J. Phys. Chem. B 2005, 109, 1023-1033
1023
Understanding Electron Transfer across Negatively-Charged Aib Oligopeptides Roberto Improta,†,§ Sabrina Antonello,‡ Fernando Formaggio,‡ Flavio Maran,*,‡ Nadia Rega,† and Vincenzo Barone*,† Dipartimento di Chimica, UniVersita` di Napoli “Federico II”, Complesso UniVersitario Monte S. Angelo, Via Cintia, 80126 Napoli, Italy, Dipartimento di Scienze Chimiche, UniVersita` di PadoVa, Via Marzolo 1, 35131 PadoVa, Italy, and Istituto di Biostrutture e Bioimmagini - CNR, Via mezzocannone 16, 80134 Napoli, Italy ReceiVed: September 16, 2004; In Final Form: October 12, 2004
The physicochemical effects modulating the conformational behavior and the rate of intramolecular dissociative electron transfer in phthalimide-Aibn-peroxide peptides (n ) 0-3) have been studied by an integrated density functional/continuum solvent model. We found that three different orientations of the phthalimide ring are possible, labeled Φhel, ΦC7, and ΦpII. In the condensed phase, they are very close in energy when the system is neutral and short. When the peptide chain length increases and the system is negatively charged, Φhel becomes instead the most stable conformer. Our calculations confirm that the 310-helix is the most stable secondary structure for the peptide bridge. However, upon charge injection in the phthalimide end of the phthalimide-Aib3-peroxide, the peptide bridge can adopt an R-helix conformation as well. The study of the dependence of the frontier orbitals on the length and on the conformation of the peptide bridge (in agreement with experimental indications) suggests that for n ) 3 the process could be influenced by a 310 f R-helix conformational transition of the peptide chain.
Introduction Understanding how electrons are transferred in proteins is a challenging task requiring knowledge of many related aspects, such as the properties of the donor (D) and the acceptor (A), the effect of the surrounding medium, and the electronic coupling between the relevant states involved in the process.1 In this context, the direct use of proteins containing well-devised D and A groups has provided a substantial body of useful information.2 On the other hand, to study how fine details or specific aspects may tune electron transfer (ET) reactions in such complex environments, the use of simpler models provides a more convenient approach. Because the peptide chains are essential in assisting long-range ET in proteins,1 focusing on well-defined D-peptide-A model molecules has been the successful strategy adopted by several research groups. Prolinebased peptides have been employed extensively,3,4 although other kinds of peptide backbones have also been used.5 These studies have shown that the role of the peptide backbone is more complex than that of just providing a spacer connecting D and A. In fact, the peptide provides a bridge in which electronic states are available to support the actual ET between the D and A electronic states. Generally, when the energy of the bridge orbital is much higher than that of the ET reactant and product states, longrange ET is viewed as occurring by the superexchange mechanism.6 This is a coherent tunneling mechanism in which ET between D and A occurs without transient occupation of the states of the bridge. The mixing of the latter states with the reactant and product configurations is responsible for the increase of the electronic coupling and thus of the ET rate. * Corresponding author. E-mail:
[email protected]. † Universita ` di Napoli “Federico II”. ‡ Universita ` di Padova. § Istituto di Biostrutture e Bioimmagini - CNR.
Although this mechanism provides an efficient channel for transferring electrons, the resulting ET rate depends exponentially and thus significantly on the D/A distance. On the other hand, some bridges are liable to take part directly in the ET reaction by providing a backbone in which electrons can be transferred from D to A by an incoherent hopping mechanism.7 Electron migration takes place by using electronic states that are localized onto the units forming the bridge itself. An important feature of this ET path, stemming from the fact that this process is thermally activated and requires an initial endoergonic charge injection from D to the first bridge unit, is that the ET rate does not change significantly with the D/A distance. As the number of bridge units increases, the efficient superexchange mechanism is thus expected to be eventually overwhelmed by intrabridge electron hopping. This transition is monitored by the onset of a weaker distance dependence of the ET rate and is a function of the donor-bridge-acceptor energetics.8 Such an ET scheme has received considerable consensus for charge transfer across DNA strands.7-9 However, despite earlier suggestions or sometimes intriguing experimental data,3,4,5k-m,10 together with the outcome of some recent theoretical treatments,11,12 it is still unclear whether this scheme is actually applicable to peptides and proteins, also by taking into account the result of other theoretical studies1b,6a,13 and the role played by the nature of the peptide backbone.14 Very recently, we studied the ET from an electrogenerated phthalimide radical anion donor to a peroxide acceptor.15 The phthalimide and peroxide electrophores were attached at both ends of R-aminoisobutyric acid (Aib) homooligomers of different lengths. These peptides were chosen for their propensity to form rigid 310-helices because of steric hindrance at the R-carbon and resulting reduced torsional freedom.16 This is a feature common to oligomers based on CR-tetrasubstituted R-amino acids, making them particularly convenient spacers
10.1021/jp045797l CCC: $30.25 © 2005 American Chemical Society Published on Web 12/18/2004
1024 J. Phys. Chem. B, Vol. 109, No. 2, 2005
Improta et al.
