Nanoscale strain-hardening of keratin fibres

Mammalian appendages such as hair, quill and wool have a unique structure composed of a cuticle, a cortex and a medulla. The cortex, responsible for the mechanical properties of the fibers, is an assemblage of spindle-shaped keratinized cells bound together by a lipid/protein sandwich called the cell membrane complex. Each cell is itself an assembly of macrofibrils around 300 nm in diameter that are paracrystalline arrays of keratin intermediate filaments embedded in a sulfur-rich protein matrix. Each macrofibril is also attached to its neighbors by a cell membrane complex. In this study, we combined atomic force microscopy based nano-indentation with peak-force imaging to study the nanomechanical properties of macrofibrils perpendicular to their axis. For indentation depths in the 200 to 500 nm range we observed a decrease of the dynamic elastic modulus at 1 Hz with increasing depth. This yielded an estimate of 1.6GPa for the lateral modulus at 1 Hz of porcupine quill's macrofibrils. Using the same data we also estimated the dynamic elastic modulus at 1 Hz of the cell membrane complex surrounding each macrofibril, i.e., 13GPa. A similar estimate was obtained independently through elastic maps of the macrofibrils surface obtained in peak-force mode at 1 kHz. Furthermore, the macrofibrillar texture of the cortical cells was clearly identified on the elasticity maps, with the boundaries between macrofibrils being 40-50% stiffer than the macrofibrils themselves. Elasticity maps after indentation also revealed a local increase in dynamic elastic modulus over time indicative of a relaxation induced strain hardening that could be explained in term of a α-helix to β-sheet transition within the macrofibrils.     

Functional remineralization of dentin lesions using polymer-induced liquid-precursor process

It was hypothesized that applying the polymer-induced liquid-precursor (PILP) system to artificial lesions would result in time-dependent functional remineralization of carious dentin lesions that restores the mechanical properties of demineralized dentin matrix. 140 μm deep artificial caries lesions were remineralized via the PILP process for 7-28 days at 37°C to determine temporal remineralization characteristics. Poly-L-aspartic acid (27 KDa) was used as the polymeric process-directing agent and was added to the remineralization solution at a calcium-to-phosphate ratio of 2.14 (mol/mol). Nanomechanical properties of hydrated artificial lesions had a low reduced elastic modulus (E(R) = 0.2 GPa) region extending about 70 μm into the lesion, with a sloped region to about 140 μm where values reached normal dentin (18-20 GPa). After 7 days specimens recovered mechanical properties in the sloped region by 51% compared to the artificial lesion. Between 7-14 days, recovery of the outer portion of the lesion continued to a level of about 10 GPa with 74% improvement. 28 days of PILP mineralization resulted in 91% improvement of E(R) compared to the artificial lesion. These differences were statistically significant as determined from change-point diagrams. Mineral profiles determined by micro x-ray computed tomography were shallower than those determined by nanoindentation, and showed similar changes over time, but full mineral recovery occurred after 14 days in both the outer and sloped portions of the lesion. Scanning electron microscopy and energy dispersive x-ray analysis showed similar morphologies that were distinct from normal dentin with a clear line of demarcation between the outer and sloped portions of the lesion. Transmission electron microscopy and selected area electron diffraction showed that the starting lesions contained some residual mineral in the outer portions, which exhibited poor crystallinity. During remineralization, intrafibrillar mineral increased and crystallinity improved with intrafibrillar mineral exhibiting the orientation found in normal dentin or bone.     

