Photoinduced electron transfer on ?2-sheet cyclic peptides

Article abstract of DOI:10.1021/jp011181+

Gramicidin S analogues that contain a single pyrenyl group and a single p-nitrophenyl group at different positions were synthesized. Photoinduced electron transfer (ET) from an excited pyrenyl group located at the fourth position to a nitrophenyl group located at five different positions was investigated on the ?2-sheet chains of the cyclic peptides. The observed ET rate constants displayed a complex dependence on the number of spacer units or on the edge-to-edge distance between the two aromatic groups. The ET rate constants, however, showed a reasonable linear relationship with the equivalent ??-distances calculated from the Beratan-Onuchic tunneling pathway model, if through-hydrogen-bond ET was taken into account. The results support the applicability of the tunneling pathway model on both helix and ?2-sheet model peptides.

Full text of DOI:10.1021/jp011181+

10416
J. Phys. Chem. B 2001, 105, 10416-10423
Photoinduced Electron Transfer on â-Sheet Cyclic Peptides
†
†
,†
‡
Hiroshi Sasaki, Maki Makino, Masahiko Sisido,* Trevor A. Smith, and
Kenneth P. Ghiggino‡
Department of Bioscience and Biotechnology, Faculty of Engineering, Okayama UniVersity,
3
-1-1 Tsushimanaka, Okayama 700-8530, Japan, and School of Chemistry, UniVersity of Melbourne,
Victoria 3010, Australia
ReceiVed: March 28, 2001
Gramicidin S analogues that contain a single pyrenyl group and a single p-nitrophenyl group at different
positions were synthesized. Photoinduced electron transfer (ET) from an excited pyrenyl group located at the
fourth position to a nitrophenyl group located at five different positions was investigated on the â-sheet
chains of the cyclic peptides. The observed ET rate constants displayed a complex dependence on the number
of spacer units or on the edge-to-edge distance between the two aromatic groups. The ET rate constants,
however, showed a reasonable linear relationship with the equivalent σ-distances calculated from the Beratan-
Onuchic tunneling pathway model, if through-hydrogen-bond ET was taken into account. The results support
the applicability of the tunneling pathway model on both helix and â-sheet model peptides.
Photoinduced electron transfer (ET) on peptides and proteins
has been studied by a number of researchers, and the ET mech-
anism on these systems has been discussed widely.1,2 A simple
and practical model for predicting the ET rates on peptides and
other molecular systems has been presented by Beratan and
The cyclic peptide has antiparallel â-sheet strands that are linked
4
5
by the â-turns at the D-Phe- Pro sequences. The two â-sheet
1
strands are stabilized by four hydrogen bonds, ( Val)NsHs
3
′
1
3′
3
OdC( Leu), ( Val)CdOsHsN( Leu), ( Leu)NsHsOdC-
1
′
3
1′
( Val), and ( Leu)CdOsHsN( Val). The hydrophobic side
groups of Val and Leu are oriented to one side of the cyclic
structure, and the hydrophilic side groups of Orn are positioned
3
1
3
Onuchic. It is the tunneling pathway model that has been
4,5
2
successfully applied to several protein systems. However, the
validity of the model itself and the parameters used in it have
not been thoroughly examined on simple model peptides, such
on the other side. The unique amphiphilic structure may be
related to the antibiotic activity of this cyclic peptide. The unique
and rigid structure of GS has been employed as the framework
6
-8
as single R-helix polypeptides
and isolated â-sheet pep-
1
2
tides.9,10
for pyrenyl excimers.
In this study, the 4D-Phe unit was replaced by a D-1-
pyrenylalanine (D-pyrAla) unit and one of the four hydrophobic
8
In the previous work, we prepared model R-helical polypep-
tides that contain a single pyrenyl group and a single p-
nitrophenyl group as the donor-acceptor pair and measured the
ET rates as a function of the number of spacer units or of the
edge-to-edge distances. The ET rates were found to decrease
with the edge-to-edge distance according to an approximate
relation, kET ) 1.4 × 10 exp[-0.66(ree - 3)] (s , ree in Å).
