On the Combined Analysis of ²H and ¹⁵N/¹H Solid-State NMR Data for Determination of Transmembrane Peptide Orientation and Dynamics

Abstract

The dynamics of membrane-spanning peptides have a strong affect on the solid-state NMR observables. We present a combined analysis of ²H-alanine quadrupolar splittings together with ¹⁵N/¹H dipolar couplings and ¹⁵N chemical shifts, using two models to treat the dynamics, for the systematic evaluation of transmembrane peptides based on the GWALP23 sequence (acetyl-GGALW(LA)₆LWLAGA-amide). The results indicate that derivatives of GWALP23 incorporating diverse guest residues adopt a range of apparent tilt angles that span 5°–35° in lipid bilayer membranes. By comparing individual and combined analyses of specifically ²H- or ¹⁵N-labeled peptides incorporated in magnetically or mechanically aligned lipid bilayers, we examine the influence of data-set size/identity, and of explicitly modeled dynamics, on the deduced average orientations of the peptides. We conclude that peptides with small apparent tilt values (<∼10°) can be fitted by extensive families of solutions, which can be narrowed by incorporating additional ¹⁵N as well as ²H restraints. Conversely, peptides exhibiting larger tilt angles display more narrow distributions of tilt and rotation that can be fitted using smaller sets of experimental constraints or even with ²H or ¹⁵N data alone. Importantly, for peptides that tilt significantly more than 10° from the bilayer-normal, the contribution from rigid body dynamics can be approximated by a principal order parameter.

Introduction

Solid-state NMR provides a powerful means for characterizing the structure and behavior of transmembrane helical domains of proteins in their native phospholipid bilayer environment (1). NMR spectra of oriented lipid-bilayer systems offer access to the average orientations of membrane-spanning helical segments, namely the magnitude (τ) and direction (ρ) of helix tilt. Different NMR observables, nevertheless, have different sensitivities to helix orientation, due to different orientations in the molecular frame, sensitivities, and physical basis for each particular nuclear spin interaction. The reorientation of an isotope-labeled group during the NMR pulse sequence and data acquisition time presents another inherent issue. Although fast precession of individual transmembrane helices about the lipid bilayer-normal (2,3) does not influence the NMR signals, oscillations around the average tilt and rotation angles can produce observable effects (4,5). Here we employ ¹⁵N and ²H labels to characterize peptides that exhibit a wide range of dynamic behavior and compare different methods for assessing dynamics using individual or combined sets of restraints.

The contributions of molecular motions that are rapid on the NMR timescale often are accounted for by a scale factor (principal order parameter, S_zz) between 0 and 1. The limit S_zz = 0 corresponds to isotropic molecular motion, whereas the limit S_zz = 1 corresponds to a completely immobilized molecule. The scale factor can be a fitted parameter, although a fixed value ∼0.8 has been measured for lipids and fitted for polypeptides in magnetically aligned bilayers (q = 3.2 bicelles) (6–9). An alternative way of describing the whole-body dynamics is to model explicit motions as specific fluctuations in the tilt magnitude τ and peptide rotation or tilt direction ρ (4,10–12), using a normalized two-dimensional probability distribution for possible (τ, ρ) combinations. The sum of the elements of each resulting matrix yields a predicted motionally averaged value for each NMR signal. Very slow motions (not addressed here) may lead to broad powder lines, e.g., for large proteins (13) or molecular aggregates (14).

Methods to deduce transmembrane peptide orientation in lipid bilayers include high-resolution separated local field (SLF) PISEMA, SAMMY, or PELF experiments (12,15–18), and deuterium quadrupolar splitting measurements (2,19,20). SLF spectra correlate ¹⁵N chemical shifts (CS) with ¹⁵N/¹H dipolar couplings (DC) for the peptide backbone of a tilted α-helix, with spectral patterns often referred to as “PISA wheels”. The CS and DC principal interaction axes—namely, the σ₃₃ CS tensor component and the NH bond, respectively—are aligned close to the peptide's helix axis (see Fig. S1 A in the Supporting Material). These observables therefore undergo slight changes at small tilt angles (<10°) and more dramatic changes at larger tilt angles. Small angles between the interaction axes and helix axis dictate that, for transmembrane peptides, the CS and DC values typically undergo monotonic changes without changing sign or passing through the isotropic limit. The trends in CS and DC can be visualized on helical wave curves for the individual restraints (see Fig. S1 B).

