Elastohydrodynamic Synchronization of Adjacent Beating Flagella

Area of Science:

• Biophysics
• Fluid Dynamics
• Cell Biology

Background:

• Eukaryotic flagella and cilia typically synchronize in phase when beating in proximity.
• Hydrodynamic coupling and waveform compliance are hypothesized mechanisms for this synchrony.
• Existing low-dimensional models (bead-spring) reproduce synchrony but lack direct physical parameterization.

Purpose of the Study:

• To theoretically examine hydrodynamic coupling between extended filaments in the regime of small inter-filament distances (d/L ≪ 1).
• To develop a more realistic model for flagellar beating that incorporates elasticity and active force generation.
• To elucidate the elastohydrodynamic mechanism driving synchrony in closely spaced biological filaments.

Main Methods:

• Asymptotic analysis of hydrodynamic coupling between two extended filaments for d/L ≪ 1.
• Development of a heuristic model for flagellar beating using a single fourth-order nonlinear PDE based on symmetry and physical principles.
• Analytical and numerical studies of the proposed PDE model.

Main Results:

• The hydrodynamic coupling between closely spaced filaments is independent of the microscopic details of their internal driving forces.
• The asymptotic analysis reveals a form of mutual induction analogous to vortex filament motion.
• The heuristic PDE model successfully illustrates how elastohydrodynamic coupling leads to synchrony between a pair of filaments.

Conclusions:

• Hydrodynamic coupling plays a crucial role in the in-phase synchrony of eukaryotic flagella and cilia.
• The developed asymptotic analysis and heuristic model provide a theoretical framework for understanding this phenomenon in the biologically relevant regime of close proximity.
• This work bridges the gap between simplified models and complex continuum descriptions of flagellar dynamics and synchrony.