Kinetically Trapped Liquid-State Conformers of a Sodiated Model Peptide Observed in the Gas Phase
Markus Schneider, Chiara Masellis, Thomas Rizzo, Carsten Baldauf
KKinetically Trapped Liquid-State Conformersof a Sodiated Model Peptide Observed in theGas Phase
Markus Schneider, † , ¶ Chiara Masellis, ‡ , ¶ Thomas Rizzo, ∗ , ‡ and Carsten Baldauf ∗ , † † Fritz-Haber-Institut der Max-Planck-Gesellschaft, Theory Department, Faradayweg 4-6,D-14195 Berlin, Germany ‡ Ecole Polytechnique Fédérale de Lausanne, Laboratoire de Chimie Physique Moléculaire,EPFL SB ISIC LCPM, Station 6, CH-1015 Lausanne, Switzerland ¶ Both authors contributed equally.
E-mail: thomas.rizzo@epfl.ch; [email protected] a r X i v : . [ phy s i c s . a t m - c l u s ] A ug bstract We investigate the peptide AcPheAla LysH + , a model system for studying helix for-mation in the gas phase, in order to fully understand the forces that stabilize thehelical structure. In particular, we address the question of whether the local fixationof the positive charge at the peptide’s C-terminus is a prerequisite for forming helicesby replacing the protonated C-terminal Lys residue by Ala and a sodium cation. Thecombination of gas-phase vibrational spectroscopy of cryogenically cooled ions withmolecular simulations based on density-functional theory (DFT) allows for detailedstructure elucidation. For sodiated AcPheAla , we find globular rather than helicalstructures, as the mobile positive charge strongly interacts with the peptide backboneand disrupts secondary structure formation. Interestingly, the global minimum struc-ture from simulation is not present in the experiment. We interpret that this is dueto high barriers involved in re-arranging the peptide-cation interaction that ultimatelyresult in kinetically trapped structures being observed in the experiment. Δ E [ kc a l / m o l ] AB gas phase continuumwater ntroduction Helical secondary structural motifs, such as α and , are common in proteins. In solution,helix propensity is determined both by intramolecular interactions and protein-solvent in-teraction. Gas-phase systems offer the opportunity to study the “undamped” intramolecularinteractions that shape peptides, thereby shedding light on intrinsic helix propensities andbonding interactions. Gas-phase helices have been investigated using ion mobility spectrom-etry and vibrational spectroscopy.
The combination of these experimental techniqueswith molecular simulations based on density-functional theory (DFT) allows for structureelucidation, as it helps to interpret experimentally obtained spectra. Moreover, a rigorousexperiment-theory comparison allows for the assessment of the accuracy and predictive powerof simulation approaches. Pioneering ion-mobility experiments in the group of Jarrold examined the role of N- andC-terminal residues on gas-phase helix formation for the sequences Ala n H + , AcLysAla n H + ,and AcAla n LysH + . They concluded that Ala n H + and AcLysAla n H + adopt globular confor-mations in the gas phase independent of the length of the amino-acid chain while AcAla n LysH + is helical for n > . The identities of these structures were confirmed by theoretical and ex-perimental vibrational spectroscopy in the work of Rossi et al. and Schubert et al. , respec-tively. Similar studies focused on peptides of the form AcPheAla n LysH + with n = 1 – , ,where phenylalanine provides a UV chromophore, which allows for conformer-specific IR-UVdouble resonance spectroscopy. Vibrational signatures of individual conformers add a newdimension to peptide structural analysis beyond the orientationally averaged collisional crosssection provided by ion mobility. In these experiments, the number of residues necessary toform a helix was found to be six, but much of the hydrogen bonding pattern responsi-ble for the formation of this motif is already present even with only three residues.