SCHEME 1
because of their definite conformational preferences.17 The compounds and the ET reactions are illustrated in Scheme 1, where n represents the number of additional amino acid units, which was varied between 0 and 6. The intramolecular ET reaction depicted in Scheme 1 is a typical concerted dissociative process and, consequently, is endowed by the large inner reorganization associated with elongation of the cleaving bond.18 The reduction of the peroxides is thus irreversible and kinetically very slow.19 Because of this ET sluggishness, the electron is first injected by the electrode into the phthalimide end of the peptide, leading to the corresponding radical anion. In this case, the reaction is kinetically fast because only solvent reorganization and negligible inner reorganization are involved in the heterogeneous process. The electron is subsequently transferred, intramolecularly, to the peroxide end of the peptide. We found that the ET rate constant depends very mildly on the number of Aib units or the edge-to-edge D/A distance (dee). As a matter of fact, we were surprised to find that the ET rate was even increasing when n was varied from 1 to 3. These results were attributed to an active role played by the intramolecular H-bonds on the intramolecular ET process. In this regard, it should be mentioned that the issue of how important may be the intramolecular H-bonds in supporting the electron tunneling across peptides and other molecular systems is currently receiving much attention on both experimental20 and theoretical grounds.1b,13a,14,21 The picture emerging from these studies, however, does not seem to provide unequivocal proof of active participation of the H-bonds in these ET processes. From our side, we purposely focused on the use of peptides based on the Aib unit to control as much as possible the stiffness of the bridge connecting D and A. In fact, Aib homopeptides are well-known for their tendency to form turns and helices, assuming a regular 310-helical structure starting from the tripeptide. This is witnessed by the X-ray diffraction structures of the complete -(Aib)n- series up to n ) 11,17,22 the only peptide series for which such a result has been achieved so far, and by 1H NMR and IR spectroscopy data obtained in solution. The propensity of Aib homopeptides to adopt rigid helical conformations is much higher than that of the coded R-amino acids, which start to form helices only for relatively long oligomers. The Aib residue is thus an ideal building block for constructing rigid and tunable helical peptides with known conformation.23 Our data on the anomalous distance dependence observed with the Aib peptides15 could be, to some extent, forced to fit into the framework of the sequential hopping mechanism. This is something that needed to be tested. On the other hand, the same anomalous dependence might raise the suspicion that the observed trend is a specific feature of the selected systems. We have now started an investigation aimed at gaining some insight onto these aspects. In addition, we had another motivation, i.e., the fact that there is no specific knowledge on what happens to a peptide system, concerning both conformation and energetics, upon charge injection. For example, it is conceivable that addition of one electron should modify at least the strength of specific H-bonds and have implications on the conformational
preferences of the peptide. The purpose of this paper is thus to gain insight into the physical aspects modulating the rate of intramolecular dissociative ET as a function of the number of bridge units. In general, increasing the peptide length implies taking into account various structural and electronic aspects, which are often mutually related and whose influence on the electron transfer rate is not so easy to explain. In such a scenario, the recent advances made in the area of quantum mechanical methods,24,25 which now can provide reliable results on large size systems in solution, could be very useful. In fact, by providing direct structural and energetic information on short living compounds and/or relative energy minima, they can be a fundamental tool for understanding the most influential effects modulating ET in biological systems. In this study, we have used quantum mechanical (QM) calculations to gain insight into and rationalize the physicochemical effects modulating the rate of intramolecular dissociative ET (DET) in phthalimide-Aibn-peroxide peptides.15 In particular, we have addressed the following main issues: (i) the conformation of Aibn in the gas phase and in solution; (ii) the dependence of the conformational equilibria upon injection of one electron; (iii) the effect of the peptide chain elongation on both the peptide structure and the redox behavior of the ET antenna; (iv) the possible conformational dependence of the ET reaction across the investigated systems. The peptides were studied either in the gas phase or by simulating the presence of the same solvent used for the electrochemical experiments, N,Ndimethylformamide (DMF). The theoretical analysis provided significant insight into the peptide-length and solvent effects on the energetics of both the neutral and radical anion species. We found that the energy of the singly occupied molecular orbital (SOMO) changes along the series in agreement with the effect of the secondary structure. The results also indicate how the conformational preferences of the negatively charged peptides may differ quite significantly from those of the neutral systems, which implies interesting consequences on the ET mechanism. Computational Details All calculations were performed using the Gaussian03 package,26 the PBE0 density functional27 and standard 6-31G(d) and 6-31+G(d,p) basis sets.28 Despite the absence of adjustable parameters, PBE0 has already shown an accuracy competitive with that of the best last generation functionals and has been successfully applied to the conformational study of biomolecules.29 Solvent effects were taken into account by means of the latest implementation30 of the polarizable continuum model (PCM).31 In this model, the molecule is embedded in a cavity surrounded by an infinite dielectric, whose dielectric constant is set to the value of the electrochemical solvent, DMF ( ) 36.7). The cavity generated by the solute in the solvent is defined in terms of interlocking spheres centered on non-hydrogen atoms, whose radii are optimized according to the UAHF model.31c We recall that the solvation energies issuing from PCM computations have the status of free energies, because
