Evidence that αC region is origin of low modulus, high extensibility, and strain stiffening in fibrin fibers

Fibrin fibers form the structural scaffold of blood clots and perform the mechanical task of stemming blood flow. Several decades of investigation of fibrin fiber networks using macroscopic techniques have revealed remarkable mechanical properties. More recently, the microscopic origins of fibrin's mechanics have been probed through direct measurements on single fibrin fibers and individual fibrinogen molecules. Using a nanomanipulation system, we investigated the mechanical properties of individual fibrin fibers. The fibers were stretched with the atomic force microscope, and stress-versus-strain data was collected for fibers formed with and without ligation by the activated transglutaminase factor XIII (FXIIIa). We observed that ligation with FXIIIa nearly doubled the stiffness of the fibers. The stress-versus-strain behavior indicates that fibrin fibers exhibit properties similar to other elastomeric biopolymers. We propose a mechanical model that fits our observed force extension data, is consistent with the results of the ligation data, and suggests that the large observed extensibility in fibrin fibers is mediated by the natively unfolded regions of the molecule. Although some models attribute fibrin's force-versus-extension behavior to unfolding of structured regions within the monomer, our analysis argues that these models are inconsistent with the measured extensibility and elastic modulus.     

Postnatal development of collagen structure in ovine articular cartilage

Background  

Articular cartilage (AC) is the layer of tissue that covers the articulating ends of the bones in diarthrodial joints. Across species, adult AC shows an arcade-like structure with collagen predominantly perpendicular to the subchondral bone near the bone, and collagen predominantly parallel to the articular surface near the articular surface. Recent studies into collagen fibre orientation in stillborn and juvenile animals showed that this structure is absent at birth. Since the collagen structure is an important factor for AC mechanics, the absence of the adult Benninghoff structure has implications for perinatal AC mechanobiology. The current objective is to quantify the dynamics of collagen network development in a model animal from birth to maturity. We further aim to show the presence or absence of zonal differentiation at birth, and to assess differences in collagen network development between different anatomical sites of a single joint surface. We use quantitative polarised light microscopy to investigate properties of the collagen network and we use the sheep (Ovis aries) as our model animal.     

Stiffening of Individual Fibrin Fibers Equitably Distributes Strain and Strengthens Networks

As the structural backbone of blood clots, fibrin networks carry out the mechanical task of stemming blood flow at sites of vascular injury. These networks exhibit a rich set of remarkable mechanical properties, but a detailed picture relating the microscopic mechanics of the individual fibers to the overall network properties has not been fully developed. In particular, how the high strain and failure characteristics of single fibers affect the overall strength of the network is not known. Using a combined fluorescence/atomic force microscope nanomanipulation system, we stretched 2-D fibrin networks to the point of failure, while recording the strain of individual fibers. Our results were compared to a pair of model networks: one composed of linearly responding elements and a second of nonlinear, strain-stiffening elements. We find that strain-stiffening of the individual fibers is necessary to explain the pattern of strain propagation throughout the network that we observe in our experiments. Fiber strain-stiffening acts to distribute strain more equitably within the network, reduce strain maxima, and increase network strength. Along with its physiological implications, a detailed understanding of this strengthening mechanism may lead to new design strategies for engineered polymeric materials.     

A computational model to describe the collagen orientation in statically cultured engineered tissues

Collagen provides cardiovascular tissues with the ability to withstand haemodynamic loads. A similar network is essential to obtain in tissue-engineered (TE) samples of the same nature. Yet, the mechanism of collagen orientation is not fully understood. Typically collagen remodelling is linked to mechanical loading. However, TE constructs also show an oriented collagen network when developed under static culture. Experiments under these conditions also indicate that the tissue gradually compacts due to contractile stresses developed in the α-actin fibres of the cells. Therefore, it is hypothesised that cellular contractile stresses are responsible for collagen orientation. A model describing the cellular α-actin turnover and the stresses developed by them is integrated in a structural constitutive model describing the mechanical behaviour of collagen fibres. Results show that the model can successfully capture the sample compaction, tissue stress generation and its heterogeneous collagen arrangement.     

