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.

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

The multiscale mechanical behavior of individual fibrin fibers and fibrin clots wasmodeled by coupling atomistic simulation data and microscopic experimental data. We propose anew protofibril element composed of a nonlinear spring network, and constructed this based onmolecular simulations and atomic force microscopy results to simulate the force extension behaviorof fibrin fibers. This new network model also accounts for the complex interaction of protofibrilswith one another, the effects of the presence of a solvent, Coulombic attraction, and other bindingforces. The network model was formulated to simulate the force-extension mechanical behavior ofsingle fibrin fibers from atomic force microscopy experiments, and shows good agreement. Thevalidated 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 continuumlevel, which shows very good correlation. The results show that our network model is able to predictthe behavior of fibrin fibers as well as fibrin clots at small strains, large strains, and close to the breakstrain. We used the network model to explain why the mechanical response of fibrin clots and fibrinfibers deviates from worm-like chain behavior, and instead behaves like a nonlinear spring.

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.

Physiochemical Effects of Nanoparticles on Cell Nuclear Complex Pore Transport: A Coarse-Grained Computational Model.

Understanding and controlling the interaction between nanoparticles and cell nuclei is critical to the development of the biomedical applications such as gene delivery, cellular imaging, and tumor therapy. Recent years have witnessed growing evidence that the size, shape, and the grafting density of the karyopherins ligands of nanoparticles provide a significant influence on the uptake mechanism of nanoparticles into cells; however, there is a lack of investigation into how these physical factors play a role in cellular nuclear uptake and how the nanoparticle enters the nucleus. Here, we build a computational framework to parametrically evaluate the effects of the size, shape, and the grafting density of the karyopherins ligands of designed nanoparticles on their transport through the nuclear pore complex of a cell nucleus so as to provide a novel scheme for nanoparticle design and precise nucleus-targeted therapy. Simulation results indicate that smaller spherical nanoparticles need to overcome a lower energy barrier than larger ones and also that nanoparticles with large grafting density exhibited greatly altered dynamics during the active transport process. Moreover, we observed that the shape and morphology of nanoparticles unambiguously determined their nuclear uptake pathways. Nuclear uptake is determined by an intricate interplay between physicochemical particle properties and nucleus properties. Our work provides a systematic understanding for nuclear uptake of nanoparticles, viruses, and bacteria and opens up a controllable design strategy for manipulating nanoparticle-nucleus interaction, with numerous applications in medicine, bioimaging, and biosensing.

Molecular insights into the irreversible mechanical behavior of sickle hemoglobin.

Sickle cell disease is caused by the amino acid substitution of glutamic acid to valine, which leads to the polymerization of deoxygenated sickle hemoglobin (HbS) into long strands. These strands are responsible for the sickling of red blood cells (RBCs), making blood hyper-coagulable leading to an increased chance of vaso-occlusive crisis. The conformational changes in sickled RBCs traveling through narrow blood vessels in a highly viscous fluid are critical in understanding; however, there are few studies that investigate the origins of the molecular mechanical behavior of sickled RBCs. In this work, we investigate the molecular mechanical properties of HbS molecules. A mechanical model was used to estimate the directional stiffness of an HbS molecule and the results were compared to adult human hemoglobin (HbA). The comparison shows a significant difference in strength between HbS and HbA, as well as anisotropic behavior of the hemoglobin molecules. The results also indicated that the HbS molecule experienced more irreversible mechanical behavior than HbA under compression. Further, we have characterized the elastic and compressive properties of a double stranded sickle fiber using six HbS molecules, and it shows that the HbS molecules are bound to each other through strong inter-molecular forces.

Flow plate separation of cells based on elastic properties: a computational study.

Medical studies have consistently shown that the best defense against cancer is early detection. Due to this, many efforts have been made to develop methods of screening patient blood quickly and cheaply. These methods range from separation via differences in size, electrostatic potential, chemical potential, antibody-binding affinity, among others. We propose a method of separating cells which have similar size and outer coatings, but which differ in their elastic properties. Such a method would be useful in detecting cancerous cells, which may have similar properties to leukocytes or erythrocytes but differ in their stiffness and deformation response. Here, we use coarse-grained model of a cell with membrane, cytoskeleton, and inner fluid to determine how small changes in the cell stiffness may be used to quickly and efficiently separate out irregular cells such as circulating tumor cells from a sample of blood. We focus specifically on the effects of volumetric flux and plate geometry on the ability of a separation plate to differentiate cells of similar but disparate stiffnesses. We show that volumetric flux is crucial in determining the stiffness cutoff for separating out cells of similar sizes, while the angle of the separation plate plays a less important role. With this work, we provide a comprehensive approach to the design factors of cell separation via elastic properties and hope to offer a guideline for the development of novel cytometry devices for the detection of irregular cells such as circulating tumor cells.