An application of nanoindentation technique to measure bone tissue Lamellae properties

Measuring the microscopic mechanical properties of bone tissue is important in support of understanding the etiology and pathogenesis of many bone diseases. Knowledge about these properties provides a context for estimating the local mechanical environment of bone related cells thait coordinate the adaptation to loads experienced at the whole organ level. The objective of this study was to determine the effects of experimental testing parameters on nanoindentation measures of lamellar-level bone mechanical properties. Specifically, we examined the effect of specimen preparation condition, indentation depth, repetitive loading, time delay, and displacement rate. The nanoindentation experiments produced measures of lamellar elastic moduli for human cortical bone (average value of 17.7 +/- 4.0 GPa for osteons and 19.3 +/- 4.7 GPa for interstitial bone tissue). In addition, the hardness measurements produced results consistent with data in the literature (average 0.52 +/- 0.15 GPa for osteons and 0.59 +/- 0.20 GPa for interstitial bone tissue). Consistent modulus values can be obtained from a 500-nm-deep indent. The results also indicated that the moduli and hardnesses of the dry specimens are significantly greater (22.6% and 56.9%, respectively) than those of the wet and wet and embedded specimens. The latter two groups were not different. The moduli obtained at a 5-nm/s loading rate were significantly lower than the values at the 10- and 20-nm/s loading rates while the 10- and 20-nm/s rates were not significantly different. The hardness measurements showed similar rate-dependent results. The preliminary results indicated that interstitial bone tissue has significantly higher modulus and hardness than osteonal bone tissue. In addition, a significant correlation between hardness and elastic modulus was observed.     

The effect of Glisson's capsule on the superficial elasticity measurements of the liver

In the past decade, novel tools for surgical planning and disease diagnosis have been developed to detect the liver's mechanical properties. Some tools utilize superficial indentation type measurements to determine the elasticity of the liver parenchyma and to assume material homogeneity. In fact, the liver is a soft tissue covered with a connective sheathing that is called Glisson's capsule. This article quantifies the effect of this capsule on the measured or "effective" elastic modulus obtained by indentation with a spherical geometry. Two sets of parametric computational studies in which the Glisson capsule thickness and elasticity were varied, demonstrated the relationship between the measured elastic response and the underlying parenchymal elastic response. Previously reported in vivo indentation data on the human liver were utilized to determine the elasticity of its parenchyma. The results indicated a linear relationship between the effective (measured) elastic response and the underlying parenchyma for the Glisson capsule thicknesses considered. When previously published human liver indentation data were analyzed, the measured elastic modulus was nearly 6.9% greater than the underlying parenchyma elastic modulus. Although the analyzed data were obtained from a single liver and yet displayed a significant variation, the Glisson capsule elasticity induced a significant but systematic error as well. The Glisson capsule thickness error was negligible for capsule parameters associated with a normal liver. Based on this work, an emphasis on the Glisson capsule's contribution to the mechanical response of the liver would enhance the clinical potential of indentation-based novel tools for liver care.     

Stiffness and heterogeneity of the pulmonary endothelial glycocalyx measured by atomic force microscopy

The mechanical properties of endothelial glycocalyx were studied using atomic force microscopy with a silica bead (diameter ～18 μm) serving as an indenter. Even at indentations of several hundred nanometers, the bead exerted very low compressive pressures on the bovine lung microvascular endothelial cell (BLMVEC) glycocalyx and allowed for an averaging of stiffness in the bead-cell contact area. The elastic modulus of BLMVEC glycocalyx was determined as a pointwise function of the indentation depth before and after enzymatic degradation of specific glycocalyx components. The modulus-indentation depth profiles showed the cells becoming progressively stiffer with increased indentation. Three different enzymes were used: heparinases III and I and hyaluronidase. The main effects of heparinase III and hyaluronidase enzymes were that the elastic modulus in the cell junction regions increased more rapidly with the indentation than in BLMVEC controls, and that the effective thickness of glycocalyx was reduced. Cytochalasin D abolished the modulus increase with the indentation. The confocal profiling of heparan sulfate and hyaluronan with atomic force microscopy indentation data demonstrated marked heterogeneity of the glycocalyx composition between cell junctions and nuclear regions.     