Strain tunes proteolytic degradation and diffusive transport in fibrin networks

Proteolytic degradation of fibrin, the major structural component in blood clots, is critical both during normal wound healing and in the treatment of ischemic stroke and myocardial infarction. Fibrin-containing clots experience substantial strain due to platelet contraction, fluid shear, and mechanical stress at the wound site. However, little is understood about how mechanical forces may influence fibrin dissolution. We used video microscopy to image strained fibrin clots as they were degraded by plasmin, a major fibrinolytic enzyme. Applied strain causes up to 10-fold reduction in the rate of fibrin degradation. Analysis of our data supports a quantitative model in which the decrease in fibrin proteolysis rates with strain stems from slower transport of plasmin into the clot. We performed fluorescence recovery after photobleaching (FRAP) measurements to further probe the effect of strain on diffusive transport. We find that diffusivity perpendicular to the strain axis decreases with increasing strain, while diffusivity along the strain axis remains unchanged. Our results suggest that the properties of the fibrin network have evolved to protect mechanically loaded fibrin from degradation, consistent with its function in wound healing. The pronounced effect of strain upon diffusivity and proteolytic susceptibility within fibrin networks offers a potentially useful means of guiding cell growth and morphology in fibrin-based biomaterials.     

Critical conditions for pattern formation and in vitro tubulogenesis driven by cellular traction fields

In vitro angiogenesis assays have shown that tubulogenesis of endothelial cells within biogels, like collagen or fibrin gels, only appears for a critical range of experimental parameter values. These experiments have enabled us to develop and validate a theoretical model in which mechanical interactions of endothelial cells with extracellular matrix influence both active cell migration--haptotaxis--and cellular traction forces. Depending on the number of cells, cell motility and biogel rheological properties, various 2D endothelial patterns can be generated, from non-connected stripe patterns to fully connected networks, which mimic the spatial organization of capillary structures. The model quantitatively and qualitatively reproduces the range of critical values of cell densities and fibrin concentrations for which these cell networks are experimentally observed. We illustrate how cell motility is associated to the self-enhancement of the local traction fields exerted within the biogel in order to produce a pre-patterning of this matrix and subsequent formation of tubular structures, above critical thresholds corresponding to bifurcation points of the mathematical model. The dynamics of this morphogenetic process is discussed in the light of videomicroscopy time lapse sequences of endothelial cells (EAhy926 line) in fibrin gels. Our modeling approach also explains how the progressive appearance and morphology of the cellular networks are modified by gradients of extracellular matrix thickness.     

Tension is required for fibripositor formation

Embryonic tendon cells (ETCs) have actin-rich fibripositors that accompany parallel bundles of collagen fibrils in the extracellular matrix. To study fibripositor function, we have developed a three-dimensional cell culture system that promotes and maintains fibripositors. We show that ETCs cultured in fixed-length fibrin gels replace the fibrin during ~6 days in culture with parallel bundles of narrow-diameter collagen fibrils that are uniaxially aligned with fibripositors, thereby generating a tendon-like construct. Fibripositors occurred simultaneously with onset of parallel collagen fibrils. Interestingly, the constructs have a tendon-like crimp. In initial experiments to study the effects of tension, we showed that cutting the constructs resulted in loss of tension, loss of fibripositors and the appearance of immature fibrils with no preferred orientation.     

A constitutive model for the time-dependent,nonlinear stress response of fibrin networks

Blood clot formation is important to prevent blood loss in case of a vascular injury but disastrous when it occludes the vessel. As the mechanical properties of the clot are reported to be related to many diseases, it is important to have a good understanding of their characteristics. In this study, a constitutive model is presented that describes the nonlinear viscoelastic properties of the fibrin network, the main structural component of blood clots. The model is developed using results of experiments in which the fibrin network is subjected to a large amplitude oscillatory shear (LAOS) deformation. The results show three dominating nonlinear features: softening over multiple deformation cycles, strain stiffening and increasing viscous dissipation during a deformation cycle. These features are incorporated in a constitutive model based on the Kelvin–Voigt model. A network state parameter is introduced that takes into account the influence of the deformation history of the network. Furthermore, in the period following the LAOS deformation, the stiffness of the networks increases which is also incorporated in the model. The influence of cross-links created by factor XIII is investigated by comparing fibrin networks that have polymerized for 1 and 2 h. A sensitivity analysis provides insights into the influence of the eight fit parameters. The model developed is able to describe the rich, time-dependent, nonlinear behavior of the fibrin network. The model is relatively simple which makes it suitable for computational simulations of blood clot formation and is general enough to be used for other materials showing similar behavior.     

