Charge-transfer mechanism for cytochrome c adsorbed on nanometer thick films. Distinguishing frictional control from conformational gating

Article abstract of DOI:10.1021/ja034719t

Using nanometer thick tunneling barriers with specifically attached cytochrome c, the electron-transfer rate constant was studied as a function of the SAM composition (alkane versus terthiophene), the ω-terminating group type (pyridine, imidazole, nitrile), and the solution viscosity. At large electrode-reactant separations, the pyridine terminated alkanethiols exhibit an exponential decline of the rate constant with increasing electron-transfer distance. At short separations, a plateau behavior, analogous to systems involving -COOH terminal groups to which cytochrome c can be attached electrostatically, is observed. The dependence of the rate constant in the plateau region on system properties is investigated. The rate constant is insensitive to the mode of attachment to the surface but displays a significant viscosity dependence, change with spacer composition (alkane versus terthiophene), and nature of the solvent (H₂O versus D₂O). Based on these findings and others, the conclusion is drawn that the charge-transfer rate constant at short distance is determined by polarization relaxation processes in the structure, rather than the electron tunneling probability or large-amplitude conformational rearrangement (gating). The transition in reaction mechanism with distance reflects a gradual transition between the tunneling and frictional mechanisms. This conclusion is consistent with data from a number of other sources as well.

Full text of DOI:10.1021/ja034719t

Published on Web 06/03/2003
Charge-Transfer Mechanism for Cytochrome c Adsorbed on
Nanometer Thick Films. Distinguishing Frictional Control from
Conformational Gating
Dimitri E. Khoshtariya,† Jianjun Wei, Haiying Liu, Hongjun Yue, and
David H. Waldeck*
Contribution from the Chemistry Department, UniVersity of Pittsburgh,
Pittsburgh, PennsylVania 15260
Received February 17, 2003; E-mail: dave@pitt.edu
Abstract: Using nanometer thick tunneling barriers with specifically attached cytochrome c, the electron-
transfer rate constant was studied as a function of the SAM composition (alkane versus terthiophene), the
ω-terminating group type (pyridine, imidazole, nitrile), and the solution viscosity. At large electrode-reactant
separations, the pyridine terminated alkanethiols exhibit an exponential decline of the rate constant with
increasing electron-transfer distance. At short separations, a plateau behavior, analogous to systems
involving -COOH terminal groups to which cytochrome c can be attached electrostatically, is observed.
The dependence of the rate constant in the plateau region on system properties is investigated. The rate
constant is insensitive to the mode of attachment to the surface but displays a significant viscosity
dependence, change with spacer composition (alkane versus terthiophene), and nature of the solvent (H2O
versus D2O). Based on these findings and others, the conclusion is drawn that the charge-transfer rate
constant at short distance is determined by polarization relaxation processes in the structure, rather than
the electron tunneling probability or large-amplitude conformational rearrangement (gating). The transition
in reaction mechanism with distance reflects a gradual transition between the tunneling and frictional
mechanisms. This conclusion is consistent with data from a number of other sources as well.
1. Introduction
and numerous studies of its electron-transfer rate have been
performed, both homogeneous2,3 and heterogeneous.4,5
A large number of studies have compared cytochrome c’s
electron-transfer kinetics with contemporary theoretical models.
The nonadiabatic (tunneling) charge-transfer mechanism6 pre-
dicts the exponential decay of the charge-transfer rate constant
with the electron-transfer distance Re
Because of their diversity and rich behavior, the kinetics and
mechanism of biochemical charge-transfer processes are often
difficult to identify, and many aspects of a protein’s microscopic
mechanism remain unclear because of the complex and inho-
mogeneous character of biomolecular systems. Nevertheless,
experimental and theoretical studies have shown that elementary
electron-transfer events involving redox-active proteins can be
understood in the light of contemporary theoretical models for
molecular charge-transfer reactions. Cytochrome c is a small,
“model”, redox protein1 with a well-known molecular structure,
ket exp[-â(Re - Ro)]
(1)
where Ro is a minimal electron donor-acceptor distance and â
is a decay parameter whose value depends on the intervening
atomic and molecular structure.7 The observation of an expo-
nential distance dependence for a given reaction series provides
strong evidence for the nonadiabatic (tunneling) mechanism.
The exponential dependence arises from the dependence of the
rate constant on the electronic coupling |V| between the electron
† Permanent address: Institute of Molecular Biology and Biophysics,
Georgian Academy of Sciences, Gotua 14, Tbilisi 380060, Georgia.
(1) (a) Fedurco, M. Coord. Chem. ReV. 2000, 209, 263. (b) Scott, R. A. In
Cytochrome C: A Multidisciplinary Approach; Scott, R. A., Mauk, A. G.,
Eds.; University Science Books: Sausalito, CA, 1996; p 515.
(2) (a) Meade, T. J.; Gray, H. B.; Winkler, J. R. J. Am. Chem. Soc. 1989, 111,
4353. (b) Zhou, J. S.; Rodgers, M. A. J. J. Am. Chem. Soc. 1991, 113,
7728. (c) Casimiro, D. R.; Richards, J. H.; Winkler, J. R.; Gray, H B. J.
Phys. Chem. 1993, 97, 13073. (d) Mines, G. A.; Bjerrum, M. J.; Hill, M.
G.; Casimiro, D. R.; Chang, I.-J.; Winkler, J. R.; Gray, H. B. J. Am. Chem.
Soc. 1961, 118, 1961. (e) Luo, J.; Reddy, K. B.; Salameh, A. S.; Wishart,
J. F.; Isied, S. S. Inorg. Chem. 2000, 39, 2321.
(3) (a) McLendon, G. Acc. Chem. Res. 1988, 21, 160. (b) Harris, M. R.; Davis,
D. J.; Durham, B.; Millett, F. Biochim. Biophys. Acta 1997, 1319, 147. (c)
Mei, H.; Wang, K.; Peffer, N.; Weatherly, G.; Cohen, D. S.; Miller, M.;
Pielak, G.; Durham, B.; Millett, F. Biochemistry 1999, 38, 6846. (d) Ivkovic´-
Jensen, M. M.; Kostic´, N. M. Biochemistry 1997, 36, 8135. (e) Pletneva,
E. V.; Fulton, D. B.; Kohzuma, T.; Kostic´, N. M. J. Am. Chem. Soc. 2000,
122, 1034. (f) Overfield, R. E.; Wraight, C. A.; DeVault, D. FEBS Lett.
1979, 105, 137.
(4) (a) Tarlow, M. J.; Bowden, F. F. Am. Chem. Soc. 1991, 113, 1847. (b)
Song, S.; Clark, R. A.; Bowden, F. F.; Tarlow, M. J. J. Phys. Chem. 1993,
97, 6564. (c) Feng, Z. Q.; Imabayashi, S.; Kakuichi, T.; Niki, K. J. Chem.
Soc., Faraday Trans. 1997, 93, 1367. (d) Avila, A.; Gregory, B. W.; Niki,
K.; Cotton, T. M. J. Phys. Chem. B 2000, 104, 2759.
(5) Wei, J.; Liu, H.; Khoshtariya, D. E.; Yamamoto, H.; Dick, A.; Waldeck,
D. H. Angew. Chem., Int. Ed. 2002, 41, 4700.
(6) (a) Barbara, P. F.; Meyer, T. J.; Ratner, M. A. J. Phys. Chem. 1996, 100,
13148. (b) Curry, W. B.; Grabe, M. D.; Kurnikov, I. V.; Skourtis, S. S.;
Beratan, D. N.; Regan, J. J.; Aquino, A. J. A.; Beroza, P.; Onuchic, J. N.
J. Bioenerg. Biomembr. 1995, 27, 285. (c) Closs, G. L.; Miller, J. R. Science
1998, 240, 440.
(7) Beratan, D. N.; Betts, J. N.; Onuchic, J. N. Science 1991, 252, 1285.