Mechano-acoustic determination of Young's modulus of articular cartilage

The compressive stiffness of an elastic material is traditionally characterized by its Young's modulus. Young's modulus of articular cartilage can be directly measured using unconfined compression geometry by assuming the cartilage to be homogeneous and isotropic. In isotropic materials, Young's modulus can also be determined acoustically by the measurement of sound speed and density of the material. In the present study, acoustic and mechanical techniques, feasible for in vivo measurements, were investigated to quantify the static and dynamic compressive stiffness of bovine articular cartilage in situ. Ultrasound reflection from the cartilage surface, as well as the dynamic modulus were determined with the recently developed ultrasound indentation instrument and compared with the reference mechanical and ultrasound speed measurements in unconfined compression (n=72). In addition, the applicability of manual creep measurements with the ultrasound indentation instrument was evaluated both experimentally and numerically. Our experimental results indicated that the sound speed could predict 47% and 53% of the variation in the Young's modulus and dynamic modulus of cartilage, respectively. The dynamic modulus, as determined manually with the ultrasound indentation instrument, showed significant linear correlations with the reference Young's modulus (r(2)=0.445, p<0.01, n=70) and dynamic modulus (r(2)=0.779, p<0.01, n=70) of the cartilage. Numerical analyses indicated that the creep measurements, conducted manually with the ultrasound indentation instrument, were sensitive to changes in Young's modulus and permeability of the tissue, and were significantly influenced by the tissue thickness. We conclude that acoustic parameters, i.e. ultrasound speed and reflection, are indicative to the intrinsic mechanical properties of the articular cartilage. Ultrasound indentation instrument, when further developed, provides an applicable tool for the in vivo detection of cartilage mechano-acoustic properties. These techniques could promote the diagnostics of osteoarthrosis.     

Nanomechanical and structural properties of native cellulose under compressive stress

Cellulose is an important biopolymer with applications ranging from its use as an additive in pharmaceutical products to the development of novel smart materials. This wide applicability arises in part from its interesting mechanical properties. Here we report on the use of high pressure X-ray diffraction and Raman spectroscopy in a diamond anvil cell to determine the bulk and local elastic moduli of native cellulose. The modulus values obtained are 20 GPa for the bulk modulus and 200-355 and 15 GPa for the crystalline parts and the overall elastic (Young's) modulus, respectively. These values are consistent with those calculated from tensile measurements. Above 8 GPa, the packing of the cellulose chains within the fibers undergoes significant structural distortion, whereas the chains themselves remain largely unaffected by compression.     

Endothelial, cardiac muscle and skeletal muscle exhibit different viscous and elastic properties as determined by atomic force microscopy

This study evaluated the hypothesis that, due to functional and structural differences, the apparent elastic modulus and viscous behavior of cardiac and skeletal muscle and vascular endothelium would differ. To accurately determine the elastic modulus, the contribution of probe velocity, indentation depth, and the assumed shape of the probe were examined. Hysteresis was observed at high indentation velocities arising from viscous effects. Irreversible deformation was not observed for endothelial cells and hysteresis was negligible below 1 μm/s. For skeletal muscle and cardiac muscle cells, hysteresis was negligible below 0.25 μm/s. Viscous dissipation for endothelial and cardiac muscle cells was higher than for skeletal muscle cells. The calculated elastic modulus was most sensitive to the assumed probe geometry for the first 60 nm of indentation for the three cell types. Modeling the probe as a blunt cone–spherical cap resulted in variation in elastic modulus with indentation depth that was less than that calculated by treating the probe as a conical tip. Substrate contributions were negligible since the elastic modulus reached a steady value for indentations above 60 nm and the probe never indented more than 10% of the cell thickness. Cardiac cells were the stiffest (100.3±10.7 kPa), the skeletal muscle cells were intermediate (24.7±3.5 kPa), and the endothelial cells were the softest with a range of elastic moduli (1.4±0.1 to 6.8±0.4 kPa) depending on the location of the cell surface tested. Cardiac and skeletal muscle exhibited nonlinear elastic behavior. These passive mechanical properties are generally consistent with the function of these different cell types.     