Fibrin-fiber architecture influences cell spreading and differentiation

ABSTRACT

The mechanical and structural properties of the extracellular matrix (ECM) play an important role in regulating cell fate. The natural ECM has a complex fibrillar structure and shows nonlinear mechanical properties, which are both difficult to mimic synthetically. Therefore, systematically testing the influence of ECM properties on cellular behavior is very challenging. In this work we show two different approaches to tune the fibrillar structure and mechanical properties of fibrin hydrogels. Addition of extra thrombin before gelation increases the protein density within the fibrin fibers without significantly altering the mechanical properties of the resulting hydrogel. On the other hand, by forming a composite hydrogel with a synthetic biomimetic polyisocyanide network the protein density within the fibrin fibers decreases, and the mechanics of the composite material can be tuned by the PIC/fibrin mass ratio. The effect of the changes in gel structure and mechanics on cellular behavior are investigated, by studying human mesenchymal stem cell (hMSC) spreading and differentiation on these gels. We find that the trends observed in cell spreading and differentiation cannot be explained by the bulk mechanics of the gels, but correlate to the density of the fibrin fibers the gels are composed of. These findings strongly suggest that the microscopic properties of individual fibers in fibrous networks play an essential role in determining cell behavior.     

Coarse-grained molecular dynamics simulations of fibrin polymerization: effects of thrombin concentration on fibrin clot structure

Studies suggest that patients with deep vein thrombosis and diabetes often have hypercoagulable blood plasma, leading to a higher risk of thromboembolism formation through the rupture of blood clots, which may lead to stroke and death. Despite many advances in the field of blood clot formation and thrombosis, the influence of mechanical properties of fibrin in the formation of thromboembolisms in platelet-poor plasma is poorly understood. In this paper, we combine the concepts of reactive molecular dynamics and coarse-grained molecular modeling to predict the complex network formation of fibrin clots and the branching of fibrin monomers. The 340-kDa fibrinogen molecule was converted into a coarse-grained molecule with nine beads, and using our customized reactive potentials, we simulated the formation and polymerization process of a fibrin clot. The results show that higher concentrations of thrombin result in higher branch-point formation in the fibrin clot structure. Our results also highlight many interesting properties, such as the formation of thicker or thinner fibers depending on the thrombin concentration. To the best of our knowledge, this is the first successful molecular polymerization study of fibrin clots to focus on thrombin concentration.     

Multiscale mechanobiology: Coupling models of adhesion kinetics and nonlinear tissue mechanics

The mechanical behavior of tissues at the macroscale is tightly coupled to cellular activity at the microscale. Dermal wound healing is a prominent example of a complex system in which multiscale mechanics regulate restoration of tissue form and function. In cutaneous wound healing, a fibrin matrix is populated by fibroblasts migrating in from a surrounding tissue made mostly out of collagen. Fibroblasts both respond to mechanical cues, such as fiber alignment and stiffness, as well as exert active stresses needed for wound closure.Here, we develop a multiscale model with a two-way coupling between a microscale cell adhesion model and a macroscale tissue mechanics model. Starting from the well-known model of adhesion kinetics proposed by Bell, we extend the formulation to account for nonlinear mechanics of fibrin and collagen and show how this nonlinear response naturally captures stretch-driven mechanosensing. We then embed the new nonlinear adhesion model into a custom finite element implementation of tissue mechanical equilibrium. Strains and stresses at the tissue level are coupled with the solution of the microscale adhesion model at each integration point of the finite element mesh. In addition, solution of the adhesion model is coupled with the active contractile stress of the cell population. The multiscale model successfully captures the mechanical response of biopolymer fibers and gels, contractile stresses generated by fibroblasts, and stress-strain contours observed during wound healing. We anticipate that this framework will not only increase our understanding of how mechanical cues guide cellular behavior in cutaneous wound healing, but will also be helpful in the study of mechanobiology, growth, and remodeling in other tissues.     

Early stiffening and softening of collagen: interplay of deformation mechanisms in biopolymer networks

Collagen networks, the main structural/mechanical elements in biological tissues, increasingly serve as biomimetic scaffolds for cell behavioral studies, assays, and tissue engineering, and yet their full spectrum of nonlinear behavior remains unclear. Here, with self-assembled type-I collagen as model, we use metrics beyond those in standard single-harmonic analysis of rheological measurements to reveal strain-softening and strain-stiffening of collagen networks both in instantaneous responses and at steady state. The results show how different deformation mechanisms, such as deformation-induced increase in the elastically active fibrils, nonlinear extension of individual fibrils, and slips in the physical cross-links in the network, can lead to the observed complex nonlinearity. We demonstrate how comprehensive rheological analyses can uncover the rich mechanical properties of biopolymer networks, including the above-mentioned softening as well as an early strain-stiffening, which are important for understanding physiological response of biological materials to mechanical loading.     

