Secondary structure of Ac-Ala n -LysH + polyalanine peptides ( n =5,10,15) in vacuo: Helical or not?
M. Rossi, V. Blum, P. Kupser, G. von Helden, F. Bierau, K. Pagel, G. Meijer, M. Scheffler
SSecondary structure of Ac-Ala n -LysH + polyalanine peptides ( n =5,10,15) in vacuo:Helical or not? M. Rossi , V. Blum , P. Kupser , G. von Helden , F. Bierau , K. Pagel , ∗ , G. Meijer , and M. Scheffler Fritz-Haber-Institut der Max-Planck-Gesellschaft, D-14195, Berlin, Germany and Freie Universit¨at Berlin, Institut f¨ur Chemie und Biochemie,Takustr. 3, 14195 Berlin, Germany ∗ The polyalanine-based peptide series Ac-Ala n -LysH + ( n =5-20) is a prime example that a sec-ondary structure motif which is well-known from the solution phase (here: helices) can be formed invacuo . We here revisit this conclusion for n =5,10,15, using density-functional theory (van der Waalscorrected generalized gradient approximation), and gas-phase infrared vibrational spectroscopy. Forthe longer molecules ( n =10,15) α -helical models provide good qualitative agreement (theory vs. ex-periment) already in the harmonic approximation. For n =5, the lowest energy conformer is not asimple helix, but competes closely with α -helical motifs at 300 K. Close agreement between infraredspectra from experiment and ab initio molecular dynamics (including anharmonic effects) supportsour findings. It is often said that the structure of peptides andproteins can not be understood without the actionof a solvent, and this statement is certainly true forthe full three-dimensional (tertiary) structure of pro-teins. However, their secondary structure level (helices,sheets, turns) is predominantly shaped by intramolecu-lar interactions—most importantly, hydrogen bonds. Forthese interactions, benchmark experiment-theory com-parisons under well-defined “clean-room” conditions invacuo can furnish critical information towards a com-plete, predictive picture of peptide structure and dy-namics. For example, first-principles approaches such asdensity-functional theory (DFT) with popular exchange-correlation functionals do not account for van der Waals(vdW) interactions. For peptide studies, precise experi-mental calibration points for different, actively developedtheoretical remedies [1–5] would be extremely useful— ifthe same structure as in the solution phase can be formed .In a seminal ion-mobility spectrometry study morethan a decade ago, Hudgins, Ratner, and Jarrold (HRJ)[6] reported the formation of just such a secondary struc-ture motif known from the solution phase (helical) invacuo for a series of designed, charged polyalanine-basedpeptides Ac-Ala n -LysH + ( n =5-20). While much follow-up work has been done after the original HRJ study(e.g., Refs. [7–14]) the “helical” nature of the exact se-ries Ac-Ala n -LysH + is so far still established only indi-rectly by comparing ion-mobility cross-sections to resultsfrom force-field based molecular dynamics. A helical as-signment for polyalanine is thus plausible and easily ac-cepted, but different structural conclusions are not en-tirely ruled out. This fact is strikingly evidenced by ad-ditional ion-mobility experiments with microsolvation [9],which indicate that the secondary structure is not yet he-lical for n <
8. On the other hand, a spectroscopic studyof Ac-Phe-Ala -LysH + [12] inferred structures with “he-lical” H-bond rings ( α - or 3 -helix-like) as the dominantconformers.The key goal of the present work is to unambiguouslyverify the structure of the n =5, 10, and 15 members of the original HRJ series, both experimentally and theo-retically. This is an important task, as safely knowingthe correct structure is a key prerequisite for any furtherphysical conclusions. Obviously, this is a broadly impor-tant statement for a wide part of physics and chemistry—surface science and catalysis, alloys and compounds,semiconductor properties etc.—but for a benchmark sys-tem such as the HRJ series, such safe knowledge is par-ticularly crucial. On the theory side, we employ DFTin the PBE [15] generalized gradient approximation cor-rected for vdW interactions[5] with an accuracy that iscritical for the success of our work. We thereby confirmthe helical assignment for n =10 and 15, but for n =5,the lowest energy structure is indeed not a simple he-lix. Even for such a relatively short molecule, there isthen an enormous structural variety to navigate, an ef-fort which one must not shun (see below). We verify ourfindings against experimental infrared multiple photondissociation (IRMPD) spectra of the vibrational modesin the 1000-2000 cm − region, which pertain to finite T ≈