Inconjunction with computational vibrational spectroscopy based on DFT, such spectraallowed for determining detailed molecular structures and critically examining evidence forhelix formation of peptides in isolation. 3 ) AcPheAla LysH + c) AcPheAla + Na + a) Stabilizing factors of a helix he li x m a c r o - d i po l e m o m en t δ - δ + capping of carbonylgroups near C-terminusdue to protonatedlysine side-chainintra-molecularhydrogen bonds H C CH CH CH CH CH ⊕ H NOHNOHN OOHNOHNOHNOHN HOO HN CH H C CH CH CH CH CH OHNOHN OOHNOHNOHNOHN HOO HN ⊕ Na Figure 1: Illustration of helix-stabilizing factors for peptides in the gas phase (a) andstructural formulas of (b) AcPheAla LysH + and (c) AcPheAla + Na + .Figure 1(a) illustrates the helix-stabilizing factors in polyalanine peptides, shown for thespecific case of AcPheAla LysH + . Work by the groups of Jarrold, Rizzo, and Blum showed that intramolecular hydrogen bonds play an important role and that the designconcept can even be transferred to non-natural peptides. Hoffmann et al. could showthat deleting a single hydrogen bond had little impact on the overall helix stability. Inaddition to their energetic stability, hydrogen bonds are aligned in helices, and the resultingmacro-dipole favorably interacts with the positive charge of the protonated lysine (Lys) side-chain at the C-terminus. Moreover, the capping of the “dangling” carbonyl groups near theC-terminus by the Lys side-chain provides additional stability.To investigate the importance of the charge fixed at the C-terminus, we focus on the well-studied system of AcPheAla LysH + and compare it to AcPheAla + Na + (Figures 1(b)and 1(c), respectively). In the latter, Lys is formally replaced by alanine (Ala) and a sodiumcation (Na + ) in order to introduce a freely movable positive charge. The resulting richpossibilities for electrostatic interaction can locally disrupt hydrogen-bonding networks andinduce unconventional backbone conformations. Consequently, the cation-binding site,and hence the conformation as a whole, is not a priori obvious. Ion mobility studies onmetallated peptides ( e.g. sodiated species of Ala n + M + 22 ) suggest that the cation plays the4ame role as the charged Lys side-chain in AcAla n LysH + for peptides with n > . For shorterpeptides, calculated collisional cross sections (CCS) for globular and helical structures areboth in agreement with the experimental CCS, preventing a definitive structural assignment.In the present work, we couple IR-UV double resonance spectroscopy and theory in orderto unravel the structure of the system of AcPheAla + Na + with the aim of understandingwhether a freely movable cation is sufficient to stabilize helix formation or if the C-terminallocalization is a prerequisite for that. Experimental Setup
The experimental setup has been described in detail elsewhere. In brief, a nano-electrosprayion source is combined with a cooled ion trap ( ) for spectroscopic studies of gas-phaseions. Conformer-selective IR spectra are recorded by applying IR-UV double resonance.A measurement is performed by fixing the wavenumber of the UV laser to a line in theelectronic spectrum and scanning the wavenumber of an infrared laser. When the IR pulseis in resonance with a vibrational transition of the ion, part of the population is removedfrom the ground state, leading to a decrease in UV-induced fragmentation. Scanning the IRwavenumber, one obtains a conformer-specific vibrational spectrum. Performing the sameexperiment on each line of the electronic spectrum allows for assignment of each UV spectralfeature to a particular conformer.
Computational Methods
The applied conformational search algorithm is similar to the one used by Rossi et al. First,a global conformational search is performed on the force field (FF) level using
CHARMM22 and OPLS-AA , separately. To that end, a basin-hopping approach was applied us-ing the scan program of the TINKER molecular modeling package.
For the system ofAcPheAla LysH + (AcPheAla + Na + )
603 280 (
626 829 ) conformers were found using
CHARMM22
643 938 (
635 120 ) conformers were found using
OPLS-AA . Single-point energy calculationsat the generalized-gradient approximated (GGA) DFT level of theory have been performedfor all these FF conformers. All DFT calculations were done using the all-electron/full-potential electronic structure code package
FHI-aims . To be more precise, energies werecomputed at the PBE+vdW level, i.e. using the PBE functional and a pair-wise van derWaals correction scheme (vdW). Furthermore,
FHI-aims -specific tier 1 basis sets and light settings have been used that are provided out-of-the-box to control the computa-tional accuracy intended to give reliable energies energy for screening purposes. For thetwo FFs individually, the 500 conformers with the lowest FF energy and the 500 conformerswith the lowest DFT energy, i.e. a grand total of 2000 conformers, have been selected. The2000 selected conformers were then geometry optimized at the PBE+vdW level using tier1 basis sets and light settings. A hierarchical clustering scheme was applied in order torule out duplicates. Further relaxation was then accomplished at the PBE+vdW level using
FHI-aims -specific tier 2 basis sets and tight settings that are intended to provide meV -level accurate energy differences, i.e. within .