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7704
J. AM. CHEM. SOC. 2003, 125, 7704-7714
10.1021/ja034719t CCC: $25.00 © 2003 American Chemical Society

Charge Transfer for Cytochrome c at Short Distances
A R T I C L E S
Chart 1. Molecular Structures Are Shown for the Different
donor and acceptor
Receptor-Based Tethering Molecules
2
ket |V|
(2)
and the exponential decrease of the exchange interaction that
causes |V|, such that
â
2
|V| ) V0 exp - (Re - Ro)
(3)
[
]
where V0 is the value of |V| at the minimum distance Ro. The
same model predicts an activation free energy for the rate
constant
∆Ga
ket exp -
(4)
[
]
RT
that depends quadratically on the reaction free energy ∆Go,
these studies have provided a wealth of information and indicate
biases toward one or more of the characteristic features
quantified by eqs 1, 5, or 6, they do not probe the dependence
of the intrinsic charge-transfer mechanism on the reaction
conditions. Except for a few reports (Vide infra), these studies
do not explore the possible change in the mechanism from the
nonadiabatic limit to the adiabatic limit. This deficiency reflects
the difficulty in varying the fundamental parameters, Re, |V|,
and ∆G0 in an independent and quantifiable manner. Hetero-
geneous bioelectrochemical systems in which cytochrome c or
other redox proteins exchange electrons with a metal electrode
by tunneling through insulating self-assembled monolayer
(SAM) films promises to allow such studies.4,5,11 Electrochemi-
cal methods are well proven for the determination of rate
constants and intrinsic mechanisms in chemical studies.10,12
The present work is an extension of earlier studies from this
group that probes the electron-transfer kinetics of cytochrome
c that is linked to nanometer thick monolayer films by direct
binding with the protein’s heme unit.5,11 This report presents
new data on the viscosity dependence and deuterium isotope
dependence of the electron-transfer rate constant for the systems
described earlier and presents data for new types of tethers,
including a conjugated linker (Chart 1). In addition to these
new data, a comprehensive and self-consistent analysis of the
results is presented. In particular, the data show a clear change
in the reaction mechanism with the distance of the protein from
the electrode, and the analysis compares the description by a
unified charge-transfer theory with that by a conformational
gating model.
namely
(λ - ∆Go)2
∆Ga )
- |V|
(5)
4λ
Assuming that the reorganization free energy, λ, is constant
within a reaction series, a bell-shaped dependence of log(ket)
vs ∆Go should be observed, at least for “homogeneous”
unimolecular rate constants (for electrode processes eq 5 is
approximately valid within the range of |∆Go| e λ, Vide infra8).
An alternative description of the electron-transfer rate constant
is required when the electronic interaction between the electron
donor and electron acceptor is large enough and is referred to
as the adiabatic limit. In this limit, the rate constant is no longer
controlled by the magnitude of the electronic coupling but rather
by the frictional coupling between the changing charge distribu-
tion of the reactants and the polarization of the surrounding
medium. This frictional coupling is most often characterized
by a characteristic relaxation time of the medium τs or a viscosity
η for the medium. Phenomenological and theoretical models,
based on the Kramers treatment,9 have been used to treat the
reaction rate constant in this limit. When the frictional coupling
to the medium is very strong, the rate constant decreases as
1/τs or 1/η. Empirically, a power law form is often found to
describe the friction dependence of the rate constant; for
example,
ket η-γ
(6)
where γ is an “empirical” parameter with typical values within
the range 0< γ e 1.10
2. Experimental Section
The electron-transfer kinetics of cytochrome c in “homoge-
neous” systems, including bimolecular reactions of the protein
with natural or artificial counterparts3 and unimolecular reactions
of an unnatural cytochrome that has low-molecular weight redox
partners covalently attached,2 have been performed. Although
Reagents and Materials. Water for the experiments was purified
by using a Barnstead-Nanopure system and had a resistivity of 18
MΩ cm. 1,3-Dicyclohexylcarbodiimide, DCC, (99%) was purchased
from Alfa Aesar. All mercaptoalkanes were purchased from Aldrich
and used without further purification. Imidazole (99%), 6-mercapto-
1-hexanol, 11-bromo-1-undecanol (98%), 1-nonadecanol, isonicotinic
acid (99%), docosanedioic acid (85%), methanolic iodine (99%), sodium
bisulfite (99%), thiourea (99+%, A.C.S. reagent), K2CO3 (99+%,
A.C.S. reagent), NaOH (97%), and MgSO4 (99%) were purchased from
Aldrich. 4-Pyridinecarbaldehyde and 2-bromothiophene, 4-bromopy-
(8) (a) Finklea, H. O. In Electroanalytical Chemistry; Bard, A. J., Rubinstein,
I., Eds.; Marcel Dekker: New York, 1996; Vol. 19, p 109. (b) Chidsey, C.
E. D. Science 1991, 251, 919. (c) Miller, C. J. In Physical Methods in
Electrochemistry; Rubinstein, I., Ed. Wiley: New York, 1995; p 27.
(9) Kramers, H. A. Physica 1940, 7, 284.
(10) (a) Weaver, M. J.; McManis, G. E. Acc. Chem. Res. 1990, 23, 294. (b)
Weaver, M. J. Chem. ReV. 1992, 92, 463. (c) Fawcett, W. R.; Opallo, M.
Angew. Chem., Int. Ed. Engl. 1994, 33, 2131. (d) Williams, M. E.; Crooker,
J. C.; Pyati, R.; Lyons, L. J.; Murray, R. W. J. Am. Chem. Soc. 1997, 119,
10249. (e) Fu, Y.; Cole, A. S.; Swaddle, T. W. J. Am. Chem. Soc. 1999,
121, 10410. (f) Khoshtariya, D. E.; Dolidze, T. D.; Krulic, D.; Fatouros,
N.; Devilliers, D. J. Phys. Chem. B 1998, 102, 7800.
(11) (a) Wei, J.; Liu, H.; Dick, A. R.; Yamamoto, H.; He, Y.; Waldeck, D. H.
J. Am. Chem. Soc. 2002, 124, 9591. (b) Yamamoto, H.; Liu, H.; Waldeck,
D. H. Chem. Comm. 2001, 1032.
(12) Bard, A. J.; Faulkner, L. R. Electrochemical Methods; Wiley: New York,
1980.
9
J. AM. CHEM. SOC. VOL. 125, NO. 25, 2003 7705

A R T I C L E S
Khoshtariya et al.
ridine anhydrous N,N-dimethylformamide (DMF) were bought from
Fluka. Absolute ethanol was purchased from Pharmcoproducts, Inc.;
Dextrose ((+)-D-glucose anhydrous, 99%) was purchased from Sigma.
Cytc (Sigma C 7752, from horse heart, minimum 95% based on
molecular weight 12 384) was purified using a cation exchange column
(CM-52, carboxymethyl-cellulose from Whatman) in a manner
described previously.11 The purified cytochrome c was stored under
an argon atmosphere in a freezer with dry ice until use.
The solution used in the voltammetry study was 20 mM sodium
phosphate buffer solution at pH 7. The viscosity of the solutions was
varied by using glucose concentrations of 0 g/L, 200 g/L, and 400 g/L.
The solution viscosities were measured to be 0.98 cP, 1.76 cP, and
3.88 cP, respectively. The measurements were performed at room
temperature with an Ubbelohde viscometer.
Electrode Preparation. More details of preparation and character-
ization of the gold electrode can be found elsewhere.11 Only a brief
outline of the procedure is given here. A gold wire (0.5 mm diameter,
99.99%) was cleaned by reflux in nitric acid (68-70%) at 130 °C
overnight and then was washed with deionized water. The tip of the
gold wire was heated and annealed in a gas flame to form a ball of
about 0.06-0.12 cm2 surface area. Chemically modified electrodes were
prepared by immersion in an ethanol or THF solution that contained 1
mM -S(CH2)nOOC(C5H4N) and -S(CH2)n-2CH3 (the mole ratio of
-S(CH2)nOOC(C5H4N) to -S(CH2)n-2CH3 was 1:9). The electrode
remained in this solution for 1 day to form the mixed SAM. The
electrode was taken out from the solution, first rinsed with absolute
ethanol (or THF), then rinsed with the supporting buffer solution (20
mM phosphate buffer pH 7), and finally dried by a stream of argon
gas. The electrode was characterized, as previously,11 and then immersed
in a 100 µM cytochrome c solution (purged with argon gas) for 30-
60 min in order to immobilize the cytochrome on the SAM-coated
electrode. These electrodes were immediately used in voltammetry
studies.
Electrochemical Measurements. Electrochemical measurements
were performed by using an EG&G PAR-283 potentiostat controlled
by a PC computer running version 4.3 of PARC’s 270 software and a
GPIB board. The three-electrode cell was composed of a platinum spiral
counter electrode, an Ag/AgCl (3 M NaCl) reference electrode, and
the SAM-coated Au as a working electrode. The voltammetry measure-
ments were performed in 20 mM phosphate buffer solution (pH of 7.0)
at different viscosities under an argon atmosphere. To study the isotope
effects, the SAM modified gold electrodes were incubated in cyto-
chrome c D2O buffer solution to immobilize protein and then measured
in both D2O and H2O buffer solution.
C. Bis(16-hydroxyhexadecyl)disulfide: 16-Mercaptohexadecanol
was prepared by reducing 16-mercaptohexadecanoic acid in ethyl ether
using LiAlH4. Diluted NaOH solution was used to quench the reaction.
The resulting solution was dissolved in 0.2 M HCl and extracted with
CH2Cl2. The solvent was removed under vacuum. Purification of the
resulting crude 16-mercaptohexadecanol was performed by flash
1
chromatography (CH3Cl). H NMR (300 MHz) CDCl3 δ 3.646 (t,J )
6.615, 2H); 2.527 (q, J ) 7.34, 2H); 1.603 (m, 6H); 1.327 (broad,
23H). Bis(16-hydroxyhexadecyl)disulfide is insoluble in common
solvents, such as CH2Cl2, and NMR data were not obtained.
