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.     

Chemical modification of insulin in amyloid fibrils

We have investigated the chemical modification of insulin under conditions that promote the conversion of the soluble protein into amyloid fibrils. The modifications that are incorporated into the fibrils include deamidation of Asn A21, Asn B3, and Gln B4. In order to prepare fibrils with minimal deamidation of these residues, the kinetics of aggregation were accelerated by seeding with aliquots of a solution containing preformed fibrils. The resulting fibrils were then reincubated to determine the extent to which chemical modification occurs in the fibril itself. The deamidation of Asn A21 in particular could be followed in detail. Deamidation of this residue in the fibrillar form of insulin was found to occur in only 52 +/- 5% of molecules. This result indicates that there are at least two different packing environments of insulin molecules in the fibrils and suggests that the characterization of chemical modifications may be a useful probe of the environment of polypeptide chains within amyloid fibrils.     

Controlling the dimensions of amyloid fibrils: toward homogenous components for bionanotechnology

Amyloid fibrils have been recognized as having potential in a variety of bionanotechnological applications. However, realization of these applications is constrained by a lack of control over morphology and alignment, both crucial for potential end uses. This article focuses on the use of growth and storage conditions to control the length of amyloid fibrils formed from bovine insulin, with length distributions constructed from transmission electron microscopy (TEM) images. Growth temperature, pH, protein concentration, and storage conditions were examined and were seen to offer a range of conditions that favor different length distribution. The use of amyloid fibrils as nanowires is one area where control of fibril dimensions is desirable, for experimental setup and endpoint applications. The conductive properties of fibrils formed from bovine insulin are presented, with these insulin fibrils being shown to have high resistivity in their unmodified state, with current values in the nanoamp range. These low current values can be increased via modification, or the fibrils used in their native state in applications where low current values are desirable. These findings, coupled with the ability to predict and select for various insulin amyloid fibril dimensions, enhances their utility as nanomaterials.     

Evaluation of the influence of growth medium composition on cell elasticity

Recently, there has been an increasing interest in using the biomechanical properties of cells as biomarkers to discriminate between normal and cancerous cells. However, few investigators have considered the influence of the growth medium composition when evaluating the biomechanical properties of the normal and diseased cells. In this study, we investigated the variation in Young's modulus of non-malignant MCF10A and malignant MDA-MB-231 breast cells seeded in five different growth media under controlled experimental conditions. The average Young's modulus of MDA-MB-231 cells was significantly lower (p<0.0001) than the mean Young's modulus of MCF10A cells when compared in identical medium compositions. However, we found that growth medium composition affected the elasticity of MCF10A and MDA-MB-231 cells. The average Young's modulus of both cell lines decreased by 10-18% when the serum was reduced from 10% to 5% and upon addition of epidermal growth factor (EGF, 20 ng/ml) to the medium. Though these elasticity changes might have some biological impact, none was statistically significant. However, the elasticity of MCF10A was significantly more responsive than MDA-MB-231 cells to the medium composition supplemented with EGF, cholera toxin (CT), insulin (INS) and hydrocortisone (HC), which are recommended for routine cultivation of MCF10A cells (M5). MCF10A cells were significantly softer (p<0.002) when grown in medium M5 compared to a standard MDA-MB-231 medium (M1). The investigation of the effects of culture medium composition on the elastic properties of cells highlights the need to take these effects into consideration when interpreting elasticity measurements in cells grown in different media.     

Structural and mechanical properties of TTR105-115 amyloid fibrils from compression experiments

Amyloid fibrils, originally associated with neurodegenerative diseases, are now recognized to have interesting mechanical properties. By using synchrotron x-ray diffraction at high pressure in a diamond anvil cell we determined the bulk modulus of TTR105-115 amyloid fibrils in water and in silicone oil to be 2.6 and 8.1 GPa, respectively. The compression characteristics of the fibrils are quite different in the two media, revealing the presence of cavities along the axis of the fibrils, but not between the β-sheets, which are separated by a dry interface as in a steric zipper motif. Our results emphasize the importance of peptide packing in determining the structural and mechanical properties of amyloid fibrils.     

