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Collagen-based mechanical anisotropy of the tectorial membrane: implications for inter-row coupling of outer hair cell bundles.

Gavara N, Chadwick RS - PLoS ONE (2009)

Bottom Line: We found that the TM's large mechanical anisotropy results in a marked transmission of deformations along the direction that maximizes sensory cell excitation, whereas in the perpendicular direction the transmission is greatly reduced.Computational results, based on our values of elastic moduli, suggest that the TM facilitates the directional cooperativity of sensory cells in the cochlea, and that mechanical properties of the TM are tuned to guarantee that the magnitude of sound-induced tip-link stretching remains similar along the length of the cochlea.Furthermore, we anticipate our assay to be a starting point for other studies of biological tissues that require directional functionality.

View Article: PubMed Central - PubMed

Affiliation: Auditory Mechanics Section, National Institute on Deafness and Other Communication Disorders, NIH, Bethesda, MD, USA.

ABSTRACT

Background: The tectorial membrane (TM) in the mammalian cochlea displays anisotropy, where mechanical or structural properties differ along varying directions. The anisotropy arises from the presence of collagen fibrils organized in fibers of approximately 1 microm diameter that run radially across the TM. Mechanical coupling between the TM and the sensory epithelia is required for normal hearing. However, the lack of a suitable technique to measure mechanical anisotropy at the microscale level has hindered understanding of the TM's precise role.

Methodology/principal findings: Here we report values of the three elastic moduli that characterize the anisotropic mechanical properties of the TM. Our novel technique combined Atomic Force Microscopy (AFM), modeling, and optical tracking of microspheres to determine the elastic moduli. We found that the TM's large mechanical anisotropy results in a marked transmission of deformations along the direction that maximizes sensory cell excitation, whereas in the perpendicular direction the transmission is greatly reduced.

Conclusions/significance: Computational results, based on our values of elastic moduli, suggest that the TM facilitates the directional cooperativity of sensory cells in the cochlea, and that mechanical properties of the TM are tuned to guarantee that the magnitude of sound-induced tip-link stretching remains similar along the length of the cochlea. Furthermore, we anticipate our assay to be a starting point for other studies of biological tissues that require directional functionality.

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Related in: MedlinePlus

Setup to measure mechanical anisotropy.Point-like forces (ΔF) were imposed to indent the surface of the TM using a spherical tip. Since our experimental approach required controlled lateral forces, the AFM was tilted with respect to the stage. Surface displacements (Δd) were detected by tracking fluorescent beads deposited onto the surface of the TM. A set of measurements consisted of several indentation measurements performed at increasing tip-bead distances (r).
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pone-0004877-g002: Setup to measure mechanical anisotropy.Point-like forces (ΔF) were imposed to indent the surface of the TM using a spherical tip. Since our experimental approach required controlled lateral forces, the AFM was tilted with respect to the stage. Surface displacements (Δd) were detected by tracking fluorescent beads deposited onto the surface of the TM. A set of measurements consisted of several indentation measurements performed at increasing tip-bead distances (r).

Mentions: Elastic moduli determine the way a material deforms in response to an applied force. Analogous to the way a deformation pattern is transmitted along the surface of a bed when someone sits on it, deformations of the surface of the TM will also be observed when an AFM tip is used to impose forces on it. Clearly, those displacements must decay with increasing distance to the point of force application. A representative relation between applied forces, ΔF, and resulting displacements Δd, is , involving an elastic modulus and the distance r between the points of force application and observation. This kind of behavior for the transmission of deformations is found for a transversely anisotropic material. For such a material, the relationship between forces and deformations is described by a surface Green's tensor , which contains the three elastic moduli of the material, and whose elements represent surface displacements in the ith direction that result from a unit point force at the origin acting in the jth direction. Interestingly, for a transversely isotropic material, Gij = Gji,, i.e. Green's surface tensor is symmetric, so there are only six independent elements, albeit they are very mathematically complex in general. Along special directions however, some elements are given by simple functions that involve only one elastic modulus. We have used those tensor elements to readily estimate the elastic moduli of the material. Therefore, when designing our experimental setup (Fig. 2), the direction of forces that were applied as well as the direction of displacements measured, on the surface were carefully chosen to correspond to the tensor elements that provided direct computation of the elastic moduli (Fig. 1, lower row). It should be noted that the experimental design required forces to be exerted in the surface plane of the TM. Current AFMs, however, provide actual estimates of force only in the vertical direction. Therefore, we modified our AFM by placing it over a custom-made wedge, with a 10 degree tilt. By tilting the AFM head, we could apply a controlled component of the force in the plane of the stage (X–Y plane). Nevertheless, when the AFM head was tilted the applied force still retained a component in the vertical direction. Consequently, measurements were repeated in a non-tilted configuration to subtract the displacement resulting from vertical forces. The wedge could also be rotated, enabling the force on the X–Y plane to be directed parallel or perpendicular to the TM's fibers. To detect force-induced displacements, fluorescent beads were deposited onto the surface of the TM and tracked with nanometer resolution (Fig. 3 and 4). We then used our anisotropy model to compute the three elastic moduli from the applied forces, the observed bead displacements and the tip-bead distances.


