Best of Two Worlds? How MD Simulations of ... - ACS Publications

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Cite This: J. Chem. Theory Comput. XXXX, XXX, XXX−XXX

Best of Two Worlds? How MD Simulations of Amphiphilic Helical Peptides in Membranes Can Complement Data from Oriented SolidState NMR Sabine Reißer,†,∥ Erik Strandberg,‡ Thomas Steinbrecher,§,⊥ Marcus Elstner,§ and Anne S. Ulrich*,‡,† †

Institute of Organic Chemistry, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 6, 76131 Karlsruhe, Germany Institute of Biological Interfaces (IBG-2), KIT, P.O. Box 3640, 76012 Karlsruhe, Germany § Institute of Physical Chemistry, KIT, Fritz-Haber-Weg 6, 76131 Karlsruhe, Germany

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‡

S Supporting Information *

ABSTRACT: The membrane alignment of helical amphiphilic peptides in oriented phospholipid bilayers can be obtained as ensemble and time averages from solid state 2H NMR by fitting the quadrupolar splittings to ideal α-helices. At the same time, molecular dynamics (MD) simulations can provide atomistic insight into peptide−membrane systems. Here, we evaluate the potential of MD simulations to complement the experimental NMR data that is available on three exemplary systems: the natural antimicrobial peptide PGLa and the two designer-made peptides MSI-103 and KIA14, whose sequences were derived from PGLa. Each peptide was simulated for 1 μs in a DMPC lipid bilayer. We calculated from the MD simulations the local angles which define the side chain geometry with respect to the peptide helix. The peptide orientation was then calculated (i) directly from the simulation, (ii) from back-calculated MD-derived NMR splittings, and (iii) from experimental 2H NMR splittings. Our findings are that (1) the membrane orientation and secondary structure of the peptides found in the NMR analysis are generally well reproduced by the simulations; (2) the geometry of the side chains with respect to the helix backbone can deviate significantly from the ideal structure depending on the specific residue, but on average all side chains have the same orientation; and (3) for all of our peptides, the azimuthal rotation angle found from the MDderived splittings is about 15° smaller than the experimental value.

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INTRODUCTION Membrane-active peptides have diverse biological functions, such as antimicrobial, cytotoxic, cell penetrating, fusogenic, or amyloidogenic functions. To elucidate these mechanisms of action, it is particularly important to understand not only the peptide structures but also their molecular interactions with the lipids. These interactions are quite subtle, and the use of model systems like detergent micelles provides less information compared to the data obtained in more realistic lipid bilayers.1−3 A powerful method to study peptides with high resolution in quasi-native membranes is solid-state NMR (SSNMR), based on macroscopically aligned bilayers at ambient temperature under saturating hydration conditions.4−9 This approach has been used by other groups and ourselves to study numerous antimicrobial peptides,10−18 cell-penetrating agents,19−22 and fusion peptides.23−26 In principle, by sitespecific labeling of the peptide with NMR-active isotopes at different positions, it is possible to get near-atomic resolution information about the peptide in the membrane-bound form. However, an entire set of peptides with site-selective labels at different positions must be tediously synthesized, purified, and reconstituted, and the label itself often represents a © XXXX American Chemical Society

conservative mutation. With a judicious choice of labels, it is usually possible to describe the conformation of the peptide, its orientation in the membrane, and its dynamic behavior, as well as its tendency for oligomerization, self-assembly, and/or aggregation.4−7 However, we have also encountered certain scenarios in which it was necessary but quite impractical to use some 10 labels or more positions.11,19,20,22,27 Especially, an unusual peptide conformation, a high mobility, or simply an unfortunate alignment can lead to ambiguous or even insufficient information about the system.28 An obvious alternative method that can, in principle, give complete information about a peptide−lipid system is molecular dynamics simulations (MD). This approach is becoming increasingly popular because computers got more powerful, simulation packages more user friendly, and simulation time cheaper.29−36 However, for MD, many factors can influence the results, in particular, the choice of force fields.37 To speed up simulations, certain approximations are used in these force fields. Sometimes the peptides or lipid Received: March 21, 2018

A

DOI: 10.1021/acs.jctc.8b00283 J. Chem. Theory Comput. XXXX, XXX, XXX−XXX

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Journal of Chemical Theory and Computation matrix are even approximated by coarse-grained models,38−41 and then, the system is not atomistically described. It has also been shown that the simulation trajectories must be quite long in order to capture the critical aspects of the system.42 It is therefore essential to compare MD results with experiments to make sure that the simulation fits with reality. By complementing SSNMR with all-atom MD, it is possible to combine the strengths of both methods. Very fine details, like short-lived hydrogen bonds between lipids and peptides or small fluctuations in the peptide backbone structure can be captured from the simulation. SSNMR, on the other hand, provides time-averaged ensemble properties, such as peptide dynamics and local orientational angles in the membrane.43,44 The studies where NMR data and MD simulations were combined can be divided into two groups: (i) NMR data were used as restraints in the simulation.45−48 (ii) NMR data were directly compared with back-calculated spectra from unrestrained MD.49,50 For the latter group, however, the analyzed simulation timespans are mostly short (up to 200 ns)41,51−53 or they were done on transmembrane peptides that are not amphiphilic54 or were performed using coarse-grained simulations.41,55 In the present study, we have run long unrestrained all-atom MD on three exemplary α-helical amphipathic peptides in a DMPC bilayer: the antimicrobial peptide (AMP) PGLa from the African frog Xenopus laevis,56 the designer-made 21-mer MSI-103 that is based on the PGLa sequence,57 and a short 14mer version of MSI-103 called KIA14.58 The MD results were compared with 2H NMR data collected on the same peptides in oriented lipids. We have systematically compared the structure and orientation of these three related peptides as studied by the two complementary methods in order to find similarities as well as differences. A direct comparison was made by back-calculating the putative 2H NMR quadrupolar splittings from the molecular coordinates in the simulation trajectories and then analyzing these MD-derived splittings in the same way as the NMR data to derive the alignment parameters of the peptide. An indirect comparison was made by calculating the peptide orientation directly from the simulation and comparing this behavior with the results from the NMR data analysis. The orientation of a helical peptide in the lipid bilayer can be defined by two angles, τ and ρ, as described in Figure 1 and explained in the Supporting Information. The tilt angle τ denotes the angle between the helix axis and the membrane normal, while the azimuthal angle ρ describes the rotation of the peptide around the helix axis (with respect to a defined residue as a reference point). Since the peptide is not fixed but can move in the membrane, these two orientational parameters tend to fluctuate around an average value with a certain distribution function. The peptide conformation can be defined by a set of internal angles. The backbone is described by dihedral angles Φ and ψ, and the relative orientation of the side chains is described by torsion angles. In the case of Ala-d3 side chains, the orientation of the Cα-CD3 bond that is relevant for the quadrupolar splitting is denoted within the framework of the helix by the three angles α, β, and Θ.59,60 These angles are illustrated in Figure 1, and their meaning is explained in detail in the Supporting Information. Briefly, β is the angle between the helix axis and the Cα-CD3 bond of Ala-d3, α describes the geometry of the same bond within a plane perpendicular to the helix axis, and Θ is the angle between the Cα atoms of two