Deuterium NMR spectra of the methyl groups in Ala-d₄ residues offer a sensitive metric of transmembrane peptide behavior (2,21). The C_α-C_β bond geometry dictates that the methyl quadrupolar splittings (QS) pass through the isotropic nodes twice for transmembrane helices and four times for interfacial helices. The signs of the QS interactions cannot be measured.

The aforementioned restraints can be used individually or in combination. Examples of combined orientational analysis include the antimicrobial peptide distinctin (CS alone (22) or with QS (23)), the peptaibol alamethicin (11) (CS, DC, and QS) and the model peptide WALP23 (10) (QS, ¹³C-¹⁵N DC, ¹³C, and ¹⁵N CS anisotropies). The topology of the distinctin heterodimer was deduced from five labels, with a disulfide bridge and the amphipathic character of both helices allowing improbable topologies to be eliminated (23). The orientation of alamethicin in C_14:0 bicelles was implied from a single aminoisobutyric acid, labeled with ¹⁵N and ²H. Close angles between the C_α-C_β1/C_α-C_β2 bond vectors and B₀ precluded resolution of QS from the two methyl groups, thus leaving only three NMR observables and a fairly large solution area (11). The introduction of ¹³C-based restraints is promising (10), yet requires knowledge of ¹³C CS tensor orientations. Although the ²H labels for WALP23 covered the majority of the α-helix, the ¹³C and ¹⁵N labeling was sparse, reducing the contributions from these restraints (10). Indeed, each earlier study was performed with only a few labeled sites, making it difficult to compare the value of each individual type of restraint for determining molecular orientation and dynamics. An alternative approach uses CS and DC data for structural and topological constraints (24,25). Nevertheless, oriented solid-state NMR data for such calculations have to be complemented by other methods to provide the distance restraints.

In this article, we report systematic analysis of several transmembrane peptides, based on acetyl-GGALW(LA)₆LWLAGA-amide (GWALP23) with single Trp interfacial anchor residues (26) in lipid bilayer membranes. GWALP23 shows particularly systematic behavior in a series of lipid bilayer membranes (27). The peptides chosen for this investigation cover a variety of ranges of dynamics and orientation (Table 1). Extensive isotope labeling (employing up to 29 total restraints) made it possible to compare experimentally the sensitivities of different individual restraints toward the dynamic averaging. We compare the semistatic (variable S_zz) or explicit Gaussian (τ, ρ distributions) methods for treating the peptide dynamics and identify those cases where the methods converge to similar results or diverge to quite different outcomes. The goal of this work is to provide a framework for analysis of molecular orientation and whole-body dynamics using solid-state NMR data for oriented lipid/protein systems while identifying potential pitfalls.

Table 1.

Peptide sequences and best-fit peptide orientations and dynamics in DMPC/DHPC bicelles

Peptide	Sequence	τ0 Deg.∗	ρ0 Deg.	στ Deg.	σρ Deg.
GWALP23	GGALWLALALALALALALWLAGA	18	311	15	54
KWALP23	GKALWLALALALALALALWLAKA	19	307	13	53
WWALP23†	GWALWLALALALALALALWLAWA	22†	135†	0†	140†
		10†	133†	21†	70†
GW3,21ALP23-R14	GGWLALALALALARALALALWGA	34	267	15	30

In separate synthetic samples, ²H-labeled Ala residues, usually two per peptide, were incorporated in each position between the innermost Trp residues. The ¹⁵N-labeled Leu and Ala residues employed in selected peptides are underlined.All peptides include N-acetyl and C-amide groups.

^∗Best-fit values of τ₀, ρ₀, σ_τ, and σ_ρ from combined Gaussian dynamic analysis (see Materials and Methods in the Supporting Material) of available QS + DC + CS data (see Table S1 in the Supporting Material) for each peptide in bicelles of DMPC/DHPC. For details, and for results from fits to individual or pairs of data sets, see Table S2.

^†Result for one of several fits that give essentially equivalent minima for RMSD, with τ₀ between 10° and 22° and σ_ρ between 70° and 140° (see Table S2).

Materials and Methods

Labeled peptides (Table 1) were synthesized and purified as described previously (27,28). Samples were oriented with the bilayer normal either parallel (β = 0°) or perpendicular (β = 90°) to the magnetic field. A detailed Materials and Methods section, including descriptions of the solid-state NMR experiments and data analysis, is included in the Supporting Material.