Amyloid fibril formation from crude protein mixtures

Amyloid fibrils have potential as bionanomaterials. A bottleneck in their commercial use is the cost of the highly purified protein typically needed as a starting material. Thus, an understanding of the role of heterogeneity in the mixtures from which amyloid fibrils are formed may inform production of these structures from readily available impure starting materials. Insulin, a very well understood amyloid-forming protein, was modified by various reagents to explore whether amyloid fibrils could still form from a heterogeneous mixture of insulin derivatives. Aggregates were characterized by thioflavin T fluorescence and transmission electron microscopy. Using acetylation, reduction carboxymethylation, reduction pyridylethylation, trypsin digestion and chymotrypsin digestion, it was shown that amyloid fibrils can form from heterogeneous mixtures of modified insulin. The modifications changed both the rate of reaction and the yield of the final product, but led to fibrillar structures, some with interesting morphologies. Well defined, long, unbranched fibrils were observed in the crude reduced carboxymethylated insulin mixture and the crude reduced pyridylethylated insulin revealed the formation of "wavy" fibrils, compared with the straighter native insulin amyloid fibrils. Although trypsin digestion inhibited fibrils formation, chymotrypsin digestion of insulin produced a mixture of long and short fibrils under the same conditions. We conclude that amyloid fibrils may be successfully formed from heterogeneous mixtures and, further, that chemical modification may provide a simple means of manipulating protein fibril assembly for use in bionanotechnological applications, enabling some design of overall morphology in the bottom-up assembly of higher order protein structures from amyloid fibrils.     

Mechanical properties of human patellar tendon at the hierarchical levels of tendon and fibril

Tendons are strong hierarchical structures, but how tensile forces are transmitted between different levels remains incompletely understood. Collagen fibrils are thought to be primary determinants of whole tendon properties, and therefore we hypothesized that the whole human patellar tendon and its distinct collagen fibrils would display similar mechanical properties. Human patellar tendons (n = 5) were mechanically tested in vivo by ultrasonography. Biopsies were obtained from each tendon, and individual collagen fibrils were dissected and tested mechanically by atomic force microscopy. The Young's modulus was 2.0 ± 0.5 GPa, and the toe region reached 3.3 ± 1.9% strain in whole patellar tendons. Based on dry cross-sectional area, the Young's modulus of isolated collagen fibrils was 2.8 ± 0.3 GPa, and the toe region reached 0.86 ± 0.08% strain. The measured fibril modulus was insufficient to account for the modulus of the tendon in vivo when fibril content in the tendon was accounted for. Thus, our original hypothesis was not supported, although the in vitro fibril modulus corresponded well with reported in vitro tendon values. This correspondence together with the fibril modulus not being greater than that of tendon supports that fibrillar rather than interfibrillar properties govern the subfailure tendon response, making the fibrillar level a meaningful target of intervention. The lower modulus found in vitro suggests a possible adverse effect of removing the tissue from its natural environment. In addition to the primary work comparing the two hierarchical levels, we also verified the existence of viscoelastic behavior in isolated human collagen fibrils.     

The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques

Acoustic microscopy (30-60 microm resolution) and nanoindentation (1-5 microm resolution) are techniques that can be used to evaluate the elastic properties of human bone at a microstructural level. The goals of the current study were (1) to measure and compare the Young's moduli of trabecular and cortical bone tissues from a common human donor, and (2) to compare the Young's moduli of bone tissue measured using acoustic microscopy to those measured using nanoindentation. The Young's modulus of cortical bone in the longitudinal direction was about 40% greater than (p<0.01) the Young's modulus in the transverse direction. The Young's modulus of trabecular bone tissue was slightly higher than the transverse Young's modulus of cortical bone, but substantially lower than the longitudinal Young's modulus of cortical bone. These findings were consistent for both measurement methods and suggest that elasticity of trabecular tissue is within the range of that of cortical bone tissue. The calculation of Young's modulus using nanoindentation assumes that the material is elastically isotropic. The current results, i.e., the average anisotropy ratio (E(L)/E(T)) for cortical bone determined by nanoindentation was similar to that determined by the acoustic microscope, suggest that this assumption does not limit nanoindentation as a technique for measurement of Young's modulus in anisotropic bone.     

Ab initio predictions of structural and elastic properties of struvite: contribution to urinary stone research

In the present work, we carried out density functional calculations of struvite--the main component of the so-called infectious urinary stones--to study its structural and elastic properties. Using a local density approximation and a generalised gradient approximation, we calculated the equilibrium structural parameters and elastic constants C(ijkl). At present, there is no experimental data for these elastic constants C (ijkl) for comparison. Besides the elastic constants, we also present the calculated macroscopic mechanical parameters, namely the bulk modulus (K), the shear modulus (G) and Young's modulus (E). The values of these moduli are found to be in good agreement with available experimental data. Our results imply that the mechanical stability of struvite is limited by the shear modulus, G. The study also explores the energy-band structure to understand the obtained values of the elastic constants.     

