Dipole and Coulomb Forces in Electron Capture Dissociation and

Article pubs.acs.org/JPCA

Dipole and Coulomb Forces in Electron Capture Dissociation and Electron Transfer Dissociation Mass Spectroscopy ́ Iwona Swierszcz, Piotr Skurski,†,‡ and Jack Simons*,‡ †

Department of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland Chemistry Department and Henry Eyring Center for Theoretical Chemistry, University of Utah, Salt Lake City, Utah 84112, United States

‡

ABSTRACT: Ab initio electronic structure calculations were performed on a doubly charged polypeptide model H+−Lys(Ala)19−CO−CH(NH2)−CH2−SS−CH2−(NH2)CH−CO−(Ala)19− Lys−H+ consisting of a C-terminal protonated Lys followed by a 19-Ala α-helix with a 20th Alalike unit whose side chain is linked by a disulfide bond to a corresponding Ala-like unit connected to a second 19-Ala α-helix terminated by a second C-terminal-protonated Lys. The Coulomb potentials arising from the two charged Lys residues and dipole potentials arising from the two oppositely directed 72 D dipoles of the α-helices act to stabilize the SS bond’s σ* orbital. The Coulomb potentials provide stabilization of 1 eV, while the two large dipoles generate an additional 4 eV. Such stabilization allows the SS σ* orbital to attach an electron and thereby generate disulfide bond cleavage products. Although calculations are performed only on SS bond cleavage, discussion of N− Cα bond cleavage caused by electron attachment to amide π* orbitals is also presented. The magnitudes of the stabilization energies as well as the fact that they arise from Coulomb and dipole potentials are supported by results on a small model system consisting of a H3C-SS-CH3 molecule with positive and negative fractional point charges to its left and right designed to represent (i) two positive charges ca. 32 Å distant (i.e., the two charged Lys sites of the peptide model) and (ii) two 72 D dipoles (i.e., the two α-helices). Earlier workers suggested that internal dipole forces in polypeptides could act to guide incoming free electrons (i.e., in electron capture dissociation (ECD)) toward the positive end of the dipole and thus affect the branching ratios for cleaving various bonds. Those workers argued that, because of the huge mass difference between an anion donor and a free electron, internal dipole forces would have a far smaller influence over the trajectory of a donor (i.e., in electron transfer dissociation (ETD)). The present findings suggest that, in addition to their effects on guiding electron or donor trajectories, dipole potentials (in combination with Coulomb potentials) also alter the energies of SS σ* and amide π* orbitals, which then affects the ability of these orbitals to bind an electron. Thus, both by trajectory-guiding and by orbital energy stabilization, Coulomb and dipole potentials can have significant influences on the branching ratios of ECD and ETC in which disulfide or N−Cα bonds are cleaved.

I. INTRODUCTION The mechanisms by which an excess electron, either from an anion donor in electron-transfer dissociation1−5 (ETD) or as a free electron as in electron-capture dissociation6−9 (ECD), attaches to a multiply positively charged gas-phase peptide and induces bond cleavages within the charge-reduced peptide have been the focus of much of our recent research.10 The central issues in these studies include: 1 Identifying where in the peptide (and into what kind of orbital and with what cross-section) the excess electron is initially bound 2 Characterizing to where, over what distances, and at what rates the electron may subsequently migrate within the peptide 3 Understanding how the excess electron’s presence causes specific bonds (e.g., disulfide and backbone N−Cα bonds are found to preferentially break) to be cleaved and with what intensities. ECD and ETD are relatively new yet extremely promising analytical techniques that are found to generate significantly higher backbone cleavage fractions than collisional or infrared © 2012 American Chemical Society

activation techniques, while doing so with great specificity (i.e., in peptides, primarily N−Cα and S−S bonds are cleaved). Why these bonds cleave and why they do throughout such a large fraction of the backbone need to be explained, and this is the focus of much of the theoretical work in this area. A. The Utah Washington (UW) Mechanism. As a result of our earlier studies and those of the Turecek and other groups,11−39 one mechanistic picture has evolved within which it is the attachment of an electron to an amide π* or disulfide σ* orbital that causes the N−Cα or SS bond cleavage. The amide π* or disulfide σ* orbitals that are “amenable” to electron attachment are determined by the local intramolecular electrostatic potentials stabilizing the orbitals (if the potential is not strong enough, electron attachment cannot occur). In addition to contributing to the electrostatic potential within the peptide, the positive sites within the charged peptide provide Rydberg orbitials that act as antennas to initially attach the Received: November 13, 2011 Revised: January 25, 2012 Published: January 26, 2012 1828

