We address three problems that limit the use of the atomic force microscope when measuring elastic moduli of soft materials at microscopic scales. The first concerns the use of sharp cantilever tips, which typically induce local strains that far exceed the linear material regime. We show that this problem can be alleviated by using microspheres as probes, and we establish the criteria for their use. The second relates to the common use of the Hertz contact mechanics model, which leads to significant errors when applied to thin samples. We develop novel, simple to use corrections to apply for such cases. Samples that are either bonded or not bonded to a rigid substrate are considered. The third problem concerns the difficulty in establishing when contact occurs on a soft material. We obtain error estimates for the elastic modulus resulting from such uncertainty and discuss the sensitivity of the estimation methods to error in contact point. The theoretical and experimental results are compared to macroscopic measurements on poly(vinyl-alcohol) gels.

The atomic force microscope (AFM) has found wide applicability as a nanoindentation tool to measure local elastic properties of soft materials. An automated approach to the processing of AFM indentation data, namely, the extraction of Young's modulus, is essential to realizing the high-throughput potential of the instrument as an elasticity probe for typical soft materials that exhibit inhomogeneity at microscopic scales. This paper focuses on Hertzian analysis techniques, which are applicable to linear elastic indentation. We compiled a series of synergistic strategies into an algorithm that overcomes many of the complications that have previously impeded efforts to automate the fitting of contact mechanics models to indentation data. AFM raster data sets containing up to 1024 individual force-displacement curves and macroscopic compression data were obtained from testing polyvinyl alcohol gels of known composition. Local elastic properties of tissue-engineered cartilage were also measured by the AFM. All AFM data sets were processed using customized software based on the algorithm, and the extracted values of Young's modulus were compared to those obtained by macroscopic testing. Accuracy of the technique was verified by the good agreement between values of Young's modulus obtained by AFM and by direct compression of the synthetic gels. Validation of robustness was achieved by successfully fitting the vastly different types of force curves generated from the indentation of tissue-engineered cartilage. For AFM indentation data that are amenable to Hertzian analysis, the method presented here minimizes subjectivity in preprocessing and allows for improved consistency and minimized user intervention. Automated, large-scale analysis of indentation data holds tremendous potential in bioengineering applications, such as high-resolution elasticity mapping of natural and artificial tissues.

The conventional theory about the snail shell shape of the mammalian cochlea is that it evolved essentially and perhaps solely to conserve space inside the skull. Recently, a theory proposed that the spiral's graded curvature enhances the cochlea's mechanical response to low frequencies. This article provides a multispecies analysis of cochlear shape to test this theory and demonstrates that the ratio of the radii of curvature from the outermost and innermost turns of the cochlear spiral is a significant cochlear feature that correlates strongly with low-frequency hearing limits. The ratio, which is a measure of curvature gradient, is a reflection of the ability of cochlear curvature to focus acoustic energy at the outer wall of the cochlear canal as the wave propagates toward the apex of the cochlea.inner ear ͉ function ͉ mammalian evolution ͉ spiral I t is often thought that mammalian cochleae are coiled to pack a longer organ into a small space inside the skull and that the cochlear coil increases the efficiency of blood and nerve supply through a central shaft (1). Although these spatial advantages of a coiled cochlea have been generally accepted, understanding the effect of shape on hearing itself has been a challenge.Cochlear coiling is absent in reptiles, birds, and monotreme mammals, and it appears to have originated in the marsupial and placental mammal lines (2). Coiling allowed the cochlea to become longer, increasing the potential octave range, whereas uncoiled cochleae have been associated with relatively limited hearing ranges. Earlier studies suggested that the evolution of coiling enhanced high-frequency hearing (3). This suggestion, however, is not wholly satisfactory for several reasons. Above all, increased hearing ranges extended both high-frequency and low-frequency (LF) hearing abilities in mammals compared with birds and reptiles and improved sensitivities compared with even LF specialist fishes (4). Further, the highest-frequency waves are resolved near the base (entrance) before they propagate far enough into the spiral to ''feel'' the cochlear curvature; it is the lowest-frequency waves that propagate along the cochlea's coils.Earlier work on land mammal ear anatomy (5) found a strong correlation between the LF hearing limit of each species and the product of basilar membrane length and number of spiral turns, but did not adduce a mechanistic explanation for this relationship. Other data suggested also that longitudinal curvature of the cochlear duct generates radial fluid pressure gradients (6) and enhances radial movement of hair cells (1, 7).Recently, a new theory proposed that the cochlea's graded curvature actually enhances LF hearing (8), similar to a whispering gallery in which sounds cling to the concave surface of the lateral wall (9). The cochlear spiral shape redistributes wave energy toward the outer wall, particularly along its innermost, tightest, apical turn, and thereby enhances sensitivity to lowerfrequency sounds.In this article, we test this theory morphometrically. W...

The behavior of two dimensional patches of piezoelectric material bonded to the surface of elastic distributed structures and used as vibration actuators is analytically investigated. A static analysis is used to estimate the loads induced by the piezoelectric actuator to the supporting elastic structure. The theory is then applied to develop an approximate dynamic model for the vibration response of a simply supported elastic rectangular plate excited by a piezoelectric patch of variable rectangular geometry. The results demonstrate that modes can be selectively excited and that the geometry of the actuator shape markedly affects the distribution of the response among modes. It thus appears possible to tailor the shape of the actuator to either excite or suppress particular modes leading to improved control behavior.