Figure 1. (A, B) Definition of the helix tilt angle τ and the azimuthal rotation angle ρ, which fully describe the orientation of the amphiphilic object with respect to the membrane normal. Note that according to our convention we chose residue 12 in the middle of a typical peptide to define ρ = 0°. (C) Definition of βi, the angle between the helix axis (N-terminus to C-terminus) and the Cα,i−Cβ,i bond. (D) Definition of αi, the angle between the radial connection from the helix center through the Cα,i atom and the Cα,i−Cβ,i bond, viewed in the projection onto the plane perpendicular to the helix axis (C-terminus is in the back); definition of the helix pitch Θi,i+1, the angular distance of two subsequent Cα atoms. (E) Definition of δi, the angle between the membrane plane and the Cα,i−Cβ,i bond.

consecutive residues around the helix axis. Of particular importance here is our assumption in the NMR data analysis that the peptides are described by ideal α-helices. This means that the values of Φ, ψ, α, β, and Θ are treated as constants that do not change over time and are the same for all residues in the peptide. It is a necessary approximation because the NMR spectra usually do not provide enough information to determine these angles for each residue, and the data reflect time averages over the experimental time scale. In MD, on the other hand, these angles are not constant, and they will change over time and also be different for each residue in the peptide. Therefore, they are given indices such that Φi, ψi, αi, βi, and Θi,i+1 are the angles that fully describe the instantaneous geometry of any individual residue i. By averaging the angles over different time intervals, it is possible to study how the averages converge and to get an estimate of how long a simulation should be performed to give useful results. It is also possible to find out whether the angles are consistently different for different types of residues or whether they are different closer to the termini of the peptide due to partial unravelling, as these aspects cannot easily be determined by NMR61 but are important for the NMR interpretation. Thus, the 2H NMR data give experimental constraints that can be used to test the MD results, and vice versa MD can be used to improve the experimental picture by giving more accurate values for the structure-defining angles to be employed in the NMR data analysis.

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METHODS Simulations. Three helical peptides were simulated, which have been studied comprehensively in the past by SSNMR: (i) the 21-mer PGLa from X. laevis [charge +5, GMASKAGAIAGKIAKVALKAL-NH2];5,13,56,62−71 (ii) the 21-mer MSI103 whose sequence was derived from PGLa to obtain an ideal amphiphilic structure [charge +7, (KIAGKIA) 3 NH2];12,57,58,72−74 (iii) the shorter 14-mer KIA14 with the same repeat sequence as MSI-103 [charge +5, (KIAGKIA)2NH2].58,61,73,74 All peptides were initially modeled as ideal αhelices using the xleap tool from the AmberTools modeling suite,75 with dihedral angles of Φ0 = −57° (Ci‑1, Ni, Cα,i, Ci) and ψ0 = −47° (Ni, Cα,i, Ci, Ni+1). B


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Table S1. Separate tables for each simulated peptide with all splittings, αi, βi, and Θi,i+1, can be found in Tables S2−S4. Table 1 summarizes for each of the three peptides the averages of the angles αi, βi, and Θi,i+1 calculated from the last

MD simulations were conducted in a DMPC bilayer consisting of 128 lipids with 4500−5700 TIP3P water molecules.76 The SLIPID force field77 was used for the lipids, and the AMBER99SB-ILDN force field78 for everything else. First, the peptide−membrane complexes were constructed by conducting unrestrained membrane binding simulations of 10−20 ns length, at an elevated temperature of 480 K to speed up insertion (simulation protocol from ref 37). Here, a single peptide helix was placed parallel to pre-equilibrated lipid bilayers at a distance of 2 nm. During the high temperature insertion, H-bonds in the helix backbone were restrained using distance restraints of 1000 kJ/(mol nm2) to prevent unfolding. After cooling to 303 K, a short equilibration run of 500 ps with position restraints of 1000 kJ/(mol nm2) on the membraneinserted peptide was performed to allow temperature and volume to stabilize. Then, the system was simulated without any restraints at 303 K for 1 μs in the NPT ensemble (constant pressure P, temperature T, and number of particles N), using a Nosé−Hoover thermostat79 and Parrinello−Rahman barostat at 1 bar80 with semi-isotropic pressure coupling. A time step of 2 fs was used for all simulations, together with the LINCS algorithm81 to constrain all bonds. Long range electrostatics were treated via particle-mesh Ewald82 combined with a 1.4 nm direct space cutoff for van der Waals and Coulomb interactions. Snapshots were saved every 50 ps. The calculation of the angles τ, ρ, αi, βi, and Θi,i+1 (and the additional angle Δδi,i+1, which is explained below) is described in the Supporting Information. The helicity for each residue i over a given time interval is calculated as the percentage of snapshots, in which the dihedral angles Φi and ψi are within 30° around the starting values of Φ0 = −57° and ψ0 = −47°.

Table 1. Average Values for Fit Parameters α, β, and Θ from MD Simulationsa Peptide

⟨α⟩ (deg)

⟨β⟩ (deg)

⟨Θ⟩ (deg)

⟨Δδ⟩ (deg)b

Δρ (deg)c

PGLa MSI-103 KIA14

39 ± 13 39 ± 14 39 ± 9

122 ± 8 121 ± 9 122 ± 6

100 ± 16 100 ± 18 98 ± 7

99 ± 14 100 ± 15 99 ± 13

11 14 14

a

Averages were calculated over all residues in the helical region over the simulation period from 200−1000 ns. Details on the calculation of the angles are found in the Supporting Information. bAverage difference between the δ angles (Figure 1) for two subsequent residues i, i + 1. cDifference between ρ calculated directly from the MD coordinates and ρ from the best fit of the MD-derived splittings, fitted with the old value of α = 53.2° and β = 121.1°.

800 ns of the simulations and averaged over all helical residues. The averaged quantities are denoted as ⟨α⟩, etc. The averages for each of the four intervals for each residue are shown in Tables S2−S4. It can be noted that the individual values for the different residues are quite different and that there is also a variation between the time intervals. However, the averages over all residues (last row in Tables S2−S4) are very similar for each interval, showing that the simulations have converged. The values are also very similar among the three peptides, suggesting that these average angles are the same in all amphipathic peptides. The values for ⟨β⟩ are very close to the one used in fitting the helical wave curves earlier (121.1°). However, the value of ⟨α⟩ obtained from the MD simulations is generally 11° to 14° lower than what was used for analyzing the splittings (53.2°). This difference in the value of α does not influence the RMSD, which represents the quality of the fit, but it will lead to a change in the resulting ρ angle. The splitting depends on the angle δ, which in turns depends on the sum of ⟨α⟩ and ρ (see eqs S1−S5 in the Supporting Information); thus, decreasing ⟨α⟩ with 14° will lead to an increase of ρ with 14°. Table 1 shows the average helix pitch angle ⟨Θ⟩, which is the pitch between the Cα atom positions of two consecutive residues. In Tables S2−S4, it can also be seen that for individual sites Θi,i+1 can be very different, and sometimes it is consistently higher or lower than the average for all intervals. This could be due to insufficient sampling for single positions, or it may reflect a real variation in Θi,i+1 depending on the residue and its environment. The splitting Δνq is calculated from δ, which is defined in Figure 1. It contains a sum of the three angles Θ, α, and ρ (see eqs S4 and S5 in the Supporting Information). Therefore, for the calculation of the MD-derived splittings the pitch Δδ between two subsequent δ angles is actually the most relevant parameter. Δδ was extracted from each snapshot, and the average values for each position over each interval are listed in Tables S2−S4. We find that the deviation in Θ is slightly compensated by a deviation in α, or vice versa, so that in many cases Δδi,i+1 is closer to the ideal value of 100° than Θi,i+1. The average values ⟨Θ⟩ and ⟨Δδ⟩ are shown in Table 1, and both are very close to the ideal value of 100° used in the fitting. For PGLa and MSI-103, the lower standard deviations in Δδ show that this angle is fluctuating slightly less than Θ.