dx.doi.org/10.1021/jp210915c | J. Phys. Chem. A 2012, 116, 1828−1837

The Journal of Physical Chemistry A

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either the enolimine or the more stable amide. (It is possible that the proton is abstracted prior to cleavage of the N−Cα bond, in which case formation of the enolimine would be favored. Some experimental infrared spectroscopic evidence exists34 providing evidence that the amide is formed, but this is not conclusive support proving that the proton is transferred after N−Cα bond cleavage, because the enolimine, if formed first, could subsequently rearrange to the thermodynamically more stable amide.) The proton can be abstracted either from the N-terminal or C-terminal direction (likely from the most proximal site of low proton affinity). B. Coulomb Stabilization Energy. As noted above, the UW mechanistic model requires the SS σ* or amide π* orbital to have an electron binding energy BE* that exceeds that of the Rydberg orbital (BERydberg) from which the electron is transferred. As stated20 in our initial 2003 work on this subject, it is endothermic to vertically attach a free electron into an SS σ* orbital. Electron transmission experiments have been interpreted to mean that vertical electron attachment into SS σ* or amide π* orbitals is ca. 1 or 2.0−2.5 eV endothermic,40 respectively, in the absence of any influence that would act to differentially stabilize the electron-attached species. So, how then do SS σ* or amide π* orbitals become capable of extracting an electron from a Rydberg orbital in the charge-reduce peptide? In our 2003 paper on this subject,20 we suggested that the Coulomb potential C

electron and subsequently serve to transfer the electron to amenable amide π* or disulfide σ* orbitals over distances determined by the radial sizes of the Rydberg orbitals. The N−Cα and SS bond cleavage processes are viewed in the UW model as taking place as follows: 1 In both ECD and ETD, the electron most likely first attaches to a Rydberg orbital localized on a positively charged site (e.g., a protonated side chain) of the parent peptide. 2 Energy conservation and Landau−Zener estimates of the electron attachment cross sections suggest that the accessible Rydberg principal quantum numbers (n) are limited to n = 3 and 4 in ETD (we assume a value for the electron binding energy BEDonor of 0.6 eV (i.e., that of the commonly used fluoranthene anion) to characterize ETD, and a value of 0.0 eV is used to characterize the free electron used in ECD) and n = 3, 4, 5, and 6 in ECD, with approximately equal populations entering each Rydberg level. 3 An excess electron captured into such a Rydberg orbital can subsequently undergo prompt (i.e., faster than relaxation within the Rydberg orbital manifold) intramolecular electron transfer to any SS σ* or amide π* orbital that lies within a radial “shell” of average size ⟨r⟩ and width T that characterizes each Rydberg orbital and has an electron binding energy sufficient to overcome the electron binding energy of that Rydberg orbital. 4 Once the electron enters an SS σ* orbital, cleavage of the associated disulfide bond is prompt because the σ2σ*1 anionic electronic state is repulsive. If the electron enters an amide π* orbital, cleavage of the associated N−Cα bond can occur by surmounting a thermally accessible barrier that is much smaller than the barrier needed to homolytically cleave this N−Cα bond in the absence of the excess electron. The route by which such N−Cα cleavage is thought to occur is shown in Scheme 1

M

C=

∑ J=1

14.4 eV RJ(Å)

(1)

produced by the M positively charged sites within the peptide at distances RJ from an SS σ* or amide π* orbital act to differentially stabilize an SS σ* electron-attached state, thus rendering electron attachment exothermic if C is large enough. At essentially the same time in 2005, Turecek16 and we23 extended this Coulomb stabilization concept to amide π* orbitals. As a result, within the UW model, one has to have C > 1 eV + BERydberg

Scheme 1

(2)

(where BERydberg is the binding energy of the Rydberg orbital from which the electron transfers) for an SS σ* orbital or C > 2.0−2.5 eV + BERydberg

(3)

for an amide π* orbital. It is this condition on the Coulomb stabilization energy that is refined in the present work.

II. PRINCIPLES UNDERLING THE UW MODEL OF ELECTRON ATTACHMENT AND ELECTRON TRANSFER A. Crossing of Energy Surfaces. At certain critical donor anion (or electron)−peptide distances Rcrossing, the energy of the anion−peptide collision pair matches the energy of the system after the electron has attached to a Rydberg orbital of the peptide. In the Landau−Zener model, it is at such distances the electron trasfer can most efficiently take place. If the crossings occur at large enough distances, the interaction of the anion with the peptide’s dipole and polarization potentials can be neglected compared to the anion−peptide Coulomb potential in which case we can estimate the crossing distances41

After the electron attaches to the amide π* orbital, the N−Cα bond is weakened because cleaving it allows a new C−N π bond to form; this is why the barrier to cleavage is reduced. The −O−CNH anion site can abstract a proton to form

R crossing = 1829

14.4 eV Å (BERydberg − BEdonor) eV

(4)



