Influence of whole-body dynamics on 15N PISEMA NMR spectra of membrane proteins: a theoretical analysis

Abstract

Membrane proteins and peptides exhibit a preferred orientation in the lipid bilayer while fluctuating in an anisotropic manner. Both the orientation and the dynamics have direct functional implications, but motions are usually not accessible, and structural descriptions are generally static. Using simulated data, we analyze systematically the impact of whole-body motions on the peptide orientations calculated from two-dimensional polarization inversion spin exchange at the magic angle (PISEMA) NMR. Fluctuations are found to have a significant effect on the observed spectra. Nevertheless, wheel-like patterns are still preserved, and it is possible to determine the average peptide tilt and azimuthal rotation angles using simple static models for the spectral fitting. For helical peptides undergoing large-amplitude fluctuations, as in the case of transmembrane monomers, improved fits can be achieved using an explicit dynamics model that includes Gaussian distributions of the orientational parameters. This method allows extracting the amplitudes of fluctuations of the tilt and azimuthal rotation angles. The analysis is further demonstrated by generating first a virtual PISEMA spectrum from a molecular dynamics trajectory of the model peptide, WLP23, in a lipid membrane. That way, the dynamics of the system from which the input spectrum originates is completely known at atomic detail and can thus be directly compared with the dynamic output obtained from the fit. We find that fitting our dynamics model to the polar index slant angles wheel gives an accurate description of the amplitude of underlying motions, together with the average peptide orientation.

Figure 1

Orientational and dynamic parameters for an α-helical peptide in a lipid bilayer. A pair of angles, tilt (τ) and azimuthal rotation (ρ), are sufficient to define the peptide orientation. τ is the angle formed between the molecular long axis of the helix (H) and the membrane normal (N). We define ρ as the angle between the direction of the peptide tilt and a vector perpendicular to H, pointing through the C^α atom of a reference residue (here the first residue of the peptide).

Figure 2

Geometry and definition of parameters used to calculate the chemical shift and dipolar splitting for each peptide plane. δ₁₁, δ₂₂, and δ₃₃ are the principal components of the CSA tensor, with δ₂₂ aligned along the normal to the peptide plane, N_i. The ¹⁵N axis frame is related to the ¹H-¹⁵N dipolar tensor by the angle β. θ_i is the angle between each N-H_i bond and the projection of the magnetic field vector B₀ onto the peptide plane, and λ_i is the angle between B₀ and N_i.

Figure 3

PISA wheels corresponding to mean tilt angles of 10° (A, D, and G), 30° (B, E, and H), and 90° (C, F, and I), calculated for various dynamic fluctuation modeled by Gaussian distributions. In each PISA wheel a reference peak is marked with a solid dot, corresponding to a signal from the same residue. Left column (A–C): effect of wagging fluctuations of τ, with σ_τ = 0° (solid line), 10° (dashed line), and 20° (dotted line). Middle column (D–F): effect of azimuthal fluctuations of ρ, with σ_ρ = 0° (solid line), 20° (dashed line), and 100° (dotted line). Right column (G–I): effect of simultaneous wagging and azimuthal fluctuations. Shown are σ_τ/σ_ρ pairs of 0°/0° (solid line), 0°/50° (dashed line), 20°/0° (dashed-dotted line), and 20°/50° (dotted line).

Figure 4

Analysis of the deviations encountered on fitting a mobile peptide with a static model. Best-fit τ-values as a function of the actual mean tilt of the reference peptide, which is a virtual case with a rotation angle of 180° undergoing wagging fluctuations with σ_τ^ref = 10° (dashed line), 20° (dashed-dotted line), 30° (dotted-dashed line), and 40° (dotted line). The solid line corresponds to the perfect fit for σ_τ^ref = 0°.

Figure 5

Virtual PISEMA spectra of WLP23 in a dimyristoylphosphatidylcholine membrane calculated from the trajectories of an atomistic MD simulation (30). (A) All signals corresponding to the 17 leucine residues of the peptide are shown, with those of the six residues used here for the fits (positions 10–15) marked with solid circles. (B) Best-fit PISA wheels to the virtual PISEMA spectrum of WLP23. The six quasiexperimental signals of residues 10–15, used here for the fits, are marked with open circles. The dashed line is the best-fit PISA wheel corresponding to a static model, where the positions of the fitted signals are marked with solid squares. The solid line is the best-fit wheel calculated with a dynamic model (explicit fluctuations of τ and ρ), where the fitted signals are marked with crosses.