Glucose Concentration Affects Fibrin Clot Structure and Morphology as Evidenced by Fluorescence Imaging and Molecular Simulations.

Although in vivo studies have been conducted in the past to determine hyperglycemic effects and influence on clotting risk in patients with diabetes, the true extent of hyperglycemia on unstable and spontaneous clot formation remains highly debated. Factors such as increased glycation, elevated fibrinogen concentration, elevated prothrombin levels, and decreased plasminogen are known to influence fibrin conversion, clot morphology, and thrombus formation in these individuals. In this regard, the isolated effects of hyperglycemia on irregular fibrin clot formation were investigated in a controlled fibrinogen system. In this study, fibrin clot characteristic differences at 3 glucose concentrations were analyzed to determine the effects of glucose concentration on fibrinogen glycation and fibrin clot morphology using confocal microscopy, glycation quantification, molecular simulations, and image processing methods. Algorithms coupled with statistical analysis support in vivo findings that hyperglycemia increases fibrinogen glycation, with ensuing altered fibrin clot structure characteristics. Our experimental and molecular simulation results consistently show an increased glucose adsorption by fibrinogen with increased glucose concentration. Significant differences in clot structure characteristics were observed, and the results of this work can be used to further develop diagnostic tools for evaluating clotting risk in individuals with hypercoagulable and hyperglycemic conditions.

Human cathepsins K, L, and S: Related proteases, but unique fibrinolytic activity.

BACKGROUND: Fibrin formation and dissolution are attributed to cascades of protease activation concluding with thrombin activation, and plasmin proteolysis for fibrin breakdown. Cysteine cathepsins are powerful proteases secreted by endothelial cells and others during cardiovascular disease and diabetes. Their fibrinolytic activity and putative role in hemostasis has not been well described. METHODS: Fibrin gels were polymerized and incubated with recombinant human cathepsins (cat) K, L, or S, or plasmin, for dose-dependent and time-dependent studies. Dissolution of fibrin gels was imaged. SDS-PAGE was used to resolve cleaved fragments released from fibrin gels and remnant insoluble fibrin gel that was solubilized prior to electrophoresis to assess fibrin α, ß, and γ polypeptide hydrolysis by cathepsins. Multiplex cathepsin zymography determined active amounts of cathepsins remaining. RESULTS: There was significant loss of α and ß fibrin polypeptides after incubation with cathepsins, with catS completely dissolving fibrin gel by 24 h. Binding to fibrin stabilized catL active time; it associated with cleaved fibrin fragments of multiple sizes. This was not observed for catK or S. CatS also remained active for longer times during fibrin incubation, but its association/binding did not withstand SDS-PAGE preparation. CONCLUSIONS: Human cathepsins K, L, and S are fibrinolytic, and specifically can degrade the α and ß fibrin polypeptide chains, generating fragments unique from plasmin. GENERAL SIGNIFICANCE: Demonstration of cathepsins K, L, and S fibrinolytic activity leads to further investigation of contributory roles in disrupting vascular hemostasis, or breakdown of fibrin-based engineered vascular constructs where non-plasmin mediated fibrinolysis must be considered.

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.

ELECTROMAGNETICALLY INDUCED DISTORTION OF A FIBRIN MATRIX WITH EMBEDDED MICROPARTICLES.

Blood clots occur in the human body when they are required to prevent bleeding. In pathological states such as diabetes and sickle cell disease, blood clots can also form undesirably due to hypercoagulable plasma conditions. With the continued effort in developing fibrin therapies for potential life-saving solutions, more mechanical modeling is needed to understand the properties of fibrin structures with inclusions. In this study, a fibrin matrix embedded with magnetic micro particles (MMPs) was subjected to a magnetic field to determine the magnitude of the required force to create plastic deformation within the fibrin clot. Using finite element (FE) analysis, we estimated the magnetic force from an electromagnet at a sample space located approximately 3 cm away from the coil center. This electromagnetic force coupled with gravity was applied on a fibrin mechanical system with MMPs to calculate the stresses and displacements. Using appropriate coil parameters, it was determined that application of a magnetic field of 730 A/m on the fibrin surface was necessary to achieve an electromagnetic force of 36 nN (to engender plastic deformation).

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.

Molecular dynamics simulations indicate that deoxyhemoglobin, oxyhemoglobin, carboxyhemoglobin, and glycated hemoglobin under compression and shear exhibit an anisotropic mechanical behavior.

