A modular fibrinogen model that captures the stress-strain behavior of fibrin fibers

Interplay of fibrinogen αEC globular domains and factor XIIIa cross-linking dictates the extensibility and strain stiffening of fibrin networks

BACKGROUND

Fibrinogen is a plasma protein forming the fibrin scaffold of blood clots. Its mechanical properties therefore affect the risk of bleeding as well as thrombosis. There has been much recent interest in the biophysical mechanisms controlling fibrin mechanics; however, the role of molecular heterogeneity of the circulating fibrinogen in determining clot mechanical function remains poorly characterized.

OBJECTIVES

By comparing 2 fibrinogen variants where the only difference is the Aα-chain length, with one variant having a globular domain at its C-terminus, this study aimed to reveal how the molecular structure impacts the structure and mechanics of fibrin networks.

METHODS

We characterized the mechanical response to large shear for networks formed from 2 recombinant fibrinogen variants: the most prevalent variant in circulation with a molecular weight of 340 kDa (recombinant human fibrinogen [rFib] 340) and a minor variant with a molecular weight of 420 kDa (rFib420).

RESULTS

We show that the elastic properties of the 2 variants are identical when fibrin is cross-linked with factor XIIIa but differ strongly in its absence. Uncross-linked rFib420 networks are softer and up to 3-fold more extensible than rFib340 networks. Electron microscopy imaging showed that the 2 variants formed networks with a comparable structure, except at 4 mg/mL, where rFib420 formed denser networks.

CONCLUSION

We propose that the αEC domains of rFib420 increase the extensibility of uncross-linked fibrin networks by promoting protofibril sliding, which is blocked by FXIIIa cross-linking. Our findings can help explain the functional role of different circulating fibrinogen variants in blood clot mechanics and tissue repair.

Combined computational modeling and experimental study of the biomechanical mechanisms of platelet-driven contraction of fibrin clots

While blood clot formation has been relatively well studied, little is known about the mechanisms underlying the subsequent structural and mechanical clot remodeling called contraction or retraction. Impairment of the clot contraction process is associated with both life-threatening bleeding and thrombotic conditions, such as ischemic stroke, venous thromboembolism, and others. Recently, blood clot contraction was observed to be hindered in patients with COVID-19. A three-dimensional multiscale computational model is developed and used to quantify biomechanical mechanisms of the kinetics of clot contraction driven by platelet-fibrin pulling interactions. These results provide important biological insights into contraction of platelet filopodia, the mechanically active thin protrusions of the plasma membrane, described previously as performing mostly a sensory function. The biomechanical mechanisms and modeling approach described can potentially apply to studying other systems in which cells are embedded in a filamentous network and exert forces on the extracellular matrix modulated by the substrate stiffness.

The Story of the Fibrin(ogen) αC-Domains: Evolution of Our View on Their Structure and Interactions

Although much has been established concerning the overall structure and function of fibrinogen, much less has been known about its two αC regions, each consisting of an αC-connector and an αC-domain, but new information has been accumulating. This review summarizes the state of our current knowledge of the structure and interactions of fibrinogen's αC regions. A series of studies with isolated αC regions and their fragments demonstrated that the αC-domain forms compact ordered structures consisting of N- and C-terminal subdomains including β sheets and suggested that the αC-connector has a poly(L-proline) type II structure. Functionally, the αC-domains interact intramolecularly with each other and with the central region of the molecule, first demonstrated by electron microscopy and then quantified by optical trap force spectroscopy. Upon conversion of fibrinogen into fibrin, the αC-domains switch from intra- to intermolecular interactions to form ordered αC polymers. The formation of αC polymers occurs mainly through the homophilic interaction between the N-terminal subdomains; interaction between the C-terminal subdomains and the αC-connectors also contributes to this process. Considerable evidence supports the idea that the αC-regions accelerate fibrin polymerization and affect the final structure of fibrin clots. The interactions between αC-regions are important for the mechanical properties of clots, increasing their stiffness and extensibility. Conversion of fibrinogen into fibrin results in exposure of multiple binding sites in its αC regions, providing interaction of fibrin with different proteins and cell types during hemostasis and wound healing. This heretofore mysterious part of the fibrinogen molecule is finally giving up its secrets.

Computational Biomechanical Modeling of Fibrin Networks and Platelet-Fiber Network Interactions

Fibrin deformation and interaction of fibrin with other blood components play critical roles in hemostasis and thrombosis. In this review, computational and mathematical biomechanical models of fibrin network deformation and contraction at different spatio-temporal scales as well as challenges in developing and calibrating multiscale models are discussed. There are long standing challenges. For instance, applicability of models to identify and test potential mechanisms of the biomechanical processes mediating interactions between platelets and fiber networks in blood clot stretching and contraction needs to be examined carefully. How the structural and mechanical properties of major blood clot components influences biomechanical responses of the entire clot subjected to external forces, such as blood flow or vessel wall deformations needs to be investigated thoroughly.

