and Beratan and co-workers
5
(OB) associated to each
of these pathways an additive contribution to H
DA
allowing for
a selection of those with the optimum coupling strengths.
The limitations of both theories are well-known. Briefly,
Dutton’s model simply does not rely upon a microscopic
description of proteins, while, as we will show below, OB’s
approximation largely underestimates the contributions of
through-space (TS) interactions. An accurate determination of
H
DA
must include the complete structural and energetic com-
plexity of proteins into the electronic Hamiltonian, which has
to be treated exactly.
6
To date, only a very limited number of
such studies exists.
7
It is therefore difficult to appreciate the
whole behavior of H
DA
in ET proteins. A lucid discussion of
the present status of the theory has been given by Friesner.
8
In this paper, we re-examine the available experimental data,
including the most recent ones, on the k
max
-Vs-d correlation.
Our compilation clearly distinguishes between the photosynthetic
reaction center (PRC) and other ET protein systems. By
analyzing, on a variety of proteins, the possible energetic and
structural origins of the observed behaviors, we show that there
is no influence of the protein’s structure on the aVerage
distance-decay rate of H
DA
. However, experimental data
support the notion of a large dispersion of the electronic energy
levels of the protein as reflected by the important scatter of the
data.
According to theory, k
max
is related to H
DA
through the
semiclassical Marcus expression for the ET rate constant k:
9
where k
B
is the Boltzmann constant, T is the temperature, λ is
the nuclear reorganization energy accompanying ET, and ΔG°
is the reaction free-energy change. k
max
is reached at vanishing
activation energy (∆G° )-λ),
where the numerical estimate of k
max
(in s
-1
) as a function of
H
DA
(in cm
-1
) holds for a typical reorganization energy λ ) 1
eV at T ) 300 K. H
DA
reflects the influence of the intervening
medium on the ET rate.
Table 1 presents an up-to-date compilation of k
max
Versus d
for 23 ET protein systems studied in the literature.
10-20
These
†
Present address: Service de Ge ´ne ´tique Me ´dicale, Ho ˆpital Sainte-Justine,
3175, Chemin Co ˆte Sainte-Catherine, Montre ´al (Que ´bec) H3T 1C5, Canada.
X
Abstract published in AdVance ACS Abstracts, February 1, 1997.
(1) Moser, C. C.; Keske, J. M.; Warncke, K.; Farid, R. S.; Dutton, P. L.
Nature 1992, 355, 796-802.
(2) Beratan, D. N.; Onuchic, J. N.; Winkler, J. R.; Gray, H. B. Science
1992, 258, 1740-1741 and references therein.
(3) Evenson, J. W.; Karplus, M. Science 1993, 262, 1247-1249.
(4) Farid, R. S.; Moser, C. C.; Dutton, P. L. Curr. Opin. Struct. Biol.
1993, 3, 225-233.
(5) Onuchic, J. N.; Beratan, D. N.; Winkler, J. R.; Gray, H. B. Annu.
ReV. Biophys. Biomol. Struct. 1992, 21, 349-377 and references therein.
Betts, J. N.; Beratan, D. N.; Onuchic, J. N. J. Am. Chem. Soc. 1992, 114,
4043-4046. Regan, J. J.; Risser, S. M.; Beratan, D. N.; Onuchic, J. N. J.
Phys. Chem. 1993, 97, 13083-13088. Skourtis, S. S.; Regan, J. J.; Onuchic,
J. N. J. Phys. Chem. 1994, 98, 3379-3388.
(6) Stuchebrukhov, A. A.; Marcus, R. A. J. Phys. Chem. 1995, 99, 7581-
7590. Stuchebrukhov, A. A. Chem. Phys. Lett. 1994, 225, 55-61.
(7) Kuki, A.; Wolynes, P. G. Science 1987, 236, 1647-1652. Gruschus,
J. M.; Kuki, A. J. Phys. Chem. 1993, 97, 5581-5593. Siddarth, P.; Marcus,
R. A. J. Phys. Chem. 1993, 97, 13078-13082 and references therein. Okada,
A.; Kakitani, T.; Inoue, J. J. Phys. Chem. 1995, 99, 2946-2948.
(8) Friesner, R. A. Structure 1994, 2, 339-343.
(9) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265-
322.
(10) McLendon, G.; Miller, J. R. J. Am. Chem. Soc. 1985, 107, 7811-
7816.
k )
2π
p
|H
DA
|
2
1
4πλk
B
T
e
-(∆G°+λ)
2
/4λk
B
T
(1)
k
max
)
2π
p
|H
DA
|
2
1
4πλk
B
T
≈ (2.575 × 10
8
)|H
DA
|
2
(2)
1978 J. Am. Chem. Soc. 1997, 119, 1978-1980
S0002-7863(96)01978-6 CCC: $14.00 © 1997 American Chemical Society