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The reaction-diffusion basis of animated patterns in eukaryotic flagella

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  • James F. Cass

    (University of Bristol)

  • Hermes Bloomfield-Gadêlha

    (University of Bristol)

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.

Suggested Citation

  • James F. Cass & Hermes Bloomfield-Gadêlha, 2023. "The reaction-diffusion basis of animated patterns in eukaryotic flagella," Nature Communications, Nature, vol. 14(1), pages 1-14, December.
    • Handle: RePEc:nat:natcom:v:14:y:2023:i:1:d:10.1038_s41467-023-40338-2
    DOI: 10.1038/s41467-023-40338-2
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    References listed on IDEAS

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    1. N. J. Carter & R. A. Cross, 2005. "Mechanics of the kinesin step," Nature, Nature, vol. 435(7040), pages 308-312, May.
    2. Sushil Khanal & Miguel Ricardo Leung & Abigail Royfman & Emily L. Fishman & Barbara Saltzman & Hermes Bloomfield-Gadêlha & Tzviya Zeev-Ben-Mordehai & Tomer Avidor-Reiss, 2021. "A dynamic basal complex modulates mammalian sperm movement," Nature Communications, Nature, vol. 12(1), pages 1-11, December.
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