Nanomechanics of Blood Clot and Thrombus Formation

Mechanical properties have been extensively studied in pure elastic or viscous materials; however, most biomaterials possess both physical properties in a viscoelastic component. How the biomechanics of a fibrin clot is related to its composition and the microenvironment where it is formed is not yet fully understood. This review gives an outline of the building mechanisms for blood clot mechanical properties and how they relate to clot function. The formation of a blood clot in health conditions or the formation of a dangerous thrombus go beyond the mere polymerization of fibrinogen into a fibrin network. The complex composition and localization of in vivo fibrin clots demonstrate the interplay between fibrin and/or fibrinogen and blood cells. Studying these protein–cell interactions and clot mechanical properties may represent new methods for the evaluation of cardiovascular diseases (the leading cause of death worldwide), creating new possibilities for clinical diagnosis, prognosis, and therapy.

Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Why fibrin biomechanical properties matter for hemostasis and thrombosis

Polymeric fibrin displays unique structural and biomechanical properties that contribute to its essential role of generating blood clots that stem bleeds. The aim of this review is to discuss how the fibrin clot is formed, how protofibrils make up individual fibrin fibers, what the relationship is between the molecular structure and fibrin biomechanical properties, and how fibrin biomechanical properties relate to the risk of thromboembolic disease. Fibrin polymerization is driven by different types of bonds, including knob-hole interactions displaying catch-slip characteristics, and covalent crosslinking of fibrin polypeptides by activated factor XIII. Key biophysical properties of fibrin polymer are its visco-elasticity, extensibility and resistance to rupture. The internal packing of protofibrils within fibers changes fibrin biomechanical behavior. There are several methods to analyze fibrin biomechanical properties at different scales, including AFM force spectroscopy, magnetic or optical tweezers and rheometry, amongst others. Clinically, fibrin biomechanical characteristics are key for the prevention of thromboembolic disorders such as pulmonary embolism. Future studies are needed to address unanswered questions regarding internal molecular structure of the fibrin polymer, the structural and molecular basis of its remarkable mechanical properties and the relationship of fibrin biomechanical characteristics with thromboembolism in patients with deep vein thrombosis and ischemic stroke.

Strength, deformability and toughness of uncrosslinked fibrin fibers from theoretical reconstruction of stress-strain curves

Structural mechanisms underlying the mechanical properties of fibrin fibers are elusive. We combined tensile testing of uncrosslinked fibrin polymers in vitro and in silico to explore their material properties. The experimental stress (σ) - strain (ε) curves for fibrin fibers are characterized by elastic deformations with a weaker elastic response for ε<160% due to unraveling of αC tethers and straightening of fibrin protofibrils, and a stronger response for ε>160% owing to unfolding of the coiled coils and γ nodules in fibrin monomers. Fiber rupture for strains ε>212% is due to dissociation of the knob-hole bonds and rupture of D:D interfaces. We developed the Fluctuating Bilinear Spring model to interpret the σ-ε profiles in terms of the free energy for protofibril alignment ΔG0 = 10.1-11.5 kBT, Young's moduli for protofibril alignment Yu = 1.9-3.2 MPa and stretching Ya = 5.7-9.7 MPa, strain scale ε˜≈ 12-40% for fiber rupture, and protofibril cooperativity m= 3.6-8. We applied the model to characterize the fiber strength σcr≈ 12-13 MPa, deformability εcr≈ 222%, and rupture toughness U≈ 9 MJ/m3, and to resolve thermodynamic state functions, 96.9 GJ/mol entropy change for protofibril alignment (at room temperature) and 113.6 GJ/mol enthalpy change for protofibril stretching, which add up to 210.5 GJ/mol free-energy change. Fiber elongation is associated with protofibril dehydration and sliding mechanism to create an ordered protofibril array. Fibrin fibers behave like a hydrogel; protofibril dehydration and water expulsion account for ∼94-98% of the total free-energy changes for fiber elongation and rupture. STATEMENT OF SIGNIFICANCE: Structural mechanisms underlying the mechanical properties of fibrin fibers, major components of blood clots and obstructive thrombi, are elusive. We performed tensile testing of uncrosslinked fibrin polymers in vitro and in silico to explore their material properties. Fluctuating Bilinear Spring theory was developed to interpret the stress-strain profiles in terms of the energy for protofibril alignment, elastic moduli for protofibril alignment and stretching, and strain scale for fiber rupture, and to probe the limits of fiber strength, extensibility and toughness. Fibrin fibers behave like a hydrogel. Fiber elongation is defined by the protofibril dehydration and sliding. Structural rearrangements in water matrix control fiber elasticity. These results contribute to fundamental understanding of blood clot breakage that underlies thrombotic embolization.

