Lipid Dynamics Studied by Calculation of 31P ... - ACS Publications

Apr 16, 2014 - Mikkel Vestergaard , Johan F. Kraft , Thomas Vosegaard , Lea Thøgersen , and Birgit Schiøtt ... Daniel M. Dawson and Sharon E. Ashbro...
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Lipid Dynamics Studied by Calculation of 31P Solid-State NMR Spectra Using Ensembles from Molecular Dynamics Simulations Sara K. Hansen,† Mikkel Vestergaard,† Lea Thøgersen,†,‡ Birgit Schiøtt,† Niels Chr. Nielsen,† and Thomas Vosegaard*,† †

Center for Insoluble Protein Structures (inSPIN), Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark ‡ Center for Membrane Pumps in Cells and Diseases, Bioinformatics Research Centre, Aarhus University, DK-8000 Aarhus C, Denmark S Supporting Information *

ABSTRACT: We present a method to calculate 31P solid-state NMR spectra based on the dynamic input from extended molecular dynamics (MD) simulations. The dynamic information confered by MD simulations is much more comprehensive than the information provided by traditional NMR dynamics models based on, for example, order parameters. Therefore, valuable insight into the dynamics of biomolecules may be achieved by the present method. We have applied this method to study the dynamics of lipid bilayers containing the antimicrobial peptide alamethicin, and we show that the calculated 31P spectra obtained with input from MD simulations are in agreement with experiments under a large range of different sample conditions, including vesicles and oriented samples with and without peptides. We find that the changes in the 31P spectra upon addition of peptide stem from lipids with reduced diffusion due to peptide−lipid interactions.

1. INTRODUCTION Lipid bilayer membranes of living organisms are highly flexible. The importance of their mobility is manifested by the plethora of functions and processes involving lipids, including formation of permeability barriers of cells and subcellular organelles as well as accommodation of membrane and lipid-anchored proteins.1 Accordingly, the lipid environment is essential for the function of membrane-associated polypeptides. Investigation of the structure and dynamics of membrane proteins and peptides in their native surroundings remains a challenging, though important, task for understanding their function, where the interactions between lipids and membrane-associated polypeptides also play a central role. Because of this complexity, there exists no “golden method” to characterize the structure and dynamics of membrane proteins and membrane-associated peptides. Molecular dynamics (MD) simulations are widely used and are a well-accepted method for modeling biological systems on the time scale of nano- to microseconds, even up to milliseconds in a few cases.2 Numerous successful examples of MD simulations of biological macromolecules can be found in the literature, targeting, for example, protein folding,3 conformational changes,4−6 selectivity of membrane channels,7 and pore formation studies.8,9 It is essential for the credibility of MD simulations that they are in agreement with experimental observations. Numerous studies have used MD in combination with experiments, e.g. NMR, to study the structure and dynamics of various biological macromolecules.10−13 © 2014 American Chemical Society

Through several decades, NMR spectroscopy has been a prevalent tool to study dynamics of proteins. In the liquid state, the widely used model-free analysis separates the global rotational diffusion of the macromolecules from the internal motions.14−16 In solids, both magic-angle spinning (MAS) experiments of powdered protein samples and static-sample experiments of uniaxially oriented membrane proteins have proven a powerful tool for studying membrane proteins.17−21 For oriented-sample solid-state NMR, various bilayer mimics and modes of orientation have been developed, including hydrated lipid bilayers on cover glasses,22 bicelles,23,24 macrodiscs,25 and spinning samples using hydrated bilayers on cover glasses26 or polymer foils27 (magic-angle oriented-sample spinning). Recently, a number of oriented-sample solid-state NMR studies of small membrane proteins have revealed the importance of including information about protein/lipid dynamics in structural studies of such samples.28−32 Since the lipid environment is perturbed by the proteins it accommodates, it is possible to use the lipids as “spy” reporters on the behavior of the proteins. In a couple of recent studies, 31 P oriented-sample solid-state NMR studies of the lipids have revealed details on the membrane-bound conformation of antimicrobial peptides (AMPs) as well as on the reduced dynamics of the lipids in such systems.33,34 In the present study, Received: January 2, 2014 Revised: April 16, 2014 Published: April 16, 2014 5119