The application of the tunneling pathway model to the R-helix
showed that the ET rates may be reasonably interpreted when
through-hydrogen-bond (HB) electron jumps were taken into
consideration.
4
′
amino acids, or the D-Phe was replaced by a L- or D-p-
nitrophenylalanine (ntrPhe) unit, respectively. The GS analogues
are named as P4Tm (m ) 1, 3, 1′, 3′, and 4′), where m indicates
the position of the ntrPhe unit. A GS analogue that contains an
isolated pyrenyl group at the fourth position was also synthesized
and named as P4. As has been described in our previous study,7
the pyrenyl group acts as the donor and the nitrophenyl group
works as an electron acceptor. Since the fluorescence lifetime
of the pyrenyl group is very long (242 ns at -58°), the relatively
slow ET process that occurs across the edge-to-edge distance
of up to about 18 Å can be followed on the â-sheet framework.
9
-1
,8
As for the â-sheet conformation, however, a similar model
study is not easy to do because there is no isolated â-sheet
peptide. Very often, â-sheet conformations are found as a part
of protein structure or a part of large peptide assemblies. Some
cyclic peptides are exceptional cases in which two â-sheet chains
are folded and stabilized with interstrand hydrogen bonds. A
typical example is gramicidin S (GS).11 GS is a well-known
C2-symmetric cyclic decapeptide of the following amino acid
sequence:
Experimental Section
Synthesis of the GS Analogues that Contain a D-pyrAla
Unit at the Fourth Position and a ntrPhe Unit at the 1, 3,
4
′
5′
1
′, 3′, or 4′ Position. A linear peptide, Fmoc- D-Ph-- Pro-
1
2
3
4
5
1′
2′
Val- Orn(Boc)- Leu- D-pyrAla- Pro- Val- Orn(Boc)-
Leu-OH and its analogues that contain a single ntrPhe unit
3
′
at the 1, 3, 1′, 3′, or 4′ position were synthesized by the solid-
phase method on a Fmoc/PyBOP protocol. The Fmoc protecting
group of the linear peptides was removed, and the free peptides
were cyclized with HATU in DMF. The crude cyclic peptides
were purified first by gel chromatography and then by HPLC
5
′
1
2
3
4
Pro- Val- Orn- Leu- D-Phe
|
|
4
′
3′
2′
1′
5
D-Phe- Leu- Orn- Val- Pro
(
C4 column/0.1% aqueous TFA + acetonitrile). The purified
cyclic peptides were characterized by TOF mass spectroscopy
PE Biosystems Voyager DE Pro). The wild-type GS peptide
*
Corresponding author. Tel: +81-86-251-8218. Fax: +81-86-251-8219.
(
E-mail: sisido@cc.okayama-u.ac.jp.
†
‡
with Boc-protected Orn units [GS(Boc)2] was prepared by the
Boc protection of the commercial GS peptide. Detailed proce-
Okayama University.
University of Melbourne.
1
0.1021/jp011181+ CCC: $20.00 © 2001 American Chemical Society
Published on Web 10/03/2001

Electron Transfer on â-Sheet Peptides
J. Phys. Chem. B, Vol. 105, No. 42, 2001 10417
Figure 1. CD spectra of the GS analogues in the amide absorption region (left) and pyrenyl absorption region (right). TMP solution, [peptide] )
-
4
1
0
M, at 25 °C.
dures for the peptide synthesis and the spectroscopic data are
described in the Supporting Information.
Spectroscopic Measurements. Absorption and CD spectra
were recorded on a Jasco U-best 560 instrument and a Jasco
J720WI instrument, respectively, in DMF and in trimethyl
phosphate (TMP). Fluorescence spectra were recorded on a
Jasco FP777 instrument in argon-saturated DMF solution. The
-
6
concentration of the peptide was adjusted to be 2.4 × 10 M.
