Anisotropic swelling due to hydration constrains anisotropic elasticity in biomaterial fibers.

Naturally occurring protein fibers often undergo anisotropic swelling when hydrated. Within a tendon, a hydrated collagen fibril's radius expands by 40% but its length only increases by 5%. The same effect, with a similar relative magnitude, is observed for single hair shafts. Fiber hydration is known to affect elastic properties. Here we show that anisotropic swelling constrains the anisotropic linear elastic properties of fibers. First we show, using data from disparate previously reported studies, that anisotropic swelling can be described as an approximately linear function of water content. Then, under the observation that the elastic energy of swelling can be minimized by the anisotropic shape, we relate swelling anisotropy to elastic anisotropy - assuming radial (transverse) symmetry within a cylindrical geometry. We find an upper bound for the commonly measured axial Poisson ratio νzx<1/2. This is significantly below recently estimated values for collagen fibrils extracted from tissue-level measurements, but is consistent with both single hair shaft and single collagen fibril mechanical and hydration studies. Using νzx, we can then constrain the product γ≡(1-νxy)Ez/Ex - where νxy is the seldom measured transverse Poisson ratio and Ez/Ex is the ratio of axial to radial Young's moduli.

Histological staining alters circular dichroism SHG measurements of collagen.

Circular dichroism second harmonic generation microscopy (CDSHG) is a powerful imaging technique, which allows three-dimensional visualization of collagen fibril orientation in tissues. However, recent publications have obtained contradictory results on whether CDSHG can be used to reveal the relative out-of-plane polarity of collagen fibrils. Here we compare CDSHG images of unstained tendon and tendon which has been stained with hematoxylin and eosin. We find significant differences in the CDSHG between these two conditions, which explain the recent contradictory results within the literature.

An interferometric-based tensile tester to resolve damage events within reconstituted multi-filaments collagen bundles.

Understanding how mechanical damage propagates in load-bearing tissues such as skin, tendons and ligaments, is key to developing regenerative medicine solutions for when these tissues fail. For collagenous tissues in particular, damage is typically assessed after mechanical testing using a broad range of microscopy techniques because standard tensile testing systems do not have the time and force sensitivity to resolve mechanical damage events. Here we introduce an interferometric detection scheme to measure the displacement of a cantilever with a resolution of 0.03% of full scale at a sampling rate of 5000 samples/s. The system is validated using collagen fibers engineered to mimic mammalian tendons. The system can detect sudden decrease in force due to slippage between collagen filaments, one to five microns in diameter, within a fiber in air. It can also detect yield events associated with local collagen unfolding or sliding within collagen fibrils within a fiber in liquid. This is opening the road to the sub-failure study of damage propagation within a broad range of hierarchical biomaterials.

Torsion and bistability of double-twist elastomers.

We investigate the elastic properties of anisotropic elastomers with a double-twist director field, which is a model for collagen fibrils or blue phases. We observe a significant Poynting-like effect, coupling torsion (fibril twist) and extension. For freely-rotating boundary conditions, we identify a structural bistability at very small extensional strains which undergoes a saddle-node bifurcation at a critical strain - at approximately 1% strain for a parameterization appropriate for collagen fibrils. With clamped boundary conditions appropriate for many experimental setups, the bifurcation is not present. We expect significant helical shape effects when fixed torsion does not equal the equilibrium torsion of freely-rotating boundary conditions, due to residual torques.

Multifilament Collagen Fiber Bundles with Tendon-like Structure and Mechanical Performance.

Collagen multifilament bundles comprised of thousands of monofilaments are prepared by multipin contact drawing of an entangled polymer solution consisting of collagen and poly(ethylene oxide) (PEO). The multifilament bundles are hydrated in graded concentrations of PEO and phosphate buffered saline (PBS) to promote assembly of collagen fibrils within each monofilament while preserving the structure of the multifilament bundle. Multiscale structural characterization reveals that the hydrated multifilament bundle contains properly folded collagen molecules packed in collagen fibrils containing microfibrils, staggered by exactly one-sixth of the microfibril D-band spacing to produce a periodicity of 11 nm. Sequence analysis predicts that in this structure, phenylalanine residues are close enough within and between microfibrils to become ultraviolet C (UVC) crosslinked. In agreement with this analysis, the ultimate tensile strength (UTS) and Young's modulus of the hydrated collagen multifilament bundles crosslinked by UVC radiation increase nonlinearly with total UVC energy to reach values in the range of native tendons without damage to the collagen molecules. This fabrication method recapitulates the structure of a tendon across multiple length scales and offers tunability in tensile properties using only collagen molecules and no other chemical additives in addition to PEO, which is almost entirely removed during the hydration process.