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randomly mutating lipids to DHPC until a DMPC/DHPC ratio of 3.2 was obtained, resulting in 1719 DMPC and 537 DHPC molecules in the bicelle. The disc was solvated with water to obtain a total lipid concentration of 300 mM (105280 CG-water beads), minimized, and simulated for 2500 ns using GROMACS 4.5.443 with the MARTINI 2.1P force field44 and a time step of 25 fs. The polarizable water model in MARTINI45 was employed for all CG simulations, as it has proved essential for modeling DHPC micelles correctly.46 The Lennard-Jones potential was cutoff at 12 Å with a shift potential starting at 9 Å, while the Coulomb potential was shifted to zero over the interval from 0 to 12 Å. As the random mixture of lipids within the bicelle had to equilibrate, the initial 2000 ns were considered as equilibration and 50000 snapshots equally distributed over the last 500 ns were used for the analysis. An isotropic pressure was applied by employing the Berendsen weak coupling algorithm47 with a time constant of 3.0 ps, a compressibility of 3 × 10−5 bar−1, and a target pressure of 1.0 bar. The temperature was kept at 308 K by use of Langevin dynamics with a coupling constant of 1.0 ps−1. Likewise, a DMPC bilayer consisting of 1000 lipids was simulated for 2000 ns using the polarizable water model in MARTINI.45 The pressure was controlled semiisotropically with the same coupling constants as employed in the bicelle simulation, while the temperature was kept at 298 K by a Berendsen thermostat with a time constant of 0.3 ps. 2.3. Sample Preparation for NMR Experiments. The macroscopically aligned samples were obtained by dissolving DMPC (and alamethicin) in MeOH and distributing the solution on 20 glass slides. The glass slides were allowed to dry at room temperature. Subsequently, the residual solvent was evaporated for 2 h in vacuo, and the sample was rehydrated at 100% relative humidity. The glass slides were carefully stacked, wrapped with parafilm, and packed in a small plastic bag to maintain hydration level, prior to each experiments. The bicelle sample (28% w/vol, q = 3.2) was prepared by dissolving dry DMPC powder in 10 mM phosphate buffer by vortexing until a homogeneous suspension was achieved. The suspension was added to the short-chained DHPC lipid and vortexed. Five cool/heat (4 °C/50 °C) cycles were performed to attain bicelle formation. The vesicle sample was prepared by suspending dry DMPC lipids in water. The sample was vortexed and ultrasonicated until it formed a homogeneous suspension. Five freeze/thaw cycles were applied to the sample to increase the size of the vesicles. 2.4. Solid-State NMR Experiments. All solid-state NMR experiments were conducted on a Bruker-400 Avance widebore spectrometer at 162.0 MHz (Bruker BioSpin, Rheinstetten, Germany). All 31P experiments on hydrated samples were performed in a Bruker flat-coil probe tuned in double resonance mode to 1H and 31P. The spectra of hydrated samples were recorded using a standard single-pulse experiment at 310 K, which is well above the gel-to-liquid crystalline phase transition at 297 K for DMPC. The 31P powder spectrum of DMPC was recorded in a 4 mm triple-resonance Bruker MAS probe operated in doubleresonance mode. The powder spectrum was obtained using a spin−echo pulse sequence with an interpulse delay of 1 ms and acquisition of the whole echo. 50 kHz CW decoupling was employed during the echo delay and acquisition. The experiment was performed at 298 K with a repetition delay of 30 s.

we will adopt the same idea, but rather than restricting the analysis to simple geometrical models for the lipid dynamics, we will exploit the detailed dynamics of the molecular species provided by MD simulations as input to calculation of solidstate NMR spectra and compare the result with experimental 31 P solid-state NMR spectra. To thoroughly investigate the influence of details in the underlying dynamics, we used allatom (AA) and coarse-grained (CG) MD simulations and find that both types of simulations can explain all characteristic spectral features of 31P solid-state NMR spectra of lipids in vesicles, bicelles, and hydrated bilayers with and without membrane inserted peptides.

2. EXPERIMENTAL SECTION 2.1. Computational Methods for All-Atom MD Simulations. A pure bilayer with dimensions of 120 Å × 120 Å was constructed by use of the membrane builder plugin for VMD35 giving a total of 406 1,2-dimyristoyl-sn-glycero-3phosphatidylcholine (DMPC) lipids. Likewise, a bilayer with alamethicin inserted in a transmembrane conformation was built by placing 20 alamethicin molecules (the A monomer of the pdb-file 1AMT36) in a hexagonal pattern in a DMPC bilayer with dimensions of 137 Å x 137 Å and removing the three DMPC lipids in each leaflet closest to each of the peptides. This resulted in a system containing 405 DMPC lipids and 20 alamethicin molecules, which led to a peptide-lipid ratio of approximately 1:20. Both systems were solvated with water. We modeled alamethicin in its neutral state, since it has previously been shown in MD simulations that alamethicin pores are more stable when the peptide is neutral37 and that pores can form spontaneously with the Glu19 variant.9 Furthermore, it is known that two natural variants exist either with Glu or Gln in position 19 pointing toward a neutral polar residue as this position holding hydrogen bond accepting and donating characteristics.38 Since alamethicin is neutral, no counterions were added. The MD simulations were conducted in NAMD 2.739 by use of the CHARMM22 force field with CMAP40 correction for the peptides and CHARMM3641 for the lipids. The nonstandard amino acids were parametrized as previously described.9 The water was described by the TIP3P water model.42 Both systems were minimized and equilibrated for 500 ps in the NVT ensemble with everything except the tails of the lipids position restrained. The alamethicin system evolved for another 500 ps in the NPT ensemble with only the peptides restrained, to let the DMPC lipids pack around them. Finally, both systems were minimized followed by a 1 ns equilibration without restraints and a 300 ns production run in the NPT ensemble. 300000 snapshots distributed evenly over the production run were used in the analysis. The simulations were run with a 1 fs time step with the nonbonded short-range interactions, full electrostatics PME, and neighbor list being updated every second, fourth, and 20th step, respectively. A switching function was used for the short-range nonbonded interactions starting at 10 Å with a cutoff at 12 Å, while the pair list distance was set to 14 Å. The temperature of the simulations were kept at 310 K by a Langevin thermostat with a damping constant of 0.5 ps−1 while the pressure was controlled anisotropically by a Nosé− Hoover Langevin barostat with a piston period of 100 fs, a decay time of 50 fs and a target pressure of 1.01325 bar. 2.2. Computational Methods for Coarse-Grained MD Simulations. A bicelle was constructed by cutting a disc with a radius of 15 nm from an equilibrated DMPC bilayer and 5120