Finite element analysis of blood clots based on the nonlinear visco-hyperelastic model

Mechanical thrombectomy has become the standard treatment for patients with an acute ischemic stroke. In this approach, to remove blood clots, mechanical force is applied using thrombectomy devices, in which the interaction between the clot and the device could significantly affect the clot retrieval performance. It is expected that the finite element method (FEM) could visualize the mechanical interaction by the visualization of the stress transmission from the device to the clot. This research was aimed at verifying the constitutive theory by implementing FEM based on the visco-hyperelastic theory, using a three-dimensional clot model. We used the visco-hyperelastic FEM to reproduce the mechanical behavior of blood clots, as observed in experiments. This study is focused on the mechanical responses of clots under tensile loading and unloading because in mechanical thrombectomy, elongation is assumed to occur locally on the clots during the retrieval process. Several types of cylindrical clots were created by changing the fibrinogen dose. Tensile testing revealed that the stiffness (E_0.45-value) of clots with fibrinogen could be more than three times higher than that of clots without fibrinogen. It was also found that the stiffness was not proportional to the fibrinogen dose. By fitting to the theoretical curve, it was revealed that the Mooney-Rivlin model could reproduce the hyperelastic characteristics of clots well. From the stress-relaxation data, the three-chain Maxwell model could accurately fit the experimental viscoelastic data. FEM, taking the theoretical models into account, was then carried out, and the results matched well with the experimental visco-hyperelastic characteristics of clots under tensile load, reproducing the mechanical hysteresis during unloading, the stress dependence on the strain rate, and the time-dependent stress decrease in the stress-relaxation test.

Physical forces regulating hemostasis and thrombosis: Vessels, cells, and molecules in illustrated review

This illustrated review focuses on the physical forces that regulate hemostasis and thrombosis. These phenomena span from the vessel to the cellular to the molecular scales. Blood is a complex fluid with a viscosity that varies with how fast it flows and the size of the vessel through which it flows. Blood flow imposes forces on the vessel wall and blood cells that dictates the kinetics, structure, and stability of thrombi. The mechanical properties of blood cells create a segmented flowing fluid whereby red blood cells concentrate in the vessel core and platelets marginate to the near-wall region. At the vessel wall, shear stresses are highest, which requires a repertoire of receptors with different bond kinetics to roll, tether, adhere, and activate on inflamed endothelium and extracellular matrices. As a thrombus grows and then contracts, forces regulate platelet aggregation as well as von Willebrand factor function and fibrin mechanics. Forces can also originate from platelets as they respond to the external forces and sense the stiffness of their local environment.

Fracture mechanics analysis of fibrin fibers using mesoscale and continuum level methods

Computational models for simulating and predicting fibrin fiber fracture are important tools for studying bulk mechanical properties and mechanobiological response of fibrin networks in physiological conditions. In this work, we employed a new strategy to model the mechanical response of a single fibrin fiber using a collection of bundled protofibrils and modeled the time-dependent properties using discrete particle simulations. Using a systematic characterization of the parameters, this model can be used to mimic the elastic behavior of fibrin fibers accurately and also to simulate fibrin fiber fracture. In addition, a continuum model was modified and used to obtain the individual fibrin fiber fracture toughness properties. Using this model and the experimentally available fibrin mechanical properties, we predicted the range of fracture toughness (1 to k P a m ) values of a typical fibrin fiber of diameter 100 nm and its critical flaw size to rupture (~4 nm), both of which are not currently available in the literature. The models can be collectively used as a foundation for simulating the mechanical behavior of fibrin clots. Moreover, the tunable discrete mesoscopic model that was employed can be extended to simulate and estimate the mechanical properties of other biological or synthetic fibers.

Probing fibrin's molecular response to shear and tensile deformation with coherent Raman microscopy

Blood clots are essential biomaterials that prevent blood loss and provide a temporary scaffold for tissue repair. In their function, these materials must be capable of resisting mechanical forces from hemodynamic shear and contractile tension without rupture. Fibrin networks, the primary load-bearing element in blood clots, have unique nonlinear mechanical properties resulting from fibrin's hierarchical structure. This structure provides multiscale load bearing from fiber deformation to protein unfolding. Here, we study the fiber and molecular scale response of fibrin under shear and tensile loads in situ using a combination of fluorescence and vibrational (molecular) microscopy. Imaging protein fiber orientation and molecular vibrations, we find that fiber alignment and molecular unfolding in fibrin appear at much larger strains under shear compared to uniaxial tension. Alignment levels reached at 150% shear strain were reached already at 60% tensile strain, and molecular unfolding of fibrin was only detected at shear strains above 300%, whereas fibrin unfolding began already at 20% tensile strain. Moreover, shear deformation caused progressive changes in vibrational modes consistent with increased protofibril and fiber packing that were already present even at very low tensile deformation. Together with a bioinformatic analysis of the primary fibrinogen structure, we propose a scheme for the molecular response of fibrin from low to high deformation, which may relate to the teleological origin of fibrin's resistance to shear and tensile forces.