High numerical aperture imaging allows chirality measurement in individual collagen fibrils using polarization second harmonic generation microscopy.

Second harmonic generation (SHG) microscopy is a commonly used technique to study the organization of collagen within tissues. However, individual collagen fibrils, which have diameters much smaller than the resolution of most optical systems, have not been extensively investigated. Here we probe the structure of individual collagen fibrils using polarization-resolved SHG (PSHG) microscopy and atomic force microscopy. We find that longitudinally polarized light occurring at the edge of a focal volume of a high numerical aperture microscope objective illuminated with linearly polarized light creates a measurable variation in PSHG signal along the axis orthogonal to an individual collagen fibril. By comparing numerical simulations to experimental data, we are able to estimate parameters related to the structure and chirality of the collagen fibril without tilting the sample out of the image plane, or cutting tissue at different angles, enabling chirality measurements on individual nanostructures to be performed in standard PSHG microscopes. The results presented here are expected to lead to a better understanding of PSHG results from both collagen fibrils and collagenous tissues. Further, the technique presented can be applied to other chiral nanoscale structures such as microtubules, nanowires, and nanoribbons.

Single collagen fibrils isolated from high stress and low stress tendons show differing susceptibility to enzymatic degradation by the interstitial collagenase matrix metalloproteinase-1 (MMP-1).

Bovine forelimb flexor and extensor tendons serve as a model for examining high stress, energy storing and low stress, positional tendons, respectively. Previous research has shown structural differences between the collagen fibrils of these tissues. The nanoscale collagen fibrils of flexor tendons are smaller in size, more heavily crosslinked, and respond differently to mechanical loading. Meanwhile, energy storing tendons undergo less collagen turnover compared to positional tendons and are more commonly injured. These observations raise the question of whether collagen fibril structure influences the collagen degradation processes necessary for remodelling. Atomic force microscopy was used to image dry collagen fibrils before and after 5-hour exposure to matrix metalloproteinase-1 (MMP-1) to detect changes in fibril size. Collagen fibrils from three tissue types were studied: bovine superficial digital flexor tendons, matched-pair bovine lateral digital extensor tendons, and rat tail tendons. Compared to control fibrils exposed only to buffer, a significant decrease in fibril cross-sectional area (CSA) following MMP-1 exposure was observed for bovine extensor and rat tail fibrils, with larger fibrils experiencing a greater magnitude of CSA decrease in both fibril types. Fibrils from bovine flexor tendons, on the other hand, showed no decrease in CSA when exposed to MMP-1. The result did not appear to be linked to the small size of flexor fibrils, as equivalently sized extensor fibrils were readily degraded by the enzyme. Increased proteolytic resistance of collagen fibrils from high stress tendons may help to explain the longevity of collagen within these tissues in vivo.

Effect of out of plane orientation on polarization second harmonic generation of single collagen fibrils.

Second harmonic generation (SHG) microscopy has emerged as a powerful technique for visualizing collagen organization within tissues. Amongst the many advantages of SHG is its sensitivity to collagen nanoscale organization, and its presumed sensitivity to the relative out of plane polarity of fibrils. Recent results have shown that circular dichroism SHG (CD-SHG), a technique that has been commonly assumed to reveal the relative out of plane polarity of collagen fibrils, is actually insensitive to changes in fibril polarity. However, results from another research group seem to contradict this conclusion. Both previous results have been based on SHG imaging of collagen fibrils within tissues, therefore, to gain a definitive understanding of the sensitivity of SHG to relative out of plane polarity, the results from individual fibrils are desirable. Here we present polarization resolved SHG microscopy (PSHG) data from individual collagen fibrils oriented out of the image plane by buckling on an elastic substrate. We show through correlation with atomic force microscopy measurements that SHG intensity can be used to estimate the out of plane angle of individual fibrils. We then compare the sensitivity of two PSHG techniques, CD-SHG and polarization-in, polarization-out SHG (PIPO-SHG), to the relative out of plane polarity of individual fibrils. We find that for single fibrils CD-SHG is insensitive to relative out of polarity and we also demonstrate the first direct experimental confirmation that PIPO-SHG reveals the relative out of plane polarity of individual collagen fibrils.