D. Bis(20-hydroxyeicosyl)disulfide and Bis(22-hydroxydocosyl)-
disulfide were prepared through the same procedures as that for the
preparation of Bis(16-hydroxyhexadecyl disulfide.
2. Preparation of Pyridine Derivatives. A. Bis[6-((pyridinylcar-
bonyl)oxy)hexanyl]disulfide: 1,2-dicyclohexylcarbodiimide (DCC)
(4.13 g, 20.02 mmol) was added to 20 mL of dichloromethane solution
of bis(6-hydroxyhexanyl)disulfide (2.42 g, 9.10 mmol), isonicotic acid
(2.24 g, 18.20 mmol), and 4-(dimethylamino)pyridine (0.22 g, 1.82
mmol) at 0 °C. After 1 h, the solution was allowed to warm to room
temperature, and stirring was continued for 4 days. After removal of
the precipitated dicyclohexylurea (DCU) by filtration, the solvent was
removed under reduced pressure to yield a crude solid. The solid was
recrystallized with ethanol and chromatographed on silica gel (60-
200 mesh) with ethyl acetate. Evaporation of the solvent yielded the
1
disulfide as 3.45 g of a white solid. H NMR (300 MHz) CDCl3 δ
8.789 (d, J ) 5.97, 4H); 7.849 (d, J ) 5.97, 4H); 4.362 (t, J ) 6.615,
4H); 2.695 (t, J ) 7.215, 4H); 1.802 (m, 4H); 1.723 (m, 4H); 1.488-
1.453 (m, 8H).
B. Bis[11-((4-methyl-4-pyridinylcarbony)oxy)undecyl]disulfide,
Diiodides: Bis[11-((4-pyridinylcarbonyl)oxy)undecyl]disulfide was re-
fluxed with an excess of iodomethane in ethanol for 24 h under nitrogen.
The solution was cooled to room temperature, and the precipitate that
formed was filtered and recrystallized in ethanol and acetone 3 times.
1
A brown solid was obtained. H NMR (300 MHz) CDCl3 δ 9.501 (d,
J ) 6.54, 4H); 8.515 (d, J ) 6.46, 4H); 4.834 (s, 6H); 4.449 (t, J )
6.614, 4H); 2.694 (t, J ) 7.301, 4H); 1.818 (m, 4H); 1.678 (m, 8H);
1.476-1.216 (broad, 24H).
C. Bis[11-((4-pyridinylcarbonyl)oxy)undecyl]disulfide: 1H NMR
(300 MHz) CDCl3 δ 8.810 (s, 4H); 7.901(d, J ) 5.73, 4H); 4.367 (t,
J ) 6.63, 4H); 2.684 (t, J ) 7.32, 4H); 1.789 (m, 4H); 1.675 (m, 4H);
1.43-1.29 (broad, 28H). EI-HRMS: calcd 616.3385 (C34H52N2O4S2),
found 616.3369.
D. Bis[16-((4-pyridinylcarbony)oxy)hexadecyl]disulfide: 1H NMR
(300 MHz) CDCl3 δ 8.889 (s, 4H); 7.869 (d, J ) 5.46, 4H); 4.359 (t,
J ) 6.705, 4H); 2.683 (t, J ) 7.36, 4H); 1.781 (m, 8H); 1.673
(m, 4H); 1.43-1.29 (broad, 44H). EI-HRMS: calcd 756.4896
(C44H72N2O4S2), found 756.4934.
E. Bis[22-((4-pyridinylcarbony)oxy)docosyl)disulfide: 1H NMR
(300 MHz) CDCl3 δ 8.789 (d, J ) 5.52, 4H); 7.857 (d, J ) 5.76, 4H);
4.358 (t, J ) 6.66, 4H); 2.685 (t, J ) 7.37, 4H); 1.784 (m, 4H); 1.694
(m, 4H); 1.26 (broad, 72H).
Material Preparation. Pyridine, imidazole, nitrile terminated dis-
ulfide derivatives, 2-(4-pyridine-5-terthiophene-thiol), nonadecanethiol,
and heneicosanethiol were prepared according to literature proce-
dures.11,13 12-Mercapto-1-dodecanol was prepared in the manner
reported earlier.11a 1H NMR spectra were obtained at 300 MHz, and
the coupling constant is reported in Hz.
1. Preparation of Disulfides. A. Bis(6-hydroxyhexanyl)disulfide:
6-Mercapto-1-hexanol (6.0 g, 44.696 mmol) was dissolved in 10 mL
of methanol and titrated with 0.5 M methanolic iodine until the reaction
turned from colorless to a persistent yellow. The reaction was quenched
with 10% sodium bisulfite to a colorless solution. The resulting mixture
was dissolved in distilled water and extracted with CH2Cl2, and the
solvent was removed under vacuum. Purification of the resulting crude
disulfide was performed by flash chromatography (CH3Cl) to afford
F. 2-(4-Pyridine-5-terthiophene-thiol): Details on the preparation
of the terthiophene will be reported elsewhere.
3. Results
Two different strategies have been used to adsorb cytochrome
c onto the surface of nanometer thick insulating films on metal
electrodes (see Figure 1). The first method uses carboxylate
terminated SAMs that bind the protein electrostatically, since
it is positively charged (left panel). It is believed that the ionized
lysines on the surface of the cytochrome interact with the
carboxylate groups. The second method uses SAMs that are
terminated with nitrogen containing headgroups that can bind
to the heme unit of the protein (right panel). The first method
has the advantage of providing a better mimic of the in vivo
1
the disulfide (5.35 g) as a white solid in 90% yield. H NMR (300
MHz) CDCl3 δ 3.649 (t, J ) 6.435, 4H); 2.690 (t, J ) 7.275, 4H);
1.703 (m, 4H); 1.584 (m, 4H); 1.510-1.375 (m, 8H).
B. Bis(11-hydroxyundecyl)disulfide: 1H NMR (300 MHz) CDCl3
δ 3.651 (q, J ) 6.18, 4H); 2.689 (t, J ) 7.34, 4H); 1.679 (m, 4H);
1.579 (m, 4H); 1.379-1.290 (broad, 28 H).
(13) (a) Hu, J.; Fox, M. J. Org. Chem. 1999, 64, 4959. (b) Abbotto, A.;
Bradamante, S.; Facchetti, A.; Pagani, G. J. Org. Chem. 1997, 62, 5755.
9
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Charge Transfer for Cytochrome c at Short Distances
A R T I C L E S
Figure 1. This schematic drawing shows the adsorption of the cytochrome c to the surface of self-assembled monolayer films through two different binding
motifs: (left panel) electrostatic attraction between carboxylate groups on the SAM and the protein’s positive lysine groups and (right panel) coordination
of a receptor group (pyridine) in the SAM with the heme of the protein.
environment of cytochrome c, and the distribution of lysines
on the surface leads to an adsorption geometry that has the heme
edge oriented toward the surface.14 The second method provides
control of the cytochrome c orientation on the surface and
directly “wires” the heme to the electrode but requires the
receptor group on the SAM to displace an axial ligand from
the heme, thereby causing partial unfolding. The second method
is exploited here, but comparisons are drawn with the work of
others using the first method.
The standard rate constants for electron transfer between the
SAM coated Au electrode and the attached cytochrome c were
determined through the evaluation of cyclic voltammetry data,
a standard procedure.12 Representative voltammograms for these
systems have been reported.5,11 In brief, the dependence of the
Figure 2. This diagram plots the apparent standard electron-transfer rate
observed peak potential for the faradaic current is measured as
a function of the voltage scan rate.15 Quantitative analysis of
this dependence provides the standard heterogeneous electron-
transfer rate constant, which is the heterogeneous electron-
transfer rate constant at a reaction free energy of zero. Plots of
the peak position as a function of scan rate have been reported
for the alkylpyridine systems, already.5 This method is limited
in its time resolution by the RC characteristics of the electrode.
With the small diameter (ca. 1 mm) gold ball electrodes used
in this work, rate constants up to about 10 000 Hz can be
constants for the different systems. The data for systems bound through
coordination with the heme are represented by a circle for pyridine, × for
imidazole, triangle for CN, and diamond for terthiophene. The squares are
the data for electrostatic adsorption on COOH. The dashed lines are fits to
the nonadiabatic model at a large layer thickness.
that found in other tunneling studies with saturated hydrocar-
bons. This behavior at large distance is a signature for
nonadiabatic electron transfer. Both data sets show a plateau
region at short donor-acceptor separations; however, the plateau
region spans to a larger methylene number for the pyridinal
systems. Although the behavior is qualitatively similar for these
two systems, the maximum rate constants differ by about a factor
of 2 and the rate constants in the pyridine-bound systems are
consistently higher than that for the electrostatically bound
system.