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B. Overlap Within Rydberg Orbitals’ Shells. For the electron attachment rate to be high, it is also important for the electronic coupling matrix element H1,2 between the two crossing states to be substantial. In Figure 1, we show a qualitative plot of

conclude that ETD populates n = 3 and 4 Rydberg orbitals, while ECD populates n = 3 through n = 6, and all with similar probabilities. D. Intramolecular Electron Transfer Distances and Fragment Ion Abundances. Also in earlier efforts,10 we found the rate of electron transfer from n = 3 Rydberg orbitals into SS σ* or amide π* orbitals lying within this orbital’s 3−7 Å radial shell to be ca. 1012 s−1. Moreover, we showed the rates for electron transfer from n = 4, 5, and 6 Rydberg orbitals into SS σ* or amide π* orbitals lying within those orbitals’ radial shells to be 20, 7, and 3% that of the n = 3 rate, all of which are considerably faster than the rates of relaxation from one Rydberg level to another. Therefore, in ETD, the n = 3 and n = 4 Rydberg orbitals promptly transport electrons to amide π* or disulfide σ* orbitals over distances of 3 to 12 Å (see Table I). In ECD, the n = 3 through n = 6 Rydberg orbitals promptly transfer electrons over 3 to ca. 25 Å. These observations suggest that the intensities of fragment ions formed in ECD and ETD should mimic the radial charge distributions of n = 3 and n = 4 Rydberg orbitals located on charged sites for ETD and the charge distributions of n = 3 through n = 6 orbitals for ECD. Because the accepting SS σ* and amide π* orbitals are much smaller than the very diffuse 2 of the coupling matrix element Rydberg orbitals, the square H1,2 governing the rates of electron transfer is proportional to the probability density (i.e., electron density per unit volume) of the Rydberg orbital within the volume of the accepting orbital. All of the Rydberg orbitals ψ are normalized (i.e., the integral ∫ ψ*ψr2 sin θ dr dθ dϕ is unity), and the n = 3 and n = 4 have relatively high densities within their respective “ranges” of 3−7 Å and 6− 12 Å. In contrast, the n = 5 and n = 6 orbitals have significantly lower densities within their (larger) 10−18 and 14−26 Å ranges. Thus, even in ECD, we expect a higher density of cleavage (i.e., cleavage per unit length along the backbone) within 3−12 Å of positive sites and lower density in the 10−26 Å range. E. An Example of Applying the UW Concepts. Let us now consider an example to illustrate how these concepts are applied and to show why there may be more to consider than just the Coulomb potential. In Figure 2, we show a doubly

Figure 1. Depiction of a 3s Rydberg orbital showing its large outermost radial “shell” whose size is characterized by and whose thickness is characterized by T.

the radial probability density for a 3s Rydberg orbital42 of a highly symmetric charged species such as NH4+ or MeNH3+. This orbital is characterized by the distance ⟨r⟩ = 0.529n (n+1/2) Å at which its primary maximum occurs and by the width or thickness T = ([⟨r2⟩ − ⟨r⟩2)1/2 = 0.529n(((n+(1/2))/2)Å)1/2. Each positive site within a multiply positively charged peptide possesses a series of Rydberg orbitals each characterized by a principal quantum number (and thus a radial size and thickness) and an approximate angular shape (i.e., s-, p-, d-, etc.). Our model assumes that efficient electron attachment can occur only when the crossing distance RCrossing (eq 4) lies within a radial “shell” ⟨r⟩ ± T/2 characterizing that Rydberg state. Only at such distances is the coupling matrix element H1,2 expected to be substantial, and only at such distances is the energy degeneracy condition simultaneously met. C. Limitations on Rydberg Orbitals’ Principal Quantum Number. In Table I, the Rydberg orbitals’ ranges and Table I. Rydberg Orbitals’ Ranges, Electron Binding Energies, and Crossing Distances for Principal Quantum Numbers Ranging from 3 through 6 principal quantum number n 3 4 5 6 a

orbital range ⟨r⟩ ± T/2 (Å)

BERydberg (eV)

Rcrossing (Å) for free electron

Rcrossing (Å) for BEDonor = 0.6 eV

± ± ± ±

3.5−4 1.5−2 0.75−1 36 not possiblea

5 9 14 20

2 3 4 6

Figure 2. The (AcCAjK+H)22+ polypeptide (for j = 15) showing the two protonated Lys C-termini, the two α-helices, and the bridging disulfide linkage.

charged polypeptide (AcCAjK+H)22+ containing 15 Ala units, a disulfide bond, and two C-terminal protonated Lys units. When j = 15, the distance from the Lys termini to the disulfide linkage43 is ca. 24 Å; for j = 10 or 20, the distances are 18 or 32 Å, respectively. When such doubly charged peptides were subjected to ECD analysis for j = 10, 15, and 20, abundant fragmentation was observed44,45 at the central SS bond, as well as at C-terminal N−Cα bonds belonging to the four Ala units closest to the Lys termini (these are indicated by the black lines in Figure 2). The Coulomb stabilizing potential near the SS bond can be estimated in terms of the distances to the two Lys termini to be

BEDonor exceeds BERydberg, so the electron transfer cannot occur.

binding energies are displayed for n ranging from 3 through 6. Also shown are values of Rcrossing associated with BEDonor of 0.6 and 0 eV representing ETD and ECD, respectively. For ECD, Rcrossing lies within ⟨r⟩ ± T/2 for n ranging from 3 to 6, while for ETD, Rcrossing lies within ⟨r⟩ ± T/2 only for n = 3 and 4. Our earlier work10 showed that the cross sections for forming n = 3 through n = 6, were nearly equal, leading us to 1830



