Biological tissue often achieves its function through anisotropic elastic properties. The mammalian inner ear seems to rely on an anisotropic extracellular matrix, the tectorial membrane (TM), to guide sound-induced vibrations to specific sensory hair cells. To understand the role of the TM in hearing it is helpful to outline the basic elements of the hearing process 
. The mammalian hearing epithelium, the organ of Corti, sits inside the snail-shaped cochlea on the basilar membrane (BM). The BM is graded in stiffness along the cochlea and vibrates in response to sound-induced movements of the cochlear fluids. As a result, the stereocilia bundles of outer hair cells (OHCs) are sheared against the TM, which is situated over the sensory epithelium and spans the entire length of the cochlea. The OHCs can change their length through a piezo-electric mechanism when stereocilia are deflected 
. Stereocilia deflection in OHCs and inner hair cells (IHC) stretches tip-links that open transduction channels, thereby inducing a receptor potential and modulating neurotransmitter release onto the postsynaptic spiral ganglion neurons 
Recent studies using mutant mice with altered TM organization have shown that its morphological anisotropy has a crucial role in mammalian hearing 
. This acellular matrix contains two main groups of components, collagen fibrils and non-collagenous proteins. The latter compose a striated-sheet matrix surrounding the collagen fibrils 
. Collagen fibrils are organized in thick fibers of ~1 µm diameter that run nearly radially across the TM 
. Surprisingly, the existence of TM's anisotropy in mammals is accompanied with a unique pattern and orientation of sensory cells, typically with one row of IHCs and three rows of OHCs 
. Furthermore, the collagen fibers and the OHC stereocilia bundles display a coincident slanting with respect to the radial direction 
. This suggests that the direction of collagen fibers in the TM coincides with the direction of stereocilia bundle deflection that leads to maximal sensitivity. Nevertheless, despite all these striking directional cues, the relevance of TM's mechanical anisotropy in hearing has not been established. This requires measurement of the anisotropic mechanical properties of the TM and subsequent modeling of the TM's mechanical interaction with hair cell stereocilia. It is important to emphasize that elastic moduli (as well as Young's modulus for an isotropic material) cannot be directly measured. An elasticity model is required to relate measurements of force and displacements to elastic moduli.
A number of morphological studies have noted the anisotropy of the TM and speculated about its function 
. In spite of that, many studies aimed at measuring the mechanical properties of the TM have disregarded the prominent presence of the oriented collagen fibers, which renders the TM mechanically anisotropic 
. Accordingly, the TM was modeled as an isotropic homogeneous material, and only one elastic modulus was reported. One recent study used Atomic Force Microscopy (AFM) to estimate the effective Young's modulus of the TM along different orthogonal directions 
. That study did not provide knowledge of the actual anisotropic elastic moduli of the TM, since an anisotropic elasticity model was not used.
We have previously described the TM using the simplest model of anisotropy, the transversely isotropic model, in which there is a single family of parallel fibers embedded in a matrix whose elastic properties are the same in any direction perpendicular to the fibers 
(). In such a model, the fibers correspond to the collagen fibers and the matrix corresponds to the striated-sheet matrix of non-collagenous proteins. When the material is incompressible, mechanical properties can be described by three elastic moduli, a fiber modulus (Ef
) and two shear moduli, one parallel to the fibers (μL
) and another perpendicular or transverse to them (μT
. The influence of these moduli are depicted in the upper row of , The larger the moduli the more difficult it is to deform the material in response to the applied stresses indicated by the arrows. Such elastic constants determine stress-strain relations, wave propagation speed, and the amount of stereocilia deflection when they are sheared against the TM.
Elastic moduli of transversely isotropic fiber model.
Here we report a new technique to measure the anisotropic mechanical properties of the TM by combining AFM, fluorescence microscopy and modeling. The main technical contribution of the present work was unraveling which measurements to make on the surface of the TM to find the 3 moduli (see lower row), and overcoming the essential difficulty in applying a calibrated shear force by the AFM cantilever in the surface plane of the TM. This novel approach has enabled us to measure for the first time the three anisotropic elastic moduli of the TM.