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Computer Simulation of Flagellar Movement IX. Oscillation and Symmetry Breaking in a Model for Short Flagella and Nodal Cilia

Brokaw, Charles J. (2005) Computer Simulation of Flagellar Movement IX. Oscillation and Symmetry Breaking in a Model for Short Flagella and Nodal Cilia. Cell Motility and the Cytoskeleton, 60 (1). pp. 35-47. ISSN 0886-1544. doi:10.1002/cm.20046.

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A computer model of flagella in which oscillation results from regulation of active sliding force by sliding velocity can simulate the movements of very short flagella and cilia. Of particular interest are the movements of the short (2–3 µm) nodal cilia of the mammalian embryo, which determine the development of the asymmetry of the internal organs. These cilia must generate a counterclockwise (viewed from base to tip) circling motion. A three-dimensional computer model, with active force generated by a simple mathematical formulation and regulated by sliding velocity, can generate this circling motion if a time delay process is included in the control specification. Without the introduction of a symmetrybreaking mechanism, the computer models start randomly in either direction, and maintain either clockwise or counterclockwise circling. Symmetry can be broken by at least two mechanisms: (1) control of dynein activity on one outer doublet by sliding velocity can be influenced by the sliding velocity experienced on an adjacent outer doublet, or (2) a constant twist of the axoneme caused by an off-axis component of dynein force. This second mechanism appears more reasonable, but its effectiveness is highly dependent upon specifications for the elastic resistances of the model. These symmetry-breaking mechanisms need to be present only at the beginning of circling. With these models, once a circling direction is established, it remains stable even if the symmetry-breaking mechanism is removed.

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Additional Information:© 2004 Wiley-Liss, Inc. Received 13 August 2004; accepted 7 October 2004. Article first published online: 30 Nov. 2004. I thank Professor Chris Henley, Cornell University, for comments on an earlier version of this report.
Subject Keywords:asymmetry; axoneme; chirality; dynein; embryo; microtubule rotation
Issue or Number:1
Record Number:CaltechAUTHORS:20120212-120149270
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Official Citation:Brokaw, C. J. (2005), Computer simulation of flagellar movement IX. Oscillation and symmetry breaking in a model for short flagella and nodal cilia. Cell Motility and the Cytoskeleton, 60: 35–47. doi: 10.1002/cm.20046
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:29249
Deposited By: Charles Brokaw
Deposited On:13 Feb 2012 15:42
Last Modified:09 Nov 2021 17:05

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