The reaction-diffusion basis of animated patterns in eukaryotic flagella

James F Cass, Hermes Bloomfield-Gadêlha*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)

Abstract

The flagellar beat of bull spermatozoa and C. Reinhardtii are modelled by a minimal, geometrically exact, reaction-diffusion system. Spatio-temporal animated patterns describe flagellar waves, analogous to chemical-patterns from classical reaction-diffusion systems, with sliding-controlled molecular motor reaction-kinetics. The reaction-diffusion system is derived from first principles as a consequence of the high-internal dissipation by the flagellum relative to the external hydrodynamic dissipation. Quantitative comparison with nonlinear, large-amplitude simulations shows that animated reaction-diffusion patterns account for the experimental beating of both bull sperm and C. Reinhardtii. Our results suggest that a unified mechanism may exist for motors controlled by sliding, without requiring curvature-sensing, and uninfluenced by hydrodynamics. High-internal dissipation instigates autonomous travelling waves independently of the external fluid, enabling progressive swimming, otherwise not possible, in low viscosity environments, potentially critical for external fertilizers and aquatic microorganisms. The reaction-diffusion system may prove a powerful tool for studying pattern formation of movement on animated structures.
Original languageEnglish
Article number5638
Number of pages14
JournalNature Communications
Volume14
Issue number1
DOIs
Publication statusPublished - 27 Sept 2023

Bibliographical note

Funding Information:
We express our gratitude to the authors of refs.  for making the data from their studies freely available, without which we would not have been able to proceed with this study. HBG acknowledges funding from the Engineering and Physical Sciences Research Council (EPSRC) DTP studentship for JFC’s PhD, with Grant Code: EP/R513179/1. The numerical work was carried out using the computational and data storage facilities of the Advanced Computing Research Centre, University of Bristol - http://www.bristol.ac.uk/acrc/ . ,

Funding Information:
We express our gratitude to the authors of refs. 17 ,47for making the data from their studies freely available, without which we would not have been able to proceed with this study. HBG acknowledges funding from the Engineering and Physical Sciences Research Council (EPSRC) DTP studentship for JFC’s PhD, with Grant Code: EP/R513179/1. The numerical work was carried out using the computational and data storage facilities of the Advanced Computing Research Centre, University of Bristol - http://www.bristol.ac.uk/acrc/.

Publisher Copyright:
© 2023, Springer Nature Limited.

Structured keywords

  • Engineering Mathematics Research Group

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