Fig 1.
The three dominant deformation modes correspond to three physical deformations seen in α-helices with 18 residues (L = 18).
The collections of individual atom displacements on these deformed α-helices lead to individual deformation modes. (A) The first deformation mode, Bend 1, has the largest eigenvalue and it is associated with bending of the α-helix in one plane. (B) The second deformation mode, Bend 2, has the second largest eigenvalue and it is associated with bending of the α-helix in another plane, orthogonal to the first one. (C) The third deformation mode captures the twisting of the α-helix along its principal axis, and it has the third largest eigenvalue. (A)-(C) In each subfigure, the two α-helices are individual helices from the PDB in the transmembrane α-helix dataset that represent the two extreme cases of each deformation mode. The arrows illustrate the displacement vector from each atom of a standard α-helix (with a periodicity Δθ of 3.6 residues per helix turn, a rise Δz of 1.5 Å per residue) to its corresponding atom on the deformed α-helix. The tails of these arrows are all translated to the corresponding atom on the deformed α-helix to more easily illustrate how each atom is pulled under the influence of a particular deformation mode.
Fig 2.
The ten principal components with the largest eigenvalues (λ) from 18-residue transmembrane α-helices (N = 6075), extramembrane α-helices (N = 2198), and α-helices in soluble proteins (N = 6716).
(A) The eigenvalues (λ). (B) The eigenvalues, when normalized by total variance.
Table 1.
The scaling exponents derived from a power law relationship between the eigenvalues (λ) of the first three deformation modes and the α-helix length (L).
Fig 3.
Each line represents the percentage of total variance explained by the first ten principal components for α-helices of a certain length (L).
Sixteen lines are plotted to illustrate this trend in the range 10≤L≤25. The length of the α-helix in question is represented by the colour and thickness of each line. These distributions were plotted for (A) transmembrane α-helices, (B) extramembrane α-helices, and (C) α-helices in soluble proteins. The structures of PDB entries 3JBR [24] and 5AM9 [25] are shown for illustrative purposes.
Fig 4.
The percentage of total variance explained by each of the first three principal components individually (red, blue, and green) and combined (pink) for α-helices with helix lengths (L) in the range 10≤L≤25. The red, blue, and green lines represent the contributions of Bend 1, Bend 2, and Twist modes respectively towards explaining the total variance. The pink line represents the summed contributions of the first three principal components towards explaining the total variance. These results are plotted for (A) transmembrane α-helices, (B) extramembrane α-helices, and (C) α-helices in soluble proteins. The structures of PDB entries 3JBR [24] and 5AM9 [25] are shown for illustrative purposes.