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,
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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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(
(
1
(
Sasaki, H.; Smith, T. A.; Ghiggino, K. J. Phys. Chem., submitted for
publication.
(9) (a) Gretchikhine, A. B.; Ogawa, M. Y. J. Am. Chem. Soc. 1996,
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1
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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
(