Fluorescence decay curves were measured on a time-correlated
single-photon counting instrument (Horiba NAES550), equipped
with a hydrogen discharge lamp (pulse width ) about 2.5 ns)
in argon-saturated DMF. For the P4T3 and P4T1′ peptides, a
picosecond photon counting system at the University of Mel-
8
bourne was used. The observed decay curves (λex ) 345 nm,
λem ) 375 nm) were analyzed using multicomponent exponential
functions by using a iterative reconvolution program. The
fluorescence decay curves were measured at -58°, -30°, 0°,
and +30 °C, by using an Oxford DN1704 or an Oxford Optistat
liquid-nitrogen cryostat.
Results and Discussion
Figure 2. Side-chain energy contour map of the P4 analogue. The
CD Spectra and Conformational Analysis of the GS
Analogues. CD spectra of GS(Boc)2 and the GS analogues in
TMP are shown in Figure 1. The CD profiles of the GS
analogues in the amide absorption region are very similar to
each other, indicating that the skeletal conformations of the
analogues and GS(Boc)2 are essentially the same. The small
negative peak at 243 nm observed in the analogues is assigned
to the Ba absorption band of the pyrenyl group. Relatively large
CD signals are induced at the Bb (260-280 nm) and La (320-
R
â
side-chain rotational angles of D-1-pyrenylalanine, ø
1
(C -C ) and
â
γ
ø
2
(C -C ) were varied. Ten contour lines were drawn at the interval
-1
of 1 kcal mol from the minimum point, (ø
1
2
,ø ) ) (175°,280°).
overlapped at this wavelength region, whereas no broad peak
is observed for the P4 analogue that contains no ntrPhe unit.
These CD results indicate that the CD signs of ntrPhe units are
primarily determined by the chirality of the ntrPhe unit.
CD spectra were measured also in DMF solution down to
265 nm. The CD profiles were very similar to those in TMP
solution, indicating that the skeletal and the side chain confor-
mations of the GS analogues are virtually the same in the two
solvents.
3
50 nm) absorption bands of the pyrenyl group, indicating that
the orientation of the pyrenyl group is constrained with respect
to the cyclic skeleton. At the La band where contribution of the
nitrophenyl absorption can be neglected, the signs and the
magnitudes of the CD signals are virtually the same for all GS
analogues except the P4T3 analogue. The similarity of the CD
profile suggests that the side-chain orientations of the pyrenyl
groups are also the same for all GS analogues. The different
CD profile in the P4T3 analogue may be explained in terms of
a strong exciton-type interaction between the neighboring
pyrenyl-nitrophenyl pair.
4
5
The orientation of pyrenyl group in the D-pyrAla- Pro
sequence that takes a â-turn was predicted from molecular
13
mechanics calculations under vacuum. The skeletal conforma-
tion and the side-chain orientations except for the orientation
of pyrenyl group were taken from the X-ray crystallographic
1
1
data of GS. The energy contour maps for the side-chain
R
â
â
γ
4
rotations [ø1(C -C ),ø2(C -C )] of the D-pyrAla unit of all
the GS analogues were virtually the same. As an example,
Figure 2 shows the energy contour map of the P4T1 analogue.
The map shows two major energy minima at (ø1,ø2) ) (175°,
The broad positive peak around 260-290 nm is assigned to
the contribution of the L-ntrPhe unit. In the P4T4′ analogue
4
′
that contains a D-ntrPhe unit, a broad negative peak is

10418 J. Phys. Chem. B, Vol. 105, No. 42, 2001
Sasaki et al.
Figure 3. Side-chain energy contour maps of the P4T1 (left), P4T3 (center), and P4T4′ (right) analogues. The side-chain rotational angles of
L-p-nitrophenylalanine (P4T1 and P4T3) or D-p-nitrophenylalanine (P4T4′) were varied. Ten contour lines were drawn at the interval of 1 kcal
-
1
mol from the minimum point, (ø
1
2
,ø ) ) (185°,65°) for P4T1, (175°,70°) for P4T3, and (180°,95°) for P4T4′.
2
80°; PI orientation) and (50°,75°; PII orientation). Although
map suggests that only a single energy minimum is allowed at
(175°,70°). The two contour maps, therefore, suggest that the
p-nitrophenyl side groups of the P4T1, P4T3, P4T1′, and P4T3′
analogues reside in a single orientation around (ø1,ø2) ) (180°,
70°) at low temperatures.