We developed a new mechanical model for determining the compression and shear mechanical behavior of four different hemoglobin structures. Previous studies on hemoglobin structures have focused primarily on overall mechanical behavior; however, this study investigates the mechanical behavior of hemoglobin, a major constituent of red blood cells, using steered molecular dynamics (SMD) simulations to obtain anisotropic mechanical behavior under compression and shear loading conditions. Four different configurations of hemoglobin molecules were considered: deoxyhemoglobin (deoxyHb), oxyhemoglobin (HbO2), carboxyhemoglobin (HbCO), and glycated hemoglobin (HbA1C). The SMD simulations were performed on the hemoglobin variants to estimate their unidirectional stiffness and shear stiffness. Although hemoglobin is structurally denoted as a globular protein due to its spherical shape and secondary structure, our simulation results show a significant variation in the mechanical strength in different directions (anisotropy) and also a strength variation among the four different hemoglobin configurations studied. The glycated hemoglobin molecule possesses an overall higher compressive mechanical stiffness and shear stiffness when compared to deoxyhemoglobin, oxyhemoglobin, and carboxyhemoglobin molecules. Further results from the models indicate that the hemoglobin structures studied possess a soft outer shell and a stiff core based on stiffness.

Computational predictions of cysteine cathepsin-mediated fibrinogen proteolysis.

Fibrin clot formation is a proteolytic cascade of events with thrombin and plasmin identified as the main proteases cleaving fibrinogen precursor, and the fibrin polymer, respectively. Other proteases may be involved directly in fibrin(ogen) cleavage, clot formation, and resolution, or in the degradation of fibrin-based scaffolds emerging as useful tools for tissue engineered constructs. Here, cysteine cathepsins are investigated for their putative ability to hydrolyze fibrinogen, since they are potent proteases, first identified in lysosomal protein degradation and known to participate in extracellular proteolysis. To further explore this, we used two independent computational technqiues, molecular docking and bioinformatics sequence analysis (PACMANS), to predict potential binding interactions and sites of hydrolysis between cathepsins K, L, and S and fibrinogen. By comparing the results from these two objective, computational methods, it was determined that cathepsins K, L, and S do bind and cleave fibrinogen α, ß, and γ chains at similar and unique sites. These differences were visualized experimentally by the unique cleaved fibrinogen banding patterns after incubation with each of the cathepsins, separately. In conclusion, human cysteine cathepsins K, L, and S are a new class of proteases that should be considered during fibrin(ogen) degradation studies both for disease processes where coagulation is a concern, and also in the implementation and design of bioengineered systems.

Computational imaging analysis of glycated fibrin gels reveals aggregated and anisotropic structures.

In this article, a computational imaging analysis method is presented for the evaluation of aggregation and anisotropy in both native (unglycated) and glycated fibrin matrix structures. The imaging analysis was used to test the hypothesis that glycated fibrin structures are more aggregated and anisotropic than unglycated (native) fibrin structures. Glycation of fibrinogen, and subsequently fibrin, occurs under normal physiological conditions; however, excess glycation due to disease states such as diabetes can disrupt the fibrin matrix and cause an abnormal structure and function. Studies that elucidate morphological changes in glucose incubated fibrin matrices are necessary to better understand thrombosis, which occurs due to hypercoagulable conditions. In this study, imaging algorithms were designed for the determination of aggregation of fibrin fibers within a matrix as well as preferential orientation (anisotropy) due to glycation. The results showed that glycated fibrin structures displayed an overall higher degree of aggregation and anisotropy as compared to unglycated fibrin structures. However, for glycated fibrin matrices that were polymerized utilizing extended incubation periods representative of physiological plasma glucose conditions, the results showed that fibrin aggregation and anisotropy decreased when compared to unglycated matrices. The algorithms showed that incorporation of the crosslinking agent FXIII into the fibrin matrix was shown to decrease both aggregation and anisotropy. © 2017 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 105A: 2191-2198, 2017.

Computational imaging analysis of fibrin matrices with the inclusion of erythrocytes from homozygous SS blood reveals agglomerated and amorphous structures.

