Cellular organization within a multicellular organism requires that a cell assess its relative location, taking in multiple cues from its microenvironment. Given that the extracellular matrix (ECM) consists of the most abundant proteins in animals and contributes both structure and elasticity to tissues, ECM probably provides key physical cues to cells. In vivo, in the vicinity of many tissue cell types, fibrous characteristics of the ECM are less discernible than the measurably distinct elasticity that characterizes different tissue microenvironments. As a cell engages matrix and actively probes, it senses the local elastic resistance of the ECM and nearby cells via their deformation, and — similar to the proverbial princess who feels a pea placed many mattresses below — the cell seems to possess feedback and recognition mechanisms that establish how far it can feel. Recent experimental findings and computational modeling of cell and matrix mechanics lend insight into the subcellular range of sensitivity. Continuity of deformation from the matrix into the cell and further into the cytoskeleton-caged and -linked nucleus also supports the existence of mechanisms that direct processes such as gene expression in the differentiation of stem cells. Ultimately, cells feel the difference between stiff or soft and thick or thin surroundings, regardless of whether or not they are of royal descent.

Matrix elasticity, cytoskeletal forces and physics of the nucleus: how deeply do cells ‘feel’ outside and in?

We recently presented a novel class of self-assembled diphenylalanine-based peptide nanotubes. Here, for the first time, we present their mechanical properties, which we directly measured through indentation type experiments using atomic force microscopy. We find that the averaged point stiffness of the nanotubes is 160 N/m, and that they have a correspondingly high Young's modulus of ∼19 GPa, as calculated by finite element analysis. This high value places these peptide nanotubes among the stiffest biological materials presently known, making them attractive building blocks for the design and assembly of biocompatible nanodevices.

Self-assembled peptide nanotubes are uniquely rigid bioinspired supramolecular structures.

Atomic force microscopy (AFM) allows the acquisition of high-resolution images and the measurement of mechanical properties of living cells under physiological conditions. AFM cantilevers with blunted pyramidal tips are commonly used to obtain images of living cells. Measurement of mechanical properties with these tips requires a contact model that takes into account their blunted geometry. The aim of this work was to develop a contact model of a blunted pyramidal tip and to assess the suitability of pyramidal tips for probing mechanical properties of soft gels and living cells. We developed a contact model of a blunted pyramidal tip indenting an elastic half-space. We measured Young's modulus (E) and the complex shear modulus (G*= G' +i G" ) of agarose gels and A549 alveolar epithelial cells with pyramidal tips and compared them with those obtained with spherical tips. The gels exhibited an elastic behavior with almost coincident loading and unloading force curves and negligible values of G". E fell sharply with indentation up to approximately 300 nm , showing a linear regime for deeper indentations. A similar indentation dependence of E with twofold lower values at the linear regime was obtained with the spherical tip fitted with Hertz's model. The dependence of E on indentation in cells paralleled that found in gels. Cells exhibited viscoelastic behavior with G"/G' approximately 1/4 . Pyramidal tips commonly used for AFM imaging are suitable for probing mechanical properties of soft gels and living cells.

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Probing mechanical properties of living cells by atomic force microscopy with blunted pyramidal cantilever tips.

The atomic force microscope is broadly used to study the morphology of cells, but it can also probe the mechanics of cells. It is now known that cancerous cells may have different mechanical properties to those of normal cells, but the reasons for these differences are poorly understood. Here, we report quantitatively the differences between normal and cancerous human cervical epithelial cells by considering the brush layer on the cell surface. These brush layers, which consist mainly of microvilli, microridges and cilia, are important for interactions with the environment. Deformation force curves obtained from cells in vitro were processed according to the 'brush on soft cell model'. We found that normal cells have brushes of one length, whereas cancerous cells have mostly two brush lengths of significantly different densities. The observed differences suggest that brush layers should be taken into account when characterizing the cell surface by mechanical means.

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Atomic force microscopy detects differences in the surface brush of normal and cancerous cells.