Collagen-based mechanical anisotropy of the tectorial membrane: implications for inter-row coupling of outer hair cell bundles.

Gavara N, Chadwick RS - PLoS ONE (2009)

Setup to measure mechanical anisotropy.Point-like forces (ΔF) were imposed to indent the surface of the TM using a spherical tip. Since our experimental approach required controlled lateral forces, the AFM was tilted with respect to the stage. Surface displacements (Δd) were detected by tracking fluorescent beads deposited onto the surface of the TM. A set of measurements consisted of several indentation measurements performed at increasing tip-bead distances (r).
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2654110&req=5

pone-0004877-g002: Setup to measure mechanical anisotropy.Point-like forces (ΔF) were imposed to indent the surface of the TM using a spherical tip. Since our experimental approach required controlled lateral forces, the AFM was tilted with respect to the stage. Surface displacements (Δd) were detected by tracking fluorescent beads deposited onto the surface of the TM. A set of measurements consisted of several indentation measurements performed at increasing tip-bead distances (r).
Mentions: Elastic moduli determine the way a material deforms in response to an applied force. Analogous to the way a deformation pattern is transmitted along the surface of a bed when someone sits on it, deformations of the surface of the TM will also be observed when an AFM tip is used to impose forces on it. Clearly, those displacements must decay with increasing distance to the point of force application. A representative relation between applied forces, ΔF, and resulting displacements Δd, is , involving an elastic modulus and the distance r between the points of force application and observation. This kind of behavior for the transmission of deformations is found for a transversely anisotropic material. For such a material, the relationship between forces and deformations is described by a surface Green's tensor , which contains the three elastic moduli of the material, and whose elements represent surface displacements in the ith direction that result from a unit point force at the origin acting in the jth direction. Interestingly, for a transversely isotropic material, Gij = Gji,, i.e. Green's surface tensor is symmetric, so there are only six independent elements, albeit they are very mathematically complex in general. Along special directions however, some elements are given by simple functions that involve only one elastic modulus. We have used those tensor elements to readily estimate the elastic moduli of the material. Therefore, when designing our experimental setup (Fig. 2), the direction of forces that were applied as well as the direction of displacements measured, on the surface were carefully chosen to correspond to the tensor elements that provided direct computation of the elastic moduli (Fig. 1, lower row). It should be noted that the experimental design required forces to be exerted in the surface plane of the TM. Current AFMs, however, provide actual estimates of force only in the vertical direction. Therefore, we modified our AFM by placing it over a custom-made wedge, with a 10 degree tilt. By tilting the AFM head, we could apply a controlled component of the force in the plane of the stage (X–Y plane). Nevertheless, when the AFM head was tilted the applied force still retained a component in the vertical direction. Consequently, measurements were repeated in a non-tilted configuration to subtract the displacement resulting from vertical forces. The wedge could also be rotated, enabling the force on the X–Y plane to be directed parallel or perpendicular to the TM's fibers. To detect force-induced displacements, fluorescent beads were deposited onto the surface of the TM and tracked with nanometer resolution (Fig. 3 and 4). We then used our anisotropy model to compute the three elastic moduli from the applied forces, the observed bead displacements and the tip-bead distances.

Bottom Line: We found that the TM's large mechanical anisotropy results in a marked transmission of deformations along the direction that maximizes sensory cell excitation, whereas in the perpendicular direction the transmission is greatly reduced.Computational results, based on our values of elastic moduli, suggest that the TM facilitates the directional cooperativity of sensory cells in the cochlea, and that mechanical properties of the TM are tuned to guarantee that the magnitude of sound-induced tip-link stretching remains similar along the length of the cochlea.Furthermore, we anticipate our assay to be a starting point for other studies of biological tissues that require directional functionality.

View Article: PubMed Central - PubMed

Affiliation: Auditory Mechanics Section, National Institute on Deafness and Other Communication Disorders, NIH, Bethesda, MD, USA.

ABSTRACT

Background: The tectorial membrane (TM) in the mammalian cochlea displays anisotropy, where mechanical or structural properties differ along varying directions. The anisotropy arises from the presence of collagen fibrils organized in fibers of approximately 1 microm diameter that run radially across the TM. Mechanical coupling between the TM and the sensory epithelia is required for normal hearing. However, the lack of a suitable technique to measure mechanical anisotropy at the microscale level has hindered understanding of the TM's precise role.

Methodology/principal findings: Here we report values of the three elastic moduli that characterize the anisotropic mechanical properties of the TM. Our novel technique combined Atomic Force Microscopy (AFM), modeling, and optical tracking of microspheres to determine the elastic moduli. We found that the TM's large mechanical anisotropy results in a marked transmission of deformations along the direction that maximizes sensory cell excitation, whereas in the perpendicular direction the transmission is greatly reduced.

Conclusions/significance: Computational results, based on our values of elastic moduli, suggest that the TM facilitates the directional cooperativity of sensory cells in the cochlea, and that mechanical properties of the TM are tuned to guarantee that the magnitude of sound-induced tip-link stretching remains similar along the length of the cochlea. Furthermore, we anticipate our assay to be a starting point for other studies of biological tissues that require directional functionality.

Show MeSH
Related in: MedlinePlus