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at ambient temperature. However, it should be noted that the chemical shift parameters for such samples remain essentially unchanged over a large temperature range,49 supported by our own observations that static spectra recorded at various temperatures in the range 20 to 40 °C provide 31P chemical shift parameters within the above error limits. This suggests that any significant change in the 31P chemical shift, e.g. as observed by comparing 31P spectra for dry lipids and hydrated vesicles (Figure 1b) should be explained by changes in the dynamics of the lipid molecules. Turning to a hydrated vesicle sample, the corresponding measurement (Figure 1b) reveals a considerable reduction in the width of the powder pattern and a change to axial symmetry, represented by the parameters δiso = 0 ± 3 ppm, δaniso = 32 ± 3 ppm, and η = 0.01 ± 0.09. This reduction is a result of fast rotational diffusion of the lipid molecules and will be a target in this combined MD/solid-state NMR study. Moving to oriented DMPC bilayers with the bilayer normal aligned along the B0 field the 31P solid-state NMR spectrum (Figure 1c) contains a single peak at 33 ppm corresponding to the downfield edge of the vesicle spectrum. Finally, a 31P spectrum of oriented DMPC lipids embedding the transmembrane peptide alamethicin (Figure 1d), shows a peak which is shifted upfield compared to the peak observed for a DMPC bilayer in the absence of alamethicin.34 In the following, we will investigate the detailed origin of these observations by taking advantage of the dynamics of such systems revealed by MD simulations. 3.1. Background for Calculation of 31P Solid-State NMR Spectra Using All-Atom MD Trajectories as Input. To use the information about the lipid geometry stored in the MD trajectories, we need to be able to relate the orientation of the 31P chemical shift tensor to the molecular structure. To determine exactly this property, Hauser et al.48 and Herzfeld et al.49 studied a number of lipid mimics by 31P single-crystal NMR spectroscopy. These studies revealed that the principal axis system (PAS) of the 31P chemical shift tensor is aligned approximately along the axes of a lipid-defined coordinate system (referred to as the PO4 frame) defined by having its yaxis intersecting the P−O13 and P−O14 vectors, the z-axis perpendicular to the plane spanned by these two vectors, and the x-axis perpendicular to y and z, as shown in Figure 2. The approximate coalignment of the 31P chemical shift tensor with the axes of this system may be specified by the direction cosines reported for the lipid mimic phosphodiester barium diethyl phosphate (BDEP) by Herzfeld et al.,49 and expressed by the Euler angles ΩPAS→PO4 = (−6.5°, 88.9°, 81.2°). We will use these Euler angles as a starting point for the orientation of the 31 P chemical shift tensor and use the molecular visualization program VMD35 to establish the orientation of the PO4 coordinate system in the laboratory (LAB) frame as defined by the Euler angles ΩPO4→LAB for each lipid in the MD simulation. To obtain this information, the atomic positions of each lipid in all snapshots of the trajectory are extracted, and through that the orientation of the chemical shift tensors in the LAB frame can be calculated. The 31P NMR resonance frequency is given by

All spectra were externally referenced to 85% H3PO4 at 298 K.

3. RESULTS AND DISCUSSION The appearance of 31P solid-state NMR spectra of lipid molecules relies strongly on the physical conditions of the lipids. In one extreme, the 31P spectrum of DMPC as lyophilized powder (Figure 1a) shows a broad 31P powder

Figure 1. (a) 31P powder spectrum of dry DMPC lipids with chemical shift parameters: δiso = 0 ± 5 ppm, δaniso = −113 ± 8 ppm, and η = 0.5 ± 0.1.34 (b) 31P spectrum of DMPC lipid vesicles in aqueous solution. The signal at 0 ppm stems from a minor fraction of small isotropic vesicles. (c,d) 31P spectra of hydrated DMPC bilayers aligned with the bilayer normal parallel to the magnetic field direction of (c) a pure DMPC sample and (d) a sample with the peptide alamethicin embedded at a molar ratio of P:L = 1:15.

pattern extending from −120 ppm to 100 ppm corresponding to the unscaled 31P chemical shift tensor. By fitting the experimental spectrum, we find that the chemical shift tensor may be represented by the parameters δiso = 1 ± 5 ppm, δaniso = −113 ± 8 ppm, and η = 0.50 ± 0.07,34 in good agreement with the parameters observed for lipid mimics by single-crystal NMR.48,49 A comparison of experimental and simulated spectra as well as details on the error limits can be found in the Supporting Information. The error limits are estimated as 95% confidence intervals, which seem reasonable to cover effects from various experimental uncertainties. As we exploit the results of 31P single-crystal experiments by Hauser et al.48 and Herzfeld et al.49 of lipid mimics recorded at room temperature, we have also performed 31P experiments on a dry lipid sample

δ = δiso + δanisoκ(η , Ω PAS → PO4 , Ω PO4 → LAB)

(1)

where 5121

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Figure 2. Molecular orientation of the 31P chemical shift tensor (purple ellipsoid) and coordinate system in a DMPC molecule. The DMPC molecule is shown in a ball-and-stick representation and oriented with the carbon tails pointing downward. Black arrows represent the PO4 frame, defined by P, O14, and O13 as suggested by Herzfeld et al.49 The principal axes of the 31P chemical shift tensor and the PO4 frames differ in orientation by less than 10°.