Electron Transfer in Aib Oligopeptides
J. Phys. Chem. B, Vol. 109, No. 2, 2005 1025
they take implicitly into account thermal and entropic contributions of the solvent. Unrestricted PBE0 calculations were employed for the open-shell anionic species. Even if the density functional theory (DFT) does not use, in principle, any welldefined wave function, the expectation value of the S2 operator can nonetheless be estimated by using a reference set of KS orbitals. The value of 〈S2〉 is close to 0.75, confirming that the problem of spin contamination is usually much less severe in Unrestricted DFT (UDFT) calculations than in the corresponding Unrestricted Hartree-Fock (UHF) approach.32
SCHEME 2: Schematic Drawing and Atom Labeling of the Systems under Study
Results As a first step of our analysis we characterized the minima of the potential energy surfaces of both the neutral and the anion forms of Aib0But and Aib0Me, in which the terminal tert-butyl group is substituted by a methyl group. These species correspond to the general formula illustrated in Scheme 2. The subscript of Aib0But and Aib0Me refers to the number of additional Aib units, n. In the acronyms, for the sake of simplicity, the donor and acceptor sides of the molecule (which do not change with n) are omitted. PBE0/6-31+G(d,p)//PBE0/6-31G(d) calculations (Table 1) indicate that, independently of the terminal alkyl group, three backbone conformers provide energy minima for the neutral species, the difference being the orientation of the phthalimide group with respect to the peptide backbone. In analogy with common peptide nomenclature, we label these minima as Φhel (φ ∼ -60°, ψ ∼ -40°), ΦC7 (φ ∼ -60°, ψ ∼ 60°), ΦpII (φ ∼ -60°, ψ ∼ 180°), in which the acronyms hel, C7, and pII correspond to helix, γ-turn (labeled C7 because the hydrogenbonded turn involves seven atoms), and polyproline II (i.e., the conformation adopted by a proline homopolymer with trans amide bonds),33 respectively. Being the investigated molecules achiral, each of the above minima is isoenergetic with its counterpart, exhibiting the opposite sign alternance in the backbone dihedrals. In the gas phase, the energy differences between the minima are small and they are further reduced when environmental effects (with DMF as the dielectric) are taken into account by using the PCM. In particular, Φhel, which represents the absolute energy minimum, is more stable than ΦpII by only ∼0.2 kcal/mol. Indeed, this energy difference is so small that it is plausible that the crystal-field effect could easily revert the stability order predicted by the PCM calculations for the DMF solution, explaining why Aib0But adopts a ΦpII conformation in the solid state.34 This picture, however, changes significantly upon formation of the phthalimide radical anion. Though the Φhel and ΦC7 conformers remain very close in energy, ΦpII is no longer a minimum of the potential energy surface of Aib0But. In fact, any optimization starting from the ΦpII geometry eventually falls into the ΦC7 structure. For Aib0Me the situation is similar in that although the ΦpII conformer still remains an energy minimum, it is remarkably less stable than ΦC7 and Φhel. Therefore, substitution of the tert-butyl group with the smaller methyl group does not alter significantly the main conformational features of the peptide or its radical anion. On the other hand, it is reasonable to expect that the effect of the C-terminal group on the conformational behavior of the peptide backbone should decrease as the peptide is made longer. For these reasons and for the sake of computational convenience, we have thus focused our attention only on species bearing a C-terminal methyl group. In the following, the peptides and corresponding radical anions will now be simply indicated as Aib0/Aib0-, Aib1/ Aib1-, Aib2/Aib2-, and Aib3/Aib3-, depending on the number of residues forming the core of the peptide bridge.
TABLE 1: Energy Minima for Aib0But and Aib0Me Obtained at the PBE0/6-31+G(d,p)//PBE0/6-31G(d) Level of Theorya Aib0But Φhel φ0 ψ0 ∆Egb ∆Gsc φ0(anion) ψ0(anion) ∆Eg(anion)b ∆Gs(anion)c
ΦC7
-52.8 -80.3 -39.2 52.9 0 1.29 0 1.50 -53.1 -75.2 -36.2 52.9 0 0.24 0 0.16
Aib0Me ΦpII
-52.5 142.5 0.65 0.24 converges to C7 conformer
Φhel
ΦC7
ΦpII
-59.0 -80.1 -52.2 -38.2 52.3 141.6 0 1.32 1.23 0 1.12 0.01 -61.4 -75.4 -45.9 -34.1 50.0 123.3 0 0.22 5.75 0 -0.44 2.80
a Energy (in kcal/mol) relative to the Φ hel conformer (see text for details). Experimental (X-ray) results: φ0 ) -69.9°, ψ0 ) 175.9°.b Gas phase. c DMF solution, PCM calculations.
Figure 1. Energy profile calculated at the PBE0/6-31G(d) level for Aib0 and Aib0- as a function of the variation of the ψ0 dihedral. Energy values (in kcal/mol) are relative to the Φhel conformer. The two minima in the pII region correspond to the R and L enantiomeric pair (nearly isoenergetic).
As to the conformational preferences of the terminal peroxide group, test calculations on Φhel (Aib0-) show that the g-g-t (ξ1 ∼ -60°, ξ2 ∼ -60°, and ξ3 ∼ 180°) conformer is the most stable among the possible staggered conformers. From the two possible isomers corresponding to each orientation of the phthalimide moiety, we selected the most stable one for the g-g-t conformation of the peroxy group, namely, R (φ ∼ -60°, ψ ∼ -40°) for Φhel, and L for ΦC7 (φ ∼ 60°, ψ ∼ -60°) and ΦpII (φ ∼ 60°, ψ ∼ -140°) (where R and L refers to the handness of the resulting secondary structure). Conformational Preferences of Aib0 and Aib0-. To study the effect of electron injection into Aib0, we performed a relaxed PCM/PBE0/6-31+G(d,p)//PBE0/6-31G(d) scan of the potential energy surface for different values of the ψ dihedral. The cyclic nature of the phthalimide moiety forces the φ dihedral to assume values between about (60° and (90°. The results are illustrated in Figure 1 and confirm the picture sketched above. For the neutral species, three regions of the potential energy surface are almost isoenergetic. They correspond to the helix, C7, and
1026 J. Phys. Chem. B, Vol. 109, No. 2, 2005
Figure 2. Schematic drawing of the three energy minima for Aib0: (a) ΦhelAib0 energy minimum; (b) ΦC7Aib0 energy minimum; (c) ΦpIIAib0 energy minimum. The most relevant intramolecular interactions are also evidenced (see text for details).