Elastic Behavior and Platelet Retraction in Low- and High-Density Fibrin?Gels

Fibrin is a biopolymer that gives thrombi the mechanical strength to withstand the forces imparted on them by blood flow. Importantly, fibrin is highly extensible, but strain hardens at low deformation rates. The density of fibrin in clots, especially arterial clots, is higher than that in gels made at plasma concentrations of fibrinogen (3–10 mg/mL), where most rheology studies have been conducted. Our objective in this study was to measure and characterize the elastic regimes of low (3–10 mg/mL) and high (30–100 mg/mL) density fibrin gels using shear and extensional rheology. Confocal microscopy of the gels shows that fiber density increases with fibrinogen concentration. At low strains, fibrin gels act as thermal networks independent of fibrinogen concentration. Within the low-strain regime, one can predict the mesh size of fibrin gels by the elastic modulus using semiflexible polymer theory. Significantly, this provides a link between gel mechanics and interstitial fluid flow. At moderate strains, we find that low-density fibrin gels act as nonaffine mechanical networks and transition to affine mechanical networks with increasing strains within the moderate regime, whereas high-density fibrin gels only act as affine mechanical networks. At high strains, the backbone of individual fibrin fibers stretches for all fibrin gels. Platelets can retract low-density gels by >80% of their initial volumes, but retraction is attenuated in high-density fibrin gels and with decreasing platelet density. Taken together, these results show that the nature of fibrin deformation is a strong function of fibrin fiber density, which has ramifications for the growth, embolization, and lysis of thrombi.     

Micromechanical modeling of the epimysium of the skeletal muscles

A micromechanical model has been developed to investigate the mechanical properties of the epimysium. In the present model, the collagen fibers in the epimysium are embedded randomly in the ground substance. Two parallel wavy collagen fibers and the surrounding ground substance are used as the repeat unit (unit cell), and the epimysium is considered as an aggregate of unit cells. Each unit cell is distributed in the epimysium with some different angle to the muscle fiber direction. The model allows the progressive straightening of the collagen fiber as well as the effects of fiber reorientation. The predictions of the model compare favorably against experiment. The effects of the collagen fiber volume fraction, collagen fiber waviness at the rest length and the mechanical properties of the collagen fibers and the ground substance are analyzed. This model allows the analysis of mechanical behavior of most soft tissues if appropriate experimental data are available.     

Elasticity of passive blood vessels: a new concept

The mechanical properties of passive blood vessels are generally thought to depend on the parallel arrangement of elastin and collagen with linear elasticity and collagen recruitment depending on vessel strain [hook-on (HO) model]. We evaluated an alternative model [serial element (SE) model] consisting of the series arrangement of an infinite number of elements, each containing elastin with a constant elastic modulus and collagen that switches stepwise from slack (zero stress) to fully rigid (infinite stiffness) on ongoing element strain. Both models were implemented with Weibull distributions for collagen recruitment strain (HO model) and collagen tightening strain (SE model). The models were tested in experiments on rat mesenteric small arteries. Strain-tension relations were obtained before and after two rounds of digestion by collagenase. Both models fitted the data prior to digestion. However, for the HO model, this required unrealistically low estimates for collagen recruitment or elastic modulus and unrealistically high estimates for distension of collagen fibers. Furthermore, the data after digestion were far better predicted by the SE model compared with the HO model. Finally, the SE model required one parameter less (collagen elastic modulus). Therefore, the SE model provides a valuable starting point for the understanding of vascular mechanics and remodeling of vessels.     

A physically motivated constitutive model for cell-mediated compaction and collagen remodeling in soft tissues

Collagen is the main load-bearing component of many soft tissues and has a large influence on the mechanical behavior of tissues when exposed to mechanical loading. Therefore, it is important to increase our understanding of collagen remodeling in soft tissues to understand the mechanisms behind pathologies and to control the development of the collagen network in engineered tissues. In the present study, a constitutive model was developed by coupling a recently developed model describing the orientation and contractile stresses exerted by cells in response to mechanical stimuli to physically motivated collagen remodeling laws. In addition, cell-mediated contraction of the collagen fibers was included as a mechanism for tissue compaction. The model appeared to be successful in predicting a range of experimental observations, which are (1) the change in transition stretch of periosteum after remodeling at different applied stretches, (2) the compaction and alignment of collagen fibers in tissue-engineered strips, (3) the fiber alignment in cruciform gels with different arm widths, and (4) the alignment of collagen fibers in engineered vascular grafts. Moreover, by changing the boundary conditions, the model was able to predict a helical architecture in the vascular graft without assuming the presence of two helical fiber families a priori. Ultimately, this model may help to increase our understanding of collagen remodeling in physiological and pathological conditions, and it may provide a tool for determining the optimal experimental conditions for obtaining native-like collagen architectures in engineered tissues.     