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ca. 2 × 14.4 eV Å/24 Å ≈ 1.2 eV, which is just enough to render exothermic attachment of a free electron to the SS σ* orbital. The Ala unit four amino acids from the Lys terminus is ca. 6.5 Å from that terminus, so it experiences a Coulomb potential of ca. 14.4/6.5 ≈ 2.2 eV,46 just about enough to render exothermic attachment of a free electron to its amide π* orbital. Moreover, the four Ala units nearest the C-termini and the disulfide bond all lie within the ranges of the n = 3 through n = 6 Rydberg orbitals predicted to transfer electrons in ECD. F. A Puzzle Arising in This Application. At first glance, the Coulomb stabilization concept of the UW mechanism seems to be in line with which bonds are observed to cleave under ECD. However, the SS σ* and four C-terminal amide π* orbitals discussed above would have to be sufficiently stabilized to also overcome the electron binding energy of the Rydberg orbital from which the electron transfers, and the estimates given above and the BERydberg values shown in Table I do not suggest this to be the case. One is thus left to wonder whether in the ECD experiments there are additional internal potentials acting to further stabilize the SS σ* and amide π* attached states. G. An Earlier Suggestion that Dipole Forces Need to be Considered. It is important to make it clear that the idea of internal dipole potentials playing roles in ETD and ECD was suggested earlier by others. In recent work on doubly protonated phosphorylated pentapeptides pSAAAR, ApSAAR, AApSAR, and AAApSR, assumed to be charged at the Nterminal amine and the C-terminal arginine side chain, the Turecek and Brøndsted-Nielsen groups47,48 obtained peptide fragment distributions under ETD, ECD, and electron-capture induced dissociation (ECID).49 They interpreted the distribution of fragment ions in terms of internal dipole forces acting to “guide” ECD’s free electron toward the positive end of the parent peptide’s dipole (i.e., toward the arginine50). Specifically, the distribution of fragment ions they observed (i.e., very similar distributions in ECID and ETD but different in ECD) suggested to them that in ECID, where the peptide extracts an electron from a neutral atom, the internal dipole potential has little effect on the trajectory of the peptide−atom collision pair. The data also suggested that in ETD the dipole potential acts on the incoming anion donor but has little influence on the anion’s trajectory because of the donor’s large mass, whereas in ECD, the peptide’s dipole potential has a strong influence on the electron’s trajectory. This acts to “guide” it preferentially toward the positive end of the dipole (where it then is attached to a Rydberg orbital on the arginine, which is closest to the dipole’s positive end). In the ECD experiments, those workers observed fragment ions consistent with increased capture at the arginine site compared to what was found in ETD and ECID. H. Our Proposal that Dipole Potentials Also Act to Stabilize Orbitals. In the present work, we extend the ideas of Turecek and Brøndsted-Nielsen to suggest that internal dipole potentials D not only may guide a free electron toward the positive end of the parent’s dipole but may also contribute to the stabilization of the energies of SS σ* or amide π* orbitals thus affecting these orbitals’ propensity for extracting an electron from a Rydberg orbital. Specifically, we suggest that exothermic electron transfer to such an orbital from a Rydberg orbital can occur if one has C + D > 1 eV + BERydberg

(where BERydberg is the binding energy of the Rydberg orbital from which the electron transfers) for an SS σ* orbital or C + D > 2−2.5 eV + BERydberg

(6)

for transfer to an amide π* orbital. Our approach to addressing the roles of Coulomb and dipole forces involves: (a) Carrying out ab initio calculations of the energy profiles for cleaving the central SS bond on a model of the full (AcCA20K+H)22+ peptide with and without an excess electron attached to the SS σ* orbital and b Carrying out ab initio calculations of analogous energy profiles on a very small model system consisting of a single MeSSMe molecule in the presence of two positive charges located ca. 32 Å from each S atom to simulate the Coulomb potential of the C-terminal Lys groups in (AcCA20K+H)22+ and fractional positive and negative charges positioned to simulate the dipole potential of the two α-helices in (AcCA20K+H)22+. To model the (AcCAjK+H)22+ species studied earlier in experiments,44,45 we employed H+−Lys(Ala)19−CO−CH(NH2)−CH2−SS−CH2−(NH2)CH−CO−(Ala)19−Lys−H+, a protonated Lys followed by 19 Ala residues with a 20th Ala-like unit having its side chain linked by a disulfide bond to the corresponding unit of a second identical α-helix terminated by a second protonated Lys. We refer to this system as (H-LysAla20S)22+. The two α-helices of this system produce large but opposing dipole moments (each with the negative end of the dipole near the C-terminal protonated Lys and the positive end near the N-terminus). The kind of ECD electron guiding postulated in ref 47 could be expected to have no influence on an incoming electron at very large distances because of the vanishing total dipole moment. However, once the electron reaches distances similar to the length of the α-helices, it could be directed toward the positive ends of the two opposing dipoles. As a result, the dipole forces could enhance the flux of electrons that collide near the SS bond thus increasing the fraction of events in which the electron is initially captured into an SS σ* orbital if direct capture into an SS σ* orbital were possible. However, this is not what we are studying here; we are examining to what extent the internal dipole potentials stabilize the SS σ*-attached state perhaps to an extent that allows this state to extract an electron that has initially been bound to a Rydberg orbital on one of the protonated Lys sites. That is, can the dipole potential stabilize the SS σ* orbital more than the ca. 1 eV provided by the Coulomb potential in (H-LysAla20-S)22+?