02 kcal / mol . After clustering, this resultedin 324 (159) conformers for the system of AcPheAla LysH + (AcPheAla + Na + ) in the low-energy region, i.e. within / mol from the global minimum. These conformers were thenagain locally refined at the PBE0+MBD level, i.e. using the hybrid exchange-correlation(xc) functional PBE0 augmented by a many-body dispersion (MBD) correction, using tier 2 basis sets and tight settings which resulted in 52 (23) conformers in the low-energyregion, i.e. within / mol from the global minimum. Results and Discussion
AcPheAla LysH + For our comparative study, a firm assignment of measured conformer-selective IR spectrato their calculated counterparts is of paramount importance. To that end, we first re-assess6he peptide AcPheAla LysH + and demonstrate that the applied conformational search tech-nique completely grasps the conformational space energetically close to the global minimum,and that the applied level of theory is capable of reproducing the energetics as well as thevibrational properties of the conformers. For this we compare our results to previous workon AcPheAla LysH + by Stearns et al. , where the 45 lowest-energy structures were selectedout of a set of 1,000 force-field minima and subsequently optimized using DFT with a hybridexchange-correlation (xc) functional. Even though four structures were successfully assignedto the experimental spectra, the question whether the search was complete and the whetherthese conformers are located in the global minimum region remained open. This did, inpart, motivate an exhaustive conformational search by Rossi et al. , in which conformerswere found within / mol of the global minimum on the potential-energy surface (PES).The authors were able to assign the experimentally observed structures to the global min-ima populated at low temperature by using the hybrid xc-functional PBE0, augmented bya many-body dispersion (MBD) correction, and including zero-point energy corrections.The latter were computed with the generalized-gradient approximation functional PBE and a pair-wise van der Waals correction (vdW), which proved however unsatisfying forthe prediction of vibrational spectra. It was suggested that using a hybrid xc-functionalwas necessary, which was a natural assumption since this level of theory was necessary fora correct conformational energy prediction in the first place. Furthermore, it was assumedthat an anharmonic treatment was needed to yield improved spectra.The conformational search strategy has already been laid out in detail in the previoussection, including numbers illustrating the exhaustiveness of the search. The fact that wefind two additional conformers within / mol from the lowest-energy conformer gives usconfidence in the conformational search. The corresponding hierarchy of the relative DFTenergy ∆ E on the PES is shown in Figure 2. Nine conformers were found within / mol from the global minimum.Since the experimental measurement takes place on cold ions in the gas phase, the PES7 E ∆ F(10K) ∆ F(300K)0.50.00.51.01.52.0 R e l a t i v e ene r g y [ kc a l / m o l ] Figure 2: Energy hierarchies of conformers of
AcPheAla LysH + at the PBE0+MBD energy ∆ E as well as the Helmholtz free energy ∆ F at
10 K and
300 K with harmonic vibrationalfree energy contributions calculated at the PBE+vdW level.merely allows for a rough estimate about the structures populated at low temperatures. Toconfidently assign the experimentally observed structures one needs to rely on the Helmholtzfree energy F at
10 K , as this is approximately the temperature of the observed ions. We ac-count for free energy contributions from internal degrees of freedom, consisting of vibrationsand rotations, in addition to the DFT energy E on the PES. A detailed formulaic descrip-tion is provided in the supporting information. For AcPheAla LysH + , Figure 2 shows energyhierarchies of the PBE0+MBD energy ∆ E as well as the Helmholtz free energy ∆ F at
10 K and at
300 K , always relative to conformer A (see Figure 3(b)). At this stage, harmonic vi-brational free energy contributions have been calculated at the PBE+vdW level. While the ∆ F (10 K) surface should best resemble experimental conditions of gas-phase measurementsat
10 K , the free energy hierarchy at
300 K represents an estimate of the conformers popu-lated at the early stage of the experimental process, where the molecules are electrosprayedinto the instrument at room temperature. Their low free energy at
