Computer simulation of flagellar movement IX. Oscillation and symmetry breaking in a model for short flagella and nodal cilia
Article first published online: 30 NOV 2004
Copyright © 2004 Wiley-Liss, Inc.
Cell Motility and the Cytoskeleton
Volume 60, Issue 1, pages 35–47, January 2005
How to Cite
Brokaw, C. J. (2005), Computer simulation of flagellar movement IX. Oscillation and symmetry breaking in a model for short flagella and nodal cilia. Cell Motil. Cytoskeleton, 60: 35–47. doi: 10.1002/cm.20046
- Issue published online: 30 NOV 2004
- Article first published online: 30 NOV 2004
- Manuscript Accepted: 7 OCT 2004
- Manuscript Received: 13 AUG 2004
- microtubule rotation
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 symmetry-breaking 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. Cell Motil. Cytoskeleton 60:35–47, 2005. © 2004 Wiley-Liss, Inc.