III. CALCULATIONAL METHODS The geometry optimization of the (H-LysAla20-S)22+ peptide was undertaken using the PM6 semiempirical method.51,52 The resulting optimized structure, is similar to that found earlier by Hudgins et al44 for (AcCA15K+H)22+ and by Hudgins and Jarrold53 for AcAnLysH + for n > 6 and for noncovalently linked (AcA19LysH)22+ (see Figure 8 in ref 53) in that it has α-helical Ala units and its C-terminal protonated Lys units bend backward to allow hydrogen bonding with nearby Ala CO groups. The optimized structure was used to perform a nonrelaxed scan of the energy associated with cleaving the S−S bond, within the two-layer ONIOM approach.54−56 In particular, the parent (H-LysAla20-S)22+ and charge-reduced (H-LysAla20-S)2+ species were divided into two layers treated with different model chemistries. The high layer containing the

(5) 1831



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The α-helical nature of the Ala19 moieties is clear, and the distances from each Lys to nearby Ala units and to the SS bond are as discussed earlier in this paper. By use of the ONIOM approach described earlier, we calculated the energy profiles for elongating the SS bond in this peptide model both in the absence of the attached excess electron and with the excess electron occupying the SS σ* orbital. In Figure 4, we display these energy profiles and we

central disulfide bridge with its neighboring methylene groups (−CH2−S−S−CH2−) was treated with the quadratic CI method including single and double substitutions (QCISD)57 using the 6-311G(d,p) basis set,58,59 whereas the low layer (containing the remaining atoms) was described with the Hartree−Fock (HF) method using the 4−31G basis set.60−64 For the calculations on the small model, the CH3−S−S−CH3 and (CH3−S−S−CH3)− species (in the presence of four +1/2 point charges65) were treated within the QCISD/6-311G(d,p) approach. The stabilizing positive point charges were located in two pairs at both disulfide bridge termini (see section IV for details). The internal distance between the charges constituting each pair was 32 Å, whereas the separations (s) between the +1/2 charge and its nearest sulfur atom were varied. In particular, the S−S bond energy profiles were obtained independently for the following separations: s = 2.500, 2.784, 2.808, 3.006, and 3.523 Å (the distances considered represent the nearest S−N and S−C separations as derived from the full geometry optimization of the (H-LysAla20-S)22+ model system). All calculations were performed with the Gaussian09 program.66

IV. RESULTS In Figure 3 we show two views of the geometry-optimized structure for the peptide model (H-LysAla20-S)22+ as well as the ground (3s) Rydberg orbital on one of the Lys termini. Figure 4. Variation in energy of the parent peptide (black squares) and of the SS σ*-attached species (red squares) as functions of the SS bond length in Å (with all other internal coordinates frozen at their values in the geometry-optimized parent). In the upper panel is shown the VDE as a function of this same bond length.

show how the energy difference (i.e., the vertical detachment energy, VDE) between the parent and electron-attached species varies with the SS bond length. Clearly, at the equilibrium SS bond length in the parent near 2 Å, electron attachment into the SS σ* orbital is exothermic by ca. 4 eV, but at very large distances, when the SS bond is fully cleaved, the VDE is ca. 6 eV. These results are quite surprising given the earlier discussion in which we pointed out that in the absence of stabilizing effects, vertical attachment of an electron to an SS σ* orbital is expected to be endothermic by ca. 1 eV, although the Coulomb stabilization from the two positively charged Lys termini ca. 32 Å distant should be ca. 1 eV. That is, electron attachment to the SS σ* orbital in the presence of two protonated Lys units is expected to be nearly thermoneutral, not exothermic by 4 eV. If attachment of an electron to the SS σ* orbital is exothermic by 4 eV, this orbital could easily extract an electron from an n = 6 Rydberg orbital on either of the Lys termini, thus possibly explaining the large abundance of SS bond cleavage found when (AcCAjK+H)22+ (j = 10, 15, 20) is subjected to ECD. The high abundance of SS cleavage compared to N−Cα cleaveage could be related to the fact that SS bond cleavage is prompt, whereas N−Cα cleaveage requires surmounting a barrier. However, we are left wondering what causes the SS σ*attached state to be stabilized to such an extent. The Coulomb potential alone produces only ca. 1 eV of stabilization at the equilibrium SS bond length. Where does the remaining 4 eV come from? Following the dipole-guiding suggestion put forth by Turecek and Brøndsted-Nielsen,47 we postulate that it is the