Adhesion force microscopy is sensitive to the charge distribution at the surface of single collagen fibrils.

Collagen fibrils are a key component of the extracellular matrix of mammalian tissues where they serve as structural elements and as a ligand for receptor-mediated signaling. As collagen molecules assemble into fibrils, in vitro or in vivo, they acquire a modulation of their molecular and electron densities called the D-band, with a 67 nm spacing, that can be visualized by cryo-electron microscopy. The D-band is composed of a gap region missing one-fifth of the molecules in the cross-section compared to the overlap region. This leads to the gap region having a positive potential and the overlap region a negative potential with respect to an n-doped silicon probe as observed by Kelvin Probe Force Microscopy. In this study, we use the adhesion force between an n-doped silicon probe and a collagen substrate to demonstrate the sensitivity of adhesion force towards charge distribution on the surface of collagen fibrils. We also map the charge distribution at the surface of single in vivo and in vitro assembled collagen fibrils and characterize the three-dimensional location and strength of three sub D-band regions that have been observed previously by cryo-electron microscopy. Our approach provides an adhesion fingerprint unique to each fibril type we analyzed and points to local charge variations at the sub D-band level even along a single fibril. It opens the road for a detailed analysis of collagen fibrils surface modifications due to ligand binding or the accumulation of advanced glycation end products at sub D-band resolution on a fibril by fibril basis.

Multi-pin contact drawing enables production of anisotropic collagen fiber substrates for alignment of fibroblasts and monocytes.

Type I collagen is the most abundant protein in the human body and is known to play important roles in numerous biological processes including tissue morphogenesis and wound healing. As such, it is one of the most frequently used substrates for cell culture, and there have been considerable efforts to develop collagen-based cell culture substrates that mimic the structural organization of collagen as it is found in native tissues, i.e., collagen fibers. However, producing collagen fibers from extracted collagen has been notoriously difficult, with existing methods providing only low throughput production of collagen fibers. In this study, we prepared collagen fibers using a highly efficient, bio-friendly, and cost-effective approach termed contact drawing, which uses an entangled polymer fluid to aid in fiber formation. Contact drawing technology has been demonstrated previously for collagen using highly concentrated dextran solutions with low concentrations of collagen. Here, we show that by replacing dextran with polyethylene oxide (PEO), high collagen content fibers may be readily formed from mixtures of soluble collagen and PEO, a polymer that readily forms fibers by contact drawing at concentrations as low as 0.5%wt. The presence of collagen and the formation of well-ordered collagen structures in the resulting fibers were characterized by attenuated total reflectance Fourier-transform infrared spectromicroscopy, Raman spectromicroscopy, and fluorescence microscopy. Corresponding to well-ordered collagen, the mechanical properties of the PEO-collagen fibers approximated those observed for native collagen fibers. Growth of cells on aligned PEO-collagen fibers attached to a polydimethyl siloxane support was examined for human dermal fibroblast (WS1) and human peripheral leukemia blood monocyte (THP-1) cell lines. WS1 and THP-1 cells readily attached, displayed alignment through migration and spreading, and proliferated on the collagen fiber substrate over the course of several days. We also demonstrated the retrieval of viable cells from the PEO-collagen fiber substrates through enzymatic digestion of the collagen substrate with collagenase IV.

Formation of Core-Sheath Polymer Fibers by Free Surface Spinning of Aqueous Two-Phase Systems.