Effect of Age and Cytoskeletal Elements on the Indentation-Dependent Mechanical Properties of Chondrocytes

Articular cartilage chondrocytes are responsible for the synthesis, maintenance, and turnover of the extracellular matrix, metabolic processes that contribute to the mechanical properties of these cells. Here, we systematically evaluated the effect of age and cytoskeletal disruptors on the mechanical properties of chondrocytes as a function of deformation. We quantified the indentation-dependent mechanical properties of chondrocytes isolated from neonatal (1-day), adult (5-year) and geriatric (12-year) bovine knees using atomic force microscopy (AFM). We also measured the contribution of the actin and intermediate filaments to the indentation-dependent mechanical properties of chondrocytes. By integrating AFM with confocal fluorescent microscopy, we monitored cytoskeletal and biomechanical deformation in transgenic cells (GFP-vimentin and mCherry-actin) under compression. We found that the elastic modulus of chondrocytes in all age groups decreased with increased indentation (15–2000 nm). The elastic modulus of adult chondrocytes was significantly greater than neonatal cells at indentations greater than 500 nm. Viscoelastic moduli (instantaneous and equilibrium) were comparable in all age groups examined; however, the intrinsic viscosity was lower in geriatric chondrocytes than neonatal. Disrupting the actin or the intermediate filament structures altered the mechanical properties of chondrocytes by decreasing the elastic modulus and viscoelastic properties, resulting in a dramatic loss of indentation-dependent response with treatment. Actin and vimentin cytoskeletal structures were monitored using confocal fluorescent microscopy in transgenic cells treated with disruptors, and both treatments had a profound disruptive effect on the actin filaments. Here we show that disrupting the structure of intermediate filaments indirectly altered the configuration of the actin cytoskeleton. These findings underscore the importance of the cytoskeletal elements in the overall mechanical response of chondrocytes, indicating that intermediate filament integrity is key to the non-linear elastic properties of chondrocytes. This study improves our understanding of the mechanical properties of articular cartilage at the single cell level.     

Dehomogenized Elastic Properties of Heterogeneous Layered Materials in AFM Indentation Experiments

Atomic force microscopy (AFM) is used to study mechanical properties of biological materials at submicron length scales. However, such samples are often structurally heterogeneous even at the local level, with different regions having distinct mechanical properties. Physical or chemical disruption can isolate individual structural elements but may alter the properties being measured. Therefore, to determine the micromechanical properties of intact heterogeneous multilayered samples indented by AFM, we propose the Hybrid Eshelby Decomposition (HED) analysis, which combines a modified homogenization theory and finite element modeling to extract layer-specific elastic moduli of composite structures from single indentations, utilizing knowledge of the component distribution to achieve solution uniqueness. Using finite element model-simulated indentation of layered samples with micron-scale thickness dimensions, biologically relevant elastic properties for incompressible soft tissues, and layer-specific heterogeneity of an order of magnitude or less, HED analysis recovered the prescribed modulus values typically within 10% error. Experimental validation using bilayer spin-coated polydimethylsiloxane samples also yielded self-consistent layer-specific modulus values whether arranged as stiff layer on soft substrate or soft layer on stiff substrate. We further examined a biophysical application by characterizing layer-specific microelastic properties of full-thickness mouse aortic wall tissue, demonstrating that the HED-extracted modulus of the tunica media was more than fivefold stiffer than the intima and not significantly different from direct indentation of exposed media tissue. Our results show that the elastic properties of surface and subsurface layers of microscale synthetic and biological samples can be simultaneously extracted from the composite material response to AFM indentation. HED analysis offers a robust approach to studying regional micromechanics of heterogeneous multilayered samples without destructively separating individual components before testing.     

Elastic energy storage in human articular cartilage: estimation of the elastic modulus for type II collagen and changes associated with osteoarthritis.

