The reaction-diffusion basis of animated patterns in eukaryotic flagella

Area of Science:

• Biophysics
• Theoretical Biology
• Mathematical Modeling

Background:

• Flagellar locomotion is crucial for microorganisms and sperm.
• Existing models often struggle to explain complex flagellar dynamics across different species.
• The role of internal dissipation in flagellar mechanics is not fully understood.

Purpose of the Study:

• To develop a minimal, geometrically exact reaction-diffusion model for flagellar beating.
• To investigate a unified mechanism for sliding-controlled molecular motors in flagella.
• To understand the influence of internal dissipation on flagellar wave generation.

Main Methods:

• Modeling flagellar beat using a reaction-diffusion system derived from first principles.
• Comparing model predictions with experimental data for bull spermatozoa and C. Reinhardtii.
• Analyzing spatio-temporal animated patterns generated by the model.

Main Results:

• The reaction-diffusion model accurately reproduces experimental flagellar waves for both bull sperm and C. Reinhardtii.
• Animated patterns reveal sliding-controlled molecular motor kinetics analogous to chemical patterns.
• High internal dissipation was identified as the key driver for autonomous travelling waves.

Conclusions:

• A unified mechanism for sliding-controlled motors, independent of external hydrodynamics and curvature-sensing, is proposed.
• Internal dissipation enables efficient progressive swimming in low viscosity, critical for aquatic microorganisms.
• The reaction-diffusion system offers a powerful new tool for studying pattern formation in biological movement.