The Role of Concentration on Drop Formation and Breakup of Collagen, Fibrinogen, and Thrombin Solutions during Inkjet Bioprinting

The influence of protein concentration on drop formation and breakup of aqueous solutions of fibrous proteins collagen and fibrinogen and globular protein thrombin in different concentration regimes has been investigated during drop-on-demand (DOD) inkjet printing. The capillary-driven thinning and breakup of dilute collagen, fibrinogen, and thrombin solutions, the solutions in which protein molecules are far away from each other, are predominantly resisted by inertial force. Although the capillary-driven thinning and breakup of semidilute unentangled collagen and fibrinogen solutions, the solutions in which protein molecules begin to interpenetrate each other, are predominantly resisted by inertial force on the initial onset of necking, the breakup of droplets is delayed because of the resistance of elastic force. The resistance of viscous force to the necking and breakup of both the dilute and semidilute unentangled protein solutions is negligible. Aggregates or subvisible particles (between 1 and 100 μm) constantly disrupt the formation of droplets for the semidilute unentangled protein solutions, even when their inverse Ohnesorge number (Z) is within the printability range of 4 ≤ Z ≤ 14. Although aggregates are present in the dilute protein solutions, they do not disrupt the formation of droplets.

Rheological investigation of collagen, fibrinogen, and thrombin solutions for drop-on-demand 3D bioprinting

Collagen, fibrinogen, and thrombin proteins in aqueous buffer solutions are widely used as precursors of natural biopolymers in three-dimensional (3D) bioprinting applications. The proteins are sourced from animals and their quality may vary from batch to batch, inducing differences in the rheological properties of such solutions. In this work, we investigate the rheological response of collagen, fibrinogen, and thrombin protein solutions in bulk and at the solution/air interface. Interfacial rheological measurements show that fibrous collagen, fibrinogen and globular thrombin proteins adsorb and aggregate at the solution/air interface, forming a viscoelastic solid film at the interface. The viscoelastic film corrupts the bulk rheological measurements in rotational rheometers by contributing to an apparent yield stress, which increases the apparent bulk viscosity up to shear rates as high as 1000 s^-1. The addition of a non-ionic surfactant, such as polysorbate 80 (PS80) in small amounts between 0.001 and 0.1 v/v%, prevents the formation of the interfacial layer, allowing the estimation of true bulk viscosity of the solutions. The estimation of viscosity not only helps in identifying those protein solutions that are potentially printable with drop-on-demand (DOD) inkjet printing but also detects inconsistencies in flow behavior among the batches.

Multiscale Network Modeling of Fibrin Fibers and Fibrin Clots with Protofibril Binding Mechanics

The multiscale mechanical behavior of individual fibrin fibers and fibrin clots was modeled by coupling atomistic simulation data and microscopic experimental data. We propose a new protofibril element composed of a nonlinear spring network, and constructed this based on molecular simulations and atomic force microscopy results to simulate the force extension behavior of fibrin fibers. This new network model also accounts for the complex interaction of protofibrils with one another, the effects of the presence of a solvent, Coulombic attraction, and other binding forces. The network model was formulated to simulate the force–extension mechanical behavior of single fibrin fibers from atomic force microscopy experiments, and shows good agreement. The validated fibrin fiber network model was then combined with a modified version of the Arruda–Boyce eight-chain model to estimate the force extension behavior of the fibrin clot at the continuum level, which shows very good correlation. The results show that our network model is able to predict the behavior of fibrin fibers as well as fibrin clots at small strains, large strains, and close to the break strain. We used the network model to explain why the mechanical response of fibrin clots and fibrin fibers deviates from worm-like chain behavior, and instead behaves like a nonlinear spring.

Revealing the molecular origins of fibrin's elastomeric properties by in situ X-ray scattering

Fibrin is an elastomeric protein forming highly extensible fiber networks that provide the scaffold of blood clots. Here we reveal the molecular mechanisms that explain the large extensibility of fibrin networks by performing in situ small angle X-ray scattering measurements while applying a shear deformation. We simultaneously measure shear-induced alignment of the fibers and changes in their axially ordered molecular packing structure. We show that fibrin networks exhibit distinct structural responses that set in consecutively as the shear strain is increased. They exhibit an entropic response at small strains (<5%), followed by progressive fiber alignment (>25% strain) and finally changes in the fiber packing structure at high strain (>100%). Stretching reduces the fiber packing order and slightly increases the axial periodicity, indicative of molecular unfolding. However, the axial periodicity changes only by 0.7%, much less than the 80% length increase of the fibers, suggesting that fiber elongation mainly stems from uncoiling of the natively disordered αC-peptide linkers that laterally bond the molecules. Upon removal of the load, the network structure returns to the original isotropic state, but the fiber structure becomes more ordered and adopts a smaller packing periodicity compared to the original state. We conclude that the hierarchical packing structure of fibrin fibers, with built-in disorder, makes the fibers extensible and allows for mechanical annealing. Our results provide a basis for interpreting the molecular basis of haemostatic and thrombotic disorders associated with clotting and provide inspiration to design resilient bio-mimicking materials. STATEMENT OF SIGNIFICANCE: Fibrin provides structural integrity to blood clots and is also widely used as a scaffold for tissue engineering. To fulfill their biological functions, fibrin networks have to be simultaneously compliant like skin and resilient against rupture. Here, we unravel the structural origin underlying this remarkable mechanical behaviour. To this end, we performed in situ measurements of fibrin structure across multiple length scales by combining X-ray scattering with shear rheology. Our findings show that fibrin sustains large strains by undergoing a sequence of structural changes on different scales with increasing strain levels. This demonstrates new mechanistic aspects of an important biomaterial's structure and its mechanical function, and serves as an example in the design of biomimicking materials.