Results

NMR observables for an ideal peptide helix parallel to the bilayer-normal (τ = 0°) would be nearly identical for all residues: ∼8 kHz (QS), ∼8 kHz (DC), and ∼202 ppm (CS) for samples oriented with β = 0°. The corresponding values when β = 90° (including bicelle samples) are ∼4 kHz (QS and DC) and ∼82 ppm (CS). Extensive dynamics will move the signals toward their isotropic values: 0 kHz (QS and DC) and ∼120 ppm (CS). Intermediate oscillations, which are likely, will cause reductions of QS and DC, along with a shift of CS toward the isotropic value, which in severe cases can cause a peptide with a large average τ to appear as if it has a smaller apparent τ (see Fig. S2). We consider three categories, according to the maximum observable |QS| when β = 0°. (See Fig. S1 B for corresponding ranges of DC and CS.)

Case 1: QS_max < 25 kHz (intermediate motion)

GWALP23 and acetyl-GKALW(LA) ₆LWLAKA-amide (KWALP23) exhibit similar signals in 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) bicelles, with QS values slightly larger for KWALP23 (Fig. 1). The SLF spectra are well dispersed and can be easily assigned (26). The PISA wheel of GWALP23 is somewhat crowded and marginally smaller than that of KWALP23. The KWALP23 spectrum and a high-field spectrum (see Fig. S3) enable complete assignments to be made for GWALP23. Observed values of QS, DC, and CS are in Table S1 in the Supporting Material.

Figure 1.

NMR spectra of labeled GWALP23 and KWALP23 in DMPC/DHPC bicelles. ²H NMR spectra for labeled alanines in (A) GWALP23, and (B) KWALP23. SLF spectra for backbone ¹⁵N/¹H groups in (C) GWALP23 and (D) KWALP23. Spectral assignments are indicated next to the corresponding resonances.

The topology of bicelles along with more extensive hydration can influence bilayer fluidity, sometimes accounted for by an additional parameter S_bic to achieve convergence between magnetic and mechanical sample alignment. Usually S_bic has been assigned a fixed value of ∼0.8 ± 0.05 to account for more extensive fast, small-amplitude lipid motions in bicelles at a given temperature (29–31). Nevertheless, we observe that the ²H NMR spectra for the peptides used in this study are virtually identical between DMPC/1,2-dihexanoyl-sn-glycero-3-phosphocholine (DHPC) bicelles at 40°C and DMPC glass slide samples at 50°C and β = 90° (see Fig. S4), indicating that the peptide data from the two alignment methods at the respective temperatures can be used interchangeably.

We begin the analysis using a subset of ²H and ¹⁵N data for alanines 7, 9, 11, 13, 15, and 17 in GWALP23, to have the same number of restraints of each type, with similar positions on a helical wheel projection. Variations of the chemical shift tensor components within this subset should be minimal, because all residues follow the repeating Leu_i-1−¹⁵N-Ala_i−Leu_i+1 pattern (32).

Fits using individual restraints (Fig. 2) reveal for each data set a large acceptable solution area for the Gaussian analysis (Fig. 2 A). These areas vary somewhat for the individual restraints, particularly QS. The changes are especially apparent for σ_τ in the 10°–20° range, as QS is more prohibitive for larger oscillations of τ. The order-parameter analysis reports unique minima for the DC and CS restraints, and two closely spaced minima for QS (Fig. 2 B). It is of interest that the decrease of S_zz has opposite effects on DC and CS. Lower S_zz values bring the theoretical DC values below the experimental ones and consequently move the fit toward τ = 0°. Conversely, lower S_zz values with CS favor large τ-angles, because the center of the PISA wheel approaches the isotropic CS when τ approaches the magic angle, whereas individual resonances are located both upfield and downfield.

Figure 2.

