Robust driving forces for transmembrane helix packing

Abstract

The packing structures of transmembrane helices are traditionally attributed to patterns in residues along the contact surface. In this view, besides keeping the helices confined in the membrane, the bilayer has only a minor effect on the helices structure. Here, we use two different approaches to show that the lipid environment has a crucial effect in determining the cross-angle distribution of packed helices. We analyzed structural data of a membrane proteins database. We show that the distribution of cross angles of helix pairs in this database is statistically indistinguishable from the cross-angle distribution of two noninteracting helices imbedded in the membrane. These results suggest that the cross angle is, to a large extent, determined by the tilt angle of the individual helices. We test this hypothesis using molecular simulations of a coarse-grained model that contains no specific residue interactions. These simulations reproduce the same cross-angle distribution as found in the database. As the tilt angle of a helix is dominated by hydrophobic mismatch between the protein and surrounding lipids, our results indicate that hydrophobic mismatch is the dominant factor guiding the transmembrane helix packing. Other short-range forces might then fine-tune the structure to its final configuration.

Figure 1

Coarse-grained model and angle definitions. (a) CG model of an α-helix assembled from hydrophobic beads at the core and hydrophilic beads at both ends to keep the helix transmembrane. Helical geometry is maintained by harmonic springs, angle springs, and dihedral angle potentials of principal helix beads (see the Supporting Material for details). (b) CG lipid model includes three hydrophilic headgroups and two five-bead hydrophobic tails. Water is represented explicitly by a single bead. All beads in the system are of the same size and correspond to ∼3 carbon atoms/water molecules. (c) Two positive mismatched helices in a typical crossed configuration (note that, for clarity, water particles are not displayed). (d) Tilt angle, θ, of a helix is defined as the angle between the helix major axis (blue arrow) and the bilayer normal, $+\hat{z}$. (e) Cross angle, Ω, is defined as the dihedral angle between the major axes of the two helices (blue and orange arrows). (f) Projection angle, γ, is defined as the angle between the major helix axes along the plain of the bilayer $\left(\hat{x}-\hat{y}\right)$.

Figure 2

Average tilt angle as function of hydrophobic mismatch. (a) Compares tilt angle for all unique TM helices (black line) with peripheral unique TM helices (dashed green line, see text) as obtained from the experimental data in the OPM database with CG simulation of hydrophobic helices in a lipid bilayer (purple squares). The experimental data in the OPM database give a distribution of tilt angles represented by (solid line) for the average, and (pink shading) for 1 SD (fit and SD were obtained by the LOESS method (49)). The simulated CG results are an average from system of both five-bead and six-bead tail lipids, representing two membranes with different hydrophobic thicknesses, with error-bars representing the error in average values of both systems. (b) Further compares our simulation (black squares) and OPM experimental data (black line, standard deviation represented by dashed lines) with previously published simulation results for KALP peptides. Results by Kandasamy and Larson (30) are shown for low (blue circles) and high (red triangles) protein to lipid ratio. (Magenta squares) Results of coarse-grained simulations by Monticelli et al. (45).

Figure 3

Reference cross-angle (Ω) distribution. (Dashed line) Reference cross-angle distribution of two helices with fixed tilt angles, ${\theta }_1^{\prime }$ and ${\theta }_2^{\prime }$, and random projection angle, γ; (solid line) reference cross-angle distribution of two helices with normally distributed tilt angles with mean ${\theta }_1^{\prime }$, ${\theta }_2^{\prime }$ and standard deviation σ₁, σ₂, respectively. These mean and standard deviation values correspond to the experimental tilt angles at hydrophobic mismatch ranges Δd₁ = 30 Å and Δd₂ = 10.0 Å, respectively, as extracted from Fig. 2a. These amount to ${\theta }_1^{\prime }$ = 23.6°, ${\theta }_2^{\prime }$ = 29.4°, σ₁ = 11.3°, and σ₂ = 12. 4°. A schematic sketch of helices is provided for both extremes of γ = 0° and γ = 180°.

Figure 4

Comparison of right- and left-handed experimental cross angles. (a) Frequency of cross angles along the entire range Ω ∈ [−90°, 90°] for right-handed (striped red) and left-handed (solid blue) cross angles. Error bars represent 0.9 confidence intervals. (b) Absolute cross-angle distribution for right-handed (dashed red) and left-handed (solid blue) cross angles, in which all helix vectors are treated as pointing toward +z direction and the angle between those vectors is calculated by a simple dot product (see Methods). The mean standard deviation around the density lines is 0.006.

Figure 5

Comparison of cross-angle distributions. (Gray boxes) Experimental cross-angle distribution; (purple curves) simulated cross-angle distribution; and (red dotted lines) reference cross-angle distribution. The reference distribution is based on the tilt angle distribution of the helices’ mismatch as extracted from Fig. 2. (a) Absolute cross angle of pairs of neighboring helices with hydrophobic mismatches in the ranges Δd₁ ∈ (2,5] Å and Δd₂ ∈ (4,7] Å compared to simulated helices of mismatch Δd = 3.2 Å, 7.7 Å, respectively. (b) Experimental neighboring pairs in ranges Δd₁ ∈ (0,3] Å and Δd₂ ∈ (0,3] Å compared to simulated helices of mismatch Δd = 3.2 Å, 3.2 Å, respectively. (c) Full cross-angle distribution (and not the absolute one) for the same set used in plot b. Error bars in all three plots represent 0.9 confidence intervals.

Figure 6

Comparison of cross-angle distribution of all neighboring helix pairs with the reference distribution based on their respective mismatches. (a) Distribution of all neighboring pairs (blue, with 0.9 confidence intervals as error bars) compared to the overall reference distribution (pink; see text). (b) Difference in log of probabilities between the two sets. Equivalent to the difference in estimated free energies. The plot shows higher tendency for small cross angles (−10° ≤ Ω ≤ 30°) than expected by the reference distributions and lower than expected tendency for larger cross angles absolute values (−25° < Ω < −15°), (37° < Ω < 47°), and (58° < Ω < 65°). Error bars represent 0.9 confidence intervals obtained by a 500-resample bootstrap (50) on the values of experimental cross angles. Data are omitted for |Ω| > 75° due to large uncertainty.

Figure 7

Histogram of experimental projection angles of neighboring helices (gray boxes) shows tendency toward lower (γ < 100°) angles with p-value <0.0001 (based on a binomial test). (Lines) Representative projection angle histograms from CG simulations; each line corresponds to a different pair of same-mismatch helices: Δd = 3 Å (red solid), 17 Å (blue dashed), and 21 Å (green dotted). These show that the trend of overpopulation of lower projection angles is observed in simulations as well and varies in strength and shape with mismatch. Error bars represent 0.9 confidence intervals in experimental projection-angle histogram.