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Metachronal waves for deterministic switching two-state oscillators with hydrodynamic interaction.

M Cosentino Lagomarsino1, P Jona, B Bassetti

  • 1FOM Institute for Atomic and Molecular Physics (AMOLF), Kruislaan 407, 1098 SJ Amsterdam, The Netherlands. cosentino-lagomarsino@amolf.nl

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2003
PubMed
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This study models cilia's coordinated motion using active oscillators called rowers. Metachronal waves emerge, but stability requires reversed coupling, leading to stable traveling wave packets.

Area of Science:

  • Physics of active matter
  • Biophysics
  • Fluid dynamics

Background:

  • Cilia generate coordinated motion (metachronal waves) essential for fluid transport.
  • Understanding cilia dynamics as a far-from-equilibrium process is crucial.
  • Hydrodynamic interactions govern the collective behavior of cilia.

Purpose of the Study:

  • To model coordinated cilia motion using a generic physical framework (rowers).
  • To analyze the dynamics of active oscillators in a low Reynolds number fluid.
  • To investigate the conditions for the emergence and stability of metachronal waves.

Main Methods:

  • Employing a rower model: active (two-state) oscillators interacting via hydrodynamic forces.
  • Deriving analytical solutions in the long-wavelength (continuum) limit.

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  • Performing numerical investigations in the short-wavelength limit.

    • Main Results:

    • Proving the existence of metachronal waves below a characteristic wavelength.
    • Identifying that these waves are initially unstable.
    • Demonstrating that stability is achieved by reversing the coupling sign.

    Conclusions:

    • Metachronal waves can form in systems of active oscillators.
    • Stable metachronal patterns emerge as traveling wave packets.
    • Anti-coordinated beating of rowers sustains these stable wave packets under normal hydrodynamic interaction.