Figure 3. Geometry-optimized structure of doubly charged (HLysAla20-S)22+also showing the ground 3s Rydberg orbital on one protonated Lys (left); close up view of top half of the structure showing the C-terminal Lys hydrogen bonded to a CO oxygen atom. 1832



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one negative charge of magnitude 1/2 near its carboxyl site and another of opposite charge near its amino site. In Figure 6, we

internal dipole potential that generates the additional stabilization of the SS σ*-attached state. As discussed by Hudgins and Jarrold,67 an α-helix structure produces a dipole potential equivalent to 3.5 D per 1.5 Å distance along the helix backbone. Such a dipole can be approximated by placing a negative half elementary charge at the carboxyl end and a positive half elementary charge at the amino end of each amino acid within the helix. As noted by Berendsen, et al.,67 this is equivalent to placing half elementary charges, of opposite signs, at the either ends of the full α-helix. For the (H-LysAla20-S)22+species examined here, this results in two oppositely directed dipole moments each of magnitude 72 D with each dipole consisting of one +1/2 charge separated by ca. 32 Å from a −1/2 charge (near a Lys terminus). To further explore the hypothesis that it is the internal dipole potential that is strongly stabilizing the SS σ*-attached state, as discussed in section III, we carried out a series of calculations on a small model system consisting of a MeSSMe molecule with two +1/2 charges, positioned 32 Å to the left and 32 Å to the right of the left and right S atoms (each representing the combination of a protonated Lys temini and a −1/2 charge on the carboxyl unit of the adjacent amino acid), as well as two +1/2 charges, one placed near each of two S atoms (representing the +1/2 charges on the amino end of the nearest amino acid). This combination of four charges placed as described is designed to generate a potential representative of (i) two positively charged Lys termini and (ii) two oppositely directed 72 D dipoles arising from the Ala α-helices. A few reasonable locations for the +1/2 charges closest to the S atoms were chosen from the optimized structure of the parent doubly charged peptide, a closeup of a portion of which is shown in Figure 5.

Figure 6. Plots of the parent (black) and SS σ*-attached (red) model species with the two +1/2 charges located on atoms C5 (top), N3 (center), and N4 (bottom). Also shown are plots of the vertical electron detachment energies at each SS bond length.

show the energies of the parent and SS σ*-attached species as functions of the SS bond length for these three choices for the location of the +1/2 charges near the S atoms. Not surprisingly, the energy profiles for the parent species shown in Figure 6 are essentially identical, regardless of where the two +1/2 charges nearest the S atoms are placed in forming the two 72 D dipoles. The energy profiles of the SS σ*-attached states all have identical shapes but are shifted in energy depending on where the two +1/2 charges are placed; the closer the +1/2 charges to the S atoms, the greater is the differential stabilization of the SS σ*-attached states, as expected. The closest agreement between the results on this model system and the ab initio ONIOM calculations on the full (H-LysAla20-S)22+ shown in Figure 4 is obtained when the two +1/2 charges are

Figure 5. Closeup of (H-LysAla20-S)22+ showing the region close to the disulfide linkage and giving selected interatomic distances.

Specifically, we carried out calculations with the +1/2 charge closest to S2 located on the atoms labeled C5, N3, or N4 in Figure 5 to obtain energy profiles analogous to those shown in Figure 4. These three locations were explored based on the assumption that each Ala residue can be represented in terms of 1833



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l, as it is when the excess electron is localized in the SS σ* orbital, the terms in the above sum corresponding to low j (i.e., arising from residues closer σ* orbital) contribute more than those having large j. The summation over dipole potentials given in the above expression for V can be approximated as an integral by introducing the variable x = jR/N; as j runs from 0 to N − 1, x varies from 0 to R (1−1/N)

placed on C5, but locating these charges on N3 also gives good agreement. We conclude from comparing the results in Figure 6 on this model system to the ab initio results in Figure 4 on the full (H-LysAla20-S)22+ peptide that the combination of Coulomb potentials arising from the two protonated Lys residues and potentials from the two oppositely directed internal dipoles of ca. 72 D are likely the origin of the substantial differential stabilization of the SS σ* orbital (1 eV from the Coulomb and 4 eV from the dipole potentials). However, there are important differences between how the dipole potentials guide ECD electrons (as posited in ref 47) and how they differentially stabilize SS σ* or amide π*-attached states. As we now illustrate, in terms of electron guiding, it is appropriate to think of the ECD electron as interacting with two 72 D macrodipoles, whereas when considering stabilization, it is better to think of the attached electron interacting with two quasilinear arrays each containing twenty 3.6 D dipoles. An electron very far (e.g., an “incoming” ECD electron much further from the peptide than the length R of the chain) from such a quasilinear polypeptide would experience a dipole potential proportional to D/r2, where D is the total dipole moment of the chain and r is the distance of the electron to the midpoint of the chain where the dipole is centered. At such distances, the electron would experience the same potential regardless of whether the dipole consisted of twenty dipoles each of size 3.6 D or one large dipole of magnitude 72 D. However, when an electron resides close to the positive end of the dipole, the potential it experiences is dominated by contributions from the more proximal residue-based dipoles. To illustrate, consider an electron residing a distance r to the left of the leftmost positive fractional charge along a linear chain of N alternating +1/2 and −1/2 charges. The potential experienced by this electron is the sum of its Coulombic interactions with each of the 2N fractional charges ⎫ ⎪ q ⎪ q ⎬ V= ∑ ⎨ − R R ⎪ r + j + l⎪ j=0 ⎩ r + j N ⎭ N