-
1
the PI orientation has lower energy by about 1 kcal mol and
a wider area of the allowed region than the PII orientation, the
latter cannot be neglected in the interpretation of the ET rates.
The side-chain energy contour maps of ntrPhe units were also
calculated. The maps for the P4T1, P4T3, and P4T4′ analogues
are compared in Figure 3. The maps for the P4T1′ and P4T3′
were very similar to the those for the P4T1 and P4T3,
respectively. In the case of the P4T1 analogue (left), the angles
between 80° and 170° are disallowed for ø1, due to a collision
In the case of the P4T4′ analogue (right), the map shows two
energy minima that may be almost equally populated: (180°,
95°; TI orientation) and (60°,65°; TII orientation). Since the side
4
′
group of D-ntrPhe at the â-turn can rotate without collision
with other side groups, this rotational freedom must be taken
into consideration.
1
between the aromatic ring of ntrPhe and the isobutyl group of
3
Leu. Since the p-nitrophenyl group has a C2 symmetry around
To summarize the results of the conformational calculations,
two different orientations (PI and PII) are allowed for each
pyrenyl group in all GS analogues, and two orientations (TI
and TII) are allowed for a nitrophenyl group in the P4T4′
analogue. The variations of the rotational angles and, as a
ø2, the contour map suggests only two possible orientations:
(ø1,ø2) ) (185°,65°) and (300°,130°). The former has a lower
-
1
energy by about 2 kcal mol and a much wider area of the
allowed region. In the case of the P4T3 analogue (center), the

Electron Transfer on â-Sheet Peptides
J. Phys. Chem. B, Vol. 105, No. 42, 2001 10419
TABLE 1: Edge-to-Edge Distances, ET Rate Constants in
DMF at Different Temperatures, Thermodynamic
Parameters, and the Equivalent σ-Distances According to
the Tunneling Pathway Model on the GS Analogs
kET (s-1)
-
58 °C
-30 °C
0 °C
30 °C
∆Hqa ∆Sqb σL (Å)
P4T1 (ree ) 9.8 Å for PI orientation, 7.1 Å for PII orientation)
6
6
6
6
2
.2 × 10
3.1 × 10
5.2 × 10
8.8 × 10
1.6
0.
0.0
-22
17.7
9.8
P4T3 (ree ) 4.9 Å for PI orientation, 4.1 Å for PII orientation)
8
8
8
8
4
5
6
.7 × 10
5.5 × 10
6.0 × 10
8.2 × 10
-18
P4T1′ (ree ) 9.2 Å for PI orientation, 9.3 Å for PII orientation)
8
8
8
8
.3 × 10
4.9 × 10
5.5 × 10
6.3 × 10
-18
12.4
P4T3′ (ree ) 12.8 Å for PI orientation, 12.2 Å for PII orientation)
6
7
7
7
.8 × 10
1.5 × 10
2.1 × 10
2.3 × 10
1.4
-20
18.4
P4T4′ (ree ) 17.8Å for (PI,TI) orientation, 16.8 Å for (PII,TI) orientation,
1
7.1 Å for (PI,TII) orientation, 16.4 Å for (PII,TII) orientation)
5
5
5
5
5
.8 × 10
6.8 × 10
7.2 × 10
7.6 × 10
0.1
-31
20.7
a
In kcal mol-1
b
In cal mol deg-1
-1
.
.
Figure 5. Fluorescence spectra of the GS analogues in argon-saturated
-
6
DMF at -58 °C. λex ) 345 nm, [peptide] ) 2.4 × 10 M. The inset
shows the spectra of the P4T1′ and P4 analogues that are normalized
at 376 nm. The difference between the two spectra is also shown.
consequence, the distribution of the edge-to-edge distances must
be taken into consideration in interpreting the ET data. The edge-
to-edge distances between the pyrenyl and nitrophenyl groups
for all possible combinations of the side-chain orientations were
calculated and are listed in Table 1.
Conformations of the GS analogues with the minimum-energy
side-chain orientations are illustrated in Figure 4. The pyrenyl
groups are set to the PI orientation and the nitrophenyl group
in the P4T4′ analogue is set to the TI orientation.
