J. Phys. Chem. C 2010, 114, 20809–20812
20809
Conformational Dependence of Electronic Coupling Across Peptide Bonds: A Ramachandran Map† Joseph B. Issa, Karsten Krogh-Jespersen, and Stephan S. Isied* Department of Chemistry and Chemical Biology, Rutgers, The State UniVersity of New Jersey, New Brunswick, New Jersey 08903, United States ReceiVed: July 30, 2010
Electronic coupling across peptide bonds has been determined throughout the peptide bond conformational space. Using the side chains of tyrosine (Tyr) and tryptophan (Trp) as donors (D) and acceptors (A), respectively, a plot of the electronic coupling matrix element HDA versus (φ,ψ) torsional angles has been constructed for Trp-peptide-Tyr molecules. The HDA values were obtained using the generalized Mulliken-Hush approach with electronic transition energies, permanent and transition dipole parameters derived from semiempirical quantum mechanical electronic structure calculations (INDO/S). The computed HDA values and the corresponding electron transfer (ET) rates show that specific helical peptide conformations situated in a narrow φ region of the full HDA-(φ,ψ) map play a significant role in developing strong electronic coupling for promoting ET. The HDA-(φ,ψ) map clearly defines the angular regions in space, where strong Trp-peptideTyr coupling occurs and peptide-mediated ET results, as well as regions of weak peptide coupling where the presence of the peptide has only marginal effects on electronic coupling. Introduction Rates of electron transfer (ET) in biological systems span a wide range of time scales and can occur over long distances between electron donor (D) and acceptor (A) pairs.1-3 The ET reaction rates involving such weakly interacting species are best described using the Marcus equation in the high temperature limit (eq 1). The electronic coupling matrix element, HDA, is the primary factor that determines the distance and orientation dependence of the ET rate.
kET ) 4π2 |HDA | 2
* 1 e-∆G /kBT 4πλkBT
(1)
Considerable theoretical effort has been expended to understand how HDA depends on the nature of the electron donor and acceptor, intervening molecular bridges, and solvent media.4-7 In biological ET reactions, where complex protein media are present between the donor and the acceptor, HDA can be calculated through the use of ingenious, yet simple, electron tunneling models. These models include the protein packing density8 or more elaborate bond networks, which consider contributions from covalent and H-bonds as well as throughspace jumps.9 Successful interpretations of many protein ET results have been achieved using such models. These protein models, however, did not correctly predict the ET rates observed in small D-peptide-A molecules, where equal numbers of peptide residues in different conformations separate a donor from an acceptor.10,11 Here, we introduce a computational methodology from which the electronic coupling matrix elements (HDA) may be evaluated for all peptide torsional angles (φ,ψ) throughout the entire peptide conformational energy landscape. The resulting HDA†
Part of the “Mark A. Ratner Festschrift”. * To whom correspondence should be addressed. E-mail: calsisied@ sbcglobal.net.
(φ,ψ) map clearly shows how specific geometrical and secondary structural features affect electronic coupling across the peptide. This bottom-up approach for elucidating peptide conformational dependence of ET reaction rates provides a solid quantum mechanical foundation for addressing more complex scenarios involving electronic coupling in proteins. Results and Discussion A model peptide was constructed using the side chains of tyrosine (Tyr) and tryptophan (Trp) to bracket a peptide moiety, as seen in Figure 1A. The Tyr and Trp fragments will serve as electron donors (D) and acceptors (A), respectively, in our calculations of HDA. Further enhancement of the electronic coupling across the peptide was achieved by forming a more rigid side chain-dipeptide connection through direct attachment of the phenol (Tyr) and indole (Trp) functionalities to the N and C peptide terminals, respectively (Figure 1B). These structural modifications allow one to estimate electronic coupling for a significant number of peptide bonds. Peptide conformations leading to commonly observed protein secondary structures are defined by the torsional angles φ and ψ (Figure 1B).12 These angles change (-180° e φ,ψ e 180°) depending on the nature of the amino acid side chains and the presence of hydrogen bonding, thus directly affecting peptide N to C terminal distances.13 Geometrical distance and angle changes account for the variability in D-A electronic coupling across peptides. The geometry of our model peptide (Figure 1B) was initially optimized (by energy minimization) in a β-strand conformation (φ ∼ -117°, ψ ∼ 113°) using the semiempirical AM1 model.14 Then, by systematically varying each of the (φ,ψ) torsional angles in 15° increments, a 24 × 24 matrix of conformations was generated for the model peptide (Figure 1B). A wide range of peptide structures (576 total) with significantly different conformational energies has hence been covered. Rigid rotations were applied to the optimized β-strandlike structure to ensure that any changes in electronic coupling
10.1021/jp1071764 2010 American Chemical Society Published on Web 10/15/2010
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Issa et al.
