Dataset Information

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

ABSTRACT: 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.

SUBMITTER: Gadelha H

PROVIDER: S-EPMC3725085 | biostudies-literature | 2013 Jul

REPOSITORIES: biostudies-literature

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

Gadêlha Hermes H Gaffney Eamonn A EA Goriely Alain A

Proceedings of the National Academy of Sciences of the United States of America 20130703 30

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 ...[more]

PMID: 23824293

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Project description:The high homology of its axonemal components with humans and a large repertoire of axonemal mutants make Chlamydomonas a useful model system for experiments on the structure and function of eukaryotic cilia and flagella. Using this organism, we explored the spatial arrangement of axonemal components under physiological conditions by small-angle x-ray fiber diffraction. Axonemes were oriented in physiological solution by continuous shear flow and exposed to intense and stable x rays generated in the synchrotron radiation facility SPring-8, BL45XU. We compared diffraction patterns from axonemes isolated from wild-type and mutant strains lacking the whole outer arm (oda1), radial spoke (pf14), central apparatus (pf18), or the ?-chain of the outer arm dynein (oda11). Diffraction of the axonemes showed a series of well-defined meridional/layer-line and equatorial reflections. Diffraction patterns from mutant axonemes exhibited a systematic loss/attenuation of meridional/layer-line reflections, making it possible to determine the origin of various reflections. The 1/24 and 1/12 nm(-1) meridional reflections of oda1 and oda11 were much weaker than those of the wild-type, suggesting that the outer dynein arms are the main contributor to these reflections. The weaker 1/32 and 1/13.7 nm(-1) meridional reflections from pf14 compared with the wild-type suggest that these reflections come mainly from the radial spokes. The limited contribution of the central pair apparatus to the diffraction patterns was confirmed by the similarity between the patterns of the wild-type and pf18. The equatorial reflections were complex, but a comparison with electron micrograph-based models allowed the density of each axonemal component to be estimated. Addition of ATP to rigor-state axonemes also resulted in subtle changes in equatorial intensity profiles, which could report nucleotide-dependent structural changes of the dynein arms. The first detailed description of axonemal reflections presented here serves as a landmark for further x-ray diffraction studies to monitor the action of constituent proteins in functional axonemes.

Dataset Information

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

Publications

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

Similar Datasets

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