RMSD contour plots of orientation and dynamics of GWALP23 in DMPC/DHPC bicelles, using one type of restraint from six Ala residues. Restraints are QS, DC, and CS (left to right). Here and elsewhere the RMSD contours are plotted from 0 kHz (blue) to the maximum value (red) using 10 contours for the dynamics and 15 contours for the orientation. (A) Gaussian distributions of tilt and rotation (QS_max = 9.7 kHz, DC_max = 0.7 kHz, and CS_max = 3.4 kHz). (B) Semistatic dynamics using an order parameter. (C) Average tilt and rotation from the Gaussian analysis (QS_max = 15.7 kHz, DC_max = 5.5 kHz, and CS_max = 22.7 kHz). (D) Average tilt and rotation from variable S_zz analysis (QS_max = 30.1 kHz, DC_max = 5.2 kHz, and CS_max = 21.9 kHz).

The peptide orientation corresponding to the global minimum is similar for each type of restraint and for both ways of treating the dynamics (Fig. 2, C and D). Nevertheless, the different sensitivities of QS, DC, and CS toward τ and ρ are immediately apparent. Although analysis using QS alone yields a single well-defined minimum, the acceptable solution area is larger for both DC and CS, in particular when the dynamics are treated in a semistatic way (Fig. 2 D). Due to a small dispersion between the smallest and largest dipolar couplings (0.8 kHz at β = 90°; see Table S1), the DC set does not differentiate well between different ρ-angles. Similarly, the CS fit also is less well defined in terms of ρ, due to the fairly flat helical wave curves (see Fig. S1 B).

Combining the restraints in pairwise fashion helps in locating the minimum in the case of Gaussian dynamics (see Fig. S5). It is particularly helpful to combine QS restraints with either DC or CS, because the acceptable solution areas do not completely overlap (Fig. 2 A). Thus, QS restraints provide a penalty against oscillations in ρ, whereas DC or CS discriminates against oscillations in τ. Combining DC and CS offers less improvement, due to nearly identical dynamics solutions. For a semistatic treatment of dynamics, the pairwise fits do not change significantly, because the individual restraint sets already have converged to a similar S_zz value of ∼0.75 (see Table S2).

In terms of the τ_o, the restraints paired with QS signals appear most beneficial, because of a sharp minimum for the methyl groups (Fig. 2 D). Average peptide orientation deduced from the DC and CS combination is not better defined than with DC or CS signals alone. Nevertheless, a joint DC and CS fit can be particularly useful if the peptide topology is not initially known, such that the CS contribution fit can eliminate the possibility of an interfacially bound peptide whereas the DC restraints will impose a penalty against very large (40°–60°) τ-angles. Root mean-squared deviation (RMSD) contour maps for the analysis using paired restraints are in Fig. S5.

Can the broader minima resulting from ¹⁵N-based restraints be narrowed by more extensive sampling? To address this, we analyzed a complete set of 11 ¹⁵N-labeled core sites in GWALP23 using DC or CS alone, DC and CS combined, or combined with QS, and finally using all three types of restraints simultaneously (see Table S2). Additional DC and CS data points did not significantly influence the quality of fits for the individual restraint analysis. Due to the dispersion of six Ala residues on the helical wheel, these ¹⁵N sites are sufficient to define a DC or CS helical wave with good accuracy, and five additional data points seem not to provide added insights. Furthermore, the 11 chemical shift values show larger deviation from an ideal case, suggesting small variations in the ¹⁵N chemical shift tensor between Leu and Ala.

The results of the joint analysis of 6 QS, 11 DC, and 11 CS restraints (see Table S2; Fig. 3) are presented in abbreviated form in Table 1. Notably, the average peptide orientation, defined by (τ₀, ρ₀) of (18°, 311°), remains similar to that obtained using any of the individual restraints, in particular QS. The ρ-angle is different by ∼22° from the fit of CS alone, but RMSD remains remarkably low, further highlighting the lower sensitivity of CS (and DC) to peptide rotation.

Figure 3.

RMSD contour plots of orientation and dynamics of GWALP23 in DMPC/DHPC bicelles, using the combined QS, DC, and CS restraints from Table S1. (A) Gaussian distributions of tilt and rotation (max RMSD = 5.0 kHz). (B) Semistatic dynamics using an order parameter. (C) Average tilt and rotation from the Gaussian analysis (max = 15.0 kHz). (D) Average tilt and rotation from variable S_zz analysis (max = 17.8 kHz). (E) Helical wheel plots for QS, DC, and CS (left to right). (Here and elsewhere, solid circles indicate Ala, and open circles indicate Leu.)