Robust strategies for automated AFM force curve analysis--I. Non-adhesive indentation of soft, inhomogeneous materials

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.     

Amyloid-like fibrils in elastin-related polypeptides: structural characterization and elastic properties

We report on the structural characterization of amyloid-like fibrils, self-assembled from synthetic polypentapeptides poly(ValGlyGlyLeuGly), whose monomeric sequence is a recurring, simple building block of elastin. This polymer adopts a beta-sheet structure as revealed by circular dichroism and Fourier transform infrared spectroscopy. Furthermore, Thioflavin-T and Congo red birefringence assays confirm the presence of amyloid-like structures. To analyze the supramolecular assembly and elastic properties of the fibrils, we employed atomic force microsocopy and spectroscopy, measuring also the elasticity of mature elastin for a comparative analysis. In the case of fibrils we estimated a Young's modulus ranging from 3.5 to 7 MPa, whereas for elastin it is around 1 MPa. The possibility to section individual fibrils with nanometric control by the AFM tip, realizing biomolecular gaps in the 100 nm range, is also demonstrated. These results are expected to open interesting perspectives for the fabrication of protein-inspired nanostructures with specific physical and chemical properties for applications in biotechnology and tissue engineering.     

Mechanical Properties of Black Locust (Robinia pseudoacacia L.) Wood. Size- and Age-dependent Variations in Sap- and Heartwood

Variations in the density and stiffness (Young's elastic modulus)of fresh wood samples drawn from different parts of the threemain trunks of a 32-year-old black locust tree,Robinia pseudoacacia(measuring 19.8 m at its highest point), were studied to determinewhether tree ontogeny can achieve a constant safety factor againstmechanical failure. Based on the properties of isolated woodsamples, the fresh density of sapwood decreased along radialtransects from bark to pith, while that of progressively olderheartwood samples increased, on average, towards the centreof each of the three trunks. Along the same radial transects,the Young's elastic modulus of sap- and heartwood increased.In terms of longitudinal changes in wood properties, mean woodmoduli (averages of sap- and heartwood samples) increased, onaverage, towards the base of each of the three trunks of thetree. However, the mean fresh densities of wood samples increasedtowards the top and the bottom of each trunk and were lowestroughly near trunk mid-length. The mean density-specific stiffness(the quotient of Young's modulus and fresh density) of woodwas thus lower toward the top and the bottom of the trunks andhighest near trunk mid-length. Mean values of fresh wood density-specificstiffness were used to estimate the critical buckling heightsfor sections of the trunks differing in diameter and age. Theseestimates indicated that ontogenetic variation in the physicalproperties and relative amounts of sap- and heartwood in trunkscould maintain a constant factor of safety (approximately equalto 2) as a sapling grows in height and girth into a mature tree.This expectation was supported by data from 16 black locusttrees differing in height and diameter at breast height (DBH). Wood; elastic properties; tree height; biomechanics     

An extended modeling of the micropipette aspiration experiment for the characterization of the Young's modulus and Poisson's ratio of adherent thin biological samples: numerical and experimental studies

The micropipette aspiration (MA) experiment remains a quite widely used micromanipulation technique for quantifying the elastic modulus of cells and, less frequently, of other biological samples. However, moduli estimations derived from MA experiments are only valid if the probed sample is non-adherent to the rigid substrate. This study extends this standard formulation by taking into account the influence of the sample adhesion. Using a finite element analysis of the sample aspiration into the micropipette, we derived a new expression of the aspirated length for linear elastic materials. Our results establish that (i) below a critical value, the thickness h of the probed sample must be considered to get an accurate value of its Young's modulus (ii) this critical value depends both on the Poisson's ratio and on the sample adhesivity. Additionally, we propose a novel method which allows the computation of the intrinsic Young's modulus of the adherent probed sample from its measured apparent elasticity modulus. Thanks to the set of computational graphs we derived from our theoretical analysis, we successfully validate this method by experiments performed on polyacrylamide gels. Interestingly, the original procedure we proposed allows a simultaneous quantification of the Young's modulus and of the Poisson's ratio of the adherent gel. Thus, our revisited analysis of MA experiments extends the application domain of this technique, while contributing to decrease the dispersion of elastic modulus values obtained by this method.     

