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

Decoding thrombosis through code: a review of computational models

From the molecular level up to a blood vessel, thrombosis and hemostasis involves many interconnected biochemical and biophysical processes over a wide range of length and time scales. Computational modeling has gained eminence in offering insights into these processes beyond what can be obtained from in vitro or in vivo experiments, or clinical measurements. The multiscale and multiphysics nature of thrombosis has inspired a wide range of modeling approaches that aim to address how a thrombus forms and dismantles. Here, we review recent advances in computational modeling with a focus on platelet-based thrombosis. We attempt to summarize the diverse range of modeling efforts straddling the wide-spectrum of physical phenomena, length scales, and time scales; highlighting key advancements and insights from existing studies. Potential information gleaned from models is discussed, ranging from identification of thrombus-prone regions in patient-specific vasculature to modeling thrombus deformation and embolization in response to fluid forces. Furthermore, we highlight several limitations of current models, future directions in the field, and opportunities for clinical translation, to illustrate the state-of-the-art. There are a plethora of opportunity areas for which models can be expanded, ranging from topics of thromboinflammation to platelet production and clearance. Through successes demonstrated in existing studies described here, as well as continued advancements in computational methodologies and computer processing speeds and memory, in silico investigations in thrombosis are poised to bring about significant knowledge growth in the years to come.

PEG-fibrin conjugates: the PEG impact on the polymerization dynamics

Fibrin and its modifications, particularly those with functionalized polyethylene glycol (PEG), remain highly attractive as a biomaterial in drug delivery and regenerative medicine. Despite the extensive knowledge of fibrinogenesis, there is little information on the processes occurring after its modification. Previously, we found structural differences between native fibrin and its conjugates with PEG that allows us to hypothesize that a combination of methods such as terahertz (THz) pulsed spectroscopy and rheology may contribute to the characterization of gelation and reveal the effect of PEG on the polymerization dynamics. Compared to native fibrin, PEGylated fibrins had a homogenously soft surface; PEGylation also led to a significant decrease in the gelation time: from 42.75 min for native fibrin to 31.26 min and 35.09 min for 5 : 1 and 10 : 1 PEGylated fibrin, respectively. It is worth noting that THz pulsed spectroscopy makes it possible to reliably investigate only the polymerization process itself, while it does not allow us to observe statistically significant differences between the distinct PEGylated fibrin gels. The polymerization time constant of native fibrin measured by THz pulsed spectroscopy was 14.4 ± 2.8 min. However, it could not be calculated for PEGylated fibrin because the structural changes were too rapid. These results, together with those previously reported, led us to speculate that PEG-fibrin conjugates formed homogenously distributed highly water-shelled aggregates without bundling compared to native fibrin, ensuring rapid gelation and stabilization of the system without increasing its complexity.

Towards understanding the effect of fibrinogen interactions on fibrin gel structure

Fibrin gelation involves the enzymatic conversion of the plasma protein fibrinogen to fibrin monomers which then polymerize to form the gel that is a major structural component of a blood clot. Because fibrinogen provides the material from which fibrin is made, it is generally regarded as promoting the gelation process. However, fibrinogen can bind to a site on a fibrin oligomer, preventing another fibrin oligomer from binding there, thus slowing the polymerization process. "Soluble fibrin oligomers," which are mixtures of fibrin and fibrinogen, are found in the blood plasma and serve as biomarkers for various clotting disorders, so understanding the interplay between fibrin and fibrinogen during fibrin polymerization may have medical importance. We present a kinetic gelation model of fibrin polymerization which accounts for the dual and antagonistic roles of fibrinogen. It builds on our earlier model of fibrin polymerization that proposed a novel mechanism for branch formation, which is a necessary component of gelation. This previous model captured salient experimental observations regarding the determinants of the structure of the gel, but did not include fibrinogen binding. Here, we add to that model reactions between fibrinogen and fibrin, so oligomers are now mixtures of fibrin and fibrinogen, and characterizing their dynamics leads to equations of substantially greater complexity than previously. Using a moment generating function approach, we derive a closed system of moment equations and we track their dynamics until the finite time blow-up of specific second moments indicates that a gel has formed. In simulations begun with an initial mixture of fibrin and fibrinogen monomers, a sufficiently high relative concentration of fibrinogen prevents gelation; the critical concentration increases with the branch formation rate. In simulations begun with only fibrinogen monomers that are converted to fibrin at a specified rate, the rates of conversion, fibrinogen binding to oligomers, and branch formation together determine whether a gel forms, how long it takes to form, and the structural properties of the gel that results.

Mathematical modeling to understand the role of bivalent thrombin-fibrin binding during polymerization

Thrombin is an enzyme produced during blood coagulation that is crucial to the formation of a stable clot. Thrombin cleaves soluble fibrinogen into fibrin, which polymerizes and forms an insoluble, stabilizing gel around the growing clot. A small fraction of circulating fibrinogen is the variant γA/γ′, which has been associated with high-affinity thrombin binding and implicated as a risk factor for myocardial infarctions, deep vein thrombosis, and coronary artery disease. Thrombin is also known to be strongly sequestered by polymerized fibrin for extended periods of time in a way that is partially regulated by γA/γ′. However, the role of γA/γ′-thrombin interactions during fibrin polymerization is not fully understood. Here, we present a mathematical model of fibrin polymerization that considered the interactions between thrombin, fibrinogen, and fibrin, including those with γA/γ′. In our model, bivalent thrombin-fibrin binding greatly increased thrombin residency times and allowed for thrombin-trapping during fibrin polymerization. Results from the model showed that early in fibrin polymerization, γ′ binding to thrombin served to localize the thrombin to the fibrin(ogen), which effectively enhanced the enzymatic conversion of fibrinogen to fibrin. When all the fibrin was fully generated, however, the fibrin-thrombin binding persisted but the effect of fibrin on thrombin switched quickly to serve as a sink, essentially removing all free thrombin from the system. This dual role for γ′-thrombin binding during polymerization led to a paradoxical decrease in trapped thrombin as the amount of γ′ was increased. The model highlighted biochemical and biophysical roles for fibrin-thrombin interactions during polymerization and agreed well with experimental observations.