κ(η , Ω PAS → PO4 , Ω PO4 → LAB) ⎛ Dm(2),0(Ω PO4 → LAB)⎜D0,(2)m(Ω PAS → PO4) ⎝ m =−2 2

=

∑

Figure 3. (a) Calculated chemical shifts of all 31P nuclei in the first snapshot of the all-atom MD simulation of a pure DMPC bilayer oriented with the bilayer normal parallel to the magnetic field. (b) Average frequency and the standard deviation for all lipid molecules as a function of simulation time. The standard deviation decreases with simulation time. By including more snapshots in the calculation, the dynamics of the lipids will average the position and orientation of the lipid and the standard deviation will be reduced. (c) Experimental (bottom, identical to Figure 1c) and calculated (top) 31P spectrum based on the average frequencies of 406 DMPC lipids in a 300 ns allatom MD simulation. The ppm scale for the 31P chemical shift applies to all figures.

⎞ η (2) − (D−(2) 2, m(Ω PAS → PO4) + D2, m(Ω PAS → PO4))⎟ ⎠ 6 (2)

is the geometrical factor accounting for the orientation of the tensor expressed by the second rank Wigner rotations (2) (Ωx→y)) representing the coordinate transformations (Dn,m from the PAS frame to the PO4 frame, and subsequently from the PO4 frame to the LAB frame. 3.2. Calculation of 31P NMR Spectra for a Static, Oriented Lipid Bilayer. The procedure outlined above was employed to calculate the 31P chemical shifts for all 406 lipids in the first snapshot of the all-atom MD trajectory of a DMPC lipid bilayer aligned with the bilayer normal along the z-axis of the LAB frame. This calculation reveals 406 resonances located in the spectral region of −110 to 80 ppm as shown in Figure 3a. This large spread in resonance frequencies underlines the high diversity in the orientation of the individual lipid molecules. The average frequency for the 406 DMPC molecules is δ̅ = 31 ppm with a standard deviation of 41 ppm. While the average chemical shift is close to the expected 33 ppm, there are huge differences in the conformation and orientation of each lipid. Since lipids are known to be highly dynamic, this observation is not surprising, and to take it into account in our predictions of NMR-shifts, we will include the time evolution from the MD trajectories in our calculations of the 31P chemical shifts. By calculating the time-averaged resonance frequency for each lipid as a function of the MD simulation time, we observe that the standard deviation between the time-averaged chemical shifts for the 406 lipids rapidly decreases as illustrated in Figure 3b. For the full 300 ns of production MD simulation the lipids show time-averaged (over 300000 snapshots) 31P resonance frequencies within a small standard deviation of 1.9 ppm. To establish a final calculated spectrum of the 406 lipids, we have added Gaussian peaks with a full-width at half height line width of 1 ppm at the time-averaged resonance frequency for each lipid to yield the spectrum in Figure 3c. This spectrum shows

the characteristic sharp line at ∼30 ppm, in good consistency with the peak observed in the experimental spectrum (Figures 1c and 3d). This spectrum demonstrates that in spite of the highly different orientations of the individual lipid molecules at any time, they behave similarly on a longer time scale. The calculated spectrum in Figure 3c uses the chemical shift parameters obtained from the powder spectrum of DMPC and the set of Euler angles (ΩPAS→PO4) determined for BDEP by Herzfeld et al.49 and results in a peak at δ̅ = 30 ppm, thus being close to but not exactly spot on with the experimental spectrum, which shows a sharp peak at 33 ppm. Since small deviations are observed for the magnitude of the 31P chemical shift tensors in DMPC and BDEP, we also expect that small deviations in the orientations of these tensors may occur. To accommodate these small deviations, we performed an optimization of the Euler angles ΩPAS→PO4 with the target being a simulated spectrum with a sharp peak at 33 ppm as observed experimentally. Euler angles of Ωopt PAS→PO4 = (−14°, 82°, 74°) were obtained by this optimization. They agree with Herzfeld’s values for BDEP within 10° for all three angles, so we consider this optimization step a calibration of the setup with DMPC lipids, that does not alter any conclusions or results but improves the agreement between the experimental and calculated spectra. Hence, we use the optimized Euler angles in the remaining part of the work. 5122