Core-sheath fibers have numerous applications ranging from composite materials for advanced manufacturing to materials for drug delivery and regenerative medicine. Here, a simple and tunable approach for the generation of core-sheath fibers from immiscible solutions of dextran and polyethylene oxide is described. This approach exploits the entanglement of polymer molecules within the dextran and polyethylene oxide phases for free surface spinning into dry fibers. The mechanism by which these core-sheath fibers are produced after contact with a solid substrate (such as a microneedle) involves complex flows of the phase-separating polymer solutions, giving rise to a liquid-liquid core-sheath flow that is drawn into a liquid bridge. This liquid bridge then elongates into a core-sheath fiber through extensional flow as the contacting substrate is withdrawn. The core-sheath structure of the fibers produced by this approach is confirmed by attenuated total reflection Fourier-transform infrared spectroscopy and confocal microscopy. Tuning of the core diameter is also demonstrated by varying the weight percentage of dextran added to the reservoir from which the fibers are formed.

D-band strain underestimates fibril strain for twisted collagen fibrils at low strains.

Collagen fibrils are the main structural component of load-bearing tissues such as tendons, ligaments, skin, the cornea of the eye, and the heart. The D-band of collagen fibrils is an axial periodic density modulation that can be easily characterized by tissue-level X-ray scattering. During mechanical testing, D-band strain is often used as a proxy for fibril strain. However, this approach ignores the coupling between strain and molecular tilt. We examine the validity of this approximation using an elastomeric collagen fibril model that includes both the D-band and a molecular tilt field. In the low strain regime, we show that the D-band strain substantially underestimates fibril strain for strongly twisted collagen fibrils - such as fibrils from skin or corneal tissue.

Chiral phase-coexistence in compressed double-twist elastomers.

We adapt the theory of anisotropic rubber elasticity to model cross-linked double-twist liquid crystal cylinders such as exhibited in biological systems. In mechanical extension we recover strain-straightening, but with an exact expression in the small twist-angle limit. In compression, we observe coexistence between high and low twist phases. Coexistence begins at small compressive strains and is robustly observed for any anisotropic cross-links and for general double-twist functions - but disappears at large twist angles. Within the coexistence region, significant compression of double-twist cylinders is allowed at constant stress. Our results are qualitatively consistent with previous observations of swollen or compressed collagen fibrils, indicating that this phenomenon may be readily accessible experimentally.

Predicting the Mixing Behavior of Aqueous Solutions Using a Machine Learning Framework.

The most direct approach to determining if two aqueous solutions will phase-separate upon mixing is to exhaustively screen them in a pair-wise fashion. This is a time-consuming process that involves preparation of numerous stock solutions, precise transfer of highly concentrated and often viscous solutions, exhaustive agitation to ensure thorough mixing, and time-sensitive monitoring to observe the presence of emulsion characteristics indicative of phase separation. Here, we examined the pair-wise mixing behavior of 68 water-soluble compounds by observing the formation of microscopic phase boundaries and droplets of 2278 unique 2-component solutions. A series of machine learning classifiers (artificial neural network, random forest, k-nearest neighbors, and support vector classifier) were then trained on physicochemical property data associated with the 68 compounds and used to predict their miscibility upon mixing. Miscibility predictions were then compared to the experimental observations. The random forest classifier was the most successful classifier of those tested, displaying an average receiver operator characteristic area under the curve of 0.74. The random forest classifier was validated by removing either one or two compounds from the input data, training the classifier on the remaining data and then predicting the miscibility of solutions involving the removed compound(s) using the classifier. The accuracy, specificity, and sensitivity of the random forest classifier were 0.74, 0.80, and 0.51, respectively, when one of the two compounds to be examined was not represented in the training data. When asked to predict the miscibility of two compounds, neither of which were represented in the training data, the accuracy, specificity, and sensitivity values for the random forest classifier were 0.70, 0.82 and 0.29, respectively. Thus, there is potential for this machine learning approach to improve the design of screening experiments to accelerate the discovery of aqueous two-phase systems for numerous scientific and industrial applications.

Polymer entanglement drives formation of fibers from stable liquid bridges of highly viscous dextran solutions.

Liquid bridges have been studied for over 200 years due to their occurrence in many natural and industrial phenomena. Most studies focus on millimeter scale liquid bridges of Newtonian liquids. Here, reptation theory was used to explain the formation of 10 cm long liquid bridges of entangled polymer solutions, which subsequently stabilize into polymer fibers with tunable diameters between 3 and 20 mm. To control the fiber formation process, a horizontal single-fiber contact drawing system was constructed consisting of a motorized stage, a micro-needle, and a liquid filled reservoir. Analyzing the liquid bridge rupture statistics as a function of elongation speed, solution concentration and dextran molecular weight revealed that the fiber formation process was governed by a single timescale attributed to the relaxation of entanglements within the polymer solution. Further characterization revealed that more viscous solutions produced fibers of larger diameters due to secondary flow dynamics. Verification that protein additives such as type I collagen had minimal effect on fiber formation demonstrates the potential application in biomaterial fabrication.