pII orientations of the phthalimide group, as illustrated in Figure 2 and summarized in Table 2. Not surprisingly, Aib0 exhibits a behavior similar to that of oligopeptides containing a proline residue.29b,35 The interaction between the NH group and the π electrons of the phthalimide pentaatomic ring (Figure 2, interaction A) contributes to the stability of the Φhel conformer. On the contrary, the ΦC7 conformer, whose structure is the absolute minimum for a dipeptide in the gas phase,35,36 is stabilized by the interaction between the NH group of the peptide moiety and one of the phthalimide carbonyl groups (interaction B). Finally, the ΦpII conformer (interaction C) allows minimizing the steric repulsion between the peptide moiety and the phthalimide ring, which may explain its stability in analogy to the situation encountered with peptides bearing a tertiary amide, such as proline derivatives. Independently on the conformation of the phthalimide ring, the anion of Aib0 is always bound, not only adiabatically but
Improta et al. also vertically. Phthalimide in the gas phase has indeed a rather large experimental electron affinity (1.015 eV)37 and the peptide chain stabilizes the presence of charge on the ring. As anticipated above (cf. Table 2 and Figure 1), the electron uptake leads to slight stabilization of ΦC7 and, especially, to remarkable destabilization of ΦpII. Inspection of the electronic structure of the radical anion species provides insight into the physicochemical reasons of this conformational behavior. As a matter of fact, the SOMO of Aib0- is almost completely localized onto the phthalimide system (Figure 3), with significant contribution of the pentaatomic ring carbonyl groups. This is in line with the results of QM calculations previously carried out on the SOMO of a series of ring-substituted phthalimide systems, which indicated that the charge density of the pentatomic ring is essentially -1 and that there is almost no difference between the LUMO and the SOMO.38 For the peptides, main consequence of such a localization is that interactions A and B (in which the phthalimide ring acts as H-bond acceptor) are strongly stabilized. Conversely, in the case of ΦpII the increase of the electron density on the ring leads to electronic repulsion with the lone pair electrons of the peptide carbonyl (Figure 2, interaction C). The increased stabilization stemming from interactions A and B and the destabilization caused by interaction C explain why the ΦpII conformer is much less stable for Aib0-. Not surprisingly, the ΦC7 conformer, which exhibits a hydrogen bond with one of the phthalimide carbonyls, becomes particularly stable upon electron uptake. The above considerations provide a rationale of the geometry changes occurring on the transition from Aib0 to Aib0-. Small distortion of the carbonyl groups within the phthalimide moiety is involved in the formation of the radical anion, the most relevant changes being elongation of the CO and C′O′ bonds by ∼0.06 Å and shortening of the CC and CC′ bonds by ∼0.05 Å. Concerning the peptide moiety, in ΦC7 small changes in the backbone dihedrals and in the τ0 angle of the anion (cf Table 2) decrease the distance between the NH and the C′O′ group, engaged in the intramolecular H-bond, from 1.95 to 1.73 Å. Analogously, in the Φhel conformer the NH group becomes closer to the phthalimide ring (the NH-N distance) by ∼0.1 Å. This result is mainly due to a small decrease of the τ0 bond angle. Also ΦpII exhibits a significant variation, the value of the ψ dihedral changing by ∼20°; as opposed to the other conformers, however, this variation increases the distance between the amide group and the phthalimide carbonyl, decreasing the destabilization due to interaction C (see Figure 2c). Solvent Effect on Aib0 and Aib0-. The results of the geometry optimizations performed in DMF solution on the Φhel, ΦC7, and ΦpII conformers of Aib0 and Aib0- are collected in Table 2. The solvent does not induce any significant change in the equilibrium geometry, particularly concerning the backbone conformation. Confirming previous computational results on peptides,29b-d,39 the geometrical parameters more influenced by the solvent are the CdO and CsN bond distances in the peptide amide moiety, which increase or decrease by ∼0.005 Å, respectively. These variations are due to the relative weight of the dipolar amide resonance structure, which increases with the polarity of the embedding medium. Because the solvent has no significant direct effect on the Aib0 geometry, it is not surprising that the relative stability predicted by the PCM single point calculations on the geometries optimized in vacuo is very similar to that issuing by optimizations performed in DMF. As a consequence, the solvent effect on other systems was evaluated by using geometries that were previously optimized in the gas phase. From the energetic point of view, the electron affinity
Electron Transfer in Aib Oligopeptides
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TABLE 2: Energy Minima for the Helix and the PII Minima of Aib0, Obtained at the PBE0/6-31+G(d,p)//PBE0/6-31G(d) Level of Theory in the Gas Phase and in DMF Solution (PCM Calculations)a Φhel φ0neutral ψ0 neutra τ0neutral Ox1Ox2neutral COneutral C′O′neutral N0H-N neutral rel stabc φ0anion ψ0anion τ0anion Ox1Ox2anion COanion C′O′anion N0H-Nanion rel stabc
ΦC7
ΦpII
gas phase
solution
gas phase
solution
gas phase
solution
-59.0 -38.2 110.5 1.439 1.209 1.210 2.319 0 -61.2 -34.1 110.8 1.435 1.239 1.248 2.231 0
-58.8 -39.3 110.3 1.439 1.210 1.211 2.324 0 -58.6 -38.7 110.3 1.437 1.243 1.249 2.262 0
78.7 -66.1 108.6 1.439 1.207 1.218 1.952 1.05 75.2 -60.1 110 1.436 1.237 1.260 1.725 -0.38
79.4 -66.9 108.4 1.439 1.209 1.219 1.950 1.28 (1.16d) 75.9 -62.6 109.3 1.437 1.241 1.261 1.757 0.20 (-0.35d)
55.3 -149.4 106.7 1.440 1.209 1.213 2.706b 0.18 53.4 -129.0 108.2 1.437 1.240 1.253 2.916b 5.36
56.7 -151.1 106.1 1.439 1.211 1.213 2.701b -0.43 (-0.37d) 55.2 -141.7 107.6 1.438 1.244 1.250 2.806b 2.50 (3.47d)
a Energy (in kcal/mol) relative to helix conformer (see text for details). b OAib-N distance. c ∆E in gas phase and ∆G in solution. d Single point PCM calculations on the gas-phase optimized geometries.
TABLE 3: Distance between the Nitrogen of the Phthalimide Moiety and the First Oxygen Atom of the Peroxy Group for Different Orientations of the Phthalimide Ring with Respect to the PolyAib Chain (in 310-Helix Conformation) Aib0 Aib1 Aib2 Aib3 a
-
Figure 3. Schematic drawing of the SOMO of ΦhelAib1 PBE0/631G(d) calculations.