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3.3. Calculation of 31P NMR Spectra for Nonoriented Vesicles. With a major objective of oriented-sample studies being the establishment of information on the membranebound conformation of peptides and proteins, it should be stressed that the samples need not be oriented to achieve this information. Several recent studies have demonstrated that the orientation-dependent nuclear spin interaction parameters may be observed through the rotation averaging of these interactions caused by the fast rotational diffusion of the lipid molecules around the lipid bilayer normal.50−54 This leads to reduced nuclear spin interactions, which may be detected not only in oriented samples, but also in e.g. vesicle samples. The 31 P spectrum of the lipids in nonoriented vesicles (Figure 1b) clearly illustrates this reduction when compared to the spectrum of dry lipids (Figure 1a). To calculate the spectrum for a lipid vesicle sample, we used the lipid bilayer from the all-atom MD simulation and covered a large sphere (diameter of 60 nm) with multiple copies of the same DMPC bilayer. Figure 4a shows a simplified version of

the experimental spectrum (Figure 4d bottom), with all characteristics including the axial symmetry reproduced. We note that the peak at 0 ppm in the experimental spectrum originates from a small fraction of small isotropic vesicles, which are not calculated within the present approach. 3.4. Peptide-Induced Perturbations of Oriented Lipid Bilayers. Various different modes of cell lysis through membrane disruption have been proposed based on studies of a large number of AMPs. The prevalent models are the barrel-stave, the toroidal pore, and the carpet models.56,57 To gain better understanding of these models, NMR has been extensively used to study the interaction between AMPs and lipids, both through the study of isotope labeled AMPs58−63 and through studies of the perturbations of the lipids when adding AMPs.33,34,64−66 The latter approach is particularly relevant in the present study, since 31P solid-state NMR of oriented samples has proven to be a highly sensitive reporter on the peptide-membrane interaction. When tiny amounts of peptide is added, the 31P resonance at ∼30 ppm in the spectrum of the aligned lipids shifts either upfield or downfield. This is ascribed to peptides, which introduce different order/ disorder than what the pure lipids exhibit. At higher peptide concentrations, we have observed that the peptide alamethicin induces a fraction of the lipids that behaves differently. These lipids exhibit significantly slower lateral diffusion and are attributed to the lipids being close to the peptide and involved in the membrane anchoring of alamethicin, as judged from the presence of intensity at ∼20 ppm in oriented 31P spectra at high peptide to lipid ratios.34 In order to use the present approach to investigate the effect of adding peptides to lipids, we will first use the all-atom MD simulations to derive information on the lateral diffusion coefficients of the DMPC lipids in the absence and presence of alamethicin. While the lateral and rotational diffusion coefficients are not directly available from MD data, the simulation allows us to calculate the mean square displacement of the lipids as a function of time, which relates to the lateral diffusion coefficient. Specifically, the lateral diffusion coefficient is obtained as the slope of the curve for the mean square displacement vs time67 d ⟨(r(t ) − r(0))2 ⟩ = 4D dt

(3)

For clarification, we should note that although the previous discussions in Section 3.3 concerned rotational diffusion as the mechanism with the most significant influence on the nuclear spin interaction parameters, this interest in lateral diffusion only concerns explaining the subtle changes observed in the 31P spectra with peptide present, since recent studies have pointed in this direction.33,34 In the present case, plots of the mean-square displacements (eq 3) are shown in Figure 5a. From these plots we found diffusion coefficients of D = 1.1 × 10−7 cm2/s for the pure DMPC lipids and D = 4 × 10−8 cm2/s for the DMPC/ alamethicin sample. These numbers for the lateral diffusion clearly indicate that the DMPC molecules are more restricted in the presence of alamethicin. By inspection of the MD snapshots, we have previously observed that some of the lipids are transiently involved in peptide insertion.9 But such transient effects are not expected to manifest in the time-averaged calculations used in the present approach. Hence, to investigate whether the lateral diffusion is more restricted for lipids involved in the anchoring of alamethicin, we made the same

Figure 4. (a) Illustration of an artificial vesicle constructed by covering a sphere with DMPC bilayers oriented on the basis of 100 REPULSION crystal orientations (see text).55 (b) Expansion of a region of the vesicle showing the orientation of a single bilayer. (c) A unit sphere with the 100 crystallite orientations represented as vertices, with the orientation highlighted in (b) indicated by an arrow. (d) Experimental (bottom) and simulated (top) 31P NMR spectra of vesicles. The latter was generated by use of DMPC bilayers from MD simulations and the principles outlined in (a−c). The actual simulation used 678 REPULSION crystallites to obtain a smooth, converged line shape.

the artificial vesicle reproduced by decorating a sphere with the DMPC bilayers from the MD simulation (Figure 4b). This was achieved using a list of Euler angles developed for efficient simulation of solid-state NMR experiments.55 Here, we used 678 REPULSION55 angles to distribute the bilayers efficiently on the sphere to ensure good convergence of the resulting 31P powder spectrum. As evident from Figure 4d (top), the calculated 31P vesicle spectrum of hydrated lipids is similar to 5123

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Figure 5. Mean square displacement of the lipids as a function of MD simulation time. The slope of the curve is proportional to the lateral diffusion coefficient of the lipids. (a) Comparison of the mean square displacement for a pure DMPC lipid bilayer and a DMPC lipid bilayer containing 1:20 alamethicin:lipid. The plots show a clear reduction of the diffusion rate when alamethicin is added. (b) Mean square displacement as a function of simulation time for the alamethicin simulation with the lipids subdivided into three groups according to the distance to the nearest peptide: red, 0−8 Å; green, 8−12 Å; blue, 12−20 Å.