Recent advances in computational modeling of fibrin clot formation: A review

The field of thrombosis and hemostasis is crucial for understanding and developing new therapies for pathologies such as deep vein thrombosis, diabetes related strokes, pulmonary embolisms, and hemorrhaging related diseases. In the last two decades, an exponential growth in studies related to fibrin clot formation using computational tools has been observed. Despite this growth, the complete mechanism behind thrombus formation and hemostasis has been long and rife with obstacles; however, significant progress has been made in the present century. The computational models and methods used in this context are diversified into different spatiotemporal scales, yet there is no single model which can predict both physiological and mechanical properties of fibrin clots. In this review, we list the major strategies employed by researchers in modeling fibrin clot formation using recent and existing computational techniques. This review organizes the computational strategies into continuum level, system level, discrete particle (DPD), and multi-scale methods. We also discuss strengths and weaknesses of various methods and future directions in which computational modeling of fibrin clots can advance.

Contribution of nascent cohesive fiber-fiber interactions to the non-linear elasticity of fibrin networks under tensile load

Fibrin is a viscoelastic proteinaceous polymer that determines the deformability and integrity of blood clots and fibrin-based biomaterials in response to biomechanical forces. Here, a previously unnoticed structural mechanism of fibrin clots' mechanical response to external tensile loads is tested using high-resolution confocal microscopy and recently developed three-dimensional computational model. This mechanism, underlying local strain-stiffening of individual fibers as well as global stiffening of the entire network, is based on previously neglected nascent cohesive pairwise interactions between individual fibers (crisscrossing) in fibrin networks formed under tensile load. Existence of fiber-fiber crisscrossings of reoriented fibers was confirmed using 3D imaging of experimentally obtained stretched fibrin clots. The computational model enabled us to study structural details and quantify mechanical effects of the fiber-fiber cohesive crisscrossing during stretching of fibrin gels at various spatial scales. The contribution of the fiber-fiber cohesive contacts to the elasticity of stretched fibrin networks was characterized by changes in individual fiber stiffness, the length, width, and alignment of fibers, as well as connectivity and density of the entire network. The results show that the nascent cohesive crisscrossing of fibers in stretched fibrin networks comprise an underappreciated important structural mechanism underlying the mechanical response of fibrin to (patho)physiological stresses that determine the course and outcomes of thrombotic and hemostatic disorders, such as heart attack and ischemic stroke. STATEMENT OF SIGNIFICANCE: Fibrin is a viscoelastic proteinaceous polymer that determines the deformability and integrity of blood clots and fibrin-based biomaterials in response to biomechanical forces. In this paper, a novel structural mechanism of fibrin clots' mechanical response to external tensile loads is tested using high-resolution confocal microscopy and newly developed computational model. This mechanism, underlying local strain-stiffening of individual fibers as well as global stiffening of the entire network, is based on previously neglected nascent cohesive pairwise interactions between individual fibers (crisscrossing) in fibrin networks formed under tensile load. Cohesive crisscrossing is an important structural mechanism that influences the mechanical response of blood clots and which can determine the outcomes of blood coagulation disorders, such as heart attacks and strokes.

Fibrin polymerization simulation using a reactive dissipative particle dynamics method

The study on the polymerization of fibrinogen molecules into fibrin monomers and eventually a stable, mechanically robust fibrin clot is a persistent and enduring topic in the field of thrombosis and hemostasis. Despite many research advances in fibrin polymerization, the change in the structure of fibrin clots and its influence on the formation of a fibrous protein network are still poorly understood. In this paper, we develop a new computational method to simulate fibrin clot polymerization using dissipative particle dynamics simulations. With an effective combination of reactive molecular dynamics formularies and many body dissipative particle dynamics principles, we constructed the reactive dissipative particle dynamics (RDPD) model to predict the complex network formation of fibrin clots and branching of the fibrin network. The 340 kDa fibrinogen molecule is converted into a spring-bead coarse-grain system with 11 beads using a topology representing network algorithm, and using RDPD, we simulated polymerization and formation of the fibrin clot. The final polymerized structure of the fibrin clot qualitatively agrees with experimental results from the literature, and to the best of our knowledge this is the first molecular-based study that simulates polymerization and structure of fibrin clots.

