The reaction-diffusion basis of animated patterns in eukaryotic flagella

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.

Spontaneous oscillation of an active filament under viscosity gradients

“…For a deeper, biologically pertinent understanding, future work should explore models of ciliary oscillation driven by dynein motors. 11–22…”

“…A variety of models have been proposed to elucidate the mechanisms of how dynein motors power spontaneous ciliary oscillation. 11–22 Despite these efforts to achieve mechanistic understanding, the proposed models have also facilitated the investigation on synchronisation of two active filaments 23–25 and the emergence of metachronal waves generated by multiple filaments, 26,27 focusing on inter-filament interactions. More recently, motivated by the typically non-Newtonian bodily fluids hosting cilia and flagella, research has been conducted on a spontaneously oscillating filament in viscoelastic 28 or shear-thinning/thickening fluids.…”

Mechanical guidance to self-organization and pattern formation of stem cells

“…Our proposed theoretical framework considers numerous factors that affect pattern formation. The parameters related to the motility of cells 54 and the culture environment properties determine the morphologies of pattern formation. In this section, we investigate how these parameters affect the development of diverse biological patterns.…”