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. 2018 Sep 26;8:14415. doi: 10.1038/s41598-018-32686-7

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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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(A) Model for extended-extended mode of motion. Both bundles are left-handed and the motor torque of 2000 pN nm is applied in positive x-directions for each bundle. (B) Rigid body rotation of the flagellum in wrapped mode. (C) Rolling rotation of the filament representing the bundle in wrapped mode; the filament maintains its position relative to the cell body and material points on a cross section move around the cross section. (D) Model showing extended-wrapped swimming with both bundles left-handed while both motors rotate counterclockwise with same torque, set at 2000 pN nm here. (E) Swimming speed and body rotation rate as a function of undetermined rolling rotation rate of wrapped bundle filament. (F) Rigid-body rotation rates of each bundle as a function of undetermined rolling rotation rate. (G) Model showing extended-wrapped swimming with wrapped bundles right-handed while both motors rotate counterclockwise with same torques as in D. (H) Swimming speed and body rotation rate as a function of undetermined rolling rotation rate of wrapped bundle. (I) Rigid-body rotation rates of each bundle as a function of undetermined rolling rotation rate.