Phase reduction approach to elastohydrodynamic synchronization of beating flagella.

Area of Science:

• Biophysics
• Fluid Dynamics
• Dynamical Systems

Background:

• Beating flagella exhibit complex dynamics often modeled by infinite-dimensional systems.
• Understanding flagellar phase dynamics is crucial for biological processes like locomotion and synchronization.

Purpose of the Study:

• To formulate a systematic theory for the phase reduction of beating flagella.
• To develop a method for analyzing flagellar dynamics using a single phase variable.
• To investigate phase synchronization between flagella via hydrodynamic interactions.

Main Methods:

• Developed a phase reduction theory for limit-cycle solutions of partial differential equations.
• Derived the phase sensitivity function to quantify responses to perturbations.
• Analyzed phase synchronization using the derived phase sensitivity function.

Main Results:

• A novel theory for phase reduction of beating flagella was established.
• The phase sensitivity function was derived, quantifying perturbation effects.
• Phase synchronization between two flagella was analyzed under low Reynolds number conditions.

Conclusions:

• The phase reduction theory provides a systematic framework for studying flagellar dynamics.
• The phase sensitivity function is a key tool for analyzing flagellar interactions and synchronization.
• Hydrodynamic interactions play a significant role in flagellar phase synchronization.