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. 2018 Mar 20;8:4882. doi: 10.1038/s41598-018-22502-7

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© The Author(s) 2018

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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Cyclization profiles for five molecules in which bend-angle and helicity are varied to counteract changes in helical repeat. For helical repeats 10.4 and 10.6, we use Pitch/Circumf = ±0.584 according to (12) and bend angle of 90 + 14.3(0.584) = 98.4 degrees according to (13). Similarly, for helical repeats 10.35 and 10.65, we use Pitch/Circumf = ±0.876 and bend angle 90 + 14.3(0.876) = 102.5. In each case, the values of Pitch/Circumf and bend angle determine helical parameters α and ψ shown in the legend, according to (26) and (27).