⎫ ⎧ ⎪ ⎪ N ⎪ ql ⎬≈ ∑ ⎨ 2 R ⎪ ⎪ R j=0 ⎪ r + j ⎪ ⎭ ⎩ N

N−1 ⎪

(

(

)

⎫ ⎪ ⎬ ⎪ ⎭

(10)

For values of r much larger than R, this expression reduces to V≈

Nql ⎛ 1 ⎞⎟ ⎜1 − 2 ⎝ ⎠ N r

(11)

which is of the dipole form and reflects a total dipole moment of Nql. For r ≪ R, which is more appropriate when the excess electron resides in the SS σ* orbital, the expression reduces to

V≈

Nql Rr

(12)

which is a Coulomb interaction (since Nl is of the order of R) with a fractional charge q a distance r away. The above analysis shows that it is not the macrodipole moment of the α-helices that plays the key role in producing the 4 eV additional stabilization of the SS σ*-attached state. It is more so the interaction of the electron with the dipoles of the proximal Ala units. This is why the agreement between the ab initio energy profile for (H-LysAla20-S)22+ (Figure 4) and for our model system MeSSMe (Figures 6) depends upon where the +1/2 charge is placed on the closest Ala unit. Thus, although dipole forces contribute both to ECD electron guiding and attached-electron stabilization, it is the macrodipole that acts in the former case while more proximal dipoles are more important in the latter. To make the application of these ideas to the system at hand more concrete, consider two different ways of evaluating the interaction of an electron residing at the midpoint of the SS bond with a dipole of magnitude 72 D located to the right of the SS bond. First, we calculate the interaction as

(7)

where q is the magnitude of each fractional charge ( /2 in our case), R/N is the distance between each residue, and l is the distance between pairs of partial charges (1.5 Å in our case) within a residue. Writing r + j(R/N) + l as [r + j(R/N)]{1 + (l/ (r + j(R/N))} and expanding {1 + (l/(r + j(R/N))}in powers of l/(r + j(R/N)) allows V to be rewritten as ⎡ ⎤⎫ ⎪ q ⎥⎪ q ⎢ l V= ∑ ⎨ − + ...⎥⎬ ⎢1 − R R R r + j ⎢⎣ r+j ⎥⎦⎪ j=0 ⎪ ⎩ r + jN ⎭ N N N−1 ⎧

N−1 ⎪

)

(9)

⎧ N ⎪1 1 V ≈ ql ⎨ − 1 R ⎪r r+R 1− ⎩ N

1

(

∫

where dx = R/N dj has been used (with dj = unity). This integral can be carried out and produces the following approximation to the potential V

N−1 ⎧

⎫ ⎧ ⎪ ⎪ ⎪ ql ⎬ = ∑ ⎨ + ... 2 ⎪ R j=0 ⎪ ⎪ ⎪ r+j ⎭ ⎩ N

)

x = R(1 − 1 ) ql dx N x=0 (r + x)2

μe r (8)

2

=

3.00μDebyes 2 rÅ

(eV) =

3.00x 72 162

= 0.84 eV (13)

which is the interaction of a dipole of magnitude 72 D located at the midpoint of the 32 Å long α-helix. Based on this estimate, we expect an electron occupying an SS σ* orbital to experience a stabilization of 1 eV from the two protonated Lys units plus 1.68 eV from the two 72 D dipoles, for a total of 2.68 eV. This is substantially less than the total stabilization of ca. 5 eV reflected in the VDE data of Figures 4 and 6.

This shows how V can be viewed in terms of N dipole potentials, each of magnitude ql, with the jth dipole located a distance r + jR/N from the electron. When r greatly exceeds R, all N terms in the above sum are approximately equal to ql/r2 and add up to Nql/r2, the interaction with a macrodipole of magnitude Nql. However, when r is comparable to R/N and to 1834



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Now, let us compute the interaction of an electron residing at the midpoint of the SS bond (whose length is ca. 2 Å) with the 20 individual dipoles lying on one side of the SS bond. We place one charge of magnitude +1/2 on the atom labeled C5 in Figure 5, which locates it 2.5 Å from the nearest S atom and thus 3.5 Å from the midpoint of the SS bond. We then place the corresponding −1/2 charge 5.0 Å from the midpoint (i.e., 1.5 Å from the +1/2 charge) to form the first dipole. The second dipole has its two fractional charges located at 5.0 and 6.5 Å, the third dipole’s charges are at 6.5 and 8.0 Å, and so on until the 20th dipole whose charges are at 30.5 and 32 Å. Within this picture, the interaction energy (in eV) is calculated as 1 2

