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Nonlinear dynamics of cilia and flagella

Andreas Hilfinger1,*, Amit K. Chattopadhyay1,2,†, and Frank Jülicher1,‡

  • 1Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany
  • 2Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom

  • *Present address: Department of Systems Biology, Harvard University, 200 Longwood Ave., Boston, MA 02115, USA.
  • †Present address: Department of Physics and Astrophysics, University of Delhi, Delhi 110 007, India.
  • ‡julicher@pks.mpg.de
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Phys. Rev. E 79, 051918 – Published 21 May, 2009

DOI: https://doi.org/10.1103/PhysRevE.79.051918

Abstract

Cilia and flagella are hairlike extensions of eukaryotic cells which generate oscillatory beat patterns that can propel micro-organisms and create fluid flows near cellular surfaces. The evolutionary highly conserved core of cilia and flagella consists of a cylindrical arrangement of nine microtubule doublets, called the axoneme. The axoneme is an actively bending structure whose motility results from the action of dynein motor proteins cross-linking microtubule doublets and generating stresses that induce bending deformations. The periodic beat patterns are the result of a mechanical feedback that leads to self-organized bending waves along the axoneme. Using a theoretical framework to describe planar beating motion, we derive a nonlinear wave equation that describes the fundamental Fourier mode of the axonemal beat. We study the role of nonlinearities and investigate how the amplitude of oscillations increases in the vicinity of an oscillatory instability. We furthermore present numerical solutions of the nonlinear wave equation for different boundary conditions. We find that the nonlinear waves are well approximated by the linearly unstable modes for amplitudes of beat patterns similar to those observed experimentally.

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Phys. Rev. E 79, 051918– Published 21 May, 2009
  • Received 5 March 2009

© 2009 American Physical Society

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