(EA) of Aib0 increases, the energy difference among the three conformers of the radical anion Aib0- decreases and Φhel becomes the most stable conformer (see Table 2 and Figure 1). The solvent effect on the conformational equilibrium of Aib0 can be explained on the same grounds described in the preceding paragraph. A polar solvent, such as DMF, decreases the importance of the intramolecular hydrogen bonds characterizing A and B, thereby favoring the ΦpII conformation over Φhel and ΦC7, and Φhel over ΦC7. Due to the strong intramolecular hydrogen bonding, ΦC7 exhibits a more rigid structure, which is less affected by the presence of the solvent. This feature explains why ΦC7 is relatively destabilized over ΦpII and Φhel by geometry optimizations in DMF. Effect of Peptide Chain Elongation. Experimental40 and computational studies36,41 have convincingly shown that, for polyAib chains, the secondary structures falling in the R region of the Ramachandran plot (i.e., R- and 310-helices) are much more favored than others. Consequently, when studying the compounds Aib1, Aib2, and Aib3 we excluded from our analysis other secondary structures, such as the β-strand, the pII, and the repeated γ-turn. PBE0/6-31G(d) geometry optimizations predict that, independently of the orientation of the phthalimide moiety, the polyAib moiety adopts a 310-helix secondary structure (the backbone dihedrals corresponding to different orientations of the donor are provided in the Supporting Information). On the average, the φ and ψ dihedral angles of the compounds examined are quite similar. In addition, they are close to the
Φhel
ΦC7
ΦpII
4.87 6.39 8.00 10.22 (7.35a)
4.46 5.61 7.43 9.81
5.57 5.60 6.41 9.68 (6.56a)
PolyAib chain adopting an R-helix structure.
TABLE 4: Relative Energies (∆E in Gas Phase, ∆G in Solution in kcal/mol) of Different Conformers of Phthalimide-Aibn-Peroxide by PBE0/6-31+G(d,p)// PBE0-6-31G(d) Calculations gas phase Φhel Aib0 Aib1 Aib2 Aib3 Aib0Aib1Aib2Aib3a
ΦC7
DMF solution ΦpII
0 1.05 0.18 0 2.94 -0.18 0 3.83 0.29 0 3.76 0.31 0 -0.38 5.36 0 5.05 5.76 0 5.38 5.83 0 (8.64a) 5.69 5.48 (12.3a)
Φhel
ΦC7
ΦpII
0 1.16 -0.37 0 3.86 0.07 0 4.30 0.10 0 4.59 0.32 0 -0.35 3.47 0 4.39 3.51 0 4.97 3.43 0 (7.03) 4.93 3.45 (8.84a)
PolyAib chain adopting an R-helix structure.
values optimized for a polyAib infinite polymer by DFT calculations employing periodic boundary conditions.36 The structure of the Aib peptide bridge is thus essentially unaffected by the terminal peroxy group or by the orientation of the phthalimide moiety. In other words, from a structural point of view the peroxide behaves as the corresponding ester-terminated peptide, in which the peroxy oxygen on the peptide side (Ox1 in Scheme 2) is simply replaced by a CO group. Because of these features, it is not surprising that the D/A distance is affected only marginally by the orientation of the phthalimide group, as summarized for the Aib0-Aib3 series in Table 3. From an energetic point of view, the most important consequence brought about by the elongation of the peptide chain is the significant destabilization experienced by the C7 conformer of the phthalimide moiety (Table 4): when only one Aib unit is added to Aib0, ΦC7 is destabilized by a few kcal mol-1 relative to Φhel and ΦpII, whereas the relative energy of
1028 J. Phys. Chem. B, Vol. 109, No. 2, 2005
Figure 4. Schematic drawing of the ΦhelAib1 energy minimum.
the latter two conformers is not affected significantly. The effect is even more pronounced when we consider the corresponding radical anions, thus highlighting the conformational consequences brought about by reduction of the donor side of the peptide. Inspection of Figure 4 helps understanding the behavior depicted above. For both Φhel and ΦpII, the passage from Aib0 to Aib1 allows forming a hydrogen bond between the NH group of the second peptide unit and one of the two phthalimide carbonyls (Figure 4, interaction D). As to ΦC7, because the carbonyl group of the phthalimide moiety is already involved in a hydrogen bond with the first peptide unit, this interaction is not possible. Therefore, it is not surprising that the relative destabilization of ΦC7 is of the same order of magnitude as that corresponding to a hydrogen bond and that this effect is particularly important in Aib1-, in which the hydrogen bond involves the carbonyl group of a negatively charged phthalimide ring. In the polar DMF solvent, although for the neutral molecules the importance of intramolecular hydrogen bonds is similar to that calculated for the gas phase, for the anions, the effect is slightly reduced. This picture remains almost unchanged when one goes to Aib2 and Aib3. Though, for the neutral system, Φhel and ΦpII are always very close in energy, for the anions, Φhel is more stable than ΦpII by ∼5.5 (gas phase) or 3.5 kcal mol-1 (DMF). On the other hand, ΦC7 is consistently less stable than Φhel by ∼4-5 kcal mol-1. Charge Effect on the Peptide Secondary Structure. In the final step of our conformational analysis, we checked the possibility that the peptide chain adopts an R-helix conformation in the Φhel and ΦpII systems. As a matter of fact, the R-helix secondary structure is more compact than that of the 310-helix (the vertical pitches associated with the increase of the peptide backbone by one amino acid unit are 1.56 and 1.94 Å, respectively)16b and the corresponding decrease of the D/A distance could be an important issue affecting the rate of electron tunneling across the peptide bridge. Furthermore, although allAib peptides so far examined exhibit a 310-helix conformation,36,41,42 the energy difference between 310- and R-helices is not large.36,41 We found that for Aib1 and Aib2 the R-helix is not a minimum energy structure, for both Φhel and ΦpII. Interestingly, when the ψ dihedrals are frozen to a value of -45° (i.e., the value assumed in an infinite Aib polymer adopting an R-helix secondary structure, according to DFT calculations empolying periodic boundary conditions),36 the peptide chain
