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Elastohydrodynamic Synchronization of Adjacent Beating Flagella.

Raymond E Goldstein1, Eric Lauga1, Adriana I Pesci1

  • 1Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.

Physical Review Fluids
|May 12, 2018
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Summary
This summary is machine-generated.

Nearby eukaryotic flagella and cilia synchronize due to hydrodynamic coupling. This study analyzes this interaction for closely spaced filaments, revealing a universal coupling mechanism that explains synchrony in biological systems.

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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.