The viscoelastic mechanical properties of normal and osteoarthritic articular were analyzed based on data reported by Kempson [in: Adult Articular Cartilage (1973)] and Silver et al. (Connect. Tissue Res., 2001b). Results of the analysis of tensile elastic stress-strain curves suggest that the elastic modulus of cartilage from the superficial zone is approximately 7.0 GPa parallel and 2.21 GPa perpendicular to the cleavage line pattern. Collagen fibril lengths in the superficial zone were found to be approximately 1265 microm parallel and 668 microm perpendicular to the cleavage line direction. The values for the elastic modulus and fibril lengths decreased with increased extent of osteoarthritis. The elastic modulus of type II collagen parallel to the cleavage line pattern in the superficial zone approaches that of type I collagen in tendon, suggesting that elastic energy storage occurs in the superficial zone due to the tensile pre-tension that exists in this region. Decreases in the elastic modulus associated with osteoarthritis reflect decreased ability of cartilage to store elastic energy, which leads to cartilage fibrillation and fissure formation. We hypothesize that under normal physiological conditions, collagen fibrils in cartilage function to store elastic energy associated with weight bearing and locomotion. Enzymatic cleavage of cartilage proteoglycans and collagen observed in osteoarthritis may lead to fibrillation and fissure formation as a result of impaired energy storage capability of cartilage.     

Correlations between indentation modulus and mineral density in bone-fracture calluses

The mechanical properties of a healing bone fracture depend not only on the geometry of the fracture callus but also on the material properties of the callus tissues. Despite the biomechanical importance of callus tissues in restoring mechanical integrity to the injured bone, little is known about the material properties of these tissues and whether these properties can be estimated non-invasively. This study used nanoindentation to quantify the spatial variations in indentation modulus throughout the fracture callus and correlated the measurements of modulus with measurements of tissue mineral density (TMD) obtained from images from micro-computed tomography (μCT). Fracture calluses were harvested from rats 24 days following creation of a full-thickness, transverse osteotomy in the femoral mid-diaphysis. Calluses were imaged using μCT, and the average TMD and the median grayvalue (X-ray attenuation) of five, pre-defined volumes of interest (VOIs) in each callus were computed. Nanoindentation was then performed at multiple, regularly spaced locations across 150 μm-thick, sagittal sections of the calluses. The indentation modulus ranged from 0.51 to 1680 MPa throughout the callus, with the highest moduli in the center of the fracture gap and the lowest in the periphery of the gap (P < 0.05). TMD was also highest in the center of the gap (P < 0.05). An increasing trend in both modulus and TMD was observed in the regions of the callus adjacent to the periosteal surfaces of the cortex. While no correlation was found between the average indentation modulus in a given VOI and the median grayvalue of that VOI, the average indentation modulus and the average TMD were positively correlated (R = 0.70, P < 0.05). Together, these findings establish the spatial heterogeneity in the mechanical behavior of tissues in fracture calluses and indicate that the indentation modulus of these tissues can be estimated by non-invasive measurements of tissue mineralization.     

Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue

The ability to determine trabecular bone tissue elastic and failure properties has biological and clinical importance. To date, trabecular tissue yield strains remain unknown due to experimental difficulties, and elastic moduli studies have reported controversial results. We hypothesized that the elastic and tensile and compressive yield properties of trabecular tissue are similar to those of cortical tissue. Effective tissue modulus and yield strains were calibrated for cadaveric human femoral neck specimens taken from 11 donors, using a combination of apparent-level mechanical testing and specimen-specific, high-resolution, nonlinear finite element modeling. The trabecular tissue properties were then compared to measured elastic modulus and tensile yield strain of human femoral diaphyseal cortical bone specimens obtained from a similar cohort of 34 donors. Cortical tissue properties were obtained by statistically eliminating the effects of vascular porosity. Results indicated that mean elastic modulus was 10% lower (p<0.05) for the trabecular tissue (18.0+/-2.8 GPa) than for the cortical tissue (19.9+/-1.8 GPa), and the 0.2% offset tensile yield strain was 15% lower for the trabecular tissue (0.62+/-0.04% vs. 0.73+/-0.05%, p<0.001). The tensile-compressive yield strength asymmetry for the trabecular tissue, 0.62 on average, was similar to values reported in the literature for cortical bone. We conclude that while the elastic modulus and yield strains for trabecular tissue are just slightly lower than those of cortical tissue, because of the cumulative effect of these differences, tissue strength is about 25% greater for cortical bone.     