Improta et al. retains the hydrogen-bond pattern i f i + 3 typical of the 310helix, even though this preference induces remarkable distortions of the φ dihedrals. This result is not unexpected because the R-helix can form one hydrogen bond less than the 310-helix involving the same number of residues. The influence of this feature on the relative stability of the two helices is obviously larger for short peptides, which exhibit a smaller number of hydrogen bonds. On going to Aib3, however, the results of our computations strongly depend on the charge present on the phthalimide ring. In fact, whereas for the neutral compound the geometry optimizations starting from the R-helix converge to the 310-helix (Figure 5, case a), our calculations predict that the R-helix is a true energy minimum of both ΦhelAib3- and ΦpIIAib3- (hereafter, ΦhelAib3(R)- and ΦpIIAib3(R)-, respectively: see cases b and c of Figure 5). Both ΦhelAib3(R)- and ΦpIIAib3(R)- exhibit two hydrogen bonds between the Aib chain (involving the NH groups of the second and third amide units) and the same phthalimide carbonyl, whereas a third hydrogen bond involves the first and last amide unit. The structure of ΦpIIAib3-(R) is particularly interesting because both hydrogen bonds involving the phthalimide carbonyl group should be strong, as the N(H)-O distance is rather short, ∼1.95 Å, and the C′O′ bond length, 1.263 Å, is larger than that found when the carbonyl is not involved in hydrogen bonds (for example, see ΦpII and Φhel conformers in Table 2). Furthermore, although one of the hydrogen bonds should involve the oxygen atom lone pair (NH is coplanar with the amide moiety), the other one has the NH group that points toward the SOMO of the phthalimide moiety. Because of the two hydrogen bonds involving the same phthalimide carbonyl, the R-helix structure is indeed expected to be stabilized by the presence of a negative charge on the ring. From the point of view of the D/A distance, the effect of this transition would be quite significant, as the dee value decreases by ∼3 Å (Table 3). It should be noticed that the PCM/PBE0/6-31+G(d,p) calculations predict that in DMF ΦpIIAib3(R)- is ∼5.4 kcal mol-1 less stable than its 310-helix counterpart, ΦpIIAib3(310)-. Although the solvent effect is important (ΦpIIAib3(R)- is ∼ 3.5 kcal mol-1 relatively more stable in DMF as compared to the gas phase), the minimum offered by the R-helix would still appear to be a bit too high in energy to provide an appealing mechanistic path. On the other hand, recent studies suggest that DFT calculations could underestimate the stability of the R-helix with respect to its 310 counterpart.43-45 Whereas this feature is more significant for extended basis sets, PBE0/6-31G(d) results are often closer to those of the most refined post-HF calculations.45 It is thus worth noting that according to our computations at the 6-31G(d) level, ΦpIIAib3(R)- is only 3.6 kcal mol-1 less stable than ΦpIIAib3(310)-. Intramolecular Dissociative ET. How do the conformational effects we have presented in the preceding sections modulate the rate of the dissociative ET to the peroxide moiety? This is not a trivial task, requiring, by itself, a specific and thorough study of the dependence of the lowest energy excited electronic state on the peptide conformation. We here present the basis for this forthcoming study by analyzing how the peptide conformation affects the shape and the energy of the frontier orbitals (those most likely involved in the ET process). Whereas the SOMO is localized on the phthalimide ring, PBE0 calculations predict that the three lowest unoccupied orbitals of the systems under study can be described as (i) a π* orbitals localized on the phthalimide ring, (ii) the O-O σ* orbital of the peroxide moiety, and (iii) a combination of the π* orbital
Electron Transfer in Aib Oligopeptides
J. Phys. Chem. B, Vol. 109, No. 2, 2005 1029
Figure 5. Schematic drawing of three different energy minima of Aib3-: (a) ΦhelAib3(310)-; (b) ΦhelAib3(R)-; (c) ΦpIIAib3(R)- (see text for details).
of the Aib peptide groups. These two latter orbitals are the most relevant for the DET, because the O-O bond breaking depends on the electron injection into the O-O σ* orbital, whereas the peptide orbitals could be involved in a sequential hopping mechanism. Because the main source of reorganization energy associated with DET is the stretching of the cleaving bond,18,46 the energy of the lowest energy unoccupied orbitals of the peptides was calculated as a function of the elongation of the O-O bond, all the other geometrical features being frozen at their equilibrium value. Confirming previous computational results on similar peroxide systems,38 an increase of the O-O bond length, which for our compounds has an equilibrium length of 1.43 Å, causes significant stabilization of the O-O σ* bond orbital of the peroxide moiety. At the same time the SOMO localized onto the phthalimide end and the orbitals localized on the bridge are essentially unaffected by this stretching. When the bond is elongated by 0.25-0.30 Å (the precise value depending on the actual peptide length and phthalimide orientation), the O-O σ* orbital is nearly isoenergetic with the SOMO on the phthalimide end, and the molecule is now set up for an efficient intramolecular DET. The extent of O-O bond elongation is in agreement with the outcome of other analyses or computational studies.19b,d,38 When the peptide chain lengthens, though the energy of the O-O σ* orbital does not change significantly, the SOMO is remarkably stabilized by the formation of extra hydrogen bonds (vide supra). Interestingly, an increase of the number of peptide units gives rise to the formation of a π* orbital delocalized on the peptide bridge due to the interaction of the π* orbital of the individual peptide units (see Figure 6). However, although the energy of this orbital is stabilized when going from Aib0 to Aib3, it always remains at least 2 eV higher than that of the O-O σ* orbital (represented in Figure 6b). Finally, it is important to highlight that in Aib3- the energy of the O-O σ* orbital is significantly stabilized (∼0.3 eV) by the 310 f R-helix
transition of the peptide bridge, confirming that this conformational transition could indeed play an important role in the DET. As we have stated above, although these considerations are to be considered as qualitative, they are confirmed by preliminary time-dependent PBE0/6-31G(d) calculations.47 For a fixed O-O bond distance (1.63 Å) we have checked that when the chain adopts a 310-helix conformation the energy of the electronic transition shifting one electron from the phthalimide SOMO to the O-O σ* bond increases from 0.78 to 1.66 eV when going from Aib0- to Aib3-. Instead, the energy associated with electronic transitions toward the orbitals localized on the peptide bridge is much higher (∼3 eV). This is an important result showing that ET to the bridge is highly disfavored, therefore ruling out the likeliness of a sequential hopping mechanism for these systems. Interestingly, our calculations indicate that the transition energy significantly drops (from 1.66 to 1.23 eV) when the peptide chain of Aib3- passes from the 