An important caveat in using voltammetric peak shifts to
obtain rate constants is the presence of iR drop in the solution.
At faster voltage scan rates the current is higher so that the
voltage drop associated with the solution resistance increases.
The importance of this effect was evaluated by studying the
voltammetry for cytochrome c linked to the electrode by way
of a pyridine terminated tether of six methylene groups. Of the
alkane tethered structures, this system would be expected to
show the largest iR artifact. A 10-fold increase in the phosphate
buffer concentration (the ionic strength) causes a 10% increase
in the measured rate constant (data are provided in the
0
measured. The standard heterogeneous rate constants ket for
the different systems are summarized in Tables 1-3.
In Figure 2, the measured heterogeneous rate constant is
plotted as a function of the methylene number of the tethering
group for the different SAMs studied here and for the -COOH
terminated SAMs; see Niki.4 At large electrode-reactant
separations, the pyridine terminated alkanes and the COOH
terminated SAMs display an exponential dependence on the
charge-transfer distance (see eqs 1 and 3) with a decay constant
of about one per methylene. This decay constant is similar to
(14) (a) Edmiston, P. L.; Lee, J. E.; Cheng, S.-S.; Saavedra, S. S. J. Am. Chem.
Soc. 1997, 119, 560. (b) Dick, L. A.; Haes, A. J.; van Duyne, R. P. J.
Phys. Chem. B 2000, 104, 11752.
(15) (a) Napper, A. M.; Liu, H.; Waldeck, D. H. J. Phys. Chem. B 2001, 105,
7699. (b)Tender, L.; Carter, M. T.; Murray, R. W. Anal. Chem. 1994, 66,
3173. (c) Weber, K.; Creager, S. E. Anal. Chem. 1994, 66, 3166. (d)
Honeychurch, M. J. Langmuir 1999, 15, 5158.
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A R T I C L E S
Khoshtariya et al.
Table 1. Rate Constant Data for Cytochrome c Immobilized on
Different Mixed SAMsa
k°
(Hz)
E°
(mV)
no. of
trials
k°
(Hz)
E°
(mV)
no. of
trials
system
system
C6py/C5
C11py/C10 1150
C12py/C11 785
C16py/C15
C20py/C19
C22py/C20
1580
-175
6
C11CN/C8 1000 -415
2
4
2
-168 14 C11Im/C8
860 -346
-172
-158 12
4
Terpy/C7
4200 -188
52
0.50 -156
0.032 -145
3
2
a In each case, the diluent SAM is an alkanethiol and the measurement
is made in aqueous buffer. The data are the average of experimental results
obtained on different days with different electrode preparations.
supplemental information). Whether this dependence represents
the effect of iR drop or change in the protein’s electron-transfer
rate with ionic strength is currently under study. Even if this
change represents the effect of iR drop, it represents a minor
contribution to the experimental rate constant and cannot explain
the weak distance dependence of the electron-transfer rate
between six methylene and twelve methylene thick films (see
Table 1).
Figure 3. Viscosity dependences of the observed electron-transfer rate
constant are shown for three different alkanethiol chain lengths: the triangles
are C6, the circles are c11, and the squares are C16. The dashed line has
zero slope.
Table 2. Rate Constants of Immobilized Cytochrome c for
Different Solution Viscositiesa
η ) 0.98 cP
η ) 1.76 cP
no. of
η ) 3.88 cP
no. of
no. of
Figure 2 also shows new data on the cytochrome c adsorbed
through three other tethers in the region of the plateau. In two
of these systems, the C11 tether is retained, but the receptor
group has been modified from a pyridine to an imidazole and
from a pyridine to a nitrile unit. These headgroups cause a quite
different apparent redox potential but have a minor effect on
the standard electron-transfer rate constant. The shift in the
apparent redox potential is consistent with solution studies of
cytochrome c’s redox potential shift when it binds small ligands.
In particular, the immobilized cytochrome c studies give -172
mV for the pyridine headgroup, whereas a cytochrome c solution
with pyridine added has a -294 mV shift.1a,16a The imidazole
tether causes an apparent redox potential of -346 mV, and the
nitrile causes -415 mV, which should be compared to -426
mV and -665 mV for cytochrome c solutions containing
imidazole and cyanide, respectively.1a,16b,c The addition of an
exogenous ligand to the solution may cause a conformational
change in the protein that might contribute to the redox potential
shift, or it may ligate to the heme and cause a shift in the redox
potential. A recent study by Fan et al.16a distinguishes these
two contributions for the case of pyridine and finds that the
heme bound pyridine has a redox potential of -161 mV and
that the larger negative redox potential of -294 mV should be
associated with a non-native protein conformation. Their find-
ings corroborate the view of cytochrome c adsorption that is
illustrated in Figure 1, in which the cytochrome c binds to the
pyridine in a nativelike conformation rather than a denatured
form. Despite these large changes in the apparent redox
potentials, the standard electron-transfer rate constants for the
three C11 systems lie within 30% of each other (see Table 1).
The other tether is a terthiophene oligomer with a pyridinal head
unit. It displays an apparent redox potential that is similar to
that found for the alkylpyridine systems, but the rate constant
shows a factor of 4 increase (see Table 1), demonstrating the
importance of tether composition on the electron-transfer rate.
system
runs
k° (Hz)
runs
k° (Hz)
runs
k° (Hz)
C6py/C5
C11py/C10
C16py/C15
3
2
2
1512
1155
60
4
5
2
1050
990
60
3
4
2
670
780
61
a Data are only obtained from the viscosity measurement, which may
not be identical to the average data of all measurements, provided in Table
1.
C6Py, C11Py, and C16Py SAM systems. Fits of the data to the
power law form of eq 6 gives γ values of 0.58 for C6Py, 0.28
for C11Py, and ∼0 for C16Py. The dependence on the viscosity
correlates with the chain length of the alkane linker. The
viscosity dependence is seen in the plateau region of the distance
dependence, whereas the rate constant is independent of the
viscosity in the large distance regime. The viscosity indepen-
dence of the rate constant for the C16Py system is consistent
with the nonadiabatic mechanism being operative in this regime
and demonstrates that the experimental procedure for changing
the viscosity is not causing some other change in the protein or
its adsorbed state. The “maximal” value of γ ≈ 0.58 found for
the plateau region is typical for viscosity dependent protein
processes and small molecule reactions.17 Although the rate
constants for C11Py and C6Py are similar, the viscosity
dependence for the C6Py system is significantly steeper than
that found for the C11Py system. The observation of a viscosity
dependence for the electron-transfer rate constant was observed
previously for cytochrome c adsorbed electrostatically to
carboxylic acid terminated films4d and for the Fe(CN)6
3-/4-
couple in contact with very thin alkane based monolayer films.18
Clearly, a viscosity linked process becomes important in the
plateau region of the data in Figure 2 and demonstrates a change
in the mechanism of the electron-transfer reaction with dis-
tance.19
Table 3 provides data that displays a shift in the electron-
transfer rate constant for cytochrome c when it has been exposed
to heavy water.20 These experiments show that long time
0
Figure 3 and Table 2 present the dependence of ket on the
solution viscosity, varied by the addition of glucose, for the
(17) (a) Waldeck, D. H. Chem. ReV. 1991, 91, 415. (b) Fayer, M. D. Annu.
ReV. Phys. Chem. 2001, 52, 315. (c) Frauenfelder, H.; Wolynes, P. G.;
Austin, R. H. ReV. Mod. Phys. 1999, 71, S419.
(18) Khoshtariya, D. E.; Dolidze, T. D.; Zusman, L. D.; Waldeck, D. H. J. Phys.
Chem. A 2001, 105, 1818.
(16) (a) Fan, C.; Gillespie, B.; Wang, G.; Heeger, A. J.; Plaxco, K. W. J. Phys.
Chem. B 2002, ASAP. (b) Battistuzzi, G.; Borsari, M.; Cowan, J. A.;
Ranieri, A.; Sola, M. J. Am. Chem. Soc. 2002, 124, 5315. (c) Battistuzzi,
G.; Borsari, M.; Ranieri, A.; Sola, M. J. Am. Chem. Soc. 2002, 124, 26.
9
7708 J. AM. CHEM. SOC. VOL. 125, NO. 25, 2003

Charge Transfer for Cytochrome c at Short Distances
A R T I C L E S
Table 3. D2O Dependence of the Rate Constant Data for
for the pyridinal case. The steepness of the decline is similar
for the two systems, 1.19 per CH2 for the pyridinal SAMs and
1.22 per CH2 for the COOH SAMs, and agrees with the fall
off found for tunneling through saturated hydrocarbons.8 The
shift between the two cases can be understood by considering
the different binding modes of cytochrome on the two film types.
