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. 2019 Mar 29;9:5321. doi: 10.1038/s41598-019-41766-1

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Collective TM-helix motions. (a) Bending (θ) and swivel (Φ) angles, which characterize the orientation of the ε-sites-carrying TM-C helix segment I47-M51 in relation to the TM-N segment I31-M35. (b) Representative conformations (overlaid at I31-M35) as determined by K-means clustering of θ and Φ angles (blue, TM-C segment I47-M51; red, TM-N segment I31-M35; orange, I45T mutation; green, G37 and G38; green sphere, C_α atom of G33). (c) Probability distributions of bending angles. (d) Probability of hinge motion types. Motions coordinated by a single hinge are referred to as type B and T, respectively. Motions around a pair of hinges are characterized by combinations of bending and twisting (BB, BT, TB, TT). (e) Probability by which a residue is identified as a hinge site in a single (B + T) and double-hinge (BB + BT + TB + TT) motion.