310- to the R-helix. It is also worth stressing that the transition energy becomes even smaller than that found with Aib1-, 1.38 eV, in nice agreement with the trend experimentally observed for the ET rates.15 Discussion and Conclusions This study originates from the experimental observation that the distance dependence of the DET rate in the phthalimideAibn-peroxide system of Scheme 1 is significantly different from the exponential dependence usually encountered with other peptide bridges.15 As a matter of fact, the ET rate even increases slightly (by ∼0.5 log k unit) on going from Aib1 to Aib3. To gain insight into this intriguing and potentially very important behavior, we employed quantum mechanical calculations and studied peptides that had exactly the same features as those of the molecules previously used in the electrochemical experiments. The focus was on the two degrees of freedom that we expected to be particularly influential in modulating the ET in the above systems, namely the orientation of the donor moiety
1030 J. Phys. Chem. B, Vol. 109, No. 2, 2005
Improta et al.
Figure 7. Dependence of the computed adiabatic EA pertaining to the Φhel, ΦC7, ΦpII structures (PBE0/6-31G(d) calculations in DMF solution) and the experimental phthalimide standard potential (E°)15 on the number of Aib units, as defined in Scheme 2. All the energy values are relative to Aib0. The dashed lines are meant to underline the experimental and computed trends.
Figure 6. (a) Schematic drawing of the molecular orbital of ΦhelAib3corresponding to the lowest energy orbital among those localized in the peptide bridge (b) Schematic drawing of the molecular orbital of ΦhelAib3- corresponding to the O-O σ* orbital.
(the phthalimide N-terminal group) with respect the peptide bridge and the secondary structure adopted by the bridge itself. The calculations took into proper account the role of DMF solvent used in the original experiments. We studied the conformational behavior of the neutral and the anionic peptides, the latter being the actual “starting points” of the intramolecular DET. Three different orientations of the phthalimide ring, labeled Φhel, ΦC7, and ΦpII, are possible. The relative energy of these conformers depends on the length of the peptide and on its charge. When the peptide is short and unable to form the 310-helix typical of oligo-Aib peptides, i.e., for Aib0, the energies of the three conformers in solution are quite similar. However, as soon as the formation of the first intramolecular hydrogen bond corresponding to the 310-helix becomes possible (for n ) 1), the ΦC7 conformer is significantly destabilized. Upon electron injection into the phthalimide end
of the peptide, the ΦpII conformer is also remarkably destabilized independently of the value of n. In addition, as for the neutral peptides, destabilization also affects the ΦC7 conformer for n g 1. These results are in keeping with the fact that the SOMO of the peptide is mostly localized onto the pentaatomic phthalimide ring, which strengthens the “best” possible intramolecular hydrogen bond involving one of the phthalimide carbonyls. The above results highlight some general features that should be taken into account when ET processes are studied across peptides. Although the negative charge is always localized on the phthalimide ring, the conformational behavior of our system remarkably depends on the charge present on the peptide. This implies that it cannot be taken for granted that structures issued from experimental and computational studies on the neutral system provide a firm basis for understanding the behavior of the negatively charged compound. Concerning the shortest species Aib0-, for which the fastest intramolecular DET rate was measured,15 our calculations suggest that both Φhel and ΦC7 conformers, having similar energies, may be important in the ET mechanism. Besides the fact that the D/A distance is shorter than for the other peptides, both conformers are characterized by specific hydrogen-bond interactions with the phthalimide pentaatomic ring, where the SOMO and thus the donor charge is localized. These interactions would contribute to increase the overall electronic coupling between the D and A moieties, in line with the expectations based on the multiple pathway model.1b,2,48 As the peptide is made longer, other important issues emerge. Increasing the peptide length stabilizes the SOMO significantly, making anionic species more stable. Figure 7 shows the dependence of adiabatic electron affinities (EA) pertaining to the 310 and pII structures and the phthalimide standard potential (E°)15 on the number of Aib units, n. The computed trend is in good agreement with the electrochemical behavior, the correlation coefficients of the computed EA vs E° plots being, for both structures, r2 ) 0.972, confirming the reliability of the adopted computational strategy and ruling out the possibile involvement of C7 structures in the DET. Our previous experimental study showed that the peroxide dissociative E° is made more negative as soon as the first intramolecular hydrogen bond forms. The peroxide E° shift is negative because the intramolecular H-bonding develops a partial negative charge in proximity of the peroxide group. This is also in line with the significant dipole moment that develops across the axis of the
Electron Transfer in Aib Oligopeptides 310-helix structure (4.5 D per additional residue),14 the negative end of the dipole being oriented toward the peroxide side. Because of these thermodynamic effects, the intramolecular ET process is thus disfavored by the increase of the peptide length. In principle, this should be true also from the point of view of the ET kinetics, as the electronic coupling between the reactant and product states is expected to decrease exponentially with the D/A distance, in agreement with the superexchange mechanism. Even in the framework of the sequential hopping mechanism the rate should slightly decrease. In fact, our calculations indicate that the latter mechanism should be discarded because of the large energy gap between the SOMO and the first bridge orbital; this is an important outcome of the present study. Therefore, the question now is why the ET rate increases on going from Aib1 to Aib3? The analysis of our computational results suggests that the orientation of the donor is liable to influence the intramolecular ET process in different ways. First, the three conformers are characterized by different hydrogen-bond arrangements with respect to the peptide backbone. For Aib1, Aib2, and Aib3, the 310-helix structure, which