Geometric somersaults of helical chains through twist propagation

Shiori Uda, Mengyun Li, Tomohiro Yanao*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This study is concerned with the rotary motions of helical chains that play essential roles in the functions of molecular motors in biological systems. While the standard pictures for the rotary motions of molecular motors may be more or less like the rotations of rigid bodies, this study explores a qualitatively different mechanism for the rotary motions. We take a simple model of a helical chain and highlight its geometric angle shifts induced by internal twist propagation. Such angle shifts, which we call geometric somersaults, can generally arise even under the conditions of zero total angular momentum, and are thereby analogous to the somersault of a falling cat. Helical chirality of the chain and the direction of twist propagation are the decisive factors that determine the direction of the resulting somersaults. As an application, we argue that the geometric somersaults of the helical chain may serve as a prototypical model for the rotary motions of the central shaft of ATP synthase.

Original languageEnglish
Pages (from-to)28-33
Number of pages6
JournalArtificial Life and Robotics
Issue number1
Publication statusPublished - 2018 Mar 1


  • ATP synthase
  • Chirality
  • Helical chain
  • Molecular motors
  • Somersault
  • Twist propagation

ASJC Scopus subject areas

  • Biochemistry, Genetics and Molecular Biology(all)
  • Artificial Intelligence


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