10 K and the relativelylarge gap to alternative structures at
300 K indicate why the species observed in experimentshould be among the four conformers within .
25 kcal / mol from the global minimum. Ofcourse we are aware of the limitation of not taking into account anharmonicity and thepossibility of solvation-memory effects ( i.e. kinetic trapping).High computational costs prohibited the systematic use of hybrid xc-functionals for the8 E ∆ F(10K) ∆ F(300K)0.40.30.20.10.00.10.2 R e l a t i v e ene r g y [ kc a l / m o l ] a)b) ABCD
A B C D c) ABCDExp.Exp. I R i n t en s i t y [ a r b . un i t] Wavenumber [cm -1 ] Figure 3: (a) Relative DFT energies ∆ E as well as relative Helmholtz free energies ∆ F at
10 K and
300 K for the lowest-energy conformers of AcPheAla LysH + at the PBE0+MBDlevel. (b) The four lowest-energy conformers on the ∆ F (10 K) scale. Hydrogen bonds areindicated with dashed lines. The labeling of the conformers follows Stearns et al. (c) Twomeasured conformer-selective IR spectra ( traces ) are compared to harmonic vibrational cal-culations ( sticks ). Calculated spectra are uniformly scaled by a factor of . .calculation of harmonic vibrations in the previous study by Rossi et al. To complete thepicture, we repeat the harmonic vibrational free energy calculations at the PBE0+MBD level,confirming the already obtained result. Figure 3(a) shows the energy hierarchies for ∆ E , ∆ F (10 K) , and ∆ F (300 K) for the four lowest-energy conformers illustrated in Figure 3(b).Conformers A and B are virtually identical near the C-terminus, but differ near the N-terminus by a tilted Phe side chain. The difference between conformers C and D is similar.All four conformers show helical structure motifs: conformer C possesses one - and two α -helical turns, conformer D features one - and one α -helical turn, and conformers A and B each possess two - and one α turn.For this work, the original IR-UV double resonance experiment by Stearns et al. hasbeen repeated to allow conformer-selective IR spectra to be compared to their theoreticalcounterparts calculated at the PBE0+MBD level. The affiliated UV spectrum including peakassignments to their corresponding conformers is provided in the supporting information.9he conformer-selective IR spectra are shown in Figure 3(c). Conformers A and B could beattributed to their corresponding observed IR spectra. While the agreement is very good, thematch between experimental and theoretical IR spectra is not perfect. This discrepancy iscommonly attributed to two factors: (i) The effect of a possible incomplete characterizationof electron exchange and correlation, despite the use of the hybrid functional PBE0, and(ii) the treatment of anharmonic vibrations and nuclear quantum effects. Both of theseeffects are corrected for solely by applying a scale factor to the vibrational frequencies. Theassumption of a uniform overestimation of the harmonic vibrational modes with respectto experiment is debatable as they depend on the theoretical method, the used basis set,and the system itself.
In this work, we focus on the frequency region of − to − which is sensitive to N − H · · · O hydrogen bonding, where a uniform scaling factorof . yields very good agreement.The exhaustive conformational search presented here for AcPheAla LysH + , and the rig-orous treatment of harmonic vibrations at the hybrid xc level allowed for (i) reproducingthe known energy hierarchy and finding additional conformers in the low-energy region and(ii) calculating well-fitting harmonic IR spectra for the conformers in the low-energy region.In this way we confirm the conformers predicted by Stearns et al. and Rossi et al. and canrule out any other competing conformers. This also shows that calculating computationallycostly anharmonic IR spectra is not required in this case. Now that we have confirmed theaccuracy of our simulation approach, we tackle AcPheAla + Na + , a more challenging systembecause of the additional conformational degrees of freedom due to the “unfixed” cation. AcPheAla + Na + Figure 4 shows the energy hierarchies of the relative PBE0+MBD energies ∆ E as well as therelative Helmholtz free energies ∆ F at
10 K and
300 K with harmonic vibrational free energycontributions at the PBE+vdW level that were obtained for AcPheAla + Na + . The four pre-sumably dominant conformers are presented in Figure 5(b). Of the four conformer-selective10R spectra that were recorded, two of them correspond to conformers with particularly highintensity in the UV spectrum (see Figure S2, supporting information). The measured IRspectra of these two conformers, IIa and
IIb , show very good agreement with the IR spec-tra calculated at the PBE0+MBD, which uses a scale factor of . . Both conformers arenearly identical, differing only in the tilt of the Phe side chain near the N-terminus. Theyare globular with the peptide being “wrapped around” the Na + cation with four partiallynegatively charged C −− O groups pointing towards the positively charged cation, restrictingthem from forming the hydrogen bonds necessary for helix formation. Indeed, no similari-ties are observed comparing these structures to the helical motifs of AcPheAla LysH + . TheC-terminal fixation of the charge by the Lys side-chain seems to be a prerequisite to effec-tively cap the helix. The “freely movable” charge prevents helix formation in this system andinstead induces a globular motif. All conformers found in the low-energy region ( i.e. within / mol from the global minimum) show a globular conformation. ∆ E ∆ F(10K) ∆ F(300K)0.00.51.01.52.02.53.03.5 R e l a t i v e ene r g y [ kc a l / m o l ] Figure 4: Energy hierarchies of conformers of AcPheAla + Na + at the PBE0+MBD energy ∆ E as well as the relative Helmholtz free energy ∆ F at