Formation of low-dimensional crystalline nucleus region during insulin amyloidogenesis process

Insulin, as other amyloid proteins, can form amyloid fibrils at certain conditions. The self-assembled aggregation process of insulin can result in a variety of conformations, starting from small oligomers, going through various types of protofibrils, and finishing with bundles of fibrils. One of the most common consensuses among the various self-assembly processes that are suggested in the literature is the formation of an early stage nucleus conformation. Here we present an additional insight for the self-assembly process of insulin. We show that at the early lag phase of the process (prior to fibril formation) the insulin monomers self-assemble into ordered nanostructures. The most notable feature of this early self-assembly process is the formation of nanocrystalline nucleus regions with a strongly bound electron-hole confinement, which also change the secondary structure of the protein. Each step in the self-assembly process is characterized by an optical spectroscopic signature, and possesses a narrow size distribution. By following the spectroscopic signature we can measure the potency of amyloid fibrils inhibitors already at the lag phase. We further demonstrate it by the use of epigallocatechin gallate, a known inhibitor for insulin fibrils. The findings can result in a spectroscopic-based application for the analysis of amyloid fibrils inhibitors.     

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.     

Fibrillin microfibrils are stiff reinforcing fibres in compliant tissues

Fibrillin-rich microfibrils have endowed tissues with elasticity throughout multicellular evolution. We have used molecular combing techniques to determine Young's modulus for individual microfibrils and X-ray diffraction of zonular filaments of the eye to establish the linearity of microfibril periodic extension. Microfibril periodicity is not altered at physiological zonular tissue extensions and Young's modulus is between 78 MPa and 96 MPa, which is two orders of magnitude stiffer than elastin. We conclude that elasticity in microfibril-containing tissues arises primarily from reversible alterations in supra-microfibrillar arrangements rather than from intrinsic elastic properties of individual microfibrils which, instead, act as reinforcing fibres in fibrous composite tissues.     

Anisotropic Poisson's ratio and compression modulus of cortical bone determined by speckle interferometry

Young's modulus and Poisson's ratios of 6mm-sized cubes of equine cortical bone were measured in compression using a micro-mechanical loading device. Surface displacements were determined by electronic speckle pattern-correlation interferometry. This method allows for non-destructive testing of very small samples in water. Analyses of standard materials showed that the method is accurate and precise for determining both Young's modulus and Poisson's ratio. Material properties were determined concurrently in three orthogonal anatomic directions (axial, radial and transverse). Young's modulus values were found to be anisotropic and consistent with values of equine cortical bone reported in the literature. Poisson's ratios were also found to be anisotropic, but lower than those previously reported. Poisson's ratios for the radial-transverse and transverse-radial directions were 0.15+/-0.02, for the axial-transverse and axial-radial directions 0.19+/-0.04, and for the transverse-axial and radial-axial direction 0.09+/-0.02 (mean+/-SD). Cubes located only millimetres apart had significantly different elastic properties, showing that significant spatial variation occurs in equine cortical bone.     

Estimation of cell Young's modulus of adherent cells probed by optical and magnetic tweezers: influence of cell thickness and bead immersion

A precise characterization of cell elastic properties is crucial for understanding the mechanisms by which cells sense mechanical stimuli and how these factors alter cellular functions. Optical and magnetic tweezers are micromanipulation techniques which are widely used for quantifying the stiffness of adherent cells from their response to an external force applied on a bead partially embedded within the cell cortex. However, the relationships between imposed external force and resulting bead translation or rotation obtained from these experimental techniques only characterize the apparent cell stiffness. Indeed, the value of the estimated apparent cell stiffness integrates the effect of different geometrical parameters, the most important being the bead embedding angle 2gamma, bead radius R, and cell height h. In this paper, a three-dimensional finite element analysis was used to compute the cell mechanical response to applied force in tweezer experiments and to explicit the correcting functions which have to be used in order to infer the intrinsic cell Young's modulus from the apparent elasticity modulus. Our analysis, performed for an extensive set of values of gamma, h, and R, shows that the most relevant parameters for computing the correcting functions are the embedding half angle gamma and the ratio h(u)/2R, where h(u) is the under bead cell thickness. This paper provides original analytical expressions of these correcting functions as well as the critical values of the cell thickness below which corrections of the apparent modulus are necessary to get an accurate value of cell Young's modulus. Moreover, considering these results and taking benefit of previous results obtained on the estimation of cell Young's modulus of adherent cells probed by magnetic twisting cytometry (MTC) (Ohayon, J., and Tracqui, P., 2005, Ann. Biomed. Eng., 33, pp. 131-141), we were able to clarify and to solve the still unexplained discrepancies reported between estimations of elasticity modulus performed on the same cell type and probed with MTC and optical tweezers (OT). More generally, this study may strengthen the applicability of optical and magnetic tweezers techniques by insuring a more precise estimation of the intrinsic cell Young's modulus (CYM).