Strain-Induced Alignment in Collagen Gels

Collagen is the most abundant extracellular-network-forming protein in animal biology and is important in both natural and artificial tissues, where it serves as a material of great mechanical versatility. This versatility arises from its almost unique ability to remodel under applied loads into anisotropic and inhomogeneous structures. To explore the origins of this property, we develop a set of analysis tools and a novel experimental setup that probes the mechanical response of fibrous networks in a geometry that mimics a typical deformation profile imposed by cells in vivo. We observe strong fiber alignment and densification as a function of applied strain for both uncrosslinked and crosslinked collagenous networks. This alignment is found to be irreversibly imprinted in uncrosslinked collagen networks, suggesting a simple mechanism for tissue organization at the microscale. However, crosslinked networks display similar fiber alignment and the same geometrical properties as uncrosslinked gels, but with full reversibility. Plasticity is therefore not required to align fibers. On the contrary, our data show that this effect is part of the fundamental non-linear properties of fibrous biological networks.     

Effects of pdgf-bb on rat dermal fibroblast behavior in mechanically stressed and unstressed collagen and fibrin gels

The dose-response effects of platelet-derived growth factor BB (PDGF-BB) on rat dermal fibroblast (RDF) behavior in mechanically stressed and unstressed type I collagen and fibrin were investigated using quantitative assays developed in our laboratory. In chemotaxis experiments, RDFs responded optimally (P < 0.05) to a gradient of 10 ng/ml PDGF-BB in both collagen and fibrin. In separate experiments, the migration of RDFs and the traction exerted by RDFs in the presence of PDGF-BB (0, 0.1, 1, 10, or 100 ng/ml) were assessed simultaneously in the presence or absence of stress. RDF migration increased significantly (P < 0.05) at doses of 10 and 100 ng/ml PDGF-BB in collagen and fibrin in the presence and absence of stress. In contrast, the effects of PDGF-BB on RDF traction depended on the gel type and stress state. PDGF-BB decreased fibroblast traction in stressed collagen, but increased traction in unstressed collagen (P < 0.05). No statistical conclusion could be inferred for stressed fibrin, but increasing PDGF-BB decreased traction in unstressed fibrin (P < 0.05). These results demonstrate the complex response of fibroblasts to environmental cues and suggest that mechanical resistance to compaction may be a crucial element in dictating fibroblast behavior.     

The behaviour of BHK cells and neutrophil leukocytes on collagen gels of defined mechanical strength

This study demonstrates how the mechanical strength of a series of collagen/composite gels can be measured using a penetrometer. It was found that the presence of fibrin in collagen gels resulted in increased gel strength. Similarly hyaluronic acid was found to increase the strength of collagen gels. Addition of heparin weakened collagen gels as did chondroitin-6-sulphate. Neutrophil migration into collagen gels was found to be inversely proportional to gel strength. Fibrin and hyaluronic acid containing gels inhibited neutrophil migration while the presence of heparin and chondroitin sulphate increased neutrophil migration. BHK gel contraction experiments demonstrated how the presence of fibrin prevents gel contraction. Despite increasing gel strength the presence of hyaluronic acid appeared to have no effect on BHK contraction of collagen gels. Similarly the presence of heparin or chondroitin sulphate had no effect on gel contraction by BHK cells.     

Estimating the 3D Pore Size Distribution of Biopolymer Networks from Directionally Biased Data

The pore size of biopolymer networks governs their mechanical properties and strongly impacts the behavior of embedded cells. Confocal reflection microscopy and second harmonic generation microscopy are widely used to image biopolymer networks; however, both techniques fail to resolve vertically oriented fibers. Here, we describe how such directionally biased data can be used to estimate the network pore size. We first determine the distribution of distances from random points in the fluid phase to the nearest fiber. This distribution follows a Rayleigh distribution, regardless of isotropy and data bias, and is fully described by a single parameter—the characteristic pore size of the network. The bias of the pore size estimate due to the missing fibers can be corrected by multiplication with the square root of the visible network fraction. We experimentally verify the validity of this approach by comparing our estimates with data obtained using confocal fluorescence microscopy, which represents the full structure of the network. As an important application, we investigate the pore size dependence of collagen and fibrin networks on protein concentration. We find that the pore size decreases with the square root of the concentration, consistent with a total fiber length that scales linearly with concentration.