10 K and
300 K with harmonicvibrational free energy contributions calculated at the PBE+vdW level.An obvious observation is the outstanding global minimum (conformer I in Figure 5(b))that is separated by a . / mol gap from the next minimum on the ∆ F (10 K) scale. Theclear assignment of conformers IIa and
IIb to the two most intense bands in the measuredspectra suggests that both conformers may be kinetically trapped. Moreover, the most stable11 E ∆ F(10K) ∆ F(300K)0.00.51.01.52.02.53.03.5 R e l a t i v e ene r g y [ kc a l / m o l ] a)b)c) ⅠⅢⅡ a Ⅱ bExp.Exp. ⅠⅡ a ⅢⅡ b Ⅰ Ⅱ a Ⅲ Ⅱ b I R i n t en s i t y [ a r b . un i t] Wavenumber [cm -1 ] Figure 5: (a) Relative DFT energies ∆ E as well as relative Helmholtz free energies ∆ F at
10 K and
300 K for the lowest-energy conformers of AcPheAla + Na + at the PBE0+MBDlevel. (b) The four lowest-energy conformers on the ∆ F (10 K) scale. Hydrogen bonds areindicated with dashed lines. (c) Two measured conformer-selective IR spectra ( traces ) withhighest intensity are compared to harmonic vibrational calculations ( sticks ). Calculatedspectra were uniformly shifted by a factor . .12tructure I does not seem to be observed in the experiment – none of the conformer-selectivespectra fit the calculated vibrational signatures (see Figure 5(c)). The structure representingthe global minimum is globular and features a cation- π interaction between the Na + andthe Phe side chain. If that conformer were present in experiment, one would expect broadfeatures in the UV spectrum due to charge-transfer between Na + and the aromatic ring.However, no such features have been observed. The reason behind the kinetic trappingof conformers IIa and
IIb has to be sought in the experimental procedure in which themolecules are electrosprayed into the apparatus from a solution at room temperature whilethe actual measurements are taken on isolated molecules at
10 K .The energy landscape of the system may differ significantly between the system in so-lution at room temperature and in the gas phase at
10 K . This is particularly true for theglobal minima. While the global minimum in the gas phase may be energetically favoredin comparison to the other structures, kinetic constrains, i.e. high energy barriers betweenminima, may hinder proper folding while transitioning from solution to the gas phase. Thus,experimentally observed local minima in the gas phase higher in energy are yielded dueto their structural bias from aqueous solution at room temperature, resulting in kineticallytrapped structures unable to transition into the global minimum.It is obvious from comparing the ∆ F (10 K) and ∆ F (300 K) hierarchies (see Figure 5(a))that the temperature difference does not contribute to a possible kinetic trapping effect.In fact, the energy gap between the global and the next minimum even increases from . / mol at
10 K to . / mol at
300 K . Therefore, kinetic trapping must be causedby solvation effects alone. In order to estimate the magnitude of such an effect, the fourlowest-energy conformers presented in Figure 5 have been geometrically optimized withPBE0+MBD including implicit water by solving the Modified Poisson-Boltzmann (MPB)equation implemented in FHI-aims (consult the supporting information for compu-tational details). While in the gas phase conformer I is . / mol lower in DFT energythan the next minima (conformers IIa and
IIb ), the situation is reversed when including13mplicit aqueous solution; conformer I is now . / mol higher in energy. This suggeststhat they carry a structural bias from aqueous solution, i.e. the barriers are sufficiently highto kinetically trap them during the electrospray process.A similar scenario can be seen for conformer III , which is of comparable energy as con-formers
IIa and
IIb on the ∆ F (10 K) scale, but the calculated IR spectrum, presented inFigure 5(c), does not match any experimentally observed one. Consulting the ∆ F (300 K) scale (see Figure 5(a)) shows that conformer III is . / mol higher in energy than con-former IIb at room temperature. When re-relaxing the structures to the nearest minimumon the potential energy surface at the PBE0+MBD level including implicit aqueous solvationeffects as described above, conformer
III becomes further energetically penalized – it is thenmore than . / mol higher in energy compared to the other conformers. a) b) Ⅳ Exp. Ⅳ Exp. I R i n t en s i t y [ a r b . un i t] Wavenumber [cm -1 ] Figure 6: (a) For the system of AcPheAla + Na + , the two measured conformer-selectiveIR spectra ( traces ) with lowest intensity are compared to vibrational calculations ( sticks ) inharmonic approximation on the PBE0+MBD level for structure IV . Calculated spectra havebeen shifted by applying a uniform scaling factor of . . (b) Structural form of conformer IV . Hydrogen bonds are indicated with dashed lines. The highlighted vibrational mode inFigure (a) is indicated with a green arrow in Figure (b).There remain two conformers, IV and V , for which the UV spectral signatures have lowerintensity (see Figure S2), suggesting that they have smaller populations. The correspondingIR spectra, shown in Figure 6(a), could not be assigned to their calculated counterparts forany structure within / mol from the global minimum on the ∆ F (10 K) scale. Similarly,as for IIa and