Sickle cell disease is a single point mutation disease that is known to alter the coagulation system, leading to hypercoagulable plasma conditions. These hypercoagulable conditions can lead to complications in the vasculature, caused by fibrin clots that form undesirably. There is a need to understand the morphology and structure of fibrin clots from patients with sickle cell disease, as this could lead to further discovery of treatments and life-saving therapies. In this work, a computational imaging analysis method is presented to evaluate fibrin agglomeration in the presence of erythrocytes (RBCs) homozygous for the sickle cell mutation (SS). Numerical algorithms were used to determine agglomeration of fibrin fibers within a matrix with SS RBCs to test the hypothesis that fibrin matrices with the inclusion of SS RBCs possess a more agglomerated structure than native fibrin matrices with AA RBCs. The numerical results showed that fibrin structures with SS RBCs displayed an overall higher degree of agglomeration as compared to native fibrin structures. The computational algorithm was also used to evaluate fibrin fiber overlap (aggregation) and anisotropy (orientation) in normal fibrin matrices compared to fibrin matrices polymerized around SS RBCs; however, there was no statistical difference. Ultrasound measurements of stiffness revealed rigid RBCs in the case of samples derived from homozygous SS blood, and densely evolving matrices, when compared to normal fibrin with the inclusion of AA RBCs. An agglomeration model is suggested to quantify the fibrin aggregation/clustering near RBCs for both normal fibrin matrices and for the altered structures. The results of this work are important in the sense that the understanding of aggregation and morphology in fibrin clots with incorporation of RBCs from persons living with sickle cell anemia may elucidate the complexities of comorbidities and other disease complications.

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.

Experimental mechanics of magnetic microparticle-induced strain on fibrin clots.

In this study, a novel technique was developed in which magnetic microparticles (MMPs) and quantum dots (QDs) were successfully incorporated into fibrin clots. The MMPs were added at concentrations of 0.1 and 1 wt % of the fibrin content in an effort to determine if a magnetic field could be used to mechanically stretch the fibrin network, simulating how cells may invade a network. The QDs were added at a dilute concentration of 0.1 wt % to determine if the mechanical properties of the fibrin network would be significantly altered and to ascertain if the overall stretch on the network could be observed. Based on strain sweep and frequency sweep rheological analysis, it was determined that both QDs and MMPs incorporated into fibrin networks at 0.1 wt % caused irreversible plastic deformation in the fibrin clot sample, as evidenced by a precipitous decline in the storage modulus value.

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

We tested what to our knowledge is a new computational model for fibrin fiber mechanical behavior. The model is composed of three distinct elements: the folded fibrinogen core as seen in the crystal structure, the unstructured α-C connector, and the partially folded α-C domain. Previous studies have highlighted the importance of all three regions and how they may contribute to fibrin fiber stress-strain behavior. Yet no molecular model has been computationally tested that takes into account the individual contributions of all these regions. Constant velocity, steered molecular dynamics studies at 0.025 Å/ps were conducted on the folded fibrinogen core and the α-C domain to determine their force-displacement behavior. A wormlike chain model with a persistence length of 0.8 nm (Kuhn length = 1.6 nm) was used to model the mechanical behavior of the unfolded α-C connector. The three components were combined to calculate the total stress-strain response, which was then compared to experimental data. The results show that the three-component model successfully captures the experimentally determined stress-strain behavior of fibrin fibers. The model evinces the key contribution of the α-C domains to fibrin fiber stress-strain behavior. However, conversion of the α-helical coiled coils to ß-strands, and partial unfolding of the protein, may also contribute.

Fatigue Response and Constitutive Behavior Modeling of Poly(ethylene terephthalate) Unreinforced and Nanocomposite Fibers Using Genetic Neural Networks.

The constitutive behavior of poly(ethylene terephthalate) (PET) unreinforced (control) and PET fibers reinforced with 5 wt% vapor-grown carbon nanofibers (VGCNFs) under uniaxial tension and subsequent to fatigue loading has been evaluated utilizing various analytical models. Two types of fatigue tests were performed: (1) Long cycle fatigue at 50 Hz (glassy fatigue) to evaluate fatigue resistance and (2) fatigue at 5 Hz (rubbery fatigue) to evaluate residual strength performance. The long cycle fatigue results at 50 Hz indicated that the PET-VGCNF sample exhibited an increased fatigue resistance of almost two orders of magnitude when compared to the PET unreinforced filament. The results of the fatigue tests at 5 Hz indicated that the constitutive response of both the PET control and PET-VGCNF samples changed subsequent to fatigue loading. The large deformation uniaxial constitutive response of the PET and PET-VGCNF fibers was modeled utilizing genetic-algorithm (GA) based training neural networks. The results showed that the large deformation uniaxial tension constitutive behavior of both PET unreinforced and PET-VGCNF samples with and without prior fatigue can be represented with good accuracy utilizing neural networks trained via genetic-based backpropagation algorithms, once the appropriate post-fatigue constitutive behavior is utilized. Experimental data of uniaxial tensile tests and experimental postfatigue constitutive data have been implemented into the networks for adequate training. The fatigue tests were conducted under tension-tension fatigue conditions with variations in the stress ratio (R), maximum stress (σmax), number of cycles (N), and the residual creep strain (εR).