300 K. Here, harmonic free-energy calculations showthat multiple conformers for n =5 (both helical and non-helical) should coexist, and are supported by calculatedvibrational spectra (harmonic and anharmonic) in closeagreement with experiment.For the experiments, the peptides were synthesized bystandard Fmoc chemistry. The experimental IR spectrawere recorded using the Fourier transform ion cyclotron(FT-ICR) mass spectrometer [16] at the free-electronlaser FELIX [17]. Ions were brought into the gas-phaseby electrospray ionization (ESI) ( ∼ µ l TFA/100 µ l H O) and mass selected and trappedinside the ICR cell which is optically accessible. Whenthe IR light is resonant with an IR active vibrationalmode of the molecule, many photons can be absorbed,causing the dissociation of the ion (IRMPD). Mass spec-tra are recorded after 4s of IR irradiation. Monitoringthe depletion of the parent ion signal and/or the frag-mentation yield as a function of IR frequency leads to anIR spectrum. a r X i v : . [ phy s i c s . b i o - ph ] M a y All DFT+vdW calculations for this work were per-formed using the FHI-aims [18] program package for anaccurate, all-electron description based on numeric atom-centered orbitals. “Tight” computational settings andaccurate tier 2 basis sets [18] were employed throughout.Harmonic vibrational frequencies, intensities and free en-ergies were computed from finite differences. For Ac-Ala -LysH + , we computed infrared intensities I ( ω ) be-yond the harmonic approximation from ab initio molec-ular dynamics (AIMD) runs >
20 ps (
N V E ensemble,with a 300 K
N V T equilibration), by calculating theFourier transform of the dipole auto-correlation function[14, 19, 20] with a quantum corrector factor to the classi-cal line shape [21, 22] proportional to ω (see Ref. [19]).For a direct comparison to experiment, it is importantto represent the “density of states” like nature of themeasured spectra also in the calculated curves. All cal-culated spectra (harmonic and anharmonic) are thereforeconvoluted with a Gaussian broadening function with avariable width of 1% of the corresponding wave num-ber, which accounts for the spectral width of the excita-tion laser. Further broadening mechanisms, e.g., due tothe excitation process, are reflected in the experimentaldata.[23].For the DFT+vdW calculations on Ac-Ala -LysH + ,we generate a large body of possible starting conforma-tions using the empirical OPLS-AA force field (as givenin Ref. [24] and references therein) in a series of basinhopping structure searches performed with the TINKER[25] package. Our particular choice of force field was notmotivated by any other reason than that an input struc-ture “generator” for DFT was needed. That said, theperformance of OPLS-AA for gas-phase Alanine dipep-tides and tetrapeptides was assessed rather favorably inearlier benchmark work.[26, 27] In the searches, specificconstraints on one or more hydrogen bonds could be en-forced. In total, we collected O (10 ) nominally differentconformers from (i) an unconstrained search, (ii) one hy-drogen bond in the Ala part constrained to remain α -helical, (iii) two hydrogen bonds in Ala constrained toform a 3 -helix, (iv) three hydrogen bonds in the Ala part constrained to form a 2 helix, or (v) one hydrogenbond in the full peptide constrained to a π -helical form.As is well known [28], conformational energy differencesbetween different types of secondary structure may varystrongly between different force fields and/or DFT. Wereduce our reliance on the energy