IIb , we assume that these conformers are kinetically trapped, which alsorenders their assignment difficult in assigning them as these conformers might be higher in14nergy, and thus no energy criterion can be applied for finding them. Instead we followan approach where we make use of information from the experiment in order to selectfrom the overall pool of structures for calculation of spectra. Candidates were picked if theyfeature a free carboxylic acid OH stretch, since the experimental IR spectra show a peak at − (see Figure 6(a)). Due to the absence of broad features in the UV spectrum, onlystructures were considered where the Na + cation was not in close proximity to the phenylring. In total, vibrational spectra for 126 conformers have been calculated. In addition tothat, local refinement on the PBE0+MBD level for all 52 found minima structures within / mol from the global minimum for the system of AcPheAla LysH + has been laid outafter formally replacing Lys with Ala + Na + , with the sodium cation being placed at theposition of the amino group nitrogen. Vibrational spectra for the resulting 28 conformers(after clustering) have been calculated as well. As explained above, computationally-costlyhybrid xc-functionals are required in order to gain enough accuracy. Only conformer IV (seeFigure 6(b)), lying . / mol higher in energy than the global minimum on the ∆ F (10 K) scale, could be assigned to one of the less populated conformers. However, one peak inthe simulated vibrational spectrum is blue shifted by
80 cm − with respect to the nearestexperimental peak, and the corresponding vibrational mode is indicated in Figure 6(b) with agreen arrow. Conformer IV is a candidate for the kinetically trapped structure only becauseof the (partially) matching IR spectra. Taking into account the large computational efforttaken, a more appropriate and computationally affordable technique for finding kineticallytrapped conformers would be certainly desirable. Conclusion
Our data indicate that the fixed location of the charge at the C-terminus is imperativefor helix formation in peptides of this length in isolation, as this stabilizes the structurethrough a cation-helix dipole interaction. In the case of the freely-movable sodium cation,15he cation-backbone and cation- π interactions seem to be stronger, leading to local distortionsof peptide structure, preventing helix stabilization. It is interesting to note the high barriersthat seem to be involved in interconverting one structure to another. Even though the cation- π interaction is energetically favored for the AcPheAla + Na + in the gas phase, the systemremains kinetically trapped in a structural state that is characterized by cation-backboneinteractions and that is energetically preferred in polar solvent. Acknowledgement
The authors thank the joint Max-Planck-EPFL Center for Molecular Nanoscience and Tech-nology for financial support. CB thanks Dr. Mariana Rossi for sharing her knowledge abouttheoretical vibrational spectroscopy and Prof. Matthias Scheffler for his continuous support.The experimental work was supported by the EPFL as well as the Swiss National ScienceFoundation through grant 200020_165908.
Supporting information available: • A detailed and technical description of the experiment and of the applied simulationsmethods as well as additional results can be found in the following sections. • Numerical details for all shown energy hierarchies as well as experimental and calcu-lated IR spectra, i.e. for Figures 2–6 and Figure 10, as well as corresponding xyz-filesof conformers are provided under this link: http://w0.rz-berlin.mpg.de/user/baldauf/carsten_pdf/Schneider_2017_Helices_SI.zip upporting Information Experimental setup in detail
The experimental setup has been described in detail elsewhere. Gas-phase protonatedpeptides are produced in a continuous fashion by nano-electrospray ionization from a . solution in 50:50 methanol-water. The ions enter the instrument through a metal-coatedborosilicate capillary and are focused by an ion funnel. The molecules are pre-trapped in ahexapole in order to generate ion packets and to match the duty cycle of the experiment. Aquadrupole mass filter selects the m / z of the ions of interest, which are deflected ◦ usingan electrostatic bender, guided though an octopole and deflected ◦ a second time beforepassing through a set of decelerating lenses and injected in a cold octopole ion trap ( ).Here, they are cooled down by collisions with cold He gas that is pulsed in before theirarrival. The He pressure is between · − and − mbar . infrared (IR) and ultraviolett(UV) beams are focused inside the trap and used to spectroscopically interrogate the coldmolecules. The charged fragments produced following UV absorption of the parent ions areextracted from the trap and deflected by a third electrostatic bender and passed througha quadrupole mass filter which selects a particular m / z ratio before they are detected by achanneltron electron multiplier. The electronic signature of the ions is recorded monitoringthe number of fragments for a particular photofragmentation channel as a function of theUV wavenumber. Each conformer present has a characteristic UV signature, so the recordedspectrum is a superimposition of lines coming from all conformations of the parent ionthat may be present in the trap. Fixing the wavenumber of the UV laser and scanningthe wavenumber of an infrared laser pulse that arrives
200 ns earlier allows for acquiringa vibrational spectrum of whatever conformer is resonant with the UV laser. When theIR pulse is in resonance with a vibrational transition of the ion, part of the populationis removed from the ground state to vibrationally excited states, leading to a decrease inUV induced fragmentation, and as the IR wavenumber is scanned one obtains a conformer-17pecific vibrational spectrum. Performing the same experiment on each line of the electronicspectrum allows for assigning each UV spectral feature to a particular conformer.