Figure 6. (a) Calculated average 31P resonance frequencies of lipids in a DMPC bilayer containing alamethicin at a molar ratio of 1:20 with the lipids sorted according to the distance to the nearest alamethicin molecule. The average resonance frequency is significantly reduced for lipids close to alamethicin. (b) Calculated (top) and experimental (bottom) 31P spectra of DMPC bilayers with alamethicin present in a molar ratio of 1:15 (see text).

relative intensities differ somewhat from the experimental ones. Whether the observed effects in the calculated spectrum are directly linked to the reduced lateral diffusion of the lipids in close proximity to the peptides or arise due to unspecific change of the dynamic behavior of some lipids is hard to judge from the present data. However, the fact that the motional averaging of the ∼200 ppm wide powder pattern of the static DMPC spectrum (Figure 1a) through dynamics as described by the MD simulations can explain all essential features of the experimental 31P spectra is very encouraging. This makes the combination of MD and 31P solid-state NMR a promising approach to provide detailed information even on effects that introduce only subtle effects in the experimental spectra. 3.5. Background for Calculations of 31P Solid-State NMR Spectra on the Basis of Coarse-Grained MD Data. One of our aspirations is to be able to understand larger biological systems. However, as the computational power needed to simulate such systems in atomistic detail on a timescale of biological interest is substantial due to the large amount of particles and the system’s many degrees of freedom, it is rarely within reach. To access information about larger molecular assemblies on the time-scale of interest, we therefore turned to coarse-grained (CG) MD simulations,44,68 which we have previously used to study peptide-lipid systems.9 The decrease in number of particles obtained when going from allatom to CG reduces the degrees of freedom resulting in faster dynamics. Simultaneously, the increased particle size enables use of larger time steps. The combination of these effects enables longer simulations approaching biological relevant time scales.69 While enabling simulations of larger molecular assemblies, CG simulations cause a problem in the present context, since we so far used the orientation of the phosphate group of the lipids (specifically the orientations of the P−O bond vectors) to calculate the orientation-dependent 31P resonance frequencies.

analysis on lipids divided into three groups depending on their average distance to the nearest peptide, as illustrated in Figure 5b. The three groups contain lipids with average distances of 0−8 Å (red), 8−12 Å (green), and 12−20 Å (blue), and the plots in Figure 5b show that the lateral diffusion does increase with the distance to the nearest peptide as expected from our recent study.34 Having addressed the overall questions on the influence of the peptides on the lateral diffusion, a remaining question is how the reduced lateral diffusion manifests itself in the calculated 31P spectrum. To address this, we have calculated the resonance frequencies for all lipids in all the snapshots of the MD simulation and binned the lipids according to their distance to the nearest peptide in the particular snapshot in 1 Ångstrøm bins. The distances between peptide and lipids were obtained by using use the molecular visualization program VMD35’s within command. From the binned data, the average frequency of all lipids in each distance bin was calculated and plotted in Figure 6a. In this plot, the distance bins are along the y-axis and the corresponding average frequencies are the along x-axis to ease the comparison with the spectra in Figure 6b. This plot supports the experimental observation that the lipids close to peptides should have a lower 31P resonance frequency as evidenced by a peak at ∼20 ppm in the experimental spectrum (see Figure 6b). When performing the same spectrum calculation, as for pure DMPC (Figure 3c), for a DMPC bilayer with alamethicin, we obtain the calculated spectrum in Figure 6b (top). The spectrum shows a broadening of the peak at ∼30 ppm with a tail toward lower ppm values and a tiny peak at ∼20 ppm as also observed in the experimental spectrum. We are very pleased to note that even subtle effects as an upfield shift of the ∼30-ppm peak and the presence of a weak peak at ∼20 ppm are present in this calculation, although the peak positions and 5124

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Figure 7. (a) Illustration of a coarse-grained DMPC bilayer from the MD simulation containing 1000 lipids with the PO4 bead in blue and the rest in gray. (b) Plot of a single CG lipid molecule (blue) indicating the NC3, PO4, GL1, GL2, C1A, and C1B beads overlaid by an all-atom lipid showing all atoms except hydrogen atoms. This figure also highlights the 31P chemical shift tensor and the CG coordinate system defined from the PO4, GL1, and GL2 beads as described in the text.