Figure 1. Natural peptide (A) and modified Trp-dipeptide-Tyr molecule (B) used for ET studies. The arrows in A indicate where incisions were made to increase model peptide rigidity. The torsional angles φ and ψ are indicated in B. The conformations shown correspond to φ ) ψ ) 180°.
computed from one rotamer to another will be due to changes solely in the (φ,ψ) dihedral angles, not to changes in other internal coordinates. We will use the generalized Mulliken-Hush method (GMH)15 to calculate HDA for the Trp-dipeptide-Tyr molecule in different (φ,ψ) conformations. The GMH method has the advantage of using pure adiabatic observables to calculate nonadiabatic quantities, and the value of HDA, calculated for a specific structure, is cumulative for two-state as well as multistate ET processes. The INDO/S semiempirical electronic structure method will be utilized to calculate the physical quantities required for a GMH evaluation of electronic coupling.16 INDO/S was specifically developed for the calculation of electronic spectroscopic properties16-18 and has been applied in GMH treatments of ET by us19 and by others.15b,20 The parameter set employed here was similar to the original set developed by Zerner et al.,16,21 as implemented in the Argus code for computer simulations.22 The physical properties necessary for a GMH treatment of electronic coupling are the donor-acceptor chargetransfer (CT) transition energy (∆E), the electronic transition dipole moment along the CT direction (µ12), and the change in permanent dipole moments between the ground and CT states (∆µ12 ) µ22 - µ11). Excited state properties were evaluated with wave functions obtained from configuration interaction (CI) calculations in which all singly excited configurations (∼ 4000) were included. For a given peptide conformation and associated computed properties, the electronic coupling matrix element HDA may be readily evaluated from the expression developed by Cave and Newton for a two-state model (eq 2).15a
HDA )
|µ12 |∆E [(∆µ12)2 + 4(µ12)2]
(2)
The ET reaction studied is the charge separation reaction schematically represented in eq 3.23 For each modified peptide conformer, the lowest energy CT state was identified from the dominance of a phenol f indole excitation in the CI expansion and a large change (>40 D) in permanent dipole moment. The computed transition energy is in the range of 5 eV for our model peptide,24 and analyses of the CI wave functions show more than 80% HOMO(Tyr) f LUMO(Trp) character (Figure 2) in the CT state. The effects exerted by the intervening peptide on the energy and intensity (transition dipole) of this CT transition
Figure 2. HOMO (tyrosine) and LUMO (tryptophan) orbitals contributing to the dominant configuration in the lowest energy chargetransfer state in Trp-dipeptide-Tyr.
are intimately related to the peptide conformation and its interaction with the donor and acceptor moieties.
Trp(Indole)-Peptide-(Phenol)Tyr f Q
x
Trp(Indole)-Peptide-(Phenol)Tyr
(3)
Thus, using Tyr and Trp as donors (D) and acceptors (A), respectively, we computed the electronic coupling between the ground state and the lowest CT state across the dipeptide bridge in 576 different conformations. The HDA matrix elements obtained are available in Table S1 of the Supporting Information,25 and they are plotted (as gray squares of varying intensities) in Figure 3 with a map of the allowed Ramachandran (φ,ψ) angles in protein structures as a backdrop.12,26 For reference, we show in Table 1 a set of average (φ,ψ) values for peptides with different secondary structures.19a,27 Individual HDA values (Table S1) range from near 0 cm-1 (e.g., φ ) -135°, ψ ) 90°) to more than 2200 cm-1 (φ ) -90°, ψ ) -45°). Assuming smooth transitions between the 576 conformational points for which HDA was evaluated, an electronic coupling HDA map, similar to the Ramachandran conformational energy map of dipeptide residues,12 was generated as a Voronoi diagram (Figure 4).28 A selected set of HDA values is presented in Table 2 with their respective angles. These HDA values provide a comparative guide for the (φ,ψ) angles representative of secondary structures in Table 1, where the HDA values can be directly read from the map shown in Figure 4. The important conclusion that peptide bonds possess the capacity for promoting electronic coupling only in Very specific conformational regions is illustrated by the limited presence
Conformational Dependence of Electronic Coupling
J. Phys. Chem. C, Vol. 114, No. 48, 2010 20811 TABLE 2: Electronic Coupling Matrix Elements, HDA, for Selected Values of (O,ψ)a φ (deg)
ψ (deg)
HDA (cm-1)
45 45 45 45 45 45 -30 -45 -45 -45 -45 -45 90 -90
180 165 -150 -135 -165 -180 -75 45 30 15 75 0 75 30
867 806 746 619 922 867 38 824 856 934 0.6 867 0.4 2
a A complete list of all HDA values is available as Table S1 in Supporting Information.