Similar analysis was performed for KWALP23 in DMPC/DHPC bicelles, which exhibits slightly larger τ₀ than GWALP23 (27). The small increase in τ₀ to ∼19°–20° is apparent in the individual or combined analyses of QS, DC, and CS (Table S2, Fig. S6). As for GWALP23, the ¹⁵N NMR observables alone offer somewhat less precision than QS, the latter being a key restraint for defining the orientation and dynamics. Interestingly, the best-fit ρ₀ differs by only 4° between KWALP23 and GWALP23, whereas the best estimates for the Gaussian (σ_τ, σ_ρ) parameters are (13°, 53°) for KWALP23 compared to (15°, 54°) for GWALP23 (Table 1 and Table S2).

Similar considerations hold for KWALP23 mechanically aligned in 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC) on glass slides. Interestingly, one ²H NMR spectrum (see Fig. S7) contains a signal from a backbone C_αD group that provides an additional restraint of similar sensitivity to helix orientation as the Ala side-chain QS. The semistatic and Gaussian analyses of this system using individual or combined restraints (29 data points total) are provided in Fig. S8. Compared to KWALP23 in DMPC, each type of restraint, individually or combined, suggests a similar ρ₀ of ∼300°, similar σ_τ of ∼10°, a small increase in τ₀ from ∼19° in DMPC to ∼21° in DLPC, and a notable decrease in σ_ρ from ∼50° in DMPC to ∼30° for KWALP23 in DLPC (see Table S2). It is of further note that similar ρ₀ and σ_τ values were deduced for KWALP23 in DMPC/DHPC bicelles and DLPC bilayers.

Case 2: QS_max < 15 kHz (extensive motion)

Single-span peptides having more than two bulky aromatic groups (Trp or Tyr residues) typically exhibit a narrow range of QS values, consistent with a small tilt angle (2,21,33). However, this result can also be caused by extensive averaging of the NMR signal, leading to a “masking” of a larger average tilt (34–36). Among such peptides, WWALP23 with four tryptophan residues has been shown to have a small apparent tilt angle in different lipid membranes using QS as a single restraint type (27). Here we complement the QS data set with the DC and CS restraints from five ¹⁵N-labeled residues (Table 1). Although the ²H NMR spectra do not exhibit unusual features in terms of line shapes or peak widths, the SLF spectrum demonstrates a single crosspeak for a peptide with five labels (Fig. 4). Although a single DC or CS value for multiple labeled sites can be observed for a peptide with τ close to zero (see above), the position of the overlapped WWALP23 resonances (3.2 kHz, 88 ppm) does not match that calculated for τ = 0° (4.1 kHz, 79.3 ppm; red circle in Fig. 4 B). Instead, the WWALP23 signal is located close to the center of PISA wheels for GWALP23 and KWALP23, implying that the narrow ranges of DC and CS among different positions in WWALP23 arise largely due to dynamics.

Figure 4.

²H NMR spectra (A), and ¹⁵N/¹H SLF NMR spectra (B) of WWALP23 in DMPC/DHPC bicelles, with assignments indicated. (B, red circle) Resonance for a zero tilt angle in the absence of the dynamics.

The analysis of WWALP23 behavior using any individual restraint set and Gaussian dynamics does not produce a definitive answer. Low RMSD values throughout the (σ_τ, σ_ρ) space make it difficult to differentiate among different solution sets (see Fig. S9 A). Although a global minimum appears to be present for the QS dynamics plot, the difference between adjacent contours is only 0.5 kHz, which is below the experimental error. Both DC and QS demonstrate similar patterns for the dynamics, with the best fits occurring for very large values of σ_τ and σ_ρ. Semistatic analyses of WWALP23 lead to single minima, although the converged S_zz values differ by 0.2 among the different sets of restraints. Notably, the DC and CS data sets point to a τ-value of 0° with an undefined ρ-angle; nevertheless, the nonidentical QS signals at different Ala positions, together with the offset of the SLF resonances from the dot in Fig. 4, reveal that the peptide is actually tilted and establish the peptide rotation ρ (see Table S2).

Unlike the GWALP23 case, where each individual restraint set already was quite informative, the combination of QS, DC and CS offers much improvement for defining the dynamics of WWALP23. The ²H data prohibit very large and very small values of σ_ρ, whereas the ¹⁵N data disfavor large σ_τ values and prohibit the combination of (small σ_ρ + small σ_τ). Together, the data sets provide a well-defined elongated minimum in (σ_τ, σ_ρ) space (Fig. 5 A). The influence of the combined restraints on semistatic analysis (Fig. 5 B) is less dramatic, as a combined fit is largely defined by QS, whereas DC and CS seem to fine-tune the S_zz value (see Table S2).

