Dipolar waves map the structure and topology of helices in membrane proteins

Abstract

Dipolar waves describe the structure and topology of helices in membrane proteins. The fit of sinusoids with the 3.6 residues per turn period of ideal alpha-helices to experimental measurements of dipolar couplings as a function of residue number makes it possible to simultaneously identify the residues in the helices, detect kinks or curvature in the helices, and determine the absolute rotations and orientations of helices in completely aligned bilayer samples and relative rotations and orientations of helices in a common molecular frame in weakly aligned micelle samples. Since as much as 80% of the structured residues in a membrane protein are in helices, the analysis of dipolar waves provides a significant step toward structure determination of helical membrane proteins by NMR spectroscopy.

Figure 1

(A) The NH bond vectors (θ_NH and φ_NH) in an α-helix are distributed on a cone tilted at an angle δ away from the helix axis (θ_av and φ_av) which has a given orientation in the frame that describes the molecular alignment and averaging. (B) This results in sinusoidal oscillations in which the location of a particular experimental measurement along the sinusoid determined the rotation of that residue about the helix axis.

Figure 2

¹H–¹⁵N dipolar couplings are simulated for (A) a straight ideal α-helix, (B) an α-helix with a 55 Å radius of curvature, and (C) an ideal α-helix with a 20° kink with their average axis tilted 15° relative to the alignment z-axis. (D, E, F) The average error per point shows that the periodicity in all cases is 3.6 except near the ends where this periodicity is disrupted. (G, H, I) The phase is also diagnostic, where the kink is evidenced by a slight change in the phase of one sinusoid relative to the other.

Figure 3

(A) Experimentally measured dipolar couplings for residues S4 through S21 in the membrane-embedded M2 peptide from the nicotinic acetylcholine receptor. Superimposed on the data are the best fitting sinusoid and the parametrized expression for the ¹H–¹⁵N dipolar coupling as a function of residue number in an α-helix. The values for S8 and L18 are highlighted demonstrate the mapping of phase in a sine wave and position in a helical wheel. (B) The RMSD to an ideal sinusoid is measured for each window of four residues as less than 180 Hz. (C) Absolute phase of the best fitted sinusoid is constant, indicative of one continuous helix. (D) The helical wheel diagram shows the mapping of the pore-forming face of the helix and how the relative rotations of those residues map to the model shown in part E. The uniaxial distribution is shown as a cone with the 14° tilt angle.

Figure 4

Experimentally measured dipolar couplings are shown for an (A) fd coat protein in completely aligned bilayers, (B) fd coat protein in weakly aligned micelles, and (C) fd^N (N-terminal 20 residues) in weakly aligned micelles. All datasets are shown with the best-fitting sinusoid and the parametrized expression yielding the tilts and rotations of the helices in the alignment frame. Shown below each dataset (D, E, F) are the RMSD to an ideal sinusoid and (G, H, I) the absolute phase of that sinusoid for each point. (J, K) Helical wheel diagrams show how the phase of the sinusoids maps to the periodicity of the helix. The residues F11, W26, and F42 are marked to show the rotation of the helices.

Figure 5

Models of the fd coat protein helices consistent with the dipolar wave results in Figure 2. (A) The uniaxial symmetry of the unaveraged dipolar couplings gives a conelike distribution of possible orientations for one helix relative to the other but fixes the orientation relative to the lipid bilayer. (B) The inherent degeneracy of RDC measurements leads to four possible models of the coat protein. The models shown here are drawn for an arbitrary alignment. Residues F11, W26, and F42 are highlighted to show the rotations of the helices about their long axes. The models most consistent with the full structure characterization of this protein are shown in red.

Figure 6

(A) Experimental ¹H–¹⁵N residual dipolar couplings measured for MerF in weakly aligned micelles. (B) The periodicity, despite some missing measurements (designated by dotted lines), is indicative of three helical segments, with a change in direction near the middle of the first helix. (C) The absolute phase of the fitted sinusoid gives an idea of the continuity of the periodicity. Four possible models of the protein are shown in D, E, F, and G. Model F is most consistent with experimental data obtained from solid-state NMR. The positions of residues C20, S36, and F53 are shown.

Figure 7

(A and B) Simulated ¹H–¹⁵N dipolar couplings for the previously determined structures KcsA with RMSDs of 3.2 Å and 2.0 Å. Simulations are performed using the FORTRAN program SIMSPEC, which takes as input the coordinates from the PDB files (protons added using MOLMOL) for the alignment shown at the top, where the protein is completely uniaxially aligned. (C and D) The same data with the best fitting sinusoids of a periodicity of 3.6 superimposed on the data. Parts E and G show that the scoring functions for a periodicity of 3.6 residues in the case of the 3.2 Å structure are not able to determine the locations of the two long helices. Parts F and H are more typical of well-fitted sinusoids showing that the score is low along all three helices and the phase is nearly constant as well.

Figure 8

Helices in membrane proteins. (A) M2 peptide in bilayers. (B) The fd coat protein in bilayers. (C) The fd coat protein in micelles. (D) N-terminal peptide of the fd coat protein in micelles. (E) MerF protein in micelles.