Conformational search approach in detail
The applied conformational search algorithm is similar to the one used by Rossi et al. First,a global conformational search is performed on the force field (FF) level using the two em-pirical fixed point charge models of
CHARMM22 and OPLS-AA , separately. To that end, abasin-hopping approach was applied using the scan program of the TINKER molecular mod-eling package.
To be detailed, all torsional modes were taken into consideration and de-fault search parameters were used, i.e. an energy threshold for local minima of
100 kcal / mol and a convergence criterion for local geometry optimizations of . / mol · Å. For thesystem of AcPheAla LysH + (AcPheAla + Na + )
603 280 (
626 829 ) conformers were foundusing
CHARMM22 and
643 938 (
635 120 ) conformers were found using
OPLS-AA . Single-pointenergy calculations on the PBE+vdW level of density-functional theory (DFT) using tier1 basis sets and light settings have been performed for all these FF conformers. All DFTcalculations were done using the all-electron/full-potential electronic structure code package
FHI-aims . For the two FFs individually, the 500 conformers with the lowest FF energyand the 500 conformers with the lowest DFT energy, i.e. a grand total of 2000 conformers,have been selected. The 2000 selected conformers were then geometrically relaxed at thePBE+vdW level using tier 1 basis sets and light settings. Relaxation was accomplishedusing a trust radius method version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) op-timization algorithm. After convergence, a clustering scheme was applied in order to ruleout duplicates. To be precise, root-mean-square deviations (RMSD) of atomic positions be-tween any two conformers were calculated using
OpenBabel . Hierarchical clustering wasthen achieved by applying the Unweighted Pair Group Method with Arithmetic Mean (UP-GMA) method implemented in Python ’s SciPy library. Following that, further relax-ation was accomplished at the PBE+vdW level using tier 2 basis sets and tight settings.18fter clustering, this resulted in 324 (159) conformers for the system of AcPheAla LysH + (AcPheAla + Na + ) in the low-energy region, i.e. within / mol from the global min-imum. These conformers were then again locally refined on the PBE0+MBD level using tier 1 basis sets and light settings. After clustering, further geometry relaxation on thePBE0+MBD level using tier 2 basis sets and tight settings resulted in 52 (23) conformersin the low-energy region, i.e. within / mol from the global minimum. Conformational search approach comparison
E(Rossi...020406080100 Δ E(own search) Δ R e l a t i v e E ne r g y [ m e V ] [ kc a l / m o l ] et al. ) Figure 7: Comparison of energy hierarchies on the PBE0+MBD level ( tier 2 basis sets and tight settings) between our own conformational search and the search performed by Rossi et al. Two additional conformers are found in the low-energy region, i.e. within / mol from the global minimum. Conformers with the same energy in both hierarchies correspondto virtually identical structures.For the system of AcPheAla LysH + , nine conformers were found in the low-energy region, i.e. within / mol from the global minimum, two more than Rossi et al. Figure 7compares the two hierarchies on the potential energy surface, i.e. on the PBE0+MBD levelusing tier 2 basis sets and tight settings. Conformers with the same energy in bothhierarchies correspond to virtually identical structures.19 elmholtz free energy
The Helmholtz free energy F per molecule in the gas phase is given by F = E + F int with E denoting the DFT energy on the potential energy surface (PES) and F int denotingthe free energy contribution due to the internal degrees of freedom, consisting of vibrationsand rotations. Assuming harmonic approximation for the intramolecular PES and neglectingany rotational-vibrational coupling, the internal free energy is given by F int = F vib + F rot with F vib = N − (cid:88) i (cid:20) ¯ hω i k B T ln(1 − exp − ¯ hω i /k B T ) (cid:21) and F rot = − k B T ln (cid:34) π / (cid:18) k B T ¯ h (cid:19) / (cid:112) I x I y I z (cid:35) , where N denotes the number of atoms, ω i denotes the vibrational frequency of normal mode i ,and I x , I y , and I z denote the moments of inertia along the three axes. The