Biophysical Mechanisms Mediating Fibrin Fiber Lysis

The formation and dissolution of blood clots is both a biochemical and a biomechanical process. While much of the chemistry has been worked out for both processes, the influence of biophysical properties is less well understood. This review considers the impact of several structural and mechanical parameters on lytic rates of fibrin fibers. The influences of fiber and network architecture, fiber strain, FXIIIa cross-linking, and particle transport phenomena will be assessed. The importance of the mechanical aspects of fibrinolysis is emphasized, and future research avenues are discussed.

Fibrin Formation, Structure and Properties

Fibrinogen and fibrin are essential for hemostasis and are major factors in thrombosis, wound healing, and several other biological functions and pathological conditions. The X-ray crystallographic structure of major parts of fibrin(ogen), together with computational reconstructions of missing portions and numerous biochemical and biophysical studies, have provided a wealth of data to interpret molecular mechanisms of fibrin formation, its organization, and properties. On cleavage of fibrinopeptides by thrombin, fibrinogen is converted to fibrin monomers, which interact via knobs exposed by fibrinopeptide removal in the central region, with holes always exposed at the ends of the molecules. The resulting half-staggered, double-stranded oligomers lengthen into protofibrils, which aggregate laterally to make fibers, which then branch to yield a three-dimensional network. Much is now known about the structural origins of clot mechanical properties, including changes in fiber orientation, stretching and buckling, and forced unfolding of molecular domains. Studies of congenital fibrinogen variants and post-translational modifications have increased our understanding of the structure and functions of fibrin(ogen). The fibrinolytic system, with the zymogen plasminogen binding to fibrin together with tissue-type plasminogen activator to promote activation to the active proteolytic enzyme, plasmin, results in digestion of fibrin at specific lysine residues. In spite of a great increase in our knowledge of all these interconnected processes, much about the molecular mechanisms of the biological functions of fibrin(ogen) remains unknown, including some basic aspects of clotting, fibrinolysis, and molecular origins of fibrin mechanical properties. Even less is known concerning more complex (patho)physiological implications of fibrinogen and fibrin.

Fibrin Fiber Stiffness Is Strongly Affected by Fiber Diameter, but Not by Fibrinogen Glycation

The major structural component of a blood clot is a mesh of fibrin fibers. Our goal was to determine whether fibrinogen glycation and fibrin fiber diameter have an effect on the mechanical properties of single fibrin fibers. We used a combined atomic force microscopy/fluorescence microscopy technique to determine the mechanical properties of individual fibrin fibers formed from blood plasma. Blood samples were taken from uncontrolled diabetic patients as well as age-, gender-, and body-mass-index-matched healthy individuals. The patients then underwent treatment to control blood glucose levels before end blood samples were taken. The fibrinogen glycation of the diabetic patients was reduced from 8.8 to 5.0 mol glucose/mol fibrinogen, and the healthy individuals had a mean fibrinogen glycation of 4.0 mol glucose/mol fibrinogen. We found that fibrinogen glycation had no significant systematic effect on single-fiber modulus, extensibility, or stress relaxation times. However, we did find that the fiber modulus, Y, strongly decreases with increasing fiber diameter, D, as Y∝D−1.6. Thin fibers can be 100 times stiffer than thick fibers. This is unusual because the modulus is a material constant and should not depend on the sample dimensions (diameter) for homogeneous materials. Our finding, therefore, implies that fibrin fibers do not have a homogeneous cross section of uniformly connected protofibrils, as is commonly thought. Instead, the density of protofibril connections, ρ_Pb, strongly decreases with increasing diameter, as ρPb∝D−1.6. Thin fibers are denser and/or have more strongly connected protofibrils than thick fibers. This implies that it is easier to dissolve clots that consist of fewer thick fibers than those that consist of many thin fibers, which is consistent with experimental and clinical observations.

Fibrin mechanical properties and their structural origins

Fibrin is a protein polymer that is essential for hemostasis and thrombosis, wound healing, and several other biological functions and pathological conditions that involve extracellular matrix. In addition to molecular and cellular interactions, fibrin mechanics has been recently shown to underlie clot behavior in the highly dynamic intra- and extravascular environments. Fibrin has both elastic and viscous properties. Perhaps the most remarkable rheological feature of the fibrin network is an extremely high elasticity and stability despite very low protein content. Another important mechanical property that is common to many filamentous protein polymers but not other polymers is stiffening occurring in response to shear, tension, or compression. New data has begun to provide a structural basis for the unique mechanical behavior of fibrin that originates from its complex multi-scale hierarchical structure. The mechanical behavior of the whole fibrin gel is governed largely by the properties of single fibers and their ensembles, including changes in fiber orientation, stretching, bending, and buckling. The properties of individual fibrin fibers are determined by the number and packing arrangements of double-stranded half-staggered protofibrils, which still remain poorly understood. It has also been proposed that forced unfolding of sub-molecular structures, including elongation of flexible and relatively unstructured portions of fibrin molecules, can contribute to fibrin deformations. In spite of a great increase in our knowledge of the structural mechanics of fibrin, much about the mechanisms of fibrin's biological functions remains unknown. Fibrin deformability is not only an essential part of the biomechanics of hemostasis and thrombosis, but also a rapidly developing field of bioengineering that uses fibrin as a versatile biomaterial with exceptional and tunable biochemical and mechanical properties.