Comparison of the equilibrium response of articular cartilage in unconfined compression,confined compression and indentation

At mechanical equilibrium, articular cartilage is usually characterized as an isotropic elastic material with no interstitial fluid flow. In this study, the equilibrium properties (Young's modulus, aggregate modulus and Poisson's ratio) of bovine humeral, patellar and femoral cartilage specimens (n=26) were investigated using unconfined compression, confined compression, and indentation tests. Optical measurements of the Poisson's ratio of cartilage were also carried out. Mean values of the Young's modulus (assessed from the unconfined compression test) were 0.80+/-0.33, 0.57+/-0.17 and 0.31+/-0.18MPa and of the Poisson's ratio (assessed from the optical test) 0.15+/-0.06, 0.16+/-0.05 and 0.21+/-0.05 for humeral, patellar, and femoral cartilages, respectively. The indentation tests showed 30-79% (p<0.01) higher Young's modulus values than the unconfined compression tests. In indentation, values of the Young's modulus were independent of the indenter diameter only in the humeral cartilage. The mean values of the Poisson's ratio, obtained indirectly using the mathematical relation between the Young's modulus and the aggregate modulus in isotropic material, were 0.16+/-0.06, 0.21+/-0.05, and 0.26+/-0.08 for humeral, patellar, and femoral cartilages, respectively. We conclude that the values of the elastic parameters of the cartilage are dependent on the measurement technique in use. Based on the similar values of Poisson's ratios, as determined directly or indirectly, the equilibrium response of articular cartilage under unconfined and confined compression is satisfactorily described by the isotropic elastic model. However, values of the isotropic Young's modulus obtained from the in situ indentation tests are higher than those obtained from the in vitro unconfined or confined compression tests and may depend on the indenter size in use.     

Variation in Young's modulus along the length of a rat vibrissa

Rats use specialized tactile hairs on their snout, called vibrissae (whiskers), to explore their surroundings. Vibrissae have no sensors along their length, but instead transmit mechanical information to receptors embedded in the follicle at the vibrissa base. The transmission of mechanical information along the vibrissa, and thus the tactile information ultimately received by the nervous system, depends critically on the mechanical properties of the vibrissa. In particular, transmission depends on the bending stiffness of the vibrissa, defined as the product of the area moment of inertia and Young's modulus. To date, Young's modulus of the rat vibrissa has not been measured in a uniaxial tensile test. We performed tensile tests on 22 vibrissae cut into two halves: a tip-segment and a base-segment. The average Young's modulus across all segments was 3.34±1.48GPa. The average modulus of a tip-segment was 3.96±1.60GPa, and the average modulus of a base-segment was 2.90±1.25GPa. Thus, on average, tip-segments had a higher Young's modulus than base-segments. High-resolution images of vibrissae were taken to seek structural correlates of this trend. The fraction of the cross-sectional area occupied by the vibrissa cuticle was found to increase along the vibrissa length, and may be responsible for the increase in Young's modulus near the tip.     

Elasticity of alveolar bone near dental implant-bone interfaces after one month's healing

Information is scarce about Young's modulus of healing bone surrounding an implant. The purpose of this preliminary study is to quantify elastic properties of pig alveolar bone that has healed for 1 month around titanium threaded dental implants, using the nanoindentation method. Two 2-year-old Sinclair miniswine were used for the study. Nanoindentation tests perpendicular to the bucco-lingual cross section were performed on harvested implant-bone blocks using the Hysitron TriboScope III. Nomarski differential interference contrast microscopy was used to identify pyramidal indentation measurements that were from bone. Reduced moduli, averaged for all anatomical regions, were found to start low (6.17 GPa) at the interface and gradually increase (slope=0.014) to a distance of 150 microm (7.89 GPa) from the implant surface, and then flatten to a slope of 0.001 from 150 to 1500 microm (10.13 GPa). Mean reduced modulus and its relationship to distance did not differ significantly by anatomic location (e.g., coronal, middle, and apical third; P>/=0.28 for all relevant tests) at 1 month after implantation.     

