Nonlinear dynamics of cilia and flagella


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.

Publication DOI:
Divisions: College of Engineering & Physical Sciences > Systems analytics research institute (SARI)
Additional Information: © 2009 The American Physical Society
Uncontrolled Keywords: cilia,flagella,eukaryotic cells,oscillatory beat patterns,microtubule doublets,axoneme,dynein motor proteins,nonlinear wave equation,fundamental Fourier mode,amplitude of oscillations,Statistics and Probability,Condensed Matter Physics,Statistical and Nonlinear Physics
Publication ISSN: 1550-2376
Last Modified: 27 Jun 2024 07:48
Date Deposited: 15 Dec 2011 11:15
Full Text Link: http://link.aps ... sRevE.79.051918
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
PURE Output Type: Article
Published Date: 2009-05-21
Authors: Chattopadhyay, Amit K. (ORCID Profile 0000-0001-5499-6008)
Hilfinger, Andreas
Jülicher, Frank



Version: Published Version

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