of 1.2 ppm. While this is very close to the experimental value of 33 ppm, we will subject the PAS → CG Euler angles to an optimization targeting the 33 ppm observed experimentally to “calibrate” the Euler angles for a real CG MD simulation. The resulting Euler angles of Ωopt PAS→CG = (9.2°, 22.4°, −35.7°) result in a resonance frequency of 33.0 ± 1.2 ppm, and they are within ±2° of the above initial values, indicating that only minor adjustments are needed in the “calibration”. We will use the optimized Euler angles for further studies. 3.6. Calculation of 31P NMR Spectra for Magnetically Aligned Bicelles. Bicelles are used as membrane mimics for structural studies of membrane-embedded peptides and proteins in combination with liquid- and oriented solid-state NMR spectroscopy. The information inferred from these studies includes orientation of single and/or multiple helices with respect to the membrane orientation,70−72 3D structures of proteins,71,73 and penetration depths of peptides by means of natural abundance 13C studies.66,74 Bicelles are formed by mixing long-chained and short-chained lipids in aqueous solution, in which case they form disc-like entities with the long-chain lipids forming a bilayer and the short-chain lipids located at the rim of the disc,75,76 covering the hydrophobic interior of the bilayer from the aqueous solvent. The size of the bicelles is defined by the molar ratio of the long- and shortchained lipids, q = [long]/[short], with the dimensions increasing with increasing q.24,77,78 In strong magnetic fields, bicelles with q ≳ 2.5 orient with the bilayer normal perpendicular to the magnetic field direction.17 Since bicelles are large molecular assemblies, especially for high q values, they are obvious targets for CG MD simulations, while exhaustive atomistic simulations are not currently feasible due to the large number of atoms. The experimental 31P solid-state NMR spectrum of DMPC/ DHPC bicelles for q = 3.2 shows two well-resolved, sharp peaks at approximately −6 and −12 ppm, which normally are assigned to DHPC and DMPC, respectively (see the inset in Figure 8d), in agreement with the assumption that DMPC forms the bilayer and DHPC forms the rim. The bilayer normal is tilted by θ = 90° relative to the magnetic field, and since the resonance frequency scales as a second rank Legendre polynomial (1/2(3cos2θ − 1) = −1/2), we would expect the bilayer peak to appear at −1/2 × 33 ppm = −16.5 ppm. The

In CG MD simulations, the phosphate group is represented by a single bead, which carries no information on the orientation of the P−O bonds. In the absence of this information, we need to search for an alternative reference system to orient the 31P chemical shift tensor with respect to the lipid molecule. To find a suitable reference system, we first compared one of the snapshots of the all-atom MD simulation and its CG counterpartner, where the positions of the beads were calculated directly as the center of mass of the atoms. Specifically, the NC3/PO4/GL1/GL2 CG beads were placed at the center of mass of the atoms (N,C12,C13,C14,C15)/ (P,O11,O12,O13,O14)/(C21,O21,O22,C2)/ (C31,O31,O32,C3), respectively, as illustrated in Figure 7b. We investigated how the beads were positioned in the PO4 coordinate system defined in Figure 2 and found that the NC3 bead displayed significant displacements, while the GL1 and GL2 beads moved significantly less. Hence, we used the PO4, GL1, and GL2 beads to define a coordinate system, which can serve as the molecular reference system to calculate the orientation of the 31P chemical shift tensor. A calculation of the orientation of the 31P chemical shift tensors (from the Euler angles used in the all-atom simulations above) in the CG coordinate system, defined in Figure 7b (with x along the PO4-GL1 bond, z perpendicular to the PO4-GL1GL2 plane, and y defined to form a right-handed coordinate system), gave average Euler angles for the PAS → CG coordinate transformation of ΩPAS→CG = (7.7°, 24.4°, 36.8°). Like for the case of the all-atom simulations, we used these parameters as a qualified guess on the orientation of the 31P chemical shift tensor with respect to the CG lipid. We do not expect the angles to be very precise because (i) the PAS → CG Euler angles represent the best average of all lipids but are not particularly precise for each individual lipid and (ii) the CG lipid structures obtained by direct conversion of the all-atom lipids to a CG representation, as explained above, are in a sterically unfavorable conformation and relax rapidly to a lowerenergy conformation under the influence of the CG force field. Applying the PAS → CG Euler angles in a calculation of the 31 P spectrum of an oriented lipid bilayer consisting of 1000 CG DMPC lipids in a 2000 ns CG simulation, for which the first snapshot is visualized in Figure 7a, resulted in a time-averaged 31 P resonance frequency of 30.0 ppm with a standard deviation 5125

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another challenge in using the present method to calculate the P spectra for large oriented bicelles: The MD force fields do not include effects of magnetic susceptibility nor do they allow to add an external magnetic field, being the essential ingredients of the magnetic alignment of large bicelles. Nonetheless, we have established an initial CG MD model of a bicelle disc consisting of 1719 DMPC and 537 DHPC molecules (q = 3.2) in a solution containing 105280 water beads (18.6 wt % lipid). During the CG simulation, the 1719 DMPC molecules always stayed in the bicelle, but the number of DHPC molecules varied between 493 and 515. Figure 8a shows a snapshot of the bicelle. This snapshot reveals an accumulation of short-chain lipids at the rim, but we also note the presence of short-chain lipids in the bilayer part. In each snapshot, the bicelle was defined to consist of the molecules with their lipid tail and glycerol linker beads being within 6 Å of each other. As there was no external magnetic field to align the molecules, we aligned the lipids in the bicelle via its inertia tensor to mimic the alignment governed by the forces between the magnetic susceptibility of the bicelle and the magnetic field. The inertia tensor was calculated according to 31

N

Ixx =

∑ mi(Δyi2 + Δzi2) i=1

(4)