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RESULTS The aim of the study is to determine the orientation of several peptides in a membrane using MD simulations and compare with results from NMR data. In the following paragraphs, for each of the four scenarios (PGLa surface-bound, PGLa tilted, MSI-103, KIA14), we set off to determine and compare the values of the helix tilt angle τ and the azimuthal rotations ρ, which were obtained in three different approaches, namely, approach i from the simulation trajectories directly, approach ii from the time-averaged MD-derived splittings, and approach iii as experimental time- and ensemble-averages from the 2H NMR splittings. To determine the orientation from NMR data and from MD-derived splittings, a model structure of the peptide is used, in which the α-helix is defined by the structural parameters αi, βi, and Θi,i+1, which describe the angles defining the orientation of the Cα−Cβ bond of Ala-d3 with respect to the helix axis. In the original NMR studies cited here, these angles were taken from a model α-helix built with the Sybyl software, and the values used were the same for all residues; α = 53.2°, β = 121.1°, and Θ = 100.0°.65 The values can also be determined from the MD simulations, which we have done here. For the MD analyses, the simulations of 1 μs were divided into five periods of 200 ns duration each. The first period, 0− 200 ns, was omitted in the evaluation to allow the system to equilibrate. For each peptide, the helicity per residue and the full set of angles (τ, ρ, αi, βi, and Θi,i+1) were calculated as averages over each of the four remaining time intervals. Additionally, the values of the theoretically expected quadrupolar splittings were calculated from the MD simulations, and averages are given in the Supporting Information, C


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terminus makes occasional contact with the head groups of the opposite bilayer leaflet. The third interval #3 shows an intermediate orientation between these two states with a nominal tilt angle of 105°. The development of τ over the course of the whole simulation is shown in Figure S5. The azimuthal rotation angle ρ is always between 105° and 120°. From our definition of ρ, this means that the 12th residue, a positively charged Lys, points up into the water phase, as expected. PGLa is thus seen to undergo a drastic reorientation within the last 300 ns of the simulation, leading to a state where the peptide is obliquely tilted into the membrane, connecting with the opposite leaflet. This tilted state agrees very well with the state measured by NMR at a higher P/L = 1:50, which has been postulated to be dimeric.13,37,63,67 The present simulations show that this state is not necessarily dimeric but can occur also for a monomer. This kind of monomeric insertion has been predicted from the 3D hydrophobic moment of PGLa in a membrane.83 However, this tilted state was not found in a previous simulation of PGLa37 and is also not seen at low peptide concentration using SSNMR.5,13,63 Therefore, it is not clear whether the tilted state is stable for a monomer; hence, a much longer simulation would be needed to investigate this in more detail. For each time interval, the theoretically predicted quadrupolar couplings were calculated (approach ii), as summarized in the complete list of Table S2. So-called “helical waves” were fitted to these MD-derived splittings in order to determine which orientation of an ideal helix matches these values best. This approach ii is based on the same kind of data analysis procedure that was originally developed and is routinely used to interpret the experimental 2H NMR splittings in approach iii.5,12,13,59,60,65 For the fit of the MD-derived splittings, the sign was taken into account, which is not possible for the 2H NMR splittings since only absolute values are available from the experiments. The best-fit helix tilt and rotation angles, obtained from the MD-derived splittings from the first two intervals, are shown in Figure 3A, together with the previously published 2H NMR data in DMPC at a peptide-to-lipid molar ratio P/L = 1:200.5,11 Also, the best fits for the individual intervals are listed in Table 2. The characteristic shape of a

In our comparison of peptide orientation determined from MD simulation and NMR, we use the values used previously for β and Θ, which are almost identical to the average values found in the simulations, but use α as found in the simulations: α = 39.0°, β = 121.1°, and Θ = 100.0°. A short discussion about the influence of the structure parameters on the fits is found in the Supporting Information. PGLa. The evaluation of the helicity for PGLa showed that the peptide unravels at the amidated C-terminus, starting from position 18 (Figure 2). When looking at the successive time

Figure 2. Helicity and orientation of PGLa (approach i). (A) Helicity along the peptide sequence as a percentage of time for four successive time intervals. The boxed region from positions 2−17 is almost perfectly α-helical. (B) Values of the helix tilt angle τ and the azimuthal rotation ρ were calculated for this helical region (positions 2−17) for each time interval of the simulation.

intervals (each 200 ns), the unraveling is more pronounced in the middle time intervals and becomes less in the last interval. The region from residues 2−17 remains almost fully helical. Therefore, in approaches i and ii, we calculated the τ and ρ angles for the helix from all residues within this well-defined helical region (Table 2). In the experimental approach iii, splittings are obviously only available for the actual 10 (or 11) deuterium-labeled positions. In approach i, we obtain for the intervals #1 and #2 a timeaveraged tilt angle τ of 99°/100° (between the helix axis and the membrane normal); i.e., the peptide is embedded almost flat in the lipid headgroup region, parallel to the membrane surface. The last interval #4, on the other hand, shows a tilted helix with an angle of 123°, where the deeply embedded C-

Table 2. Helix Tilt Angle τ and Azimuthal Rotation Angle ρ from the Simulation of PGLa Measured for the Helical Part From Positions 2−17a Calculated directly from the trajectories of positions 2−17 (approach i)

2

Interval #

Time (ns)

τ ± στ (deg)

1 2 1−2b 3 4c 1−4

200−400 400−600 200−600 600−800 800−1000 200−1000

99 ± 8 100 ± 6 99 ± 7 105 ± 10 123 ± 7 107 ± 12

c

H NMR PGLa in DMPC 1:200 (in the surface-bound state) 2 H NMR PGLa in DMPC 1:50d (in the obliquely tilted state)

Fit of all MD-derived splittings from positions 2−17 (approach ii)

ρ ± σρ (deg)

τ (deg)

ρ (deg)

Smol

RMSD (kHz)

± ± ± ± ± ±

100 101 101 107 128 108

113 109 111 122 107 113

0.84 0.83 0.83 0.79 0.87 0.79

4.4 4.3 4.2 3.5 5.4 3.4

110 107 109 120 105 110

15 16 16 20 17 18

Positions 6, 7, 8, 9, 10, 11, 13, 14, 16, 17 Positions 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 20

Fit of ∼10 experimental quadrupolar splittings (approach iii)b 97 127 0.71 4.1 127

125

0.77

1.7

a Values of τ and ρ were calculated directly from the trajectories (approach i) and from a fit of the MD-derived splittings to an ideal α-helix (approach ii). For comparison, the lower part of the table contains the fits to the experimentally determined NMR splittings (approach iii). bNMR data from ref 11. cSplittings and fits are shown in Figure 3A, representing the surface-bound state of PGLa. dSplittings and fits are shown in Figure 3B, representing the tilted state of PGLa.