Steady-State Fluorescence Spectra. Fluorescence spectra of
the GS analogues measured at -58 °C are shown in Figure 5.
The pyrenyl fluorescence is quenched by the introduction of
the nitrophenyl group and the extent of the quenching strongly
depends on the positions of the nitrophenyl group. For example,
the pyrenyl fluorescence is markedly quenched for the P4T3
analogue, in which the pyrenyl-nitrophenyl edge-to-edge
distance may be 4.1-4.9 Å. In contrast, very small quenching
is observed for the P4T4′ analogue, for which the edge-to-edge
distance is predicted to be 16.4-17.8 Å. The distance depen-
dence of the fluorescence intensity may be interpreted in terms
of the distance dependence of intramolecular ET across the
cyclic peptide. No intermolecular quenching may be expected
under the present range of concentrations.
The spectral profiles were compared in the normalized
fluorescence spectra. The profiles of the P4T1, P4T3′, and P4T4′
analogues were exactly the same as that of the P4 peptide,
indicating that no species other than the excited pyrenyl group
is present in these analogues. The spectrum of the P4T1′
analogue, however, showed an additional very weak broad band
at the long wavelength region, as shown in the inset of Figure
5
. A similar broad band was observed also for the P4T3
analogue with smaller intensity. The broad bands, although very
small, suggest that an exciplex-type species is formed in the
P4T1′ and the P4T3 analogues. Incidentally, similar exciplex-
type fluorescence has been observed in the pyrenyl-nitrophenyl
pair on a pyrAla-Glu(OChx)3-ntrPhe sequence that was built
into an R-helical polypeptide [Glu(OChx) ) γ-cyclohexyl-L-
glutamate]. Similar spectral profiles were observed at other
temperatures up to +30 °C.
Figure 4. Computer-predicted conformations of the GS analogues.
The side-chain orientations of pyrenylalanine were set to the P
orientation (ø ,ø ) ) (175°,280°). Those of p-nitrophenylalanine were
set to each minimum-energy orientation. Those in the P4T4′ analogue
were the T orientation, (ø ,ø ) ) (180°,95°). The pyrenyl-nitrophenyl
edge-to-edge distances are indicated.
I
1
2
I
1
2

10420 J. Phys. Chem. B, Vol. 105, No. 42, 2001
Sasaki et al.
Figure 8. Eyring plot of the ET rate constants at -58°, -30°, 0°, and
+30 °C in DMF.
exponential decay has been observed for the P4 analogue at all
temperatures, the multicomponent decay may be explained either
by the conformational distributions as discussed above or by
the multiplicity of the ET processes. As found in the steady-
state spectra (Figure 5), the P4T1′ and P4T3 analogues showed
a very weak broad band at long wavelengths that may be
attributed to an exciplex-type species. This additional excited-
state process may add complexity to the decay curves, although
the contribution of the exciplex-type emission is very small.
For the P4T3, P4T1′, and P4T3′ analogues that showed
multicomponent decay curves, the average decay times were
used for evaluating the ET rate constants. Although this
treatment leaves some uncertainty, the trend of the distance
dependence is not altered because the ET rate constants vary
over three-orders of magnitude (see Figure 7).
Figure 6. Fluorescence decay curves of the GS analogues in argon-
saturated DMF at -58 °C. λex ) 345 nm, [peptide] ) 2.4 × 10 M.
-
6
The ET rate constants (kET) were calculated from the decay
times of the GS analogues in the absence (P4′, t0) and presence
(P4′Tm, τ) of the ntrPhe unit
kET ) 1/τ - 1/τ
(1)
0
The rate constants measured at -58°, -30°, 0°, and +30 °C
are listed in Table 1.
