Prediction of Elastic Properties of Sperm Flagella

Schoutens, Jacques E.

doi:10.1006/jtbi.1994.1221

Cited by 14 publications

(35 citation statements)

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“…A theoretical study determined the EI of a 9+2 axoneme based on detailed calculation of its moment of inertia (Schoutens, 1994). Assuming no connections between the microtubules, a lower EI value of 680pNm 2 was determined, which is in remarkable agreement with measured values of the relaxed flagellum.…”

Section: Comparison With Literaturesupporting

confidence: 56%

Biomechanics of hair cell kinocilia: experimental measurement of kinocilium shaft stiffness and base rotational stiffness with Euler–Bernoulli and Timoshenko beam analysis

Spoon

Grant

2011

Journal of Experimental Biology

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the OL movement is transmitted to the mechanotransducing part of the hair bundle. Previous computational studies have shown that the tall and compliant kinocilia of extrastriolar bundles increase the hair cells' operating range (range of deflections over which vestibular sensory cell can encode) to several microns compared with that of striolar bundles, which is ~0.1m (Nam et al., 2005). Knowing the mechanical properties of the kinocilium will further our understanding of how these hair cells operate.Kinocilia are composed of a microtubular core, a 9+2 axoneme, composed of nine peripheral doublet microtubules encircling two central single tubules. This configuration is common to motile cilia and eukaryotic flagella (Fig.1A) but, despite their common structure, kinocilia are thought to be non-motile, unlike flagella, as they lack the inner arms of the motor protein dynein, which are essential for motility (Kikuchi et al., 1989). A limited number of spontaneous flagella-like oscillations have been observed in ampullary kinocilia but were limited in number and suggested to result from tissue Accepted 23 November 2010 SUMMARY Vestibular hair cell bundles in the inner ear contain a single kinocilium composed of a 9+2 microtubule structure. Kinocilia play a crucial role in transmitting movement of the overlying mass, otoconial membrane or cupula to the mechanotransducing portion of the hair cell bundle. Little is known regarding the mechanical deformation properties of the kinocilium. Using a force-deflection technique, we measured two important mechanical properties of kinocilia in the utricle of a turtle, Trachemys (Pseudemys) scripta elegans. First, we measured the stiffness of kinocilia with different heights. These kinocilia were assumed to be homogenous cylindrical rods and were modeled as both isotropic Euler-Bernoulli beams and transversely isotropic Timoshenko beams. Two mechanical properties of the kinocilia were derived from the beam analysis: flexural rigidity (EI) and shear rigidity (kGA). The Timoshenko model produced a better fit to the experimental data, predicting EI10,400pNm 2 and kGA247pN. Assuming a homogenous rod, the shear modulus (G1.9kPa) was four orders of magnitude less than Young's modulus (E14.1MPa), indicating that significant shear deformation occurs within deflected kinocilia. When analyzed as an Euler-Bernoulli beam, which neglects translational shear, EI increased linearly with kinocilium height, giving underestimates of EI for shorter kinocilia. Second, we measured the rotational stiffness of the kinocilium insertion () into the hair cell's apical surface. Following BAPTA treatment to break the kinocilial links, the kinocilia remained upright, and  was measured as 177±47pNmrad -1 . The mechanical parameters we quantified are important for understanding how forces arising from head movement are transduced and encoded by hair cells.

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Section: Comparison With Literaturesupporting

confidence: 56%

Biomechanics of hair cell kinocilia: experimental measurement of kinocilium shaft stiffness and base rotational stiffness with Euler–Bernoulli and Timoshenko beam analysis

Spoon

Grant

2011

Journal of Experimental Biology

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“…The nine outer doublets were designed according to Schoutens (Schoutens, 1994) as proposed in our previous study (Cibert, 2008). Black arrows represent the DAs.…”

Section: Christian Cibert 7/7mentioning

confidence: 99%

“…The rank of each outer doublet is included within the tubule A. The bending plane includes the central apparatus of the axoneme and the center of inertia (Schoutens, 1994) of the first outer doublet. The green (positive) and the red (negative) values are the dilation and the compression of the spatial frequencies of the DAs and the β-TMs calculated in Cibert 2008, when the bending angle equals π along a 10 µm long segment.…”

Section: Christian Cibert 7/7mentioning

confidence: 99%

“…From the known range of the physical characteristics (elastic constants) of the microtubules and of the ODPs (Fujime et al, 1972;Schoutens, 1994;Takano et al, 2003) one can assume that microtubules are inextensible and incompressible in the limits of normal beating cycles. However, different arguments plead in favor of their deformations during the beating cycles.…”

Section: Introductionmentioning

confidence: 99%

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Is the curvature of the flagellum involved in the apparent cooperativity of the dynein arms along the “9+2” axoneme?