The role of biophysical properties of provisional matrix proteins in wound repair

Wound healing is a complex, dynamic process required for maintaining homeostasis in an organism. Along with being controlled biochemically, wound healing is also controlled through the transduction of biophysical stimuli through cell interactions with the extracellular matrix (ECM). This review provides an overview of the ECM's role in the wound healing process and subsequently expands on the variety of roles biophysical phenomenon play.

Multi-scale strain-stiffening of semiflexible bundle networks

Bundles of polymer filaments are responsible for the rich and unique mechanical behaviors of many biomaterials, including cells and extracellular matrices. In fibrin biopolymers, whose nonlinear elastic properties are crucial for normal blood clotting, protofibrils self-assemble and bundle to form networks of semiflexible fibers. Here we show that the extraordinary strain-stiffening response of fibrin networks is a direct reflection of the hierarchical architecture of the fibrin fibers. We measure the rheology of networks of unbundled protofibrils and find excellent agreement with an affine model of extensible wormlike polymers. By direct comparison with these data, we show that physiological fibrin networks composed of thick fibers can be modeled as networks of tight protofibril bundles. We demonstrate that the tightness of coupling between protofibrils in the fibers can be tuned by the degree of enzymatic intermolecular crosslinking by the coagulation factor XIII. Furthermore, at high stress, the protofibrils contribute independently to the network elasticity, which may reflect a decoupling of the tight bundle structure. The hierarchical architecture of fibrin fibers can thus account for the nonlinearity and enormous elastic resilience characteristic of blood clots.

The Internal Dynamics of Fibrinogen and Its Implications for Coagulation and Adsorption

Fibrinogen is a serum multi-chain protein which, when activated, aggregates to form fibrin, one of the main components of a blood clot. Fibrinolysis controls blood clot dissolution through the action of the enzyme plasmin, which cleaves fibrin at specific locations. Although the main biochemical factors involved in fibrin formation and lysis have been identified, a clear mechanistic picture of how these processes take place is not available yet. This picture would be instrumental, for example, for the design of improved thrombolytic or anti-haemorrhagic strategies, as well as, materials with improved biocompatibility. Here, we present extensive molecular dynamics simulations of fibrinogen which reveal large bending motions centered at a hinge point in the coiled-coil regions of the molecule. This feature, likely conserved across vertebrates according to our analysis, suggests an explanation for the mechanism of exposure to lysis of the plasmin cleavage sites on fibrinogen coiled-coil region. It also explains the conformational variability of fibrinogen observed during its adsorption on inorganic surfaces and it is supposed to play a major role in the determination of the hydrodynamic properties of fibrinogen. In addition the simulations suggest how the dynamics of the D region of fibrinogen may contribute to the allosteric regulation of the blood coagulation cascade through a dynamic coupling between the a- and b-holes, important for fibrin polymerization, and the integrin binding site P1.

Fibrinogen, a protein found in the blood of vertebrates, when activated, aggregates and forms fibrin fibers, the basis of a blood clot. Clots are broken down by the enzyme plasmin, which cuts fibrin fibers at specific places, thus helping the regulation of clot persistence. A mechanistic understanding of fibrin degradation by plasmin is still missing. An important determinant of this process might be the flexibility of fibrinogen. The flexible nature of fibrinogen is reported, for example, by the great variety of conformations observed when fibrinogen adsorbs on material surfaces. However, limits in the spatial resolution of these experiments preclude the identification of the atomistic mechanism behind this flexibility. Here, we perform computer simulations that help identifying with atomistic detail large bending motions occurring at a specific hinge on the molecule. We show how these bending motions can explain the variable conformations observed in experiments and how they help exposing sites where plasmin can cut fibrinogen. Furthermore, our simulations let us identify cooperative effects involving several distant parts of fibrinogen that may play a role in the assembly of fibrin fibers. Both the bending and the cooperative effects, thus, represent potential mechanisms for the regulation of blood clotting.

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.