Distance Dependence of the ET Rate Constants. The
logarithms of the ET rate constants at -58 °C are plotted against
the possible ranges of the edge-to-edge distances in Figure 7
Figure 7. Dependence of the ET rate constants on the pyrenyl-
nitrophenyl edge-to-edge distances. The bold solid lines are for the
GS analogues, and the open circles are for the R-helical polypeptides
(bold solid lines). The plot shows a complex dependence on
the edge-to-edge distance. Particularly, the edge-to-edge distance
of the P4T1 analogue is predicted to be shorter than that of the
P4T1′ analogue, but the observed ET rate constant is much
higher in the latter peptide. The complex distance dependence
suggests that there exists a factor other than the edge-to-edge
distance in determining the ET rate constant.
(ref 8).
Fluorescence Decay Curves. The ET rates on the cyclic
peptides can be evaluated directly from the fluorescence decay
curves. The decay curves were measured in DMF at -58, -30,
0
, and +30 °C. Those measured at -58 °C are shown in Figure
In the same figure, the ET rate constants for the pyrenyl-
nitrophenyl pairs on the R-helical polypeptides in DMF at -58
6
. The P4 analogue that contains no nitrophenyl group showed
8
a single-exponential decay with the lifetime of 242 ns at -58
C. The introduction of the p-nitrophenyl group accelerated the
°C are also plotted. The ET rate constants measured on different
°
polypeptide structures show approximately similar distance
dependences.
fluorescence decay, and the extent of the acceleration markedly
depended on the positions of the nitrophenyl group. The decay
profiles of the P4T4′ and P4T1 analogues were essentially
single-exponential, indicating that the distributions of the
pyrenyl-nitrophenyl distances in these peptides cause little effect
on the ET rates. In the case of P4T3′, the decay curve was fitted
by two-component exponential functions. However, since the
contribution of the slow-decaying component was 83%, the ET
rates may be mainly governed by the conformation that gives
the longer pyrenyl-nitrophenyl distance. In the case of the P4T1′
and P4T3 analogues, much faster decays were observed than
decays of the other analogues, as shown in the inset of Figure
Temperature Dependence of the ET Rate Constants. The
temperature dependence of the ET rate constants are shown in
the form of an Eyring plot in Figure 8. The temperature
dependence is very small as compared with that of other
intramolecular ET systems, indicating that the skeletal structure
of the GS analogues is a rigid framework and the ET process
is mostly governed by a pure electron tunneling with small
solvent reorganization. The small temperature dependence has
8
been observed also in the R-helical polypeptides. The activation
enthalpies and entropies were calculated from the slopes and
intercepts of the Eyring plot and are listed in Table 1.
Theoretical Prediction of the ET Rates on the Basis of
the Tunneling Pathway Model. The distance dependences of
6
. The decay curves were fitted to two- or three-component
exponential functions at all temperatures. Since a single-

Electron Transfer on â-Sheet Peptides
J. Phys. Chem. B, Vol. 105, No. 42, 2001 10421
Figure 9. Optimum ET pathways on the GS analogues calculated according to the tunneling pathway model with Beratan’s parameters.

10422 J. Phys. Chem. B, Vol. 105, No. 42, 2001
Sasaki et al.
Å), the tunneling pathway model predicts that the ET rate
constants must follow the following equation:
1
3
-1
kET ) 10 exp[-0.73(σ - 3)] (s , σ in Å)
(2)
L
L
The predicted relation is indicated by a solid line in Figure 10.
The experimental data show a similar slope to that predicted,
but the absolute values seem to be a little smaller than the
predicted values.
The ET rate constants measured on the R-helical polypeptides
are also plotted in Figure 10 as open circles. The two types of
experimental data on different peptide conformations are in good
agreement with each other indicating a general applicability of
the tunneling pathway model.
Figure 10. ET rate constants of the GS analogues in DMF at -58 °C
plotted against the equivalent σ-distances calculated according to the
tunneling pathway model with Beratan’s parameters.
Conclusion
The ET rate constants on â-sheet cyclic peptides showed
complex dependence on the edge-to-edge distance. However
they exhibited reasonable correlation with the equivalent σ
distances calculated on the basis of the tunneling pathway model.