Micromechanical understanding of the cell-wall structure

For improving properties of pulp fibres, a better understanding of the relationships between its macroscopic mechanical properties, fibre ultrastructure, and properties of the wood polymers is important. This paper discusses such relations between elastic properties of fibres, their matrix structure and the wood polymer elastic constants. It is argued that an orientation of all of the wood polymers in the direction of the cellulose microfibrils is most likely. The elastic longitudinal modulus of cellulose is well described by the value of 134 GPa dominating the longitudinal fibre properties. In the transverse direction the amorphous polymers play a more important role.     

Mechanical properties of physiological and pathological models of collagen peptides investigated via steered molecular dynamics simulations

In this work we used molecular simulations to investigate the elastic properties of collagen single chain and triple helix with the aim of understanding its features starting from first principles. We analysed ideal collagen peptides, homotrimeric and heterotrimeric collagen type I and pathological models of collagen. Triple helices were found much more rigid than single chains, thus enlightening the important role of interchain stabilizing forces, like hydrophobic interaction and hydrogen bonds. We obtained Young's moduli close to 4.5GPa for the ideal model of collagen and for the physiological heterotrimer, while the physiological homotrimer presented a Young's modulus of 2.51GPa, that can be related to a mild form of Osteogenesis Imperfecta in which only the homotrimeric form of collagen type I is produced. Otherwise, the pathological model (presenting a glycine to alanine substitution) showed an elastic modulus of 4.32GPa, thus only slightly lower than the ideal model. This suggests that this mutation only slightly affects the mechanical properties of the collagen molecule, but possibly acts on an higher scale, such as the packing of collagen fibrils.     

Molecular assessment of the elastic properties of collagen-like homotrimer sequences

Knowledge of the mechanical behavior of collagen molecules is critical for understanding the mechanical properties of collagen fibrils that constitute the main architectural building block of a number of connective tissues. In this study, the elastic properties of four different type I collagen 30-residue long molecular sequences, were studied by performing stretching simulations using the molecular mechanics approach. The energy–molecular length relationship was achieved by means of the geometry optimization procedure for collagen molecule strains up to 10%. The energy was interpolated by a second order function, and the second order of the derivative with respect to the mean length corresponded to the molecule stiffness. According to the hypothesis of linear elastic behavior, except for one sequence, the elastic modulus was around 2.40 GPa. These values are larger than fibril values, and they confirm the hypothesis that tendon mechanical properties are deeply related to tendon hierarchical structure. A possible explanation of the lowest values obtained for one sequence (1.33–1.53 GPa) is provided and discussed.     

If Cell Mechanics Can Be Described by Elastic Modulus: Study of Different Models and Probes Used in Indentation Experiments

Here we investigated the question whether cells, being highly heterogeneous objects, could be described with the elastic modulus (effective Young’s modulus) in a self-consistent way. We performed a comparative analysis of the elastic modulus derived from the indentation data obtained with atomic force microscopy (AFM) on human cervical epithelial cells (both normal and cancerous). Both sharp (cone) and dull (2500-nm radius sphere) AFM probes were used. The indentation data were processed through different elastic models. The cell was approximated as a homogeneous elastic medium that had either 1), smooth hemispherical boundary (Hertz/Sneddon models) or 2), the boundary covered with a layer of glycocalyx and membrane protrusions (“brush” models). Consistency of these approximations was investigated. Specifically, we tested the independence of the elastic modulus of the indentation depth, which is assumed in these models. We demonstrated that only one model showed consistency in treating cells as a homogeneous elastic medium, namely, the brush model, when processing the indentation data collected with the dull AFM probe. The elastic modulus demonstrated strong depth dependence in all models: Hertz/Sneddon models (no brush taken into account), and when the brush model was applied to the data collected with sharp conical probes. We conclude that it is possible to describe the elastic properties of the cell body by means of an effective elastic modulus, used in a self-consistent way, when using the brush model to analyze data collected with a dull AFM probe. The nature of these results is discussed.