Much is known about the mechanotransducer (MT) channels mediating transduction in hair cells of the vertrbrate inner ear. With the use of isolated preparations, it is experimentally feasible to deliver precise mechanical stimuli to individual cells and record the ensuing transducer currents. This approach has shown that small (1–100 nm) deflections of the hair-cell stereociliary bundle are transmitted via interciliary tip links to open MT channels at the tops of the stereocilia. These channels are cation-permeable with a high selectivity for Ca2+; two channels are thought to be localized at the lower end of the tip link, each with a large single-channel conductance that increases from the low- to high-frequency end of the cochlea. Ca2+ influx through open channels regulates their resting open probability, which may contribute to setting the hair cell resting potential in vivo. Ca2+ also controls transducer fast adaptation and force generation by the hair bundle, the two coupled processes increasing in speed from cochlear apex to base. The molecular intricacy of the stereocilary bundle and the transduction apparatus is reflected by the large number of single-gene mutations that are linked to sensorineural deafness, especially those in Usher syndrome. Studies of such mutants have led to the discovery of many of the molecules of the transduction complex, including the tip link and its attachments to the stereociliary core. However, the MT channel protein is still not firmly identified, nor is it known whether the channel is activated by force delivered through accessory proteins or by deformation of the lipid bilayer.

The Physiology of Mechanoelectrical Transduction Channels in Hearing

Evidence and Implications of Inhomogeneity in Tectorial Membrane Elasticity

Knowledge of vibratory patterns in the cochlea is crucial to understanding the stimulation of mechanosensory cells. Experiments to determine the motion of the cochlear partition and surrounding fluid are extremely challenging. As a result, the motion data are incomplete and often contradictory. The bending mechanism of hair bundles, thought to be related to the shear motion and endolymphatic flow between the tectorial membrane (TM) and reticular lamina (RL), is controversial. We, therefore, extend the frequency range of our previous hybrid analytical–finite-element approach to model the basal as well as apical regions of the guinea pig cochlea. We solve the fluid-solid interaction eigenvalue problem for the axial wavenumber, fluid pressure, and vibratory relative motions of the cochlear partition as a function of frequency. A simple monophasic vibratory mode of the basilar membrane is found at both ends of the cochlea. However, this simple movement is associated with a complex frequency-dependent relative deformation between the TM and the RL. We provide evidence of a radial component of TM motion that is out of phase with the RL and that facilitates the bending of outer hair cell stereocilia at appropriate frequencies at both the cochlear base and apex.

Evidence of tectorial membrane radial motion in a propagating mode of a complex cochlear model

The cochlea transduces sound-induced vibrations in the inner ear into electrical signals in the auditory nerve via complex fluid–structure interactions. The mammalian cochlea is a spiralshaped organ, which is often uncoiled for cochlear modelling. In those few studies where coiling has been considered, the cochlear partition was often reduced to the basilar membrane only. Here, we extend our recently developed hybrid analytical/numerical micromechanics model to include curvature effects, which were previously ignored. We also use a realistic cross-section geometry, including the tectorial membrane and cellular structures of the organ of Corti, to model the apical and basal regions of a guinea-pig cochlea. We formulate the governing equations of the fluid and solid domains in a curvilinear coordinate system. The WKB perturbation method is used to treat the propagation of travelling waves along the coiled cochlear duct, and the O(1) system of the governing equations is solved in the transverse plane using finite-element analysis. We find that the curvature of the cochlear geometry has an important functional significance; at the apex, it greatly increases the shear gain of the cochlear partition, which is a measure of the bending efficiency of the outer hair cell stereocilia.

/pdf/effects-of-coiling-on-the-micromechanics-of-the-mammalian-12tvsm0edi.pdf

Effects of coiling on the micromechanics of the mammalian cochlea

We develop a hybrid approach for modeling the cochlea, in which we let the WKB method determine the axial propagation of waves and restrict the numerics to transverse planes, where we solve a fluid-solid interaction eigenvalue problem. The cochlear fluid is treated as viscous and incompressible. Viscous effects are confined to oscillatory boundary layers and the thin gap between the reticular lamina (RL) and the lower surface of the tectorial membrane (TM). Our model includes axial fluid coupling and also axial elastic coupling via a basilar membrane (BM) modeled as an orthotropic clamped plate. Three-dimensional (3D) flow is solved in two-dimensional (2D) domains, with interactions with 2D elastic domains representing the organ of Corti (OC) and the TM. The OC contains inhomogeneities representing discrete cellular structures. We have computed the interaction between the BM, TM, OC, and the cochlear fluid to find the complex-valued wavenumber-frequency relation and vibrational modes. The details of the c...

Hongxue Cai

Papers

Evidence and Implications of Inhomogeneity in Tectorial Membrane Elasticity

Evidence of tectorial membrane radial motion in a propagating mode of a complex cochlear model

Effects of coiling on the micromechanics of the mammalian cochlea

Radial Structure of Traveling Waves in the Inner Ear

Motion Analysis in the Hemicochlea