D


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iii) shows that they tend to have very different values. From the helical wave curves in Figure 3A, it can be seen that the main cause of these deviation is simply due to a phase shift of the wave curves along the x-axis by 16°. This corresponds to a considerable difference in the ρ angles and is even more so reflected in the values of the splittings. Another slight effect can be attributed to the different scaling factors Smol, which are evaluated as 0.83 in the simulations compared to 0.71 in the experiment. Yet, the actual shapes of the curves are very similar, reflecting the same α-helical conformation and only a very minor difference in τ. The RMSD, which is a measure of how well the individual data points agree with the fitted curve, is similar for the MD-derived fit and the experimental fit. Next, we proceed to interval #4 of the MD simulation, where PGLa is seen to be considerable tilted in the lipid bilayer, reaching even toward the other surface. The τ value calculated from the MD-derived splittings (approach ii) is within 5° of the one calculated directly from the trajectory (approach i), and ρ is almost identical. Figure 3B shows the best-fit wave plots from the MD-derived splittings (approach ii) and the experimental data (approach iii). In this case, the 2H NMR data correspond to experimental conditions under which the PGLa helix is known to be tilted, namely, at a relatively high peptide concentration of 1:50 in DMPC.5,11 The two helical wave curves clearly resemble each other, but again, the fit of the experimental data is phase-shifted to the left by 18°. Also here, Smol from the simulation implies a slightly lower mobility than from the experiment. The quality of the fit is higher for the experimental data, as indicated by a low RMSD of 1.7 kHz (approach iii), whereas the quality of the fit based on the MDderived splittings has deteriorated, as indicated by a high RMSD of 5.4 kHz (approach ii). The experimental data are thus in a better agreement with the underlying model of an ideal α-helix than the simulation data. MSI-103. The designer-made 21-mer MSI-103, whose sequence had been derived from PGLa, shows a behavior similar to PGLa. In both cases, the helical region ends at position 17 (Figure 4A). At the N-terminus, however, where Gly-1 and Met-2 of PGLa have been replaced by Lys and Ile,

Figure 3. Fits of the MD-derived splittings obtained from the simulations of the peptides (approach ii, black), compared with the experimental 2H NMR data (approach iii, red). For the fits of the MD-derived splittings, the sign of the splittings has been taken into account. However, for better comparison with the experimental fits, the absolute values of the splittings are shown in the helical wave curves. (A) For the surface-bound alignment of PGLa, the MDderived splittings were averaged over intervals #1 and #2 and compared with the 2H NMR data measured for PGLa in DMPC at a peptide-to-lipid ratio of 1:200. Best-fit values for the MD-derived data are τ = 101°, ρ = 111°, Smol = 0.83, and RMSD = 4.2 kHz and for the NMR data τ = 97°, ρ = 127°, Smol = 0.71, and RMSD = 4.1 kHz. (B) For the tilted orientation of PGLa, the splittings from interval #4 are compared with the 2H NMR data measured for PGLa in DMPC at a peptide-to-lipid ratio of 1:50. Best-fit values for the MD-derived data are τ = 128°, ρ = 107°, Smol = 0.87, and RMSD = 5.4 kHz and for the NMR data τ = 127°, ρ = 125°, Smol = 0.77, and RMSD = 1.7 kHz. (C) For MSI-103, the splittings were averaged over intervals #1−#4 and are compared with the 2H NMR data measured for a MSI-103 in DOPC at a peptide-to-lipid ratio of 1:200. Best-fit values for the simulation data are τ = 98°, ρ = 139°, Smol = 0.83, and RMSD = 3.5 kHz and for the NMR data τ = 96°, ρ = 148°, Smol = 0.73, and RMSD = 3.3 kHz. (D) For KIA14, the splittings were averaged over intervals #1−#4 and are compared with the 2H NMR data measured for KIA14 in DMPC at a peptide-to-lipid ratio of 1:50. Best-fit values for the simulation data are τ = 99°, ρ = 122°, Smol = 0.84, and RMSD = 1.2 kHz and for the NMR data τ = 102°, ρ = 139°, Smol = 0.67, and RMSD = 3.8 kHz.

helical wave curve is defined by the helix tilt angle τ, while the phase shift along the x-axis reflects the azimuthal rotation angle ρ.43,60 The amplitude of the curve is scaled by the so-called molecular order parameter Smol, which is a simplified way to describe the extent of motional averaging within the range of Smol = 1.0 (complete immobilization) and Smol = 0.0 (for isotropic tumbling). The MD-derived splittings from intervals #1 and #2 are very similar to the NMR data and give almost the same fit, whereas the fit for interval #3 reflects an intermediate orientational scenario as explained above. The values derived this way (approach ii) for the tilt angle τ are very close to the ones calculated directly from the peptide coordinates in the MD trajectory (approach i), differing by no more than 2°. The ρ values obtained in approach ii are 2°−3° higher than the ones calculated directly in approach i, as seen in Table 2. A comparison of the MD-derived splittings (approach ii) with those measured experimentally by 2H NMR (approach

Figure 4. (A) Helicity and (B) orientation of MSI-103 (approach i). The orientation refers to the helical region from positions 3−17. (C) Helicity and (D) orientation of KIA14 (approach i). The orientation refers to the helical region from position 3−10. Ideal α-helical regions are boxed. E


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Table 3. Helix Tilt Angle τ and Azimuthal Rotation Angle ρ from the Simulation of MSI-103 Measured for the Helical Part from Positions 3−17 Calculated directly from the trajectories of positions 3−17 (approach i) Interval #

Time (ns)

τ ± στ (deg)

1 2 3 4 1−4b

200−400 400−600 600−800 800−1000 200−1000

97 ± 7 98 ± 7 100 ± 7 98 ± 7 98 ± 7

H NMR MSI-103 in DMPC 1:200b (between surface-bound and tilted) 2 H NMR MSI-103 in DOPC 1:200c (in the surface-bound state) 2


ρ ± σρ (deg)

τ (deg)

ρ (deg)

Smol

RMSD (kHz)

± ± ± ± ±

97 97 100 98 98

130 144 138 144 139

0.85 0.86 0.87 0.81 0.83

6.3 3.0 2.6 4.9 3.5

130 144 138 145 139

18 15 16 24 19

Fit of seven experimental quadrupolar splittings (approach iii)a 111 136 0.65 1.6

Positions 7, 9, 10, 11, 13, 14, 17 Positions 7, 9, 10, 11, 13, 14, 17

96

148

0.73

3.3

NMR data from ref 72. bBeyond threshold of dimerization of MSI-103. cSplittings and fits are shown in Figure 3C.

a

Table 4. Helix Tilt Angle τ and Azimuthal Rotation Angle ρ from the Simulation of KIA14 Measured for the Helical Part from Positions 3−10 Calculated directly from the trajectories of positions 3−10 (approach i) Interval #

Time (ns)

τ ± στ (deg)

1 2 3 4 1−4a

200−400 400−600 600−800 800−1000 200−1000

100 ± 9 93 ± 9 101 ± 9 99 ± 11 98 ± 10

H NMR KIA14 in DMPC 1:50b (in the surface-bound state) 2 H NMR KIA14 in DOPC 1:50 (in the surface-bound state) 2


ρ ± σρ (deg)

τ (deg)

ρ (deg)

Smol

RMSD (kHz)

± ± ± ± ±

101 93 103 99 99

132 126 115 114 122

0.85 0.84 0.90 0.87 0.84

1.9 2.5 1.5 1.3 1.2

132 127 115 114 122

14 16 11 14 16

Positions 4, 6, 7, 9, 10, 11, 13, 14 Positions 4, 6, 7, 9, 10, 11, 13, 14

Fit of eight experimental quadrupolar splittings (approach iii)a 102 139 0.67 3.8 99

142

0.66

2.9

NMR data from ref 61. bSplittings and fits are shown in Figure 3D.