exhibits a CO(i)-NH(i+3) hydrogen-bond pattern, is the most stable conformation adopted by the peptide; this holds true both for Φhel and ΦpII orientations of the phthalimide group. Interestingly, for Φhel the first amide group is involved in an N(H)-π hydrogen bond with the phthalimide ring (Figure 4), which may provide an extra hydrogen-bond path for the electron tunneling. Although for these peptides ΦC7 is too high in energy, it appears to be an important orientation for the shortest peptide investigated, Aib0. In fact, ΦC7 is characterized by a CO(i)NH(i+2) hydrogen bond that is strengthened by an NH-ring interaction, which is a different hydrogen-bond pattern that sets up before the CO(i)-NH(i+3) hydrogen-bond network starts (for n g 1). A second issue relates to the fact that the orientation of the phthalimide ring may influence the D/A distance more than would be expected (see Table 3). In fact, only for Φhel does the distance between the nitrogen of the phthalimide ring and the first oxygen atom of the peroxy moiety increase regularly with the number of peptide units (Table 3). Furthermore, for a given number of peptide units, the three conformers may exhibit edgeto-edge distances, differing by as much as 1.6 Å. For the three longest peptides, however, even fluctuations between the two most relevant conformers (Φhel and ΦpII) do not seem to be particularly pivotal to understand the peculiar dependence of the ET rate on the peptide chain length exhibited by the compounds under study. This is because the D/A distance of Aib3 is still significantly larger that those displayed by Aib1 and Aib2. So far, we have considered that the most stable conformation adopted by the peptide backbone, the 310-helix, is the only one significantly populated. In the Introduction, we have already stressed that the peptides based on the Aib residue are characterized by their propensity to form rigid 310-helices. This conclusion stems from both experimental results on oligopeptides16 and previous theoretical studies on polypeptides.36,41 We now face a new issue, the fact that the actual species within which the ET takes place is an anion. We have seen how this feature modifies the relative energies and the conformational behavior. One result of our calculations that is particularly novel is that for the first time a minimum associated with the R-helix emerges. This is possible only because of the presence of the odd electron onto the donor end of the peptide. There are two reasons why this new aspect could be very important. First, when the Aib chain adopts the compact R-helix structure the
J. Phys. Chem. B, Vol. 109, No. 2, 2005 1031 D/A distance decreases remarkably, becoming much smaller than it would have been expected for a bridge composed by four peptide units. For example, the D/A distance in ΦpIIAib3(R)is similar to that of ΦhelAib1(310)- (Table 3). In addition, the hydrogen-bond pattern of ΦpIIAib3(R)- seems to provide a particularly suitable route for the ET reaction. The molecule can be viewed as constituted by two parallel moieties, lying at a distance of 5-6 Å and linked by two strong hydrogen bonds (Figure 5). Whereas the first of such moiety is formed by the phthalimide and the first two peptide units, the second one is formed by the last two peptide units and the peroxide group. This arrangement could allow for good overlapping between the orbitals of the donor and the acceptor moieties. It could be meaningful, for example, that the NH bond of the last peptide unit, directly bound to the peroxy group, is only 4.8 Å far from the nitrogen of the phthalimide ring (see Figure 5). The second aspect is related to the results obtained on the possible transitions from the phthalimide SOMO to the peroxide orbital. The results, obtained for a fixed elongation of the O-O bond, indicate that that the transition energy decreases when the peptide chain of Aib3- contracts from the 310- to the R-helix. Noteworthy the latter transition energy is even smaller than the one calculated for the 310-helix of the smaller Aib1- system. The results of the present study thus suggest that the ET could be conformationally gated. Aib3 is indeed the first peptide for which a conformational switch between the 310-helix and the R-helix is possible. This nuclear reorganization would yield a relatively compact structure, exhibiting a particularly favorable hydrogen-bond arrangement. For Aib2-, the other peptide for which such a reorganization could have been possible, the calculations indicate that the R-helix arrangement is not a minimum in the potential energy surface. Concerning peptides longer than Aib3, the influence of the phthalimide terminal of the peptide on the conformational equilibrium should decrease its importance as the peptide chain is made longer. In other words, the new factor introduced by the presence of the negative charge onto the phthalimide would vanish with the distance increase. Eventually, the behavior of the molecular system becomes the same as that typical of a polyAib homo-polypeptide, for which computational results predict that the stability of the 310-helix increases, with respect to the R-helix, as the number of Aib units also increase.36,41 These results, though not definitive, thus support the hypothesis that a conformational transition could be an important factor accounting for the anomalous trend of the ET rates experimentally observed. Although this conclusion requires further experimental and theoretical tests, at the present stage of the research it does not appear unlikely that under very special conditions the R-helix structure could be populated for a time long enough to be relevant for the ET process. These conditions are (i) a specific number of residues and (ii) the presence of a negatively charged moiety (the donor) involved in intramolecular hydrogen bonds characterizing the peptide secondary structure. On the other hand, there is still the possibility that Aib3- could attain a particularly favorable hydrogen-bond arrangement even when the Aib chain adopts a 310-helix conformation, as already suggested.15 A reasonable conclusion, however, is that for these systems the sequential hopping mechanism does not seem to provide an energetically appealing path. Therefore, independently of the conformational issues, the ET mechanism should proceed by the superexchange mechanism. We fail to see the exponential decrease of the rate simply because adding a new R-amino acid unit does not produce a simple distance increase but also modifies significantly the energy of the peptide
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