Figure 5.

RMSD contour plots of orientation and dynamics of WWALP23 in DMPC/DHPC bicelles, using the combined QS, DC, and CS restraints from Table S2. (A) Gaussian distributions of tilt and rotation (max RMSD = 3.4 kHz). (B) Semistatic dynamics using an order parameter. (C) Average tilt and rotation from the Gaussian analysis at point c in panel A (max = 13.8 kHz). (D) Average tilt and rotation from the Gaussian analysis at point d in panel A (max = 12.6 kHz). (E) Average tilt and rotation from variable S_zz analysis (max = 21.4 kHz). (F) Helical wheel plots for QS, DC, and CS (left to right).

Despite the better-defined range of acceptable dynamics in the Gaussian analysis, some uncertainty persists for the WWALP23 average orientation, in particular for τ₀. Due to the elongated (σ_τ, σ_ρ) solution space, the data can be equally well fitted with a number of different solutions, of which four examples in Table S2 illustrate correlations among parameters for peptide orientation and dynamics. For WWALP23 in DLPC, τ₀ can be as large as 22° if σ_ρ is ∼140° (see Table S2), or τ₀ can be as small as 10° if σ_ρ is ∼70°. The acceptable range for σ_τ is smaller, only ∼0°–20°, whereas ρ₀ remains constant at ∼134° for all of the solution sets. Because these solutions result in the identical QS, DC, and CS curves, it is not possible to differentiate among them (see Table S2, Fig. 5, C and D). The semistatic analysis of the combined restraints leads to an apparent τ that is some 5°–7° lower than the smallest τ₀ obtained with the Gaussian dynamics, similar to earlier observations with WALP19 and WALP23 (2,21), and illustrating the importance of the dynamics. Notably, WALP19, WALP23, and WWALP23 all have multiple aromatic residues that seem to compete for preferred locations within the interfacial region, perhaps causing the extensive dynamics.

Case 3: QS_max > 35 kHz (minimal motion)

Introduction of a charged residue close to the center of GWALP23 can be well tolerated in some cases (28). Recently, we have characterized a modified host peptide, GW^3,21ALP23 (37), that allows for two extra Ala labels in its hydrophobic core. The L14R mutation in this modified sequence has similar consequences on the peptide behavior as in the case of GWALP23-R14, namely an increase of ∼10° in τ₀ accompanied by a rotation change (38). For GW^3,21ALP23-R14, we observe some deviations between the ²H data in mechanically aligned glass slides and magnetically aligned bicelles, the latter yielding a larger τ, with identical ρ. Additionally, RMSD for the ²H data set is ∼2.3 kHz in bicelles (vs. 1.2 kHz in glass slides), but is lowered to ∼0.6 kHz when the most C-terminal data point Ala¹⁹ is excluded (38). Due to these considerations, we do not include restraints from Ala¹⁹ in the fits.

The large magnitudes of QS values for GW^3,21ALP23-R14 imply that τ is fairly large, irrespective of the extent of the dynamics (Fig. 6 A). The extended range of the resonances in the 2D SAMPI4 spectrum is further indicative of the large tilt magnitude (Fig. 6 B). The large dispersion of the signals also suggests only minor variations from τ₀ and ρ₀. Indeed, any individual restraint set results in a small range of acceptable σ_τ and σ_ρ values (see Fig. S10 A). The smaller σ_ρ for GW^3,21ALP23-R14 is particularly prominent when compared with GWALP23 (Fig. 2 A). The average orientation of GW^3,21ALP23-R14 (τ₀ ∼34°, ρ₀ ∼267°) is similar when deduced by any of the individual restraint sets, and also between the Gaussian and semistatic ways of treating the dynamics (see Table S2). The Gaussian parameters are notably small, ∼15° for σ_τ and ∼30° for σ_ρ (Table 1 and Table S2), reflecting the minimal peptide dynamics. Due to the enhanced amplitudes of the DC and CS helical curves, both tilt magnitude and direction are relatively well defined by the ¹⁵N restraints (see Fig. S10, C and D). As expected, the QS wave also provides an equivalent and well-defined solution.