a

i.e., in our experimental time-averaged ensembles, it was always found to tilt more readily than PGLa.12,84 This behavior leads to a fast exchange between the surface-bound state and the tilted state, similar to what is seen in the MD interval #3 of PGLa. Whereas in the MD simulation, the observed tilting of PGLa seems to have been an auspicious event, the genuine tendency of MSI-103 to start tilting in DMPC at 1:200 is reflected in its high mobility with an experimental Smol of 0.65. In another lipid system (DOPC at P/L = 1:200), where membrane insertion is known to be disfavored, the NMR data show a clean surface state where the peptide lies flat on the membrane surface,72 as observed here in the simulation. Under those experimental conditions, the alignment of MSI-103 is very similar to the present simulation. Compared to the NMR data in DOPC (approach iii), the tilt angle from the MDderived splittings (approach ii) is almost the same. Again, we note that ρ is smaller in the MD fit by 9°. The helical wave analyses of the MD-derived splittings generally yield a mobility for MSI-103 with Smol ≥ 0.8 (approach ii), similar to that of PGLa. However, the quality of the fits based on the MD-derived splittings is rather variable, with RMSDs from 2.6 to 6.3 kHz for the four different intervals. This may seem surprising since the peptide is nearly perfectly helical over positions 3−17, according to Figure 4A. Yet, the local structure of the backbone was seen to vary considerably within a range of Φ and Ψ angles that are

MSI-103 is less helical than PGLa. Hence, residues 3−17 are identified as well-folded and used to calculate the orientational angles τ and ρ of MSI-103 (Table 3). These two angles do not change much throughout the entire 1 μs simulation, as seen from the narrow distributions in Figure 4B. The helix tilt angle τ obtained directly from the trajectories (approach i) is on average 98° and close to that of PGLa in the intervals #1 and #2, indicating that also MSI-103 lies flat on the membrane surface. Likewise, the charged Lys residue at position 12 of MSI-103 is aligned toward the aqueous phase, giving a plausible average azimuthal rotation angle ρ of 139°. The MD-derived splittings calculated for the helical part of MSI-103 were fitted to an ideal α-helix (approach ii) and compared with the best fit from 2H NMR data (approach iii) in different lipids.12,72 The best fits for the four simulation intervals (approach ii) gave essentially the same value for the tilt angle τ as when this parameter was measured directly from the trajectories (approach i), as seen in Table 3. The ρ angles obtained from the fit (approach ii) are within 1° to the directly calculated ones (approach i). Notably, from the analysis of the experimental 2H NMR data in the standard lipid DMPC at P/ L = 1:200 (approach iii), the value of τ is 10° larger than from the analysis of the simulated splittings (approach ii) (see Table 3 and ref 72). We attribute the difference seen in this particular peptide−lipid system to the fact that MSI-103 is known to start tilting already at a comparatively low threshold concentration; F


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Journal of Chemical Theory and Computation nevertheless still considered to be α-helical in the helicity analysis, as described in the Methods section. A closer look at these local angles in Table S3 reveals these differences, which explains why the calculated MD-derived splittings change so much between the single intervals. Over the full simulation, intervals #1−#4, the RMSD is 3.5 kHz, similar to that found for PGLa. KIA14. In the MD simulation, the short 14-mer peptide KIA14 is seen to be helical up to position 10. As observed for PGLa and MSI-103, the last four residues seem to be frayed out. As in MSI-103, which consists of the same motif (KIAGKIA) repeated three times, the helical region starts at position 3 (Figure 4C). While the angles τ and ρ are more variable for KIA14 in intervals #1 and #2, they converge to τ ≈ 100° and ρ ≈ 115° in the last two intervals of approach i (Table 4). The average helix tilt angle τ is 98° and thus identical to that of MSI-103, while the average azimuthal rotation angle ρ is 122°, some 17° lower than for MSI-103. [Here, the position of residue 12, relative to which we define ρ, lies outside the helical region, but this was taken into account by extrapolating from the helical part of the peptide]. Once more, the tilt angles obtained from the MD-derived splittings of the helical region (approach ii) are almost identical to the ones obtained directly from the trajectories (approach i), and the ρ angles are again within 1° of those from the trajectories. The experimental 2H NMR data of KIA14 (approach iii) show roughly the same orientation in DMPC and DOPC at P/ L = 1:50.61 The tilt angle τ agrees with the results obtained from the MD-derived splittings (approach ii), but again the latter curves are shifted to lower values of ρ, as was observed also in the cases of PGLa and MSI-103. The difference in ρ between the two approaches shown in Figure 3D is 17° for KIA14. The mobility in the MD simulations with Smol values ≥0.84 is again lower than in the experiment with Smol = 0.66. Unlike what was seen for the two other peptides, in the case of KIA14, the fits of the MD data are much better, with RMSD values between 1.3 and 2.5 kHz, compared to the experimental RMSD of 3−4 kHz. RMSD Analysis. Given that the fits of the MD-derived splittings included only data from the well-folded α-helical regions of the peptides, the RMSD values are quite high. (Only for KIA14 the RMSD values are below 2 kHz.) Particularly intriguing is MSI-103, where the RMSD ranges from 2.6 to 6.3 kHz for the different intervals. To better understand the RMSD values, a more thorough analysis was carried out of the individual splittings, using MSI-103 as the example to be illustrated here (and PGLa and KIA14 in the Supporting Information). Figure 5 shows how the individual MD-derived splittings for MSI-103 deviate from the best-fit curve that was generated from this set of data. For each position in the helical part of the peptide, the corresponding splitting had been calculated as an average over all snapshots from the instantaneous angle ϑi (between the Cα−Cβ bond, as if it were a CD3-group, and the membrane normal, Figure S1C), using eq S1 (black squares in Figure 3C). A fit was performed for the whole set of these splittings, and the best-fit curve is seen in black in Figure 3C. The difference between this best-fit curve (which assumes an ideal helix with a specific tilt and azimuthal angle) and the simulated splittings then yielded the deviations shown in Figure 5. For an ideal helix geometry, the structural parameters βi, αi, and Θi,i+1 have constant values for all positions i, and successive angles δi (being the sum over ρ, αi, and Θi,i+1) between

Figure 5. Local deviations of the MD-derived splittings from the ideal α-helical wave curves calculated from the best-fit parameters for MSI103. θi is defined in eq S5. Black curves: Splittings directly calculated from ⟨ϑi⟩ values. Green curves: Splittings calculated from the fitted τ, ρ, Smol, and the individual ⟨βi⟩ and ⟨δi⟩ for each side chain. Values for the simulated interval (A) 200−400 ns, (B) 400−600 ns, (C) 600− 800 ns, and (D) 800−1000 ns. (E) Values obtained for the complete evaluation period 200−1000 ns.

residues i and i + 1 differ by 100°. In the simulation, however, the helix is not ideal, so βi varies between the different positions and successive δi are not steady. We have therefore used the average values of βi and δi for the different simulation intervals to calculate the splittings that would be expected for the best-fit values of τ, ρ, Smol, and the actual average angles βi and δi using eq S6. The green symbols and curves in Figure 5 show the deviation of these splittings from the best-fit helical wave curve. The green curves thus reflect the local perturbations due to the nonideal time-averaged geometry of the peptide. The black curves additionally include effects due to fluctuations of the structure away from the average structure, nonideal dynamics, and other contributions. The large RMSD of 6.3 kHz in interval #1 is mainly caused by positions Ile9 and Lys15, which deviate by ∼13 kHz from the best-fit curve. In intervals #2 and #3, the deviations are smaller for these and most other positions, leading to lower RMSD values of 3.0 and 2.6 kHz. In interval #4, the deviations become larger again, leading to an RMSD value of 4.9 kHz. The green and black curves are almost identical in interval #1, and they are also similar in intervals #2 and #3 but are quite different in interval #4. This shows that for intervals #1−#3, the deviations from the ideal curve (the RMSD values) are mainly caused by the local deviations of the individual βi and δi angles for each residue from the ideal values, i.e., by a deviation of the time-averaged peptide structure from ideality. In interval G