The COOH terminated groups electrostatically bind the cyto-
chrome by its lysine groups4 and the pyridine terminated
alkanethiols bind through ligation with the heme group.22
Inspection of Figure 2 shows that a shift of the COOH rate
constants by about four methylene groups to the right would
cause a good correspondence between the two data sets.
The reasonableness of such a distance shift can be probed
by estimating the physical distance between the electrode surface
and the heme unit of the protein in the two cases. Consider the
pyridine unit to coordinate at the heme and assume it contributes
little to the effective charge-transfer distance because of its
π-conjugated nature.23 The “effective” donor-acceptor separa-
tion d between the metal surface and the heme, upon the
variation of the SAM thickness, can be estimated according to
Immobilized Cytochrome ca
C11py/C10
incubant
C16py/C15
incubant
cell
k0 (Hz)
cell
k0 (Hz)
H2O
D2O
H2O
D2O
H2O
H2O
D2O
D2O
1140
1100
890
H2O
D2O
H2O
D2O
H2O
H2O
D2O
D2O
58
879
55
a Data are only obtained from the isotopic measurements and may not
be identical to the average data of all measurements, provided in Table 1.
exposure (ca. 30 min or more) of the protein to D2O changes
the observed electron-transfer rate constant in the plateau region
of Figure 2. If a C11Py/C10 coated electrode is placed in a
D2O buffer solution containing cytochrome c and allowed to
incubate to form the adsorbed state of the protein, the measured
standard electron-transfer rate constant decreases by 30%. This
decrease is independent of whether the measurement in the
electrochemical cell occurs with H2O buffer or D2O buffer. The
typical time that the electrode is in the electrochemical cell is
less than 10 minutes. These results suggest that water present
in the protein or exchangeable protons act to modulate the
electron-transfer rate constant in the plateau region. A deuterium
isotope effect was also observed by Murgida and Hildebrandt.21
In contrast, the C16Py/C15 coated electrodes do not display a
dependence on D2O versus H2O and demonstrate that the
modification of the “normal” buffer solution with D2O does
not impact the adsorbed state of the protein.
The results that are presented and summarized here cannot
be explained in terms of the nonadiabatic electron-transfer model
(eqs 1 and 2) over the whole range of systems. For methylene
chains longer than dodecane, the standard electron-transfer rate
constant declines exponentially with increasing alkane chain
length, does not display a viscosity dependence, and does not
change with the use of D2O buffer. These observations are
consistent with the nonadiabatic electron-transfer mechanism.
Further, they demonstrate that the method for changing the
viscosity and the use of D2O do not change the adsorption state
of the protein. Although the electron-transfer rate constant is
well described by the nonadiabatic model at large distances,
the reaction mechanism must change for shorter distances
because the rate constant is no longer decaying exponentially
with distance, displays a viscosity dependence, and depends on
the use of D2O versus H2O. The nature of the reaction
mechanism at short distances and the thickness at which the
mechanism changes are discussed below.
d ) 1.90 + 1.12n (Å)
(7)
where n is the number of methylenes in the alkane chain and
1.90 Å accounts for the S atom radius of the thiol.24 A similar
analysis for cytochrome c adsorbed on the COOH terminated
films requires that the tunneling pathway from the outer layer
of the SAM through the protein exterior and into the heme unit
be identified. Because of the possibility that the cytochrome
can have a range of orientation, one should more formally
consider a distance distribution; however, work by Niki25 implies
that the electron tunneling occurs mostly through the lysine 13
which lies near the heme unit. Using the cytochrome c crystal
structure, one can estimate a physical “through-space” distance
of 5.8 Å from the lysine to the heme and a “through-bond”
distance of about 20 Å. These considerations of the actual
physical distance between the electrode and the heme justify
the use of a distance shift to bring the two data sets into
correspondence.
Figure 5 presents the dependence of the heterogeneous rate
constant for the pyridinal systems as a function of the charge-
transfer distance, estimated through eq 7, and for the COOH
systems with a 5 Å shift to account for an extra “effective
tunneling distance” from the SAM edge through the protein
matrix. The good agreement between the two data sets suggests
that differences in the electron-transfer rate that is observed can
be “corrected” by accounting for differences in the electron-
transfer distance. Although it is enticing to attribute this
difference to the physical distance of the heme from the
electrode in the two situations, this may not be the most accurate
description. Rather, differences in the electronic coupling
between the heme and the electrode for the two situations,
arising from differences in the tunneling pathways, will
contribute to the “effective” donor-acceptor separation.
4. Discussion
Tunneling Mechanism at Large n and the Role of Binding
Mode. From Figure 2, one can see that at large electrode-
cytochrome c separations the data for SAM films that are
terminated with pyridinal moieties show a trend similar to that
of the -COOH terminated films, but the onset of the exponential
decline occurs at larger film thicknesses (ca. 12 methylenes)
(22) Murgida, D.; Hildebrandt, P.; Liu, H.; Wei, J.; Waldeck, D. H., in
preparation.
(19) A viscosity dependent rate constant may occur when the barrier-crossing
process has a dissipative nature, experiences frictional coupling with the
medium (solvent). For the case of “full” solute-solvent coupling, γ f 1,
the Smoluchowski limit. Deviation from this limit may be caused by weak,
or intermediate, solute-solvent coupling or a change toward a weaker
electronic coupling, as discussed later.
(23) (a) Sikes, H. D.; Smalley, J. F.; Dudek, S. P.; Cook, A. R.; Newton, M.
D.; Chidsey, C. E. D.; Feldberg, S. W. Science 2001, 291, 1519. (b) Creager,
S.; Yu, C. J.; Bamdad, C.; O’Connor, S.; Maclean, T.; Lam, E.; Chong,
Y.; Olsen, G. T.; Luo, J.; Gozin, M.; Kayyem, J. F. J. Am. Chem. Soc.
1999, 121, 1059.
(20) Some of these data were reported in ref 5.
(24) Liu, Y.-P.; Newton, M. D. J. Phys. Chem. 1994, 98, 7162.
(25) Niki, K.; Sprinkle, J. R.; Margoliash, E. Bioelectrochemistry 2002, 55, 37.
(21) Murgida, D.; Hildebrandt, P. J. Am. Chem. Soc. 2001, 123, 4062.
9
J. AM. CHEM. SOC. VOL. 125, NO. 25, 2003 7709

A R T I C L E S
Khoshtariya et al.
Friction Control versus Conformational Gating. Previous
workers4d,25 have explained the distance independent behavior
of the charge-transfer rate constant in the plateau region, for
the case of -COOH terminated SAMs, as resulting from a
change in the rate-determining step. In particular, the charge
transfer occurs by the nonadiabatic (tunneling) mechanism and
is gated by a conformational rearrangement to a precursor state
that is electroactive. This mechanism is similar to the confor-
mationally gated mechanism that has been used to describe
electron-transfer processes involving a range of processes with
cytochrome c’s.3b,26 For the COOH terminated SAMs, this may
correspond to the diffusive tumbling of the cytochrome c on
the surface to an orientation in which the protein’s heme is
closest to the surface and electron transfer occurs rapidly. Such
a scenario is not consistent with the data for the pyridine
terminated chains, which show a similar distance dependence
but do not involve reorientation of the protein on the SAM
surface.
A number of results do not support simple conformational
gating of the heterogeneous electron transfer on SAM coated
Au electrodes. First, the electrochemical data, ac impedance and
cyclic voltammetry, indicate a simple charge-transfer step. For
example, the peak potential’s shift with voltage scan rate and
symmetry of the oxidation and reduction waves suggest a simple
electrochemical reaction, rather than a mechanism involving a
preequilibrium. Second, the observation of similar limiting
values of rate constants for the different monolayer films, which
have two very different binding modes of cytochrome c,
suggests that the electron transfer is not preceded by the large-
scale protein-SAM structural rearrangement (conformationally
gated). Third, the dependence of the electron-transfer rate
constant on the amount of D2O in the adsorbed protein, rather
than D2O in the solution, is not consistent with large-scale
motion of the protein on the surface of the film. Fourth, the
larger rate constant that is found for the conjugated terthiophene
tether cannot be explained by a conformational gating mecha-
nism. These observations indicate that conformational gating
is not controlling the electron-transfer rate constant for the
pyridine terminated SAMs, but it does not discount this
mechanism for the COOH terminated SAMs nor does it discount
small amplitude conformational changes that may be linked to
the electron-transfer coordinate.
Figure 4. This Marcus plot shows the free energy dependence of
cytochrome c’s electron-transfer rate constant from a number of different
studies, mostly homogeneous solution; the data are from Gray et al. [G]2d
for Ru-modified cytochrome c; Zhou et al. [Z]2b for cytochrome c/uropor-
phyrin complexes; McLendon3a for interprotein system cytochrome c/cy-
tochrome b5 [M]; and Isied et al2e for Ru-modified cytochrome c [1]. The
open symbols (]3c, 33f, 03b, 43d, O3e) correspond to rate constants that
exhibit a dependence on the external solution viscosity. The filled circle
shows the electrochemical electron-transfer rate at short distances (plateau
region), which also displays a viscosity dependence.4d The solid curve shows
the free energy dependence expected from the Marcus model, and the dashed
curve is the same model shifted down by a factor of 10.
should not.1a,3a,27 In lieu of such experiments, electron-transfer
rate constants for many different cytochrome c systems were
obtained from the literature and analyzed as a function of free
energy.