N

Ixy = −∑ miΔxiΔyi i=1

(5)

where the summation runs over all N beads, with Δxi being the distance along x between the center of mass of the bicelle and the i’th bead. The remaining elements involving other combinations of x, y, and z are calculated in a similar fashion. Diagonalization of this tensor will reveal the size and orientation of the three principal axes of inertia. The largest principal value will be parallel to the normal of the bilayer part of the bicelle, which is known to orient perpendicular to the magnetic field direction when the bicelle is placed in a strong magnetic field. Hence, in each snapshot, we have aligned the bicelle with its largest inertia moment principal element along z and calculated the 31P resonance frequencies for the DMPC and DHPC molecules as described above for the bilayer. To account for the perpendicular orientation of the bicelle, all resulting frequencies are multiplied by the second-order Legendre polynomial at 90°: (3cos2 90° − 1)/2 = −1/2. We note that this procedure lacks a few details: (i) We cannot assess the actual degree of alignment of the bicelle in water in a magnetic field strength and (ii) The use of a simple 90° flip of the bicelle will not account for potential spectral effects of slow bicelle tumbling, since approximation will provide a spectral model corresponding to a bicelle with infinitely fast rotation around its bicelle normal. While the first issue may have consequences for our estimation of the bicelle’s orientational order parameter (vide inf ra), the latter point should actually help compensating from the limited time-averaging available because of the long MD calculation times of such large systems. Figure 8 reports the evolution as a function of simulation time of the average 31P resonance frequency and its standard deviation for the DMPC and DHPC (Figure 8b) molecules in the bicelle in the same fashion as reported for the bilayer sample in Figure 3b. Interestingly, for the production run (500 ns) the average resonance frequency of DMPC is −14 ppm, while the DHPC average resonance frequency of −8 ppm

Figure 8. (a) Illustration (front and side view) of a typical bicelle aggregate observed in a CG MD simulation containing 2256 lipids with a DMPC and DHPC mixture corresponding to q = 3.2. The bicelle contains 1719 DMPC (blue) and approximately 500 DHPC (red) molecules. The bicelle is aligned with the largest principal component of its inertia tensor horizontally. (b) Plots of the average 31 P frequencies and standard deviations of all DMPC (blue) and DHPC (red) lipids as a function of the simulation time. (c) Counts of DMPC (blue) and DHPC (red) lipids with a certain average 31P frequency. The inset shows a typical experimental 31P spectrum of a DMPC/DHPC bicelle sample of q = 3.2.

deviation from the experimentally observed chemical shift of approximately −12 ppm, is explained by the fact that bicelles exhibit an order parameter of S2 ≃ 0.8 ascribed to wobbling. The relative intensity of the two peaks is approximately proportional to the DMPC/DHPC ratio79,80 and hence, the two peaks are typically assigned accordingly. Apart from the fact that CG MD simulations lack information on the orientation of the PO4 group, we face 5126

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appears closer to the isotropic shift (0 ppm). This result is in good agreement with the experimental observation of two peaks located at approximately these frequencies. Inspection of the standard deviation for DMPC (shaded area in Figure 8b) shows the same trend as observed for the all-atom MD simulation of a DMPC bilayer (Figure 3b), that is a decrease of standard deviation as the simulation time increases, thus indicating that all long-chained lipids exhibit similar motions in a bilayer and a bicelle. The standard deviation for DHPC also shows a significant initial decrease, which levels off at longer simulation times, so the standard deviation of the frequencies for the DHPC molecules stays significantly larger than for DMPC, indicating a larger conformational heterogeneity of DHPC in bicelles. This observation is also visible from the count of average 31P resonance frequencies for the individual lipid molecules in Figure 8c. The DMPC molecules are all centered around the expected −14 ppm with a quite narrow distribution, while the DHPC molecules are distributed around a frequency of −8 ppm, in a much wider distribution. Overall, the count-plot (Figure 8c) agrees quite well with the experimental 31P spectrum of a bicelle with q = 3.2 (inset in Figure 8c) and supports the general model that DHPC is mainly located at the rim of the bicelle, where each molecule may adopt widely different internal conformations.75 The DMPC peak centered at −14 ppm is slightly shifted upfield compared to the experimental spectrum, where the peak resides at approximately −12 ppm. The experimental peak position and its deviation from the expected −1/2 × 33 ppm = −16.5 ppm has been used to deduce that the orientational order parameter of bicelles is approximately S2 ≈ 0.8. Our calculations suggest that we cannot precisely reproduce this experimental order parameter. This is not surprising, since the MD simulation does not include the alignment effect of the external magnetic field, as addressed above. Overall, our calculations show that the main features of the experimental 31P spectrum of bicelles may be confirmed with the present method involving CG snapshots, including the distinction of the DMPC and DHPC peaks. However, we also observe a significantly larger distribution of particularly the DHPC resonance frequencies than is apparent from the experimental spectrum. This observation will be subjected to further investigations beyond the scope of this paper.

Article

ASSOCIATED CONTENT

S Supporting Information *

Experimental 31P NMR spectra (static and MAS) of dry DMPC and best-fit calculations of these, including 95% confidence interval estimations of the error limits of the fitted parameters. This material is vailable free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*(T.V.) Phone: +45 8715 5929. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the Danish National Research Foundation (DNRF 0059), the Lundbeck Foundation, the Carlsberg Foundation, the Novo Nordisk Foundation, the Danish Natural Science Research Council, Lundbeckfonden, and the Danish Center for Scientific Computing (DCSC) for financial support. Johan F. Kraft is acknowledged for providing the CG simulation of the DMPC bilayer.

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REFERENCES

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dx.doi.org/10.1021/jp5000304 | J. Phys. Chem. B 2014, 118, 5119−5129