SUMMARY In eukaryotes, DNA is packaged into chromatin by canonical histone proteins. The specialized histone H3 variant CENP-A provides an epigenetic and structural basis for chromosome segregation by replacing H3 at centromeres. Unlike exclusively octameric canonical H3 nucleosomes, CENP-A nucleosomes have been shown to exist as octamers, hexamers, and tetramers. An intriguing possibility reconciling these observations is that CENP-A nucleosomes cycle between octamers and tetramers in vivo. We tested this hypothesis by tracking CENP-A nucleosomal components, structure, chromatin folding, and covalent modifications across the human cell cycle. We report that CENP-A nucleosomes alter from tetramers to octamers before replication and revert to tetramers after replication. These structural transitions are accompanied by reversible chaperone binding, chromatin fiber folding changes, and previously undescribed modifications within the histone fold domains of CENP-A and H4. Our results reveal a cyclical nature to CENP-A nucleosome structure and have implications for the maintenance of epigenetic memory after centromere replication.

The lack of practicable nonlinear elastic contact models frequently compels the inappropriate use of Hertzian models in analyzing indentation data and likely contributes to inconsistencies associated with the results of biological atomic force microscopy measurements. We derived and validated with the aid of the finite element method force-indentation relations based on a number of hyperelastic strain energy functions. The models were applied to existing data from indentation, using microspheres as indenters, of synthetic rubber-like gels, native mouse cartilage tissue, and engineered cartilage. For the biological tissues, the Fung and single-term Ogden models achieved the best fits of the data while all tested hyperelastic models produced good fits for the synthetic gels. The Hertz model proved to be acceptable for the synthetic gels at small deformations (strain < 0.05 for the samples tested), but not for the biological tissues. Although this finding supports the generally accepted view that many soft materials can be assumed to be linear elastic at small deformations, the nonlinear models facilitate analysis of intrinsically nonlinear tissues and large-strain indentation behavior.

Durotaxis is a type of directed cell migration in which cells respond to a gradient of extracellular stiffness. Using automated tracking of positional data for large sample sizes of single migrating cells, we investigated 1) whether cancer cells can undergo durotaxis; 2) whether cell durotactic efficiency varies depending on the regional compliance of stiffness gradients; 3) whether a specific cell migration parameter such as speed or time of migration correlates with durotaxis; and 4) whether Arp2/3, previously implicated in leading edge dynamics and migration, contributes to cancer cell durotaxis. Although durotaxis has been characterized primarily in nonmalignant mesenchymal cells, little is known about its role in cancer cell migration. Diffusible factors are known to affect cancer cell migration and metastasis. However, because many tumor microenvironments gradually stiffen, we hypothesized that durotaxis might also govern migration of cancer cells. We evaluated the durotactic potential of multiple cancer cell lines by employing substrate stiffness gradients mirroring the physiological stiffness encountered by cells in a variety of tissues. Automated cell tracking permitted rapid acquisition of positional data and robust statistical analyses for migrating cells. These durotaxis assays demonstrated that all cancer cell lines tested (two glioblastoma, metastatic breast cancer, and fibrosarcoma) migrated directionally in response to changes in extracellular stiffness. Unexpectedly, all cancer cell lines tested, as well as noninvasive human fibroblasts, displayed the strongest durotactic migratory response when migrating on the softest regions of stiffness gradients (2-7 kPa), with decreased responsiveness on stiff regions of gradients. Focusing on glioblastoma cells, durotactic forward migration index and displacement rates were relatively stable over time. Correlation analyses showed the expected correlation with displacement along the gradient but much less with persistence and none with cell speed. Finally, we found that inhibition of Arp2/3, an actin-nucleating protein necessary for lamellipodial protrusion, impaired durotactic migration.For all live-cell fluorescence experiments, DMEM without phenol red or FluoroBrite DMEM (GIBCO) were used, with each supplemented with a 1:100 ratio of Oxyfluor (Oxyrase, Mansfield, OH) and 10 mM DL-lactate (Sigma, St. Louis, MO) to reduce photobleaching and phototoxicity, Durotaxis by Human Cancer Cells

In most metazoan nuclei, heterochromatin is located at the nuclear periphery in contact with the nuclear lamina, which provides mechanical stability to the nucleus. We show that in cultured cells, chromatin de-compaction by the nucleosome binding protein HMGN5 decreases the sturdiness, elasticity, and rigidity of the nucleus. Mice overexpressing HMGN5, either globally or only in the heart, are normal at birth but develop hypertrophic heart with large cardiomyoctyes, deformed nuclei and disrupted lamina, and die of cardiac malfunction. Chromatin de-compaction is seen in cardiomyocytes of newborn mice but misshaped nuclei with disrupted lamina are seen only in adult cardiomyocytes, suggesting that loss of heterochromatin diminishes the ability of the nucleus to withstand the mechanical forces of the contracting heart. Thus, heterochromatin enhances the ability of the nuclear lamina to maintain the sturdiness and shape of the eukaryotic nucleus; a structural role for chromatin that is distinct from its genetic functions.