Non-equilibrium growth and twist of cross-linked collagen fibrils.

The lysyl oxidase (LOX) enzyme that catalyses cross-link formation during the assembly of collagen fibrils in vivo is too large to diffuse within assembled fibrils, and so is incompatible with a fully equilibrium mechanism for fibril formation. We propose that enzymatic cross-links are formed at the fibril surface during the growth of collagen fibrils; as a consequence no significant reorientation of previously cross-linked collagen molecules occurs inside collagen fibrils during fibril growth in vivo. By imposing local equilibrium only at the fibril surface, we develop a coarse-grained quantitative model of in vivo fibril structure that incorporates a double-twist orientation of collagen molecules and a periodic D-band density modulation along the fibril axis. Radial growth is controlled by the concentration of available collagen molecules outside the fibril. In contrast with earlier equilibrium models of fibril structure, we find that all fibrils can exhibit a core-shell structure that is controlled only by the fibril radius. At small radii a core is developed with a linear double-twist structure as a function of radius. Within the core the double-twist structure is largely independent of the D-band. Within the shell at larger radii, the structure approaches a constant twist configuration that is strongly coupled with the D-band. We suggest a stable radius control mechanism that corneal fibrils can exploit near the edge of the linear core regime; while larger tendon fibrils use a cruder version of growth control that does not select a preferred radius.

Buckling and Torsional Instabilities of a Nanoscale Biological Rope Bound to an Elastic Substrate.

Rope-like structures are ubiquitous in Nature. They are supermolecular assemblies of macromolecules responsible for the structural and mechanical integrity of plant and animal tissues. Collagen fibrils with diameters between 50 and 500 nm and their helical supermolecular structure are good examples of such nanoscale biological ropes. Like man-made laid ropes, fibrils are typically loaded in tension, and due to their large aspect ratio, they are, in principle, prone to buckling and torsional instabilities. One way to study buckling of a rigid rod is to attach it to a stretched elastic substrate that is then returned to its original length. In the case of single collagen fibrils, the observed behavior depends on the degree of hydration. By going from buckling in ambient conditions to immersed in a buffer, fibrils go from the well-known sine wave response to a localized behavior reminiscent of the bird-caging of laid ropes. In addition, in ambient conditions, the sine wave response coexists with the formation of loops along the length of the fibrils, as observed for the torsional instability of a twisted filament when tension is decreased. This work provides direct evidence that single collagen fibrils are highly susceptible to axial compression because of their helical supermolecular structure. As a result, mammals that use collagen fibrils as their main load-bearing element in many tissues have evolved mitigating strategies that protect single fibrils from axial compression damage.

Alternate soaking enables easy control of mineralized collagen scaffold mechanics from nano- to macro-scale.

The mechanical properties of biologic scaffolds are critical to cellular interactions and hence functional response within the body. In the case of scaffolds for bone tissue regeneration, engineered scaffolds created by combining collagen with inorganic mineral are increasingly being explored, due to their favourable structural and chemical characteristics. Development of a method for controlling the mechanics of these scaffolds could lead to significant additional advantages by harnessing the intrinsic mechnotransduction pathways of stem cells via appropriate control of scaffold mechanical properties. Here we present a method for controlling the macroscale flexural modulus of mineralized collagen sheets, and the radial indentation modulus of the sheets' constituent collagen fibrils. Scaffolds were created starting with sheets of highly aligned, natively structured collagen fibrils, prepared via cryosectioning of decellularized tendon. Sheets underwent an alternate soaking mineralization procedure, with sequential exposure to citrate-doped calcium and carbonate-containing phosphate solutions, both of which included poly aspartic acid. The extent of scaffold mineralization was controlled via number of repeated mineralization cycles: 0 (unmineralized), 5, 10, and 20 cycles were trialed. Following scaffold preparation, ultrastructure, macroscale flexural modulus, and nanoscale indentation modulus were assessed. Surface architecture studied by SEM, and inspection of individual extracted fibrils by TEM and AFM confirmed that fibrils became increasingly laden with mineral as the number of mineralization cycles increased. Measurements of collagen fibril nanomechanics using AFM showed that the radial modulus of collagen fibrils increased linearly with mineralization cycles completed, from 215 ± 125 MPa for fibrils from unmineralized (0 cycle) scaffolds to 778 ± 302 MPa for fibrils from the 20 mineralization cycle scaffolds. Measurements of scaffold macromechanics via flexural testing also showed a linear increase in flexural modulus with increasing number of mineralization cycles completed, from 18 ± 7 MPa for the 5 cycle scaffolds to 156 ± 50 MPa for the 20 cycle scaffolds. The process detailed herein provides a way to create mineralized collagen scaffolds with easily controllable mechanical properties.