Comparison of Homogeneous and Electrochemical Kinet-
ics. Figure 4 plots electron-transfer rate constants as a function
of ∆G0 for many different systems involving cytochrome c
0
(including the “limiting” electrochemical value, kel ). These data
include “unimolecular” systems,2 in which a redox center is
covalently attached to the cytochrome c, and bimolecular
systems.3 Because they have a well-defined metal-to-metal
separation distance, the unimolecular systems can be compared
with the electrochemical data in more detail (vide infra). An
analysis of this sort presumes that the electron-transfer rate is
determined primarily by the Franck-Condon factors (free
energy and reorganization energy) rather than the electronic
coupling and that the reorganization energy does not change
too dramatically between the different systems. Despite the
drastic nature of these assumptions, the rate constants fall
surprisingly well on a bell-shaped curve.
An adiabatic charge-transfer mechanism for the charge-
transfer kinetics in the plateau region is consistent with the
findings. In particular, the viscosity dependence of the rate and
the D2O effects can be understood through consideration of
frictional coupling in the adiabatic mechanism, whereas the
higher electron-transfer rate for the conjugated linker can be
rationalized through the effect of the electronic coupling on the
activation barrier for the reaction (eq 5). The increase in rate
constant for the conjugated system supports the adiabatic
mechanism over the conformationally gated mechanism. A
critical test for distinguishing between the two mechanisms is
to determine the free energy dependence of the reaction rate
constant. For an adiabatic electron-transfer mechanism, the rate
constant should display a Marcus bell-shaped dependence on
free energy, whereas a conformationally gated mechanism
The solid curve drawn in Figure 4 is generated by fitting the
rate data for a series of ruthenium-modified cytochrome c’s.2
This data set (G) was used because of the range of free energies
and the well-defined distances between the redox centers. The
kinetic data that are plotted with open symbols (cytochrome
c/P870 in Rb. Sphaerodis,3f cytochrome c/Ru(II)bpy,3b cyto-
chrome c/radical cation in cytochrome c peroxidase,3c zinc
cytochrome c/bean plastocyanin,3d and cytochrome c/fern
plastocyanin3e complexes) exhibit a dependence on the external
solution viscosity. The electrochemical rate data appear to follow
this Marcus free energy dependence. The electrochemical rate
constant (filled circle) measured at ∆G0 ) 0 shows a 1000-
fold reduction from the maximum rate constant but lies on the
(26) (a) Engstrom, G.; Xiao, K. H.; Yu, C. A.; Yu, L.; Durham, B.; Millett, F.
J. Biol. Chem. 2002, 277, 31072. (b) Sharp, R. E.; Chapman, S. K. Biochim.
Biophys. Acta 1999, 1432, 143. (c) Canters, G. W.; Dennison, C. Biochimie
1995, 77, 506.
(27) (a) McLendon, G.; Pardue, K.; Bak, P. J. Am. Chem. Soc. 1987, 109, 7540.
(b) Graige, M. S.; Feher, G.; Okamura, M. Y. Proc. Natl. Acad. Sci. U.S.A.
1998, 95, 11679. (c) Davidson, V. Biochemistry 2000, 39, 4924. (d)
Davidson, V. Acc. Chem. Res. 2000, 33, 87.
9
7710 J. AM. CHEM. SOC. VOL. 125, NO. 25, 2003

Charge Transfer for Cytochrome c at Short Distances
A R T I C L E S
rate constant to an electrode process at ∆G0, one finds
same curve. This observation suggests that the electrochemical
system follows the free energy dependence for electron transfer.
The observed free energy dependence of the rate data and the
viscosity-sensitive behavior for some of them (Figure 4) indicate
that the electron transfer belongs either to the totally adiabatic
(friction controlled) or, at least, to the intermediate (or mixed,
vide infra) kinetic regimes, rather than corresponding to a
conformationally gated mechanism.27d
The data in Figure 4 and the general correspondence with
the reaction free energy reflects the importance of the activation
free energy on the reaction rate constant. The large scatter in
the rate data is to be expected, since the data correspond to
cytochrome c in such different environments. The peak of the
curve corresponds to the reaction free energy magnitude that
matches the reorganization energy so that the reaction rate is at
a maximum. The dashed line in the figure was obtained by
shifting the solid curve down by an order of magnitude. The
data show that the free energy and reorganization energy
determine the rate constant to within an order of magnitude or
so. This data analysis generates a reorganization energy for the
cytochrome c of 0.8 eV. Although the reorganization energy
depends on both partners in a redox reaction, these data suggest
that the protein dominates the contribution and is fairly
consistent between systems. For the electrochemical studies, the
kinetic data probe the reorganization energy through the
dependence of ket on ∆G0 (i.e., the overpotential eê) by way of
eq 8,
2
|V|
π3RT
Fm
p 1 + g
koet )
exp(- ∆Ga/RT)
(9)
λo
x
in which Fm is the density of electronic states in the electrode
and the adiabaticity parameter g is given by
2
π3RT|V| Fmτeff
g )
(10)
pλo
g acts as a control parameter; the reaction mechanism is
nonadiabatic when g , 1, yielding the equation
2
|V|
π3RT
koNA
)
Fm
exp(- ∆Ga/RT)
(11)
p
λo
x
For long-range electron transfer in biological systems, the
weak coupling or nonadiabatic regime, in which the process is
viewed as a tunneling (“quantum friction”) mechanism, is used
for both homogeneous2 and heterogeneous4 electron-transfer
reactions. The mechanism is adiabatic when g . 1, yielding
the expression
λo
3
1
τeff
koA )
exp(- ∆Ga/RT)
(12)
xπ RT
where the characteristic time τeff is related to relaxation processes
of the solvent molecules, protein interior, and so forth. In the
approximation of a dielectric continuum and a Debye-type
dielectric response, one finds that
(eê + ꢀF - ꢀ ( λ)2
ket
∞ f(ꢀ) exp -
dꢀ
(8)
∫
[
]
-∞
4λRT
where f(ꢀ) is the Fermi-Dirac distribution function and ꢀF is
the Fermi energy.8 When |∆G0| e λ, the electrochemical data
coincides with the solid curve in Figure 4.28a
ꢀ∞ 3ηVm
τeff ≈ τL )
(13)
( )
ꢀs RT
A number of experimental and theoretical studies28,29 report
the reorganization energy of cytochrome c, and they range in
value from 0.8 eV to 0.4 eV for the protein in solution. What
portion reflects an intrinsic protein component and what portion
arises from the environment or redox partner has been addressed
through theoretical studies.29 These studies find that the inner
sphere (heme) contribution to the reorganization energy is about
0.1 eV, the protein’s “outer sphere” (interior) contribution is at
least 0.45 eV, and the solvent’s contribution is about 0.25 eV.29
The reasonable characterization of the rate data with a single
reorganization energy and the theoretical studies imply that the
reorganization energy, although the solvent affects it, is primarily
determined by the protein environment.
where τL is the longitudinal relaxation time of the solvent
polarization and η is the solvent shear viscosity.30a The other
parameters are the molar volume Vm, the static dielectric constant
ꢀS, and the high-frequency dielectric constant ꢀ∞. For the case
of more complex environments, τeff might be associated with
some conformational or molecular rearrangement that is coupled
to the electron transfer. The strong coupling, or adiabatic regime,
is often used to describe short-range electron transfer and is
viewed as solvent controlled (overdamped) motion in a single
electronic state (sometimes called the “friction mechanism”).
The experimental signature for electron transfer in this regime
is a friction (or viscosity) dependent rate constant, often
characterized by the power law form, eq 6, as mentioned in the
introductory section. To summarize, the nonadiabatic electron-
transfer mechanism displays an exponential distance dependence
and viscosity independence, whereas the adiabatic mechanism
displays a viscosity dependence but no exponential distance
dependence.
A Unified Model for the Electron Transfer. Theoretical
work30 that accounts for both the tunneling (distance controlled,
eq 1) and friction controlled (viscosity dependent, eq 6) charge-
transfer mechanisms and a gradual turnover between them is
available. Adapting the unified expression for the unimolecular
(28) (a) Terrettaz, S.; Cheung, J.; Miller, C. J. J. Am. Chem. Soc. 1996, 118,
7857. (b) Winkler, J. R.; DiBilio, A. J.; Farrow, N. A.; Richards, J. H.;
Gray, H. B. Pure Appl. Chem. 1999, 71, 1753. (c) Legrand, N.; Bondon,
A.; Simonneaux, G. Inorg. Chem. 1996, 35, 1627.