Figure 3. Plot of computed HDA values (gray squares of different intensities with higher intensity indicating larger HDA values) with a map of the allowed Ramachandran (φ,ψ) angles in protein structures as backdrop. Darker colors in the Ramachandran map represent higher populations (lower free energies) of peptides or proteins with those (φ,ψ) angles.
TABLE 1: Average Values of Torsional Angles (O,ψ) for Peptides with Different Secondary Structures structure
φ (deg)
ψ(deg)
R-helix 310-helix γ-helix Polypro II β-strand planar peptide
-67 -43 -57 -64 -117 180
-60 -24 70 126 113 180
and extent of large coupling regions (red-orange colors in Figure 4) in the HDA-(φ,ψ) map. This map also supports the following specific conclusions about electronic coupling across peptides:
(1) The large HDA values occur within a very narrow range of φ angles (adjacent to the NH group) around φ ∼ ( 50°, whereas the ψ angle (adjacent to the CO group) may vary over a much wider range while still maintaining large electronic coupling. This implies that the orientation of the nitrogen lonepair of the peptide bond is a major determinant of peptide electronic coupling. (2) The largest HDA values occur in regions of H-bonded helical secondary structures, which include regions of the Rhelix, 310-helix, and γ-helix (cf. Table 1 and Figure 4). (3) Donor-acceptor distance alone is not an accurate predictor of electronic coupling. The most compact R-helix, which projects the smallest donor-acceptor separation distance, is the least effective among the H-bonded helical structures when compared to other helices such as the 310-helix and other Hbonded helices, which project longer distances for the same number of residues. Thus, both distance and specific torsional peptide angle values are required for effective coupling. (4) The Polypro II structure has HDA values lower than the H-bonded helical peptides but significantly higher than the β-strand structure (Table 1, Figure 4). (5) Since the electronic coupling matrix element, HDA, varies over 4 orders of magnitude throughout the (φ,ψ) space and the rate constant for nonadiabatic ET (kET) is proportional to HDA2 (eq 1), rate differences as high as 8 orders of magnitude can be obtained for the same D-dipeptide-A species in different conformations, and even larger variations appear possible for larger peptides. Conclusions
Figure 4. Peptide electronic coupling map, extrapolated to all (φ,ψ) angles, showing the large variation in electronic coupling matrix element (HDA). Large and small HDA values are shown in red-orange and purple-blue colors, respectively.
In summary, we have presented a new roadmap for understanding electronic coupling across peptides with different conformations and secondary structures. This Ramachandran map of electronic coupling clearly defines the angular regions in the (φ,ψ) space where strong electronic coupling can occur and those (φ,ψ) regions where the presence of the peptide has only marginal effects on electronic coupling. We are currently extending this analysis method to determine long-range coupling in longer, D-A hydrated peptide chains and between metalsubstituted amino acid side chains29-31 in heme proteins, using protein X-ray structure data as a guide. Applications of this method to proteins will provide a new avenue for comparing calculated and experimental conformational dependence of electronic coupling, where both distance and specific torsional angles play important roles.
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Acknowledgment. We thank M. D. Newton, N. Sutin, J. F. Wishart, E. Castner, R. J. Cave, and R. M. Levy for helpful comments. Supporting Information Available: Table of computed ∆E, ∆µ12, µ12, and HDA values. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265. (2) Jortner, J.; Bixon, M. In Electron Transfer - From Isolated Molecules to Biomolecules; Prigogine, I., Rice, S. A., Eds.; John Wiley & Sons: New York, 1999; Vols. 106 and 107. (3) Electron Transfer in Chemistry; Balzani, V., Ed.; Wiley-VCH: Weinheim, Germany, 2001. (4) Newton, M. D. Chem. ReV. 1991, 91, 767. (5) Larsson, S. J. Chem. Soc., Faraday Trans. 1983, 79, 1375. (6) Jordan, K. D.; Paddon-Row, M. N. Chem. ReV. 1992, 92, 395. (7) Kurlancheek, W.; Cave, R. J. J. Phys. Chem. A 2006, 110, 14018. (8) (a) Moser, C. C.; Dutton, P. L. Biochim. Biophys. Acta 1992, 1101, 171. (b) Moser, C. C.; Keske, J. M.; Warncke, K.; Farid, R. S.; Dutton, P. L. Nature 1992, 355, 796. (c) Page, C. C.; Moser, C. C.; Chen, X.; Dutton, P. L. Nature 1999, 402, 47. (9) (a) Beratan, D. N.; Betts, J. N.; Onuchic, J. N. Science 1991, 252, 1285. (b) Beratan, D. N.; Betts, J. N.; Onuchic, J. N. J. Phys. Chem. 1992, 96, 2852. (c) Wolfgang, J.; Risser, S. M.; Priyadarshy, S.; Beratan, D. N. J. Phys. Chem. B 1997, 101, 2986. (d) Jones, M. L.; Kurnikov, I. V.; Beratan, D. N. J. Phys. Chem. A 2002, 106, 2002. (e) Prytkova, T. R.; Kurnikov, I. V.; Beratan, D. N. Science 2007, 315, 622. (10) (a) Polo, F.; Antonello, S.; Formaggio, F.; Toniolo, C.; Maran, F. J. Am. Chem. Soc. 2005, 127, 492. (b) Antonello, S.; Formaggio, F.; Moretto, A.; Toniolo, C.; Maran, F. J. Am. Chem. Soc. 2003, 125, 2874. (11) Long, Y.-T.; Abu-Irhayem, E.; Kraatz, H.-B. Chem.sEur. J. 2005, 11, 5186. (12) Ramachandran, G. N.; Ramakrishnan, C.; Sasisekharan, V. J. Mol. Biol. 1963, 7, 95. (13) Schulz, G. E.; Schirmer, R. H. Principles of Protein Structure; Springer Verlag: Berlin, 1979; Vol. 17. (14) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J. Am. Chem. Soc. 1985, 107, 3902.