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Journal of Chemical Theory and Computation #4, the structure seems to fluctuate more dramatically from the average structure, and there are probably also some contributions of non-Gaussian dynamics, which together are responsible for the large difference between the green and black curves. The analyses of the corresponding deviations for the other two peptides are shown in Figures S6 and S7. For PGLa, there are quite large contributions from nonideal geometry for Ser4, Ile9, and Gly11, while in KIA14 the deviations are quite small, except for Ala10 in interval #4. Analysis of Standard Deviations of Δνq. When looking at the standard deviations of the splittings, averaged over the total evaluated time from 200 to 1000 ns of the simulations (listed in Table S1), they range from ±8 up to ±30 kHz. This reflects the fluctuating orientations of the Cα−Cβ bonds with respect to the membrane normal (the z-axis of the simulation box). The standard deviations are clearly the lowest for splittings below −30 kHz. In Figure 6A, the standard

described in the Methods section. From SSNMR, the helicity can be determined indirectly by comparing the experimental splittings to best-fit helical wave curve to find out which part of the sequence gives splittings that fit to an ideal helix.11,61,72 It may be generally expected that the helices are less well-defined close to the termini because the terminal residues have no Hbonding partners. In the case of PGLa, previous MD simulations using different force fields have found rather different helicities. Using CHARMM,85 PGLa was found to be completely helical from the first to last residue throughout the entire simulation.37 On the other hand, with OPLS-AA,86 the central stretch of the peptide (especially around Gly7 and Gly11) had a very low helicity.37 Both of these results are questionable, as it has been proposed that the CHARMM force field overestimates the helical content of peptides,37,87 and the OPLS-AA result does not fit with experimental NMR data. Here, using another force field, a more realistic helicity was found for PGLa, which is mostly helical from positions 2−17 and becomes unravelled toward the C-terminus (Figure 2). A comprehensive set of 19FNMR data of PGLa in DOPC at P/L = 1:50 in the surfacebound state showed that the peptide is helical throughout the region from 3 to 17, as only the terminal (19F-labeled) positions Gly1, Met2, Ala20, and Ile21 did not fit well to the helical wave curve.88 A similar picture of a continuous α-helix up to position 16 is supported by 2H NMR,11 even though no data was acquired for the N-terminal positions. In MSI-103, our MD simulation shows high helicity for positions 3−17 (Figure 4A), and the existing 2H NMR data for positions 7−17 also shows a good fit to a helix, even though there was no data acquired closer to the termini.12,72 In KIA14, the helicity was quite high in our simulation for positions 3−10 (only in the last subinterval from 800 to 1000 ns it was much lower than in the other intervals) (Figure 4C). In this case, a comprehensive set of 2H NMR data is available from Ile2 to Ile14, which makes it possible to evaluate the whole length of this peptide experimentally, and it was found that the peptide is mostly helical for positions 4−14.61 Overall, our simulations agree very well with the experimental data of PGLa, MSI-103, and KIA14, with MD predicting only slightly more helicity at the N-terminus and possibly not quite enough toward the Cterminus. To be safe, in our subsequent structural analyses, however, we used only the certified helical parts of the peptides to analyze their orientation in the membrane, while the outer, more flexible parts, were excluded. The most direct way of comparing the MD simulations with the experimental data is to back calculate the theoretically expected 2H NMR quadrupolar splittings from the simulations at each position in the peptide by analyzing the orientation of the respective Cα−Cβ bond with respect to the membrane normal from the trajectory. This was done in approach ii, and these MD-derived splittings could be directly compared with the experimental quadrupolar splittings at the same positions. There are just a few limitations to this method. Experimental splittings are not available for all positions in the peptides since they must be synthesized with a selective Ala-d3 amino acid at every single position one-by-one to make the 2H NMR analysis possible, and not all positions in the peptides are suitable for replacement with Ala-d3. In particular, the cationic Lys residues have not been replaced because the overall charge of each peptide is important for its biological function. This aspect points to a second weakness, i.e., when any other amino acid is conservatively replaced by Ala-d3, the properties of the

Figure 6. (A) Standard deviations of the splittings with respect to the average splittings Δνq,i averaged over the time period given in the legend. (B) Average ϑ angles corresponding to the average splittings.

deviations are shown as a function of the average splittings. The splittings close to the theoretically most extreme value of −42 kHz have the lowest standard deviations and also the smallest spread along the y-axis for a specific x-value. For more positive splittings, the range of possible standard deviations is larger. Figure 6B shows the average ϑ angles that correspond to the splittings Δνq. Because of the relationship in eq S1, many more possible ϑ values are densely grouped within a small interval around ϑ = 90° (with almost identical splittings) compared to the density around other values of ϑ. Thus, the standard deviation for any specific splitting partly reflects the density of angular values corresponding to that splitting, and it does not per se say much about the mobility at that position. The gray values in Figure 6 show the data of the flexible, nonhelical parts of the peptides close to the N- and C-termini. As expected, the splittings obtained for these terminal positions have generally higher standard deviations than those calculated for the positions within the well-folded helical parts.

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DISCUSSION In this work, we have performed all-atom molecular dynamics simulations of three representative amphipathic peptides in lipid bilayers and compared the results with solid-state 2H NMR experimental data on the same peptides in oriented membrane samples. There are significant similarities between the results, but also some differences, which we now discuss. One important aspect of peptide structure concerns the local helicity. For the three peptides studied here, circular dichroism (CD) has shown that they form mostly α-helical structures in the presence of membranes,12,58,84 but it could not specify which residues are part of the helix. This information can be directly obtained from MD by analyzing the torsion angles as H


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Journal of Chemical Theory and Computation mutated peptide might change. To check this, circular dichroism is always used to check the labeled peptides, and in all cases considered here, the secondary structure was not affected by the introduction of Ala-d3.5,12,61 Still, when compared at the level of structural detail available in the MD study, there may be deviations. With these effects in mind, we can nevertheless cautiously interpret the similarities and differences between calculated and experimental splittings. At first sight, it seems surprising that the MD simulations cannot reproduce the splittings from the 2H NMR experiments at all, as seen from the large difference between calculated and measured splittings (black and red symbols, respectively, in Figure 3). For the native Ala positions in the sequence, where the MD analysis and the experimental Ala-d3 labels are identical (i.e., where the peptide structure in the experiment cannot be influenced by an Ala-d3 label), the back-calculated splittings from MD do not agree any better with the NMR data. One of the reasons for the bad agreement of the splittings could be an incomplete convergence of the peptide− membrane systems. It was demonstrated using a long 8 μs simulation that even a simulation time of 1 μs as used here may not be enough to reach equilibrium for a peptide−lipid system, and changes in the peptide structure may still occur after long simulation times.42 The helicity plots (Figures 2 and 4) show that the secondary structure of the peptides is indeed not fixed but rather evolves during the course of the simulations. In the future, longer simulations could help to decide whether this evolution is an intrinsic dynamic process, i.e., if it is due to random fluctuations, or if it is part of a converging process. Another systematic deviation that comes to mind is the mobility factor Smol, which is generally higher when calculated from the MD-derived fits than the experimental splittings, implying a lower mobility in the simulations. Notably, when the fits of splittings are averaged over the entire simulation (200−1000 ns), we obtain a lower Smol than the average over the Smol values of the four individual 200 ns intervals. This means that for a short 200 ns simulation, there is not enough time for the peptide to sample the whole dynamic space, which leads to an underestimation of peptide mobility. Even using 1 μs simulation time seems not to be enough to sample the full dynamics, and even longer simulation times would be better. Most interestingly, we find that the overall peptide orientations obtained by approach ii compare remarkably well with the experimental data (Figure 7), even though the experimental splittings are not reproduced by the simulations. When the MD-derived splittings are analyzed in the same way as the experimental splittings (approach iii), the resulting helix orientations are very similar in each of the three peptide systems: especially the tilt angles are almost identical. For PGLa (in the interval 200−600 ns), MD gave τ = 101°, while the NMR analysis gave τ = 97°. For MSI-103, τ = 98°, while NMR (in DOPC) gave τ = 96°. For KIA14, τ = 99°, while NMR gave τ = 102°. Thus, the simulations can reproduce the helix tilt angles of the three peptides found from the NMR data analysis to a very high accuracy. Interestingly, we observe a systematic deviation in the azimuthal angles in Figure 7, where the peptides are drawn in a helical wheel representation to illustrate the difference in ρ between the MD simulation (approach ii) and the NMR data (approach iii). For PGLa in the surface-bound state (interval 200−600 ns), the MD-derived splittings gave ρ = 111°, while NMR gave ρ = 127°, a difference of 16°. In the tilted state (interval 800−1000 ns), MD gave ρ = 107°, compared to 125°