Figure 6.

²H NMR spectra (A), and ¹⁵N/¹H SLF NMR spectra (B) of GW^3,21ALP23-R14 in DMPC/DHPC bicelles, with assignments indicated.

A combination of the orientational restraints for GW^3,21ALP23-R14 leads to only minor improvement of the Gaussian dynamics, helping marginally to localize the minimum for (σ_τ, σ_ρ). The main contribution in the dynamics refinement is the CS data set. Nevertheless, CS restraints continue to exhibit the largest deviations from the theoretical curve (perhaps reflecting subtle differences in the ¹⁵N tensors for Leu and Ala); therefore the apparent localization of the minimum RMSD solution for the Gaussian dynamics should be treated with caution (Fig. 7). The deduced average orientation of the peptide is nevertheless similar between the Gaussian and semistatic treatments and closely resembles the orientation based on the QS data alone. The DC and CS restraints alter somewhat the shape of the global minimum. Although the QS solution set is somewhat elongated in the τ₀ direction, DC and CS are less defined in ρ₀, making the combined fit appear to be more circular.

Figure 7.

RMSD contour plots of orientation and dynamics of GW^3,21ALP23-R14 in DMPC/DHPC bicelles, using the combined QS, DC, and CS restraints from Table S2. (A) Gaussian distributions of tilt and rotation (max RMSD = 11.0 kHz). (B) Semistatic dynamics using an order parameter. (C) Average tilt and rotation from the Gaussian analysis (max = 14.9 kHz). (D) Average tilt and rotation from variable S_zz analysis (max = 16.3 kHz). (E) Helical wheel plots for QS, DC, and CS (left to right).

Discussion

Membrane-spanning proteins may exhibit a variety of motions, which reflect both protein-protein and protein-lipid interactions. In this article, we have described several transmembrane α-helices that undergo small, medium, and large oscillations about their average tilt and rotation angles. Different solid-state NMR restraints were used individually or combined together to deduce the peptide behavior, and two methods to describe the peptide dynamics were compared.

The orientation and dynamics of GW^3,21ALP23-R14 are largely governed by the central arginine residue, which must be positioned in a specific way to snorkel to the membrane interface (28). The R14 residue therefore imposes a relatively large tilt angle and concomitantly restricts the dynamics to relatively small oscillations about the average molecular orientation (see Table S2). The large tilt-angle and minor dynamics can be fit using any of the QS, DC, or CS restraint sets for the data analysis (see Fig. S10). Indeed, the results from the individual restraint sets are largely similar, the only variations being small differences in the shapes of the global minima. The small extent of the dynamic averaging makes it possible to use either a semistatic or Gaussian analysis with nearly identical outcomes. One expects that minor or limited dynamics for a transmembrane segment could be dictated not only by charged residues (39), but also by helix bundles (40) or the presence of an interfacially bound domain (24). Each of these situations could restrict the motion of a membrane-spanning helix.

Such restrictions are absent for GWALP23 and KWALP23, leading to their orientations and dynamics being determined by Trp, Lys, and Gly residues at the membrane-water interface (27). The intermediate tilt accompanied by the medium oscillations can still be deduced by employing the individual QS, DC, or CS NMR data sets (see Table S2). Each individual restraint set returns similar orientation angles; however, due to the smaller dispersion of the ¹⁵N NMR data, the DC and CS restraints result in broader minima and a somewhat larger uncertainty for τ₀ and especially ρ₀ (Fig. 2). The inherently lower precision cannot be improved by more extensive data sampling. It would be beneficial therefore to include QS restraints in the analyses in cases where higher precision is required. Employing multiple types of restraints generally raises the confidence level for peptides that exhibit intermediate dynamics.

In contrast to an earlier suggestion (5,41), we do not find a specific propensity of an individual restraint set to under- or overestimate the tilt magnitudes. Nevertheless, we do observe a consistent 4°–6° tilt offset between the semistatic and Gaussian treatments of dynamics for GWALP23 and KWALP23, with the semistatic approach potentially underestimating the tilt angle. This tendency is fairly constant among the individual and combined restraint sets, and is reduced when the dynamics of the system decrease (see Table S2, KWALP23 in DLPC versus DMPC). The results highlight the importance of using identical treatments for the dynamics in cases where multiple systems are to be compared.