(29) (a) Miyashita, O.; Go, N. J. Phys. Chem. B 2000, 104, 7516. (b) Sigfridsson,
E.; Olsson, M. H. M.; Ryde U. J. Phys. Chem. B 2001, 105, 5546. (c)
Basu, G.; Kitao, A. Kuki, A.; Go, N. J. Phys. Chem. B 1998, 102, 2085.
(d) Muegge, I.; Qi, P. X.; Wand, A. J.; Chu, Z. T.; Warshel, A. J. Phys.
Chem. B 1997, 101, 825.
Equation 10 reveals that the electron-transfer mechanism
2
depends on the value of |V| compared to the other parameters
τ
eff and λo. Recent work studying the electron exchange of the
3-/4-
Fe(CN)6
redox couple with alkanethiol coated gold elec-
trodes observed the transition from the adiabatic to nonadiabatic
regime with the increasing thickness of the electron tunneling
barrier.18 For this redox couple the transition between the
nonadiabatic and adiabatic mechanisms occurred at an electron
(30) (a) Zusman, L. D. Z. Phys. Chem. 1994, 186, 1. (b) Beratan, D. N.; Onuchic,
J. N. J. Chem. Phys 1988, 89, 6195. (c) Onuchic, J. N.; Beratan, D. N.;
Hopfield, J. J. J. Phys. Chem. 1986, 90, 3707.
9
J. AM. CHEM. SOC. VOL. 125, NO. 25, 2003 7711

A R T I C L E S
Khoshtariya et al.
Figure 5. Maximum electron-transfer rate constants (eq 14) for cytochrome
c from Figure 2 are plotted as a function of the electron-transfer distance.
A constant distance of 5 Å has been added to the electrochemical data on
Figure 6. The logarithm of the ratio of the calculated nonadiabatic (simple
linear extrapolation, Figure 5) to the experimental rate constants, kNA/kEXP
) 1 + g, is plotted versus the effective charge transfer distance for the
cytochrome c systems. The solid curve represents the best fit, eqs 9 and
10. The horizontal dashed line shows the case of g ) 1.
the carboxylic acid terminated films (×, Niki et al.4c,d; +, Bowden et al.4a,b
;
*, this work) so that they coincide with the data on pyridine terminated
layers (b) and the data of Gray et al. (G).2c The solid black curves are fits
to eq 14, and the dashed line shows the predicted nonadiabatic electron-
transfer rate constant at a shorter distance.
excellent correspondence among the three data sets. The solid
black curve in Figure 5 shows a fit to eq 14, which describes
the transition between electron-transfer regimes. The dashed line
corresponds to an extrapolation of the nonadiabatic rate constant
back toward short distances. Although the good correspondence
between eq 14 and the data is compelling, it is important to
assess the values of the parameters in the model and their
reasonableness.
exchange distance of ca. 8-9 Å (distance for g ) 1) and a
relaxation time of about 50 ps in an 11 cP aqueous electrolyte
solution; of course, the actual value depends on the particulars
of the system under study. For electron-transfer processes in
highly structured media with long relaxation times τeff and small
reorganization energies λo, for example, a protein, the transition
from the adiabatic regime to the nonadiabatic regime should
occur at much smaller values of |V|, which may correspond to
relatively long distances.
The distance dependence of the electron-transfer rate constant
for cytochrome c can be quantitatively compared to eq 9. To
perform the analysis for a wider range of data (the unimolecular
data of Gray2 and the electrochemical data4), the observed
electron-transfer rate constants were converted to their maximum
(optimal) values kmax by rearrangement of eq 9
Fitting of the rate constant data in the different regimes allows
the adiabaticity parameter g to be evaluated. By fitting the
electron-transfer rate constants at large distances to the nona-
diabatic model, one can define the parameters that describe the
nonadiabatic rate. Using a reorganization energy of 0.8 eV and
a density of states for the Au electrode8b of 0.28 eV-1, one finds
an electronic coupling between the Au electrode and cytochrome
c of 0.17 cm-1 at 17 Å. This coupling magnitude and the
measured decay length at a long distance, â of 1.07/Å, can be
used to predict what the nonadiabatic rate constant would be at
shorter distances. In the plateau region of the kinetics, the fit
of the data to the adiabatic model requires that the characteristic
relaxation time for the protein’s polarization response τeff be
188 ns. This relaxation time is unusually long for a pure liquid
solvent response; however, the protein provides a highly
structured solvation environment, and its polarization relaxation
should be slower than that of a simple redox system. Note that
a change in the magnitude of kmax, arising from uncertainty in
the reorganization energy, causes a corresponding change in
the relaxation time, but it still remains in the time range of
hundreds of nanoseconds. Using eq 14, it is then possible to
extract the adiabaticity parameter g, which controls the transition
between regimes. Figure 6 plots 1 + g as a function of distance
between the redox sites, that is, the heme and the electrode.
The horizontal dashed line shows the location of g ) 1 and
marks the transition between regimes, which occurs between
16 and 17 Å. At large distances, g goes asymptotically to zero,
and at short distances, it increases exponentially. This analysis
requires that the electron-transfer mechanism for cytochrome c
lie in the strong to intermediate regimes at distances up to 17
Å.
2
|V|
π3RT
Fm
kmax ≡ koet exp(∆Ga/RT) )
(14)
p 1 + g
λo
x
This transformation removes the activation barrier from the
considerations and allows the dynamical part of the rate constant
to be studied. This procedure requires accurate knowledge of
the activation energy, however. The data in Figure 5 show this
transformation if the reorganization energy 0.8 eV, as suggested
by the Figure 4, is used for the three data sets. The value of
kmax is sensitive to uncertainty in the reorganization energy that
is used; for example, changing the reorganization energy to 0.6
eV reduces the value of kmax in Figure 5 by a factor of 7.
Given this assumption about the reorganization energy, Figure
5 plots the distance dependence of kmax for the two electro-
chemical systems and the homogeneous studies as a function
of the distance between the redox active heme of the cytochrome
and the electron donor, gold electrode and ruthenium moiety.
The •’s correspond to the rate constants of the pyridine
terminated SAMs and the G’s correspond to the unimolecular
rate constant data of Gray.2 The data for the COOH terminated
SAMs (×, *, +) did not show a good correspondence with the
other two data sets unless the electron-transfer distance was
increased by 5 Å, as discussed with regard to eq 7. This shift,
to account for an extra “effective tunneling distance”, provides
Is such a long polarization relaxation time reasonable? Most
direct studies of solvation relaxation times have been performed
for small organic molecules in neat polar liquids and have rapid
9
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Charge Transfer for Cytochrome c at Short Distances
A R T I C L E S
relaxation times, ranging from a few hundred femtoseconds in
acetonitrile to a few hundred picoseconds in n-decanol.31a In
more highly structured solvents, such as 1,3-butanediol and
alcohol glasses, the solvation times can be in the regime of
nanoseconds.31 However, relaxation times as low as 10-4-10-8
s have been reported for the myoglobin heme pocket, even at
room temperature (see refs 32 and 33). Compared to these
values, the 188 ns time required by this analysis seems
reasonable for the protein interior. For this time scale to be
physically reasonable, the polarization response must involve
some sort of quasi-diffusional conformational motion in the
protein. It is worth mentioning that this 188 ns time lies close
to the low-frequency edge for the actual conformation fluctua-
tion spectrum of native cytochrome c and near the upper bound
for helix-coil transitions of peptide chains.34 Other conforma-
tional changes that accompany the redox reaction,29,35,36 includ-
ing a shift of interglobular “catalytic water”,36 may contribute
to the frictional coupling. Alternatively, it may be that proton
transfer is linked to the electron-transfer coordinate.21 Certainly,
the D2O studies would be consistent with a reaction coordinate
that involved water(s) in the protein or proton transfer. The
results are also consistent with the finding that electron transfer
in cytochrome c can be used to trigger the folding/unfolding of
the protein, and they suggest that this process is associated with
a conformational change in the protein that modifies the
polarization along the redox reaction coordinate. The unified
model, represented by eq 14, is able to describe the distance
dependent rate constants with an effective polarization relaxation
time of 150-200 ns.
Included in this study is the linking of the protein to the gold
electrode through a terthiophene tether that is terminated with
a pyridine unit. In this case, a substantial increase of the rate
constant is observed, almost 4-fold, while the formal redox
potential remains the same as for the alkane analogue. In the
adiabatic charge transfer picture, this increase can be understood
as a decrease in the activation barrier to the electron transfer
that arises from an increased electronic coupling strength (see
eq 5). This observation is not consistent with a conformational
gating model, since the pyridine group, which is the portion of
the tether that interacts directly with the protein, is the same
for the alkane and terthiophene tethers. Using the same
parameters for the electron transfer as described previously, these
data indicate that the electronic coupling must change by 0.03
eV (ca. 250 cm-1) for a 4-fold increase in the rate constant.