Figure 7. Helix orientations have been evaluated in three different ways from the MD and NMR data of amphiphilic peptides embedded in lipid membranes. In approach i, the helix tilt angle τ and the azimuthal rotation ρ were estimated directly from the MD trajectory (values given in square brackets). It is most interesting to compare the results obtained by fitting the MD-derived splittings (approach ii, black) with those found by fitting the experimental NMR splittings (approach iii, red). In the helical wheel representations, the peptides are viewed from the N-terminus.

from NMR at P/L = 1:50, a difference of 18°. For MSI-103, ρ = 139°, while NMR (in DOPC) gave ρ = 148°, a difference of 9°. For KIA14, ρ = 122°, while NMR gave ρ = 139°, a difference of 17°. From the best-fit curves in Figure 3, it is obvious that the shape of the curves (which depends on the tilt angle) is very similar, but all MD-derived curves are phase shifted by 9°−18° along the y-axis, which directly reflects the differences in ρ. Since the difference is so similar in all three cases, it seems unlikely that this is due to a random variability; hence, there is probably a systematic error somewhere in the simulation setup. The most likely source of this error is the force field, which seems to give an apparent energy minimum with a somewhat different azimuthal rotation angle of the amphiphilic helix at the membrane−water interface than what is found in nature. The most likely reason could be either that hydrophobic groups in the peptide have different preferences for the hydrophobic environment or that the charged Lys side chains are preferentially located in a more or less polar environment, compared to a real system. We note that in a previous simulation of PGLa in DMPC bilayers, using two other force fields, a similar effect was found.37 A CHARMM force field gave ρ = 98°, and OPLS gave ρ = 106°, compared to 113° for the NMR analysis (respectively, 116° when using a different set of experimental splittings as in that paper). It should here be noted that from the present simulations, we find an average α angle for all three peptides of 39°, which is also used in the fits. In many previous NMR data analyses,5,11−13,19,20,37,43,50,63−65,67,68,72,89−92 a value of α = 53.2° was used, and therefore, the ρ angles are 14° smaller in those previous publications. In any case, three different simulations with three different force fields have systematically produced ρ values for PGLa that are 10°−18° lower than in the NMR experiments,37 and now the same effect is also seen for MSI-103 and KIA14. This finding suggests a systematic difference. On the other hand, a recent simulation of magainin 2, a related antimicrobial peptide that also forms an amphiphilic α-helix, gave only a 3° difference in the ρ value when experimental and simulated splittings were analyzed.50 In that simulation the same force field was used as I


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structure for certain residues due to steric or dynamic reasons, a fit of the simulated splittings to an ideal helix will always produce a certain RMSD between the splittings and the ideal helical wave curve (Figure 5). The RMSD values are different for different 200 ns long intervals but are generally smaller for the full 800 ns simulation. This observation indicates that deviations from the ideal α-helical structure also average out in the course of the simulation, leading to better fits for a longer simulation. RMSD values of 2−3 kHz are found here for the fits to the MD-derived as well as experimental splittings, and we can thus assume that the error for the experimental analysis is also mainly due to nonideal helices. But these deviations are small enough to still allow a reliable determination of the peptide orientation in the membrane based on ideal α-helices, which is good news for this kind of solid-state NMR structure analysis in general.

in the present study. One possible reason for the reduced discrepancy in ρ between MD and NMR could be the presence of a negatively charged Glu residue and the anionic C-terminus in magainin 2, both of which will affect the azimuthal angle, whereas all three peptides studied here carry exclusively positive charges (N-terminus and Lys residues). This juxtaposition may point to some underlying force field problem related to the charged amide groups found in the Lys side chains and the N-terminus of the peptides. For magainin 2, such problem might be compensated by the effect of negative charges. How the force fields could be modified to address this problem is, however, outside the scope of this study, though it would be interesting to use the ρ angle effects to investigate and improve the force fields. It can be argued that the shifts in ρ are not very large and thus that the simulations are still giving a considerably good picture of the peptide alignment. However, due to the steep features in the helical wave curves (Figure 3), already a small shift in ρ of 9°−18° can produce a change in the 2H NMR quadrupolar splittings of up to 30 kHz, thereby leading to a very poor fit between simulations and experiments. In other words, the splittings are very sensitive to small changes in ρ, so the experimental NMR data provide a very stringent test of the quality of the simulation. The peptide orientation in terms of τ and ρ was also determined directly from the simulation trajectories using approach i, without calculating first any quadrupolar splittings to be analyzed. A comparison between these direct orientational angles and the fitted orientation shows that the helix tilt angle is in all cases almost identical to the ones obtained in approaches ii and iii, as seen in Tables 2−4 and summarized in Figure 7. The azimuthal angles from the direct approach i are also very similar to those calculated from the MD-derived splittings. The comparison of the full coordinate space of the MD simulation with the limited set of NMR data shows that both methods are very useful and reliable to describe the alignment of peptides in membranes. We can thus conclude that an analysis of splittings is a good way of obtaining the helix orientation, even if only a limited number of experimental constraints is available. It is not a trivial fact to find that the analysis of splittings, based on an idealized model of an α-helix, gives orientations of the peptide in the membrane in good agreement with the simulation. If we analyze the structural angles αi, βi, and Θi,i+1, over the different subintervals of the simulations, we can in fact see quite large fluctuations (see for example Table S3 for values from the MSI-103 simulation). The values not only fluctuate between 200 ns long intervals, but they are also distinctly different between different positions along the peptide sequence. Some residues have values of Θi,i+1 well above the ideal value of 100° throughout the whole simulation, while others have values well below 100°, and the same is seen for αi and βi. But the average values over all positions are in the end very close to the values of an ideal αhelix; i.e., over each of the 200 ns subintervals for all the peptides, we obtain ⟨α⟩ close to 39°, ⟨β⟩ close to 121°, and ⟨Θ⟩ close to 100°. Thus, it seems that the fluctuations within the molecular structure of the helix are fast and will be well sampled during a 200 ns simulation, in contrast to the overall peptide dynamics in the membrane (see the Smol discussion above). Also, on average, the helical regions of these membrane-bound peptides are well described by an ideal αhelix. However, as there are local deviations from the average