case of T = 0 defines the zero-point energy correction where F int = (cid:80) N − i ¯ hω i .The Helmholtz free energy F is formally given by F = U − T S , with U , T , and S denotingthe internal energy, the temperature, and the entropy of the system, respectively. It is relatedto the Gibbs free energy G through G = U − T S + pV = F + pV , with p and V denoting thepressure and the volume of the system, respectively. We use Helmholtz free energies in thiswork because the experiment is essentially done at zero pressure. Furthermore, throughoutthis work we are exclusively treating relative energies, i.e. comparing energy differencesbetween different conformers (usually with respect to the global minimum) of the samesystem. Hence, the the pV term cancels. In other words, ∆ G = ∆ F .20 bserved UV spectra U V i n t en s i t y [ a r b . un i t] Wavenumber [cm -1 ] A B U V i n t en s i t y [ a r b . un i t] Wavenumber [cm -1 ] a) AcPheAla LysH + b) AcPheAla + Na + Ⅱ b Ⅱ a Ⅱ a Ⅳ Ⅴ
Figure 8: Measured UV spectra for the systems of (a) AcPheAla LysH + and (b) AcPheAla + Na + . In both cases, peaks have been assigned to their identified conformers shown in Fig-ures 3, 5, and 6.Measured UV spectra for the systems of (a) AcPheAla LysH + and (b) AcPheAla + Na + are presented in Figure 8. In both cases, peaks have been assigned to their identifiedconformers shown in Figures. 3, 5, and 6 in the paper. AcPheAla + Na + : Attempting assignemt of IR spectra ofkinetically trapped conformers IV and V As stated in the paper, for the system of AcPheAla + Na + obtained IR spectra of kinet-ically trapped conformers IV and V could not be confidently assigned to their calculatedcounterparts. For the sake of completeness, Figure 9 shows the corresponding experimen-tally obtained IR spectra along with several calculated IR spectra that share similarities.Calculations have been done on the PBE0+MBD level using tier 1 basis sets and light settings. Conformer charmm22Best500FF155865 corresponds to conformer IV illustrated in21igure 6(b) in the paper. I R i n t en s i t y [ a r b . un i t] Wavenumber [cm -1 ] StrfromLys-oplsaaBest500DFT114748StrfromLys-charmm22Best500DFT84498charmm22Best500FF153186charmm22Best500FF106517charmm22Best500FF106515charmm22Best500FF155865
Exp. a) conformer Ⅳ b) conformer Ⅴ I R i n t en s i t y [ a r b . un i t] Wavenumber [cm -1 ] StrfromLys-oplsaaBest500DFT472992StrfromLys-oplsaaBest500DFT472984oplsaaBest500FF52405charmm22Best500FF156019charmm22Best500FF147712charmm22Best500DFT278652
Exp.
Figure 9: Experimentally obtained IR spectra of kinetically trapped conformers (a) IV and(b) V . In both cases, several calculated IR spectra that share similarities are shown. Con-former charmm22Best500FF155865 corresponds to conformer IV illustrated in Fioure 6(b)in the paper. xyz -files of the conformers are provided within the SI_data.zip of this SI.
DFT calculations including implicit solvation effects
For the system of AcPheAla + Na + and the four lowest-energy conformers on the ∆ F (10 K) scale, re-relaxation was applied on the potential energy surface on the PBE0+MBD level( tier 2 basis sets, tight settings) including implicit solvation effects by solving the ModifiedPoisson-Boltzmann ( MPB ) equation implemented in
FHI-aims . Default parameters havebeen chosen while explicity setting ions_conc 0 (no ions in the electrolyte). Full relaxation22as been achieved for all conformers. Corresponding minima are still fairly similar as theroot-mean-square deviation of atomic positions is smaller than . Å in all cases. ∆ E(gas phase) ∆ E(solvation)604020020406080 R e l a t i v e ene r g y [ m e V ] -1.5-1.0-0.50.00.51.01.52.0 [ kc a l / m o l ] ⅠⅡ a Ⅱ b Ⅲ ⅠⅡ a Ⅱ b Figure 10: Comparison of energy hierarchies on the potential energy surface on thePBE0+MBD level ( tier 2 basis sets and tight settings) between gas-phase calculations andcalculations including implicit solvation effects by solving the Modified Poisson-Boltzmannequation (
MPB ) implemented in
FHI-aims . Full relaxation has been achieved for all conform-ers. Conformers have been labeled as in Figure 5. On the ∆ E (solvation) scale conformer III lies . / mol higher in energy than conformer I . References (1) Barlow, D. J.; Thornton, J. M. Helix Geometry in Proteins.
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