Rheology and morphology of no-slip sheared polymer nanocomposite under creep condition

Dissipative particle dynamics simulations are performed on wet polymer nanocomposite blends under the discrete imposed velocity profile and no-slip boundary conditions. To be able to study the chain length dependency of the rheological properties, a number of blends of mono-disperse polymer chains of lengths varying from 10 to 100 repeat units and nanoparticles of diameters 2.5 and 5 have been simulated. The wall velocity was imposed on a thin polymer layer (the no-slip layer). Linear velocity profiles for polymer confined in the pore were observed at the steady state. We found that the flow has a shear thinning effect on the chains with a radius of gyration less than the filler radius. Long chains (with a radius of gyration longer than the filler's radius), however, obey the Newtonian behavior over a much wider shear rate than that which causes shear thinning in short chains. The effect of particle-monomer interactions, polymer entanglements, chain morphology, and link formation on the shear rate dependency of the viscosity coefficient has been studied. Our results show that the particle-polymer interactions have no effect on shear thinning behavior of the blend. In contrast, the long range polymer-polymer interactions and the chain length have considerable effects on the rheological behavior of the blend. Finally, the phase diagram of the rheological properties of polymer nanocomposite as a function of strain rate and the chain length is extracted.

Integration of acoustic radiation force and optical imaging for blood plasma clot stiffness measurement

Despite the life-preserving function blood clotting serves in the body, inadequate or excessive blood clot stiffness has been associated with life-threatening diseases such as stroke, hemorrhage, and heart attack. The relationship between blood clot stiffness and vascular diseases underscores the importance of quantifying the magnitude and kinetics of blood's transformation from a fluid to a viscoelastic solid. To measure blood plasma clot stiffness, we have developed a method that uses ultrasound acoustic radiation force (ARF) to induce micron-scaled displacements (1-500 μm) on microbeads suspended in blood plasma. The displacements were detected by optical microscopy and took place within a micro-liter sized clot region formed within a larger volume (2 mL sample) to minimize container surface effects. Modulation of the ultrasound generated acoustic radiation force allowed stiffness measurements to be made in blood plasma from before its gel point to the stage where it was a fully developed viscoelastic solid. A 0.5 wt % agarose hydrogel was 9.8-fold stiffer than the plasma (platelet-rich) clot at 1 h post-kaolin stimulus. The acoustic radiation force microbead method was sensitive to the presence of platelets and strength of coagulation stimulus. Platelet depletion reduced clot stiffness 6.9 fold relative to platelet rich plasma. The sensitivity of acoustic radiation force based stiffness assessment may allow for studying platelet regulation of both incipient and mature clot mechanical properties.

Experimental and imaging techniques for examining fibrin clot structures in normal and diseased states

Fibrin is an extracellular matrix protein that is responsible for maintaining the structural integrity of blood clots. Much research has been done on fibrin in the past years to include the investigation of synthesis, structure-function, and lysis of clots. However, there is still much unknown about the morphological and structural features of clots that ensue from patients with disease. In this research study, experimental techniques are presented that allow for the examination of morphological differences of abnormal clot structures due to diseased states such as diabetes and sickle cell anemia. Our study focuses on the preparation and evaluation of fibrin clots in order to assess morphological differences using various experimental assays and confocal microscopy. In addition, a method is also described that allows for continuous, real-time calculation of lysis rates in fibrin clots. The techniques described herein are important for researchers and clinicians seeking to elucidate comorbid thrombotic pathologies such as myocardial infarctions, ischemic heart disease, and strokes in patients with diabetes or sickle cell disease.

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-based biomaterials: modulation of macroscopic properties through rational design at the molecular level

Fibrinogen is one of the primary components of the coagulation cascade and rapidly forms an insoluble matrix following tissue injury. In addition to its important role in hemostasis, fibrin acts as a scaffold for tissue repair and provides important cues for directing cell phenotype following injury. Because of these properties and the ease of polymerization of the material, fibrin has been widely utilized as a biomaterial for over a century. Modifying the macroscopic properties of fibrin, such as elasticity and porosity, has been somewhat elusive until recently, yet with a molecular-level rational design approach it can now be somewhat easily modified through alterations of molecular interactions key to the protein's polymerization process. This review outlines the biochemistry of fibrin and discusses methods for modification of molecular interactions and their application to fibrin based biomaterials.

Multiscale relationships between fibronectin structure and functional properties

Cell behavior is tightly coupled to the properties of the extracellular matrix (ECM) to which they attach. Fibronectin (Fn) forms a supermolecular, fibrillar component of the ECM that is prominent during development, wound healing and the progression of numerous diseases. This indicates that Fn has an important function in controlling cell behavior during dynamic events in vivo. The multiscale architecture of Fn molecules assembled into these fibers determines the ligand density of cell adhesion sites on the surface of the Fn fiber, Fn fiber porosity for cell signaling molecules such as growth factors, the mechanical stiffness of the Fn matrix and the adhesivity of Fn for its numerous soluble ligands. These parameters are altered by mechanical strain applied to the ECM. Recent efforts have attempted to link the molecular properties of Fn with bulk properties of Fn matrix fibers. Studies of isolated Fn fibers have helped to characterize the fiber's material properties and, in combination with models of Fn molecular behavior in the fibers, have begun to provide insights into the Fn molecular arrangement and intermolecular adhesions within the fibers. A review of these studies allows the development of an understanding of the mechanobiological functions of Fn.