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CONCLUSIONS MD simulations of three peptides in lipid bilayers were here compared with experimental solid-state NMR peptides of the same systems. The two methods can complement each other, and it is possible to combine the strengths of the two methods to get a more complete picture of the behavior of peptides in membranes. Simulations can give instantaneous structures and orientations, whereas NMR gives averages over quite long times. It was found that the geometry of the peptide converges fast; over 200 ns of simulations average values of geometric parameters are well-defined and are the same over different 200 ns blocks of the 1 μs simulations and for different peptides. These parameters can be used in the NMR analysis, giving a better starting structure than previous static models. The order parameter found in the simulation is larger than the experimental value, but it gets smaller the longer the simulation is run. This shows that peptide dynamics in the membrane is relatively slow and can be used to determine how long a simulation should be run; 1 μs seems not to be long enough. When 2H NMR splittings are back calculated from the simulations and analyzed to get peptide orientations, the result is very similar to the orientation directly determined from the simulation. This is a good sign that the NMR analysis method is not too simplistic and that it can be used to get reliable information about average peptide orientations. When simulated splittings are compared with experimental splittings, there are large difference of up to 30 kHz. However, when the splittings are analyzed to give peptide orientations, the tilt angle from simulated splittings is almost identical to those from NMR splittings, and the difference in splitting is almost fully due to a difference in azimuthal angle between simulations and experiments of 9°−18°. This has been seen using several different force fields. Thus, MD simulations can give reliable tilt angles, but force fields seem to have some systematic bias giving somewhat shifted azimuthal angles. Using NMR data, it should be possible to refine the force fields to solve this problem.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jctc.8b00283. Details about the calculations of peptide orientations from the simulations. Figure describing the orientation of PGLa over the course of the simulation. Tables of 2H J


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(12) Strandberg, E.; Kanithasen, N.; Bürck, J.; Wadhwani, P.; Tiltak, D.; Zwernemann, O.; Ulrich, A. S. Solid state NMR analysis comparing the designer-made antibiotic MSI-103 with its parent peptide PGLa in lipid bilayers. Biochemistry 2008, 47, 2601−2616. (13) Glaser, R. W.; Sachse, C.; Dürr, U. H. N.; Afonin, S.; Wadhwani, P.; Strandberg, E.; Ulrich, A. S. Concentration-dependent realignment of the antimicrobial peptide PGLa in lipid membranes observed by solid-state 19F-NMR. Biophys. J. 2005, 88, 3392−3397. (14) Salnikov, E. S.; Aisenbrey, C.; Balandin, S. V.; Zhmak, M. N.; Ovchinnikova, T. V.; Bechinger, B. Structure and alignment of the membrane-associated antimicrobial peptide arenicin by oriented solid-state NMR spectroscopy. Biochemistry 2011, 50, 3784−3795. (15) Balla, M. S.; Bowie, J. H.; Separovic, F. Solid-state NMR study of antimicrobial peptides from Australian frogs in phospholipid membranes. Eur. Biophys. J. 2004, 33, 109−116. (16) Henzler-Wildman, K. A.; Martinez, G. V.; Brown, M. F.; Ramamoorthy, A. Perturbation of the hydrophobic core of lipid bilayers by the human antimicrobial peptide LL-37. Biochemistry 2004, 43, 8459−8469. (17) Maisch, D.; Wadhwani, P.; Afonin, S.; Böttcher, C.; Koksch, B.; Ulrich, A. S. Chemical labeling strategy with (R)- and (S)triofluoromethylalanin for solid state 19F NMR analysis of peptaibols in membranes. J. Am. Chem. Soc. 2009, 131, 15596−15597. (18) Strandberg, E.; Ulrich, A. S. AMPs and OMPs: Is the folding and bilayer insertion of β-stranded outer membrane proteins governed by the same biophysical principles as for α-helical antimicrobial peptides? Biochim. Biophys. Acta, Biomembr. 2015, 1848, 1944−1954. (19) Wadhwani, P.; Strandberg, E.; van den Berg, J.; Mink, C.; Bürck, J.; Ciriello, R.; Ulrich, A. S. Dynamical structure of the short multifunctional peptide BP100 in membranes. Biochim. Biophys. Acta, Biomembr. 2014, 1838, 940−949. (20) Fanghänel, S.; Wadhwani, P.; Strandberg, E.; Verdurmen, W. P. R.; Bürck, J.; Ehni, S.; Mykhailiuk, P. K.; Afonin, S.; Gerthsen, D.; Komarov, I. V.; et al. Structure analysis and conformational transitions of the cell penetrating peptide transportan 10 in the membrane-bound state. PLoS One 2014, 9, e99653. (21) Kwon, B.; Waring, A. J.; Hong, M. A 2H solid-state NMR study of lipid clustering by cationic antimicrobial and cell-penetrating peptides in model bacterial membranes. Biophys. J. 2013, 105, 2333− 2342. (22) Zamora-Carreras, H.; Strandberg, E.; Mühlhäuser, P.; Bürck, J.; Wadhwani, P.; Jiménez, M. Á .; Bruix, M.; Ulrich, A. S. Alanine scan and 2H NMR analysis of the membrane-active peptide BP100 point to a distinct carpet mechanism of action. Biochim. Biophys. Acta, Biomembr. 2016, 1858, 1328−1338. (23) Grasnick, D.; Sternberg, U.; Strandberg, E.; Wadhwani, P.; Ulrich, A. S. Irregular structure of the HIV fusion peptide in membranes demonstrated by solid-state NMR and MD simulations. Eur. Biophys. J. 2011, 40, 529−543. (24) Afonin, S.; Dürr, U. H. N.; Glaser, R. W.; Ulrich, A. S. ’Boomerang’-like insertion of a fusogenic peptide in a lipid membrane revealed by solid-state 19F NMR. Magn. Reson. Chem. 2004, 42, 195− 203. (25) Yao, H.; Hong, M. Conformation and lipid interaction of the fusion peptide of the paramyxovirus PIV5 in anionic and negativecurvature membranes from solid-state NMR. J. Am. Chem. Soc. 2014, 136, 2611−2624. (26) Schmick, S. D.; Weliky, D. P. Major antiparallel and minor parallel beta sheet populations detected in the membrane-associated human immunodeficiency virus fusion peptide. Biochemistry 2010, 49, 10623−10635. (27) Misiewicz, J.; Afonin, S.; Grage, S. L.; van den Berg, J.; Strandberg, E.; Wadhwani, P.; Ulrich, A. S. Action of the multifunctional peptide BP100 on native biomembranes examined by solid-state NMR. J. Biomol. NMR 2015, 61, 287−298. (28) Grage, S. L.; Kara, S.; Bordessa, A.; Doan, V.; Rizzolo, F.; Putzu, M.; Kubar, T.; Papini, A. M.; Chaume, G.; Brigaud, T.; et al. Orthogonal 19F-labeling for solid-state NMR spectroscopy reveals the

NMR splittings calculated from the simulations and experimental splittings. Figures with RMSD analyses of splittings for PGLa and KIA14. (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Sabine Reißer: 0000-0003-1224-6967 Erik Strandberg: 0000-0002-2401-7478 Anne S. Ulrich: 0000-0001-5571-9483 Present Addresses ∥

S. Reißer: Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136 Trieste, Italy ⊥ T. Steinbrecher: Schrödinger GmbH, Dynamostr. 13, 68165 Mannheim, Germany Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by the Helmholtz Association program BIF-TM and by the German Research Foundation (DFG) by grants EL206/12-1 and INST 121384/58-1 FUGG.

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