A standardized method to determine the effect of polymerization shrinkage on the cusp deflection and shrinkage induced built-in stress of class II tooth models.

OBJECTIVES: Using standardized aluminum tooth models, this study: 1) measured the deflection along the cusp wall of models with a Class II cavity restored using either bulk filling or horizontal incremental filling techniques, and 2) calculated the cusp deflection and built-in stress within the restored tooth models for both filling techniques using a finite element (FE) model. METHODS: Standardized tooth models with Class II cavities 4 mm deep, 4 mm high and 6 mm wide were machined out of aluminum. The models were restored using Filtek Posterior Restorative A2 shade resin-based composite (RBC). Both bulk filling and horizontal incremental filling techniques were used to restore the tooth models. After photocuring for 20 s from a single peak wavelength light-curing unit (LCU) with a radiant exitance of 1.25 W/cm2, the deflection of the cusp wall surface was measured using a profilometer. A FE model was used to predict the cuspal deflection and built-in stress of the restored tooth models. RESULTS: The elastic modulus within the FE model was parameterized using cusp deflection data obtained on a bulk filled tooth model. An agreement was found between the measured and predicted cusp deflection only when considering partial stress relaxation within the first incremental layer for the two-layer incremental filling technique. The calculated built-in stress was significantly reduced within the RBC and along the cavity walls when the cavity was filled incrementally in a horizontal direction compared to when it was bulk filled, resulting in a significantly smaller cusp deflection. SIGNIFICANCE: The FE model was first calibrated and then validated using measured cusp deflection data. Partial stress relaxation may play a significant role in the horizontal incremental filling technique. The model can be used to predict where the built-in stress within the tooth model occurs. This study explains why for a given RBC, a horizontal incremental filling and curing technique results in lower built-in stress within the restored tooth and lower cusp deflection compared to the bulk curing technique.

A new longitudinal variation in the structure of collagen fibrils and its relationship to locations of mechanical damage susceptibility.

The hierarchical architecture of the collagen fibril is well understood, involving non-integer staggering of collagen molecules which results in a 67 nm periodic molecular density variation termed D-banding. Other than this variation, collagen fibrils are considered to be homogeneous at the micro-scale and beyond. Interestingly, serial kink structures have been shown to form at discrete locations along the length of collagen fibrils from some mechanically overloaded tendons. The formation of these kinks at discrete locations along the length of fibrils (discrete plasticity) may indicate pre-existing structural variations at a length scale greater than that of the D-banding. Using a high velocity nanomechanical mapping technique, 25 tendon collagen fibrils, were mechanically and structurally mapped along 10 µm of their length in dehydrated and hydrated states with resolutions of 20 nm and 8 nm respectively. Analysis of the variation in hydrated indentation modulus along individual collagen fibrils revealed a micro-scale structural variation not observed in the hydrated or dehydrated structural maps. The spacing distribution of this variation was similar to that observed for inter-kink distances seen in SEM images of discrete plasticity type damage. We propose that longitudinal variation in collagen fibril structure leads to localized mechanical susceptibility to damage under overload. Furthermore, we suggest that this variation has its origins in heterogeneous crosslink density along the length of collagen fibrils. The presence of pre-existing sites of mechanical vulnerability along the length of collagen fibrils may be important to biological remodeling of tendon, with mechanically-activated sites having distinct protein binding capabilities and enzyme susceptibility.