Given the small value for the electronic coupling through the
alkane tether, one can assign the change in electronic coupling
strength to the terthiophene-linked protein. By comparison with
other studies of conjugated molecular wires, one estimates an
electronic coupling for a conjugated, n ) 12 tether to be 100-
1000 times larger than that for an equivalent length alkane
chain.23 This increase is in agreement with the value found
below for the alkane tethered pyridine case (vide infra). Within
the nonadiabatic (tunneling) picture, this coupling corresponds
to a 104-106 increase in the charge transfer rate constant (see
eq 1), which is clearly not found. This rate constant for the
terthiophene linker can be rationalized by a rate-determining
charge-transfer step that operates through an adiabatic mecha-
nism, rather than a nonadiabatic mechanism.
Comparison with Other Redox Protein Systems. Only a
few reports plot the biological electron-transfer data for
comparable donor-acceptor distances below 10-15 Å, where
one expects a transition from the nonadiabatic to adiabatic
mechanism. These studies include primary electron-transfer steps
in photosynthetic reaction centers32,37 and recent data on azurin
that is adsorbed to a SAM coated gold electrode.38 The azurin
data display behavior similar to that found in cytochrome c, a
plateau region for thin SAM films. The authors of that report
restricted their discussion to the gated mechanism, which is not
appropriate for the current system, for the reasons outlined
previously. Whether the electron transfer involving cytochrome
c in the reaction centers occurs by the adiabatic mechanism is
not clear. Indeed, these natural systems may display a large
degree of inhomogeneity (see refs 32 and 37). The kinetics for
some of the electron-transfer processes is clearly not exponential,
and this behavior has been explained by a broad distribution of
nonadiabatic electron-transfer rates and by a mixed adiabatic/
nonadiabatic model.32,37 It may be that intramolecular quantum
degrees of freedom contribute significantly to the reorganization
energy for some of the primary electron-transfer steps in the
photosynthetic reaction center,37 and this could modify the onset
of the nonadiabatic to adiabatic mechanism change. In terms
of the classical model used previously, the quantum degrees of
freedom act to renormalize the electronic matrix element |V|
and shift the onset of the frictional regime to smaller donor-
acceptor distances.6 Such a condition may be crucial for the
primary steps in photosynthesis and might result from special
evolutionary forces. A manifestation of kinetically coupled
quantum modes, a significant inner sphere reorganization
contribution, causes a distortion of the bell-shaped free energy
plot, Figure 5, on the side of highly negative free energy gaps.6
No such distortion is evident in Figure 5 and indicates a minor
role for high-frequency vibrational modes in the cytochrome
electron transfer, in agreement with the results of ref 29.
(31) (a) Maroncelli, M. J. Mol. Liq. 1993, 57, 1. (b) Nandi, N.; Bhattacharyya,
K.; Bagchi, B. Chem. ReV. 2000, 100, 2013.
(32) Kotelnikov, A. I.; Ortega, J. M.; Medvedev, E. S.; Psikha, B. L.; Garcia,
D.; Mathis, P. Bioelectrochemistry 2002, 56, 3.
(33) (a) Bashkin, J. S.; McLendon, G.; Mukamel, S.; Marohn, J. J. Phys. Chem.
1990, 94, 4757. (b) Pierce, D. W.; Boxer, S. G. J. Phys. Chem. 1992, 96,
5560. (c) Beece, D.; Eisenstein, L.; Frauenfelder, H.; Good, D.; Marden,
M. C.; Reinisch, L.; Reynolds, A. H.; Sorensen, L. B.; Yue, K. T.
Biochemistry 1980, 19, 5147.
(34) Eaton, W. A.; Munoz, V.; Thompson, P. A.; Henry, E. R.; Hofrichter, J.
Acc. Chem. Res. 1998, 21, 745.
(35) (a) Banci, L.; Bertini, I.; Gray, H. B.; Luchinat, C.; Reddig, T.; Rosato,
A.; Turano, P. Biochemistry 1997, 36, 9867. (b) Qi, P. X.; Beckman, R.
A.; Wand, A. J. Biochemistry 1996, 35, 12275. (c) Moss, D.; Nabedryk,
E.; Breton, J.; Mantele, W. Eur. J. Biochem. 1990, 187, 565. (d) Yuan, X.;
Sun, S.; Hawkridge, F. M.; Chlebowski, J. F.; Taniguchi, I. J. Am. Chem.
Soc. 1990, 112, 5380. (e) Cohen, D. S.; Pielak, G. J. J. Am. Chem. Soc.
1995, 117, 1675.
(36) (a) Bertini, I.; Hajieva, P.; Luchinat, C.; Nerinovski, K. J. Am. Chem. Soc.
2001, 123, 12925. (b) Bertini, I.; Huber, J. G.; Luchinat, C.; Piccioli, M.
J. Magn. Reson. 2000, 147, 1. (c) Qi, P. X.; Urbauer, J. L.; Fuentes, E. J.;
Leopold, M. F.; Wand, A. J. Struct. Biol. 1994, 1, 378. (d) Bertini, I.;
Dalvit, C.; Huber, J. G.; Luchinat, C.; Piccioli, M. FEBS Lett. 1997, 415,
45.
Conclusions
Conventional electrochemical techniques were applied to the
electron transfer of cytochrome c protein immobilized on the
surface of SAM modified electrodes. Chemical control of the
adsorption allowed the accurate determination of heterogeneous
(37) (a) McMahon, B. H.; Mu¨ller, J. D.; Wraight, C. A.; Nienhaus, G. Ulrich;
Biophys. J. 1998, 74, 2567. (b) Nonella, M.; Schulten, K. J. Chem. Phys.
1991, 95, 2059.
(38) (a) Chi, Q.; Zhang, J.; Andersen, J. E. T.; Ulstrup, J. J. Phys. Chem. B
2001, 105, 4669. (b) Zhang, J.; Chi, Q.; Kuznetsov, A. M.; Hansen, A. G.;
Wackerbarth, H.; Christensen, H. E. M.; Andersen, J. E. T.; Ulstrup, J. J.
Phys. Chem. B 2002, 106, 1131.
9
J. AM. CHEM. SOC. VOL. 125, NO. 25, 2003 7713

A R T I C L E S
Khoshtariya et al.
unimolecular rate constants for the electron exchange between
the SAM-modified metal electrode and the cytochrome c. This
approach allowed the charge-transfer rate constant’s dependence
on distance, solution viscosity, and other parameters to be
studied in detail. The data display a change in the electron-
transfer mechanism with the distance from the electrode and
the rate constant’s dependence on viscosity, and the chemical
composition of the SAM was studied in each regime.
Analysis of these and published kinetic data for cytochrome
c with a unified model for cytochrome c’s redox kinetics is
presented. Although this analysis ignores detailed differences
between the heme environment in the data sets, it provides a
good representation of the rate constant’s distance dependence
and suggests that the electron transfer occurs very close to, or
in, the intermediate (still viscosity sensitive) regime at physi-
ologically significant distances, ca. 17 Å. This explanation
requires that the electron-transfer event be coupled to a
polarization response of the medium (the protein interior and
its environment, including the protein/water boundary hydrogen-
bonded network) with an unusually long characteristic relaxation
time of a few hundred nanoseconds. The detailed features of
this response and its molecular character remain unclear, but it
may involve a conformational motion that is linked to the
polarization response along the electron-transfer reaction coor-
dinate. Under such conditions, the transformation from adiabatic
to nonadiabatic regimes could occur at large electron-transfer
distances, ca. 17 Å or more.
What advantage arises from an adiabatic (friction controlled)
electron-transfer mechanism for cytochrome c? It may be that
the multiple functions of cytochrome c require external regula-
tory tools of mechanism switching that can be implemented
through specific protein-protein interactions. In particular,
because the reaction occurs in the frictional or intermediate
electron-transfer regime, the strong dependence of the rate
constant on the donor-acceptor distance is prevented and the
polarization response acts as a “throttle” for the reaction.
Whether these findings arise from the particular construction
of cytochrome c and are associated with its special role as a
redox protein in living cells or whether it is more generally
operative in biological systems remains an open question.
Acknowledgment. D.E.K. and D.H.W. are grateful to the
National Research Council, Office of International Affairs, for
financial support in the framework of Twinning Program Grant,
1999-2000. D.E.K. also kindly acknowledges the Collaborative
Linkage Grant (PST.CLG 975701) from the North Atlantic
Treaty Organization. D.H.W. acknowledges partial support from
the National Science Foundation, CHE-0111435, and the U.S.-
Israel Binational Science Foundation.
Supporting Information Available: Supporting Information,
which show measurements of the electron-transfer rate constant
as a function of ionic strength, is available. This material is
available free of charge via the Internet at http://pubs.acs.org.
JA034719T
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7714 J. AM. CHEM. SOC. VOL. 125, NO. 25, 2003