Effect of Thrombin and Incubation Time on Porcine Whole Blood Clot Elasticity and Recombinant Tissue Plasminogen Activator Susceptibility

Deep vein thrombosis is a major source of morbidity and mortality worldwide. Catheter-directed thrombolytics are the frontline approach for vessel recanalization, though fibrinolytic efficacy is limited for stiff, chronic thrombi. Although thrombin has been used in preclinical models to induce thrombosis, the effect on lytic susceptibility and clot stiffness is unknown. The goal of this study was to explore the effect of bovine thrombin concentration and incubation time on lytic susceptibility and stiffness of porcine whole blood clots in vitro. Porcine whole blood was allowed to coagulate at 37°C in glass pipets primed with 2.5 or 15 U/mL thrombin for 15 to 120 min. Lytic susceptibility to recombinant tissue plasminogen activator (rt-PA, alteplase) over a range of concentrations (3.15-107.00 µg/mL) was evaluated using percentage clot mass loss. The Young's moduli and degrees of retraction of the clots were estimated using ultrasound-based single-track-location shear wave elasticity and B-mode imaging, respectively. Percentage mass loss decreased and clot stiffness increased with the incubation period. Clots formed with 15 U/mL and incubated for 2 h exhibited properties similar to those of highly retracted clots: Young's modulus of 2.39 ± 0.36 kPa and percentage mass loss of 8.69 ± 2.72% when exposed to 3.15 µg/mL rt-PA. The histological differences between thrombin-induced porcine whole blood clots in vitro and thrombi in vivo are described.

Mesopore Controls the Responses of Blood Clot-Immune Complex via Modulating Fibrin Network

Formation of blood clots, particularly the fibrin network and fibrin network-mediated early inflammatory responses, plays a critical role in determining the eventual tissue repair or regeneration following an injury. Owing to the potential role of fibrin network in mediating clot-immune responses, it is of great importance to determine whether clot-immune responses can be regulated via modulating the parameters of fibrin network. Since the diameter of D-terminal of a fibrinogen molecule is 9 nm, four different pore sizes (2, 8, 14, and 20 nm) are rationally selected to design mesoporous silica to control the fibrinogen adsorption and modulate the subsequent fibrin formation process. The fiber becomes thinner and the contact area with macrophages decreases when the pore diameters of mesoporous silica are greater than 9 nm. Importantly, these thinner fibers grown in pores with diameters larger than 9 nm inhibit the M1-polorazation of macrophages and reduce the productions of pro-inflammatory cytokines and chemokines by macrophages. These thinner fibers reduce inflammation of macrophages through a potential signaling pathway of cell adhesion-cytoskeleton assembly-inflammatory responses. Thus, the successful regulation of the clot-immune responses via tuning of the mesoporous pore sizes indicates the feasibility of developing advanced clot-immune regulatory materials.

Development of a mesoscopic framework spanning nanoscale protofibril dynamics to macro-scale fibrin clot formation

Thrombi form a micro-scale fibrin network consisting of an interlinked structure of nanoscale protofibrils, resulting in haemostasis. It is theorized that the mechanical effect of the fibrin clot is caused by the polymeric protofibrils between crosslinks, or to their dynamics on a nanoscale order. Despite a number of studies, however, it is still unknown, how the nanoscale protofibril dynamics affect the formation of the macro-scale fibrin clot and thus its mechanical properties. A mesoscopic framework would be useful to tackle this multi-scale problem, but it has not yet been established. We thus propose a minimal mesoscopic model for protofibrils based on Brownian dynamics, and performed numerical simulations of protofibril aggregation. We also performed stretch tests of polymeric protofibrils to quantify the elasticity of fibrin clots. Our model results successfully captured the conformational properties of aggregated protofibrils, e.g., strain-hardening response. Furthermore, the results suggest that the bending stiffness of individual protofibrils increases to resist extension.

Investigating the two regimes of fibrin clot lysis: an experimental and computational approach

It has been observed in vitro that complete clot lysis is generally preceded by a slow phase of lysis during which the degradation seems to be inefficient. However, this slow regime was merely noticed, but not yet quantitatively discussed. In our experiments, we observed that the lysis ubiquitously occurred in two distinct regimes, a slow and a fast lysis regime. We quantified extensively the duration of these regimes for a wide spectrum of experimental conditions and found that on average, the slow regime lasts longer than the fast one, meaning that during most of the process, the lysis is ineffective. We proposed a computational model in which the properties of the binding of the proteins change during the lysis: first, the biochemical reactions take place at the surface of the fibrin fibers, then in the bulk, resulting in the observed fast lysis regime. This simple hypothesis appeared to be sufficient to reproduce with a great accuracy the lysis profiles obtained experimentally.

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 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.