The counterbend phenomenon in flagellar axonemes and cross-linked filament bundles

Gadêlha H.; Gaffney E.A.; Goriely A.

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The counterbend phenomenon in flagellar axonemes and cross-linked filament bundles

机译：The counterbend phenomenon in flagellar axonemes and cross-linked filament bundles

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Recent observations of flagellar counterbend in sea urchin sperm show that the mechanical induction of curvature in one part of a passive flagellum induces a compensatory countercurvature elsewhere. This apparent paradoxical effect cannot be explained using the standard elastic rod theory of Euler and Bernoulli, or even the more general Cosserat theory of rods. Here, we develop a geometrically exact mechanical model to describe the statics of microtubule bundles that is capable of predicting the curvature reversal events observed in eukaryotic flagella. This is achieved by allowing the interaction of deformations in different material directions, by accounting not only for structural bending, but also for the elastic forces originating from the internal cross-linking mechanics. Large-amplitude static configurations can be described analytically, and an excellent match between the model and the observed counterbend deformation was found. This allowed a simultaneous estimation of multiple sperm flagellum material parameters, namely the cross-linking sliding resistance, the bending stiffness, and the sperm head junction compliance ratio. We further show that small variations on the empirical conditions may induce discrepancies for the evaluation of the flagellar material quantities, so that caution is required when interpreting experiments. Finally, our analysis demonstrates that the counterbend emerges as a fundamental property of sliding resistance in cross-linked filamentous polymer bundles, which also suggests that cross-linking proteins may contribute to the regulation of the flagellar waveform in swimming sperm via counterbend mechanics.

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《Proceedings of the National Academy of Sciences of the United States of America》 |2013年第30期|12180-12185|共6页
作者
Gadêlha H.; Gaffney E.A.; Goriely A.;
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作者单位

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom;

Centre for Mathematical Biology, United Kingdom;

Oxford Centre for Collaborative Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX1 3LB, United Kingdom;

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收录信息美国《科学引文索引》(SCI);美国《生物学医学文摘》(MEDLINE);美国《化学文摘》(CA);
原文格式 PDF
正文语种英语
中图分类自然科学总论;
关键词
Bending rigidity; Euler-elastica buckling; Shearability; Static postbuckled deformations;

The counterbend phenomenon in flagellar axonemes and cross-linked filament bundles

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