− 14.4 3.5

1 1 1 1 1 14.4 − 14.4 14.4 − 14.4 14.4 2 2 2 2 + + + + ... + + 2

5.0

5.0

6.5

30.5

32

= −2.06 + 1.44 − 1.44 + 1.11 − 1.11 + ... + 0.23 = − 1.73 eV

(14)

This estimate predicts a total (i.e., from the two dipoles on either side of the SS bond) dipole stabilization of 3.46 eV, significantly closer to the ca. 4 eV value inferred from our ab initio calculations (i.e., 5 eV minus ca. 1 eV from the Coulomb interaction with the two Lys sites) and much larger than the 1.68 eV estimate obtained from our first estimate. This shows why it is best to think of the stabilization of an electron occupying an SS σ* or amide π* orbital in terms of its interactions with a multitude of nearby local dipoles belonging to the individual residues.

V. SUMMARY Our ab initio calculations on H+−Lys(Ala)19−CO−CH(NH 2)−CH2 −SS−CH2 −(NH2)CH−CO−(Ala)19−Lys−H+ show a total stabilization of the SS σ*-attached charge-reduced species of ca. 5 eV at the equilibrium SS bond length. Approximately 1 eV of this stabilization arises from the Coulomb potentials on the two C-terminal protonated Lys sites that are ca. 32 Å distant. The remaining 4 eV arises from the internal dipole potentials on the Ala sites within each of the two oppositely directed α-helices. This interpretation is supported by results on a small model system MeSSMe with fractional charges located at sites representative of two protonated Lys units and of the positive ends of the two most proximal Ala units. These results may explain why ECD of (AcCAjK+H)22+ produces substantial SS bond cleavage even though the Coulomb stabilization at the SS bond site of ca. 1 eV is not enough to allow the electron to be extracted from the n = 6 Rydberg orbital on the C-terminal Lys. It is the larger dipole potential that stabilizes the SS σ* orbital enough to allow it to extract the electron. Analysis of the internal dipole potential’s functional form suggests that, although a polypeptide’s macrodipole potential plays a key role in guiding an incoming ECD electron, it is the individual dipole potentials of the surrounding amino acid residues that are most important in differentially stabilizing SS σ* or amide π* orbitals. We believe the results of the present effort contribute significantly to the on going fleshing out of the UW mechanism. In closing, it may prove fruitful to suggest further experiments that could help to test the Coulomb and dipole stabilization concepts suggested here: 1 It would be interesting to perform ECD on a polypeptide of the form MeSS-Ala19-LysLys consisting of two protonated Lys residues connected to the C-terminus of an

■

α-helix of Ala units whose N-terminal side chain is connected to −SSMe. The two charged Lys sites, each ca. 32 Å from the SS bond, would stabilize the SS σ* orbital by ca. 1 eV, while the 72 D dipole from the single α-helix should provide further stabilization of ca. 2 eV. So, one would expect to see substantial SS bond cleavage in this case. Moreover, the two positive Lys sites would provide strong Coulomb stabilization to the amide π* orbitals on the Ala sites closest to these charges. Keeping in mind that an amide π* orbital requires ca. 2−2.5 eV of stabilization to allow it to bind an electron (and even more to extract the electron from a Rydberg orbital), this means the π* orbital has to be within ca. 2 × 14.4/(2 to 2.5) ≈ 11−14 Å of the charged Lys sites (even closer to allow the site to extract an electron from the Rydberg orbital). In other words, one would expect N−Cα cleavage within the Ala helix but only for those Ala units within ca. 11−14 Å of the closest Lys. 2 One should perform ETD on the polypeptide (AcCAjK +H)22+ studied in ref 44 to test the hypothesis that in ETD only n = 3 and n = 4 Rydberg orbitals play a role in attaching the electron. In such an experiment, our model would predict that the four C-terminal Ala units could still receive an electron from an n = 3 or n = 4 Rydberg orbital on one of the protonated Lys sites, so cleavage of the corresponding N−Cα bonds should still occur. However, because n = 5 and n = 6 Rydberg orbitals should not be populated, there should be no cleavage of the SS bond; its distance of 24 Å or 32 Å for the j = 15 or j = 20 species, respectively, lies well outside the ranges of the n = 3 and n = 4 orbitals that would be populated.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work has been supported by NSF Grant No. 0806160 to J.S. and NCN Grant No. DS/8371-4-0137-1 to P.S. Computer resources from the Center for High Performance Computing at the University of Utah are also acknowledged. J.S. and P.S. would like to dedicate this paper to our friend and colleague, Prof. A. I. Boldyrev, to commemorate his 60th birthday.

■

REFERENCES

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Dipole and Coulomb Forces in Electron Capture Dissociation and

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