The counterbend dynamics of cross-linked filament bundles and flagella

Research output: Contribution to journalArticlepeer-review


Cross-linked filament bundles, such as in cilia and flagella, are ubiquitous in biology. They are considered in textbooks as simple filaments with larger stiffness. Recent observations of flagellar counterbend, however, show that induction of curvature in one section of a passive flagellum instigates a compensatory counter-curvature elsewhere, exposing the intricate role of the diminutive cross-linking proteins at large scales. We show that this effect, a material property of the cross-linking mechanics, modifies the bundle dynamics and induces a bimodal L 2 - L 3 length-dependent material response that departs from the Euler-Bernoulli theory. Hence, the use of simpler theories to analyse experiments can result in paradoxical interpretations. Remarkably, the counterbend dynamics instigates counter-waves in opposition to driven oscillations in distant parts of the bundle, with potential impact on the regulation of flagellar bending waves. These results have a range of physical and biological applications, including the empirical disentanglement of material quantities via counterbend dynamics.

Original languageEnglish
Article number20170065
Number of pages9
Issue number130
Publication statusPublished - 31 May 2017

Bibliographical note

© 2017 The Author(s). This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details


  • Bending stiffness
  • Counterbend
  • Cross-linked filament bundle
  • Flagella
  • High-order diffusion
  • Relaxation dynamics
  • Biomechanical Phenomena
  • Models, Biological
  • Computer Simulation
  • Flagella/physiology

Cite this