Unlike the other peptides discussed above, WWALP23 has four Trp residues: two near the N-terminus and two near the C-terminus. Although one Trp near each end is sufficient to promote transmembrane anchoring of the peptide orientation, as observed for GWALP23, multiple Trp residues appear to compete for favorable interfacial positions, leading to extensive dynamics (27). Indeed, the complete collapse of the PISA wheel to only a single crosspeak for the five labeled positions in the WWALP23 core helix serves as a rather dramatic indicator of large-scale motions (Fig. 4 B). A notable comparison is that other peptides having small tilt angles and moderate dynamics have been observed to produce resolved SLF resonances (14). In the absence of ¹⁵N NMR data, a low S_zz value (<0.65) in the course of semistatic analysis of ²H NMR QS data may provide an alternative indication of the extensive dynamics. Despite being a sensitive gauge of the dynamics, the ¹⁵N NMR data alone are not capable of distinguishing the small tilt angles in the presence of extensive signal averaging. Depending upon the (assumed) value of S_zz (from ∼0.7 to ∼0.9), the CS and DC data alone can fit tilt angles of ∼0°–24° for WWALP23.

The explicit Gaussian dynamics analysis of the combined QS, DC and CS restraints leads to a family of solutions with τ₀ in the range of 10°–22° (see Fig. S9; Table 1 and Table S2). Conversely, the semistatic analysis of WWALP23 behavior leads to a unique solution with a fairly small τ-value of only 4°–6°. Although the different solutions have identical RMSD values, it is reasonable to assume that the semistatic analysis is (again) underestimating τ some 5°–15°.

Irrespective of the model used to describe the dynamics, the (tilt-dependent) helical wave plots for the QS, DC, and CS restraints do not alter their characteristic shapes for any of the transmembrane peptides. Comparisons of RMSD values between the semistatic and Gaussian methods for the identical systems indicate that the differences do not exceed 0.15 kHz, and typically are much less (see Table S2). Although the Gaussian approach may provide unique helical wave plots for interfacially bound helices (4), this does not appear to be the case for transmembrane helices.

We did not observe significant differences between the ²H NMR spectra from bicelles and glass plate samples (at β = 90° macroscopic orientation), indicating that the mosaic spread of the sample is similar in both cases. A likely reason for the similarity is the difference in temperature, which was ∼10° higher for the glass slide samples, leading to more extensive motions and thus bringing S_bic close to unity.

Several arguments can be made in favor of the semistatic or Gaussian analyses. Thus, the semistatic approach is essentially model-free, as the net effect of molecular motion is estimated by means of a single scaling factor. Conversely, the Gaussian method provides additional insights into the nature of the motions, but forces one to assume a particular model. Although coarse-grained molecular dynamics simulations of the XWALP23 transmembrane helices are in agreement with overall Gaussian profiles for both τ₀ and ρ₀ (28), the ρ-angle patterns for other peptides have been reported to be more complex (35,42).

An additional benefit of the semistatic analysis is the minimal requirement for only three free parameters, τ₀, ρ₀, and S_zz, each having distinct influence on the helical waves, which may allow the peptide behavior to be deduced from less extensive sampling of the data. The Gaussian approach introduces an additional free parameter due to decomposition of S_zz into σ_τ and σ_ρ components, which in turn calls for additional data points. Although the latter is a lesser problem with model Ala-rich peptides of the GWALP23 family, it can pose difficulties for investigations of biological systems. In certain cases, the QS of backbone deuterons can yield additional restraints similar in sensitivity to the QS of the Ala methyl groups (28,43). When using the C_αD QS data, nevertheless, it is advisable to scale down their contributions by a factor of approximately three, due to their weak signals and increased line widths. Within this scope, the variable S_zz approach appears to be robust, whereas the Gaussian method should be applied in cases where highly anisotropic motion of a transmembrane segment is expected.

In summary, we have employed multiple ¹⁵N and ²H solid-state NMR methods to characterize the orientations and dynamics of selected model Trp-anchored transmembrane peptides that exhibit widely varying regimes of dynamics, from minimal to moderate to very extensive whole-peptide motional averaging. Depending upon the extent of motion, either a semistatic or a Gaussian analysis of the dynamics can be employed, using QS, DC, or CS observables from the solid-state NMR. For cases where extensive peptide motion persists, Gaussian analysis and combined use of multiple types of NMR-based experimental restraints are preferred.