Fibrin polymerization simulation using a reactive dissipative particle dynamics method

Clots reveal anomalous elastic behavior of fiber networks

The adaptive mechanical properties of soft and fibrous biological materials are relevant to their functionality. The emergence of the macroscopic response of these materials to external stress and intrinsic cell traction from local deformations of their structural components is not well understood. Here, we investigate the nonlinear elastic behavior of blood clots by combining microscopy, rheology, and an elastic network model that incorporates the stretching, bending, and buckling of constituent fibrin fibers. By inhibiting fibrin cross-linking in blood clots, we observe an anomalous softening regime in the macroscopic shear response as well as a reduction in platelet-induced clot contractility. Our model explains these observations from two independent macroscopic measurements in a unified manner, through a single mechanical parameter, the bending stiffness of individual fibers. Supported by experimental evidence, our mechanics-based model provides a framework for predicting and comprehending the nonlinear elastic behavior of blood clots and other active biopolymer networks in general.

A simplified mesoscale 3D model for characterizing fibrinolysis under flow conditions

One of the routine clinical treatments to eliminate ischemic stroke thrombi is injecting a biochemical product into the patient's bloodstream, which breaks down the thrombi's fibrin fibers: intravenous or intravascular thrombolysis. However, this procedure is not without risk for the patient; the worst circumstances can cause a brain hemorrhage or embolism that can be fatal. Improvement in patient management drastically reduced these risks, and patients who benefited from thrombolysis soon after the onset of the stroke have a significantly better 3-month prognosis, but treatment success is highly variable. The causes of this variability remain unclear, and it is likely that some fundamental aspects still require thorough investigations. For that reason, we conducted in vitro flow-driven fibrinolysis experiments to study pure fibrin thrombi breakdown in controlled conditions and observed that the lysis front evolved non-linearly in time. To understand these results, we developed an analytical 1D lysis model in which the thrombus is considered a porous medium. The lytic cascade is reduced to a second-order reaction involving fibrin and a surrogate pro-fibrinolytic agent. The model was able to reproduce the observed lysis evolution under the assumptions of constant fluid