Issa et al. (15) (a) Newton, M. D.; Cave, R. J. Chem. Phys. Lett. 1996, 249, 15. (b) Rust, M.; Lappe, J.; Cave, R. J. J. Phys. Chem. A 2002, 106, 3930. (c) Mulliken, R. S. J. Am. Chem. Soc. 1952, 64, 811. (16) Ridley, J. E.; Zerner, M. C. Theor. Chim. Acta 1973, 32, 111. (17) Krogh-Jespersen, K.; Ratner, M. A. J. Phys. Chem. 1976, 65, 1305. (18) Silva-Junior, M. R.; Thiel, W. J. Chem. Theory Comput. 2010, 6, 1546. (19) (a) Shin, Y.-G. K.; Newton, M. D.; Isied, S. S. J. Am. Chem. Soc. 2003, 125, 3722. (b) Issa, J. B.; Salameh, A. S.; Castner, E. W., Jr.; Wishart, J. F.; Isied, S. S. J. Phys. Chem. B 2007, 111, 6878. (20) See, for example: (a) Wallrapp, F.; Voityuk, A.; Guallar, V. J. Chem. Theory Comput. 2009, 5, 3312. (b) Sachs, S. B.; Dudek, S. P.; Hsung, R. P.; Sita, L. R.; Smalley, J. F.; Newton, M. D.; Feldberg, S. W.; Chidsey, C. E. D. J. Am. Chem. Soc. 1997, 119, 10563. (c) Pourtois, G.; Beljonne, D.; Cornil, J.; Ratner, M. A.; Bredas, J. L. J. Am. Chem. Soc. 2002, 124, 4436. (d) Newton, M. D. Int. J. Quantum Chem. 2000, 77, 255. (21) (a) Zerner, M. C.; Loew, G. H.; Kirchner, R. F.; Mueller-Westerhoff, U. T. J. Am. Chem. Soc. 1980, 102, 589. (b) For oxygen, the resonance integral was βO )-54.0 eV, and the one-center energy for p-orbitals was UPP(O) )-15.88 eV. (22) Thompson, M. A. ArgusLab 4.0.1; Planaria Software LLC: Seattle, WA, 2004. (23) Tyr and Trp side chains and their radical cations are known to play an important role in mediating electron transfer in many biological redox reactions, see, for example: Stubbe, J.; van der Donk, W. A. Chem. ReV. 1998, 98, 705. (24) Charge transfer energies close to 8 eV were calculated in ref 19a for amino pyridine and carboxypyridine electron donor and acceptor, respectively. (25) Similar, but generally somewhat lower, HDA values were also obtained for the naturally occurring peptides in Figure 1A. (26) Laskowski, R. A.; MacArthur, M. W.; Moss, D. S.; Thornton, J. M. J. Appl. Crystallogr. 1993, 26, 283. (27) (a) Polese, A.; Mondini, S.; Bianco, A.; Toniolo, C.; Scorrano, G.; Guildi, D. M. J. Am. Chem. Soc. 1999, 121, 3446. (b) Galoppini, E.; Fox, M. A. J. Am. Chem. Soc. 1996, 118, 2299. (28) Voronoi, G. J. Reine Angew. Math. 1908, 133, 97. (29) Isied, S. S.; Kuehn, C.; Worosila, G. J. Am. Chem. Soc. 1984, 106, 1722. (30) Moreira, I.; Sun, J.; Cho, M. O.-K. P.; Wishart, J. F.; Isied, S. S. J. Am. Chem. Soc. 1994, 116, 8396. (31) Gruschus, J. M.; Kuki, A. J. Phys. Chem. B 1999, 103, 11407.
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