Cibert¹,

Ludu²

2010

Journal of Theoretical Biology

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SUMMARYIn a recent study (Cibert, C. (2008), Journal of Theoretical Biology, 253: 74-89), by assuming that the walls of the microtubules are involved in cyclic compression/dilation equilibriums as a consequence of the cyclic curvature of the axoneme, it was proposed that the local adjustments of the spatial frequencies of both the dynein arms, and the β-tubulin monomers facing series, create the propagation of joint probability waves of interaction (JPI) between these two necessary partners. Modeling the occurrence of these probable interactions along the entire length of an axoneme between each outer doublet pairs (without programming any cooperative dialog between the molecular complexes) and the cyclic attachment of two facing partners, we show that the active couples such constituted are clustered. Along a cluster the dynein arms exhibit a small phase shift with respect to the order according to which they began each their cycle after being linked to a β-tubulin monomer. The numbers of couples included in these clusters depend on the probability of interaction between the dynein arms and the β-tubulin, on the location of the outer doublet pairs around the axonemal cylinder, and on the local bending of the axoneme; around the axonemal cylinder, the faster and larger the sliding, the shorter the clusters. This mechanism could be involved in the apparent cooperativity of the molecular motors and the β-tubulin monomers, since it is partially controlled by the local curvature, and the cluster length is inversely proportional to the sliding activity of the outer doublet pairs they link.

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“…But, it is clear that because the doublets are constituted by two microtubules whose architecture is very sophisticated they must be characterized by two different moments of inertia that have been calculated [Schoutens, 1994]. Therefore, the doublets must have interesting dynamic properties with respect to their inherent nature, even if they remain basically unextensible and uncompressible.…”

Section: Introductionmentioning

confidence: 99%

Geometry drives the “deviated‐bending” of the bi‐tubular structures of the 9+2 axoneme in the flagellum

Cibert¹,

Heck²

2004

Cell Motil. Cytoskeleton

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The axoneme "9 + 2" is basically a system constituted of a cylinder of 9 microtubule doublets surrounding a central pair of microtubules. These bi-tubular structures are considered as the support system of the active molecular complexes that generate and regulate the axonemal movement. Schoutens has calculated their moments of inertia [Schoutens, 1994: Journal of Theoretical Biology 171:163-177]. The results obtained allowed us to assume that these bi-tubular systems are endowed with dynamic properties that could be involved in the regulation of the axonemal machinery. For the first time, using the finite elements methods and the resistance of material principles, we have now calculated that the curvature of the axoneme induces the deviated-bending of the bi-tubular structures of the axoneme, because of their geometry only; they behave as beams in a framework. This approach is similar to the one used to measure the deflection of a single microtubule [Kasas et al., 2004: Chem Phys Chem 5:252-257]. These behaviors induce internal movement or constraints of either couples or triplets of doublets within the axonemal cylinder that could be directly involved in a constrained or a spontaneous "convergence/divergence" equilibrium of the cylindrical generatrices that they draw along the axonemal cylinder, which could apparently regulate the activity of the axonemal motors (the dynein arms). These results are discussed here, taking into consideration the dynamic propagation of the wave train along the flagellar axoneme, and the regulated balance between the activities of the two opposite sides of the axoneme during the beat. This study raises a few questions about the architecture-activity duo of the axonemal doublets.

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Prediction of Elastic Properties of Sperm Flagella

Cited by 14 publications

References 0 publications

Biomechanics of hair cell kinocilia: experimental measurement of kinocilium shaft stiffness and base rotational stiffness with Euler–Bernoulli and Timoshenko beam analysis

Biomechanics of hair cell kinocilia: experimental measurement of kinocilium shaft stiffness and base rotational stiffness with Euler–Bernoulli and Timoshenko beam analysis

Is the curvature of the flagellum involved in the apparent cooperativity of the dynein arms along the “9+2” axoneme?

Geometry drives the “deviated‐bending” of the bi‐tubular structures of the 9+2 axoneme in the flagellum

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