The applicability of the tunneling pathway model to both R-helix
and â-sheet peptides was demonstrated, provided that the
through-hydrogen bond jumps were taken into consideration.
the ET rates of proteins and model peptides have been analyzed
on the basis of the tunneling pathway model with Beratan’s
parameters. The detail of the model and the parameters have
been described before.3-5,8 The model was applied to the GS
analogues by using the atomic coordinates predicted from the
molecular mechanics calculations (Figure 4). The product
(
ΠꢀCiꢀHBjꢀTSk) of the decaying factors for a jump across a
Acknowledgment. This work has been supported by a
Grand-in-Aid for Specially Promoted Research from the
Ministry of Education, Science, Sports and Culture, Japan
covalent bond ꢀC, for a jump across a hydrogen bond (O‚‚‚H-
N) ꢀHB, and for a jump across vacant space ꢀTS was calculated
along all possible ET pathways that connect one of the aromatic
carbons of the pyrenyl group to one of the aromatic carbons of
the nitrophenyl group. The optimum ET pathway that gave the
largest product was searched for each GS analogue. The
optimum pathways of all analogues are illustrated in Figure 9.
In the cases of P4T3′ and P4T4′, two equivalent ET pathways
were found, in which an electron jump takes place across the
antiparallel â-strands through one of the two hydrogen bondings.
In these cases, the product was evaluated as a sum of the two
products for the equivalent pathways. The product of the
decaying factors was converted to a nonintegral number of σ
bonds nσ, that gives the same value as the product for the
(No.11102003).
Supporting Information Available: Full description of the
synthesis of the cyclic peptides. This material is available free
of charge via the Internet at http://pubs.acs.org.
References and Notes
(1) For recent reviews, see: (a) Langen, R.; Colon, J. L.; Casimiro,
D. R.; Karpishin, T. B.; Winkler, J. R.; Gray, H. B. JBIC 1996, 1, 221. (b)
Gray, H. B.; Winkler, J. R. Annu. ReV. Biochem. 1996, 65, 537. (c) Kakitani,
T. Photons, Substances, Life, and Reactions from Physical and Chemical
Point of View (in Japanese); Maruzen: Tokyo, 1998.
nσ
optimum pathway (ΠꢀCiꢀHBjꢀTSk ) ꢀC ). The equivalent number
of σ bonds was then converted to the equivalent σ distance (σL
)
(
81.
2) Isied, S. S.; Ogawa, M. Y.; Wishart, J. F. Chem. ReV. 1992, 92,
3
3
1.4nσ).
(
3) (a) Beratan, D. N.; Onuchic, J. N.; Hopfield, J. J. J. Chem. Phys.
1
9
1
9
987, 86, 4488. (b) Onuchic, J. N.; Beratan, D. N. J. Chem. Phys. 1990,
2, 722. (c) Beratan, D. N.; Betts, J. N. Onuchic, J. N. Science 1991, 252,
285. (d) Beratan, D. N.; Betts, J. N.; Onuchic, J. N. J. Phys. Chem. 1992,
6, 2852.
The experimental ET rate constants must be multiplied by a
correction factor to give a maximum rate constant that is
optimized for the nuclear factor. As described before, we
8
assume the correction factor to be 9, and each observed ET
rate constant was multiplied by that factor to yield the maximum
ET rate constant kET(max). The logarithms of the maximum ET
rate constants are plotted against the equivalent σ distances in
Figure 10. The plot shows a reasonable linear correlation
between the two quantities. In particular, the large deviations
of the P4T1 and P4T1′ analogues in Figure 7 are markedly
improved in Figure 10, indicating that the ET rate is not simply
determined by the edge-to-edge distance but depends on the
ET pathways including jumps through hydrogen bonds. In the
case of the P4T1 analogue, for example, the electron must
mediate along the peptide main chain, whereas in the case of
P4T3′ and P4T4′ the inter-strand hydrogen bonds may work as
the shortcut for the electron mediation. As we have already
stressed in the case of the R-helical polypeptides, hydrogen
bonds play an important role in the electron mediation in
peptides and proteins.
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(
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(
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If we assume that the ET rate constant approaches 1013 (s-1)
when the donor and the acceptor are in the closest contact (3
(

Electron Transfer on â-Sheet Peptides
J. Phys. Chem. B, Vol. 105, No. 42, 2001 10423
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