hierarchy provided bythe force field by following up with full DFT+vdW re-laxations for a wide range of conformers, 134 in total.This range includes the lowest ∼ α -helical searches, and the lowest ∼ -constrained search, as well as the lowest few π - and 2 -helical candidates. Almost all π -helical geome-tries found in the force-field relaxed with DFT either into α or 3 helices, and all relaxed 2 helices were higherin energy than our lowest-energy conformer by at least 0.26 eV. FIG. 1: Comparison between experimental [gray full lines in(c)] and calculated, broadened harmonic vibrational spectra[black, red, and blue solid lines in (c)] for α -helices of Ac-Ala -LysH + (top), Ac-Ala -LysH + (middle) and Ac-Ala -LysH + (bottom). Also shown are the terminating H-bondnetworks used for α (a) and 3 (b). All theoretical resultsfor α - and 3 -helices have been aligned to the free C-O peakat ∼ − . Figure 1 shows the experimental IRMPD spectra forthe three lengths of peptides studied ( n =5,10,15) and cal-culated vibrational spectra in the harmonic approxima-tion for two specific types of hydrogen bond networks: α -helical (left) and 3 -helical (right). It is well known thatboth the choice of the density functional and the neglectof anharmonic effects will lead to characteristic frequencyshifts between theoretical and experimental spectra. Fora better visual comparison, all calculated spectra in thepresent work are therefore rigidly shifted to be alignedwith the approximate location of the localized free C-Ovibration at ∼ − in experiment for n =5. For ex-ample, this shift amounts to ≈
20 cm − for α -helical con-formers. All intensities were uniformly scaled to matchthe highest peak (Amide-I), but no further scaling factors(frequency or intensity) were employed. Given the limi-tations of the T =0 harmonic approximation when com-paring to room-temperature experimental spectra, theagreement is rather reasonable for the α -helical conform-ers, while this is much less the case in terms of rela-tive peak positions and fine structure for the 3 heli-cal conformers of n =10, 15. This observation correlateswith calculated energy differences, where the 3 helicalconformers are higher in energy than the α -helical onesby 0.41 eV ( n =10) and 0.82 eV ( n =15). In addition,an OPLS-AA based basin-hopping structure enumerationfor n =10 did not reveal any non- α conformers within atleast 0.15 eV. For n =15, the employed structure searchprocedure becomes prohibitive, although direct AIMDsimulations show that α -helix conformations are struc-turally stable even at high T (500 K) for at least severaltens of ps [29]. The available evidence thus points toat least predominantly α -helical secondary structure for n =10, 15. In any case, the observed disagreements for3 confirm the basic structure sensitivity of the mea-sured IRMPD spectra. FIG. 2: Geometries of Ac-Ala -LysH + : (a) g-1; (b) α -1; (c) α -2; (d) 3 -1; and (e) H-bond network of the conformers:(C-)O and N-H groups are numbered starting from the Nterminus and ending at the C terminus. For Ac-Ala -LysH + , the four lowest-energy conformersfrom our search and their H-bond networks are shown inFig. 2. Three of these conformers (labeled α -1, α -2,3 -1) are “helical”, in the sense that they contain twowell-separated terminations with the appropriate α - or3 -like H-bond loops in their Ala section. The lowest-energy conformer, labelled g-1, contains only one 2 likeloop, H-bonds to the NH +3 end of the Lys side chain, andone H-bond that runs against the normal helix dipole, ef-fectively short-circuiting the terminations. In fact, smallstructural differences in the Lys side chain lead to threenonequivalent conformers with the g-1 H-bond network,only one of which is shown here for simplicity. FIG. 3: Ac-Ala n -LysH + , n = 5 , ,
