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Instability-driven oscillations of elastic microfilaments.

Feng Ling1, Hanliang Guo1, Eva Kanso1

  • 1Department of Aerospace and Mechanical Engineering, University of Southern California , Los Angeles, CA 90089 , USA.

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|April 9, 2019
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Summary

Cilia and flagella beating patterns may arise from an open-loop instability mechanism. This study reveals how elastic filaments under compressive forces exhibit bifurcations leading to non-planar and planar oscillations, explaining complex movements.

Keywords:
Hopf bifurcationmotile cilia and flagellaplanar and non-planar beating patterns

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Area of Science:

  • Biophysics
  • Cell Biology
  • Fluid Dynamics

Background:

  • Cilia and flagella are essential organelles with diverse rhythmic beating patterns.
  • Their internal structure (axoneme, dynein motors) is known, but the mechanism driving their motion is unclear.
  • Current theories involve dynamic regulation or open-loop flutter instability.

Purpose of the Study:

  • To investigate the mechanism behind cilia and flagella beating patterns.
  • To explore the role of elastic filament instability in generating oscillations.
  • To determine if an open-loop mechanism can explain observed beating diversity.

Main Methods:

  • Nonlinear numerical analysis
  • Linear stability theory
  • Low-order bead-spring modeling
  • Simulation of elastic filaments in viscous fluid under axial forces

Main Results:

  • An elastic filament under compressive forces exhibits a Hopf bifurcation leading to non-planar spinning.
  • A second bifurcation transitions spinning to planar wave-like oscillations.
  • Beating patterns are robust to perturbations in force distribution and filament configuration.

Conclusions:

  • An open-loop, instability-driven mechanism can generate both sustained oscillations and diverse beating patterns in cilia and flagella.
  • This model provides a potential explanation for the complex dynamics observed in these organelles.
  • Findings support the flutter instability theory for cilia and flagella motility.