15: Calculated empiricalion-mobility cross sections and comparison with experiment(Ref. [6]). The solid and dashed lines serve only as a guideto the eye, and have no physical significance.TABLE I: Energy differences of the four chosen Ac-Ala -LysH + conformers wrt. g-1: Pure DFT-PBE (no vdW), DFT-PBE+vdW (PES only), and harmonic free energy F at 300 K.All energies in eV. g-1 α -1 α -2 3 -1 DFT-PBE 0.0 0.04 0.08 0.04DFT-PBE+vdW 0.0 0.09 0.11 0.19 F (300 K) 0.0 0.01 0.06 0.17 The termination-connecting H-bond of the g-1 con-former also leads to an overall volume of the g-1 con-former that is somewhat smaller than of the α -1, α -2,or 3 -1 conformers. This is quantified in Fig. 3 byway of computed empirical relative ion-mobility crosssections.[30] We show Ω=(Ω measured − . n ˚A ) as afunction of peptide chain length n , the same expressionas used by HRJ [6]. Remarkably, the g-1 conformer for n =5 together with α -helical conformers for n =10 and 15(dashed line) yields exactly the same qualitative behavioras the original data of HRJ. In contrast, our α -1 and α -2conformers would yield a much shallower drop towards n =5, whereas the 3 -1 conformer ends up too high.In Table I, we summarize our computed energy hier-archy. In DFT-PBE+vdW, the g-1 conformer is morestable than its closest competitors by 0.1-0.2 eV. On thisscale, vdW interactions are important, as seen by com-paring to the pure DFT-PBE energy hierarchy (no vdW).On the other hand, finite temperature effects reduce therelative stability of g-1. The calculated harmonic freeenergy of g-1 and α -1 at 300 K is almost equal, and α -2is only slightly ( ∼
60 meV) less stable; only 3 -1 staysnoticeably removed. The expected stability of at leastthree out of the four conformers is thus similar. We notein passing that the hierarchy for other DFT functionals (revPBE, or B3LYP at fixed geometry obtained usingthe PBE functional) is qualitatively similar, as long as avdW correction is included.[31] FIG. 4: Ac-Ala -LysH + : (a) Theoretical harmonic vibrational spectra (red line) for the four chosen conformers compared withexperiment (gray line); (b) same for anharmonic spectra from AIMD trajectories. All theoretical spectra are shifted rigidly sothat the free CO peak ( ∼ − ) is aligned. Finally, Fig.4 shows computed vibrational spectra forall four conformers compared to experiment. Again, wealign the localized free C-O vibration peak to experimentby a rigid shift and scale the intensities to match theheight of the Amide-I peak. No further scaling factorsare employed. In panel (a), spectra calculated in theharmonic approximation are shown. While there is anoverall qualitative similarity of measured and computedspectra for all four conformers, it is also clear that noneof them fit entirely—peak shifts and incorrect relativeintensities (especially those obscuring the gap betweenAmide-I and -II) abound. This situation changes whenspectra computed from ab initio molecular dynamics andthe dipole-dipole autocorrelation are considered [panel(b)]. For g-1, α -1, and α -2, nearly perfect matches to ex-periment are obtained: The relative positions of Amide-Iand Amide-II are almost exact, the interfering peaks inthe gap decrease in intensity, and even the fine structuretowards lower wave numbers is well reproduced. As oneexample, consider the experimental peak at ≈ − compared to the g-1 conformer. It coincides with a mini-mum of the harmonic spectrum, while a theoretical peaklies much closer in the anharmonic case. Consistent withthe free energy, it is thus possible and plausible that allthree conformers contribute to the experimentally ob-served signal from the ions, which were held in the iontrap at room temperature. In contrast, the features ofthe theoretical 3 -1 conformer do not match quite aswell. If 3 -1 is present in the ion trap at all, then cer-tainly with a much smaller fraction than g-1, α -1, and α -2.In summary, we demonstrate a quantitative structureprediction for Ac-Ala n -LysH + ( n =5,10,15), with strongsupport by the good agreement between calculated andmeasured vibrational spectra. Our calculations provide a direct confirmation for the proposed α -helical nature ofAc-Ala n -LysH + ( n =10,15), while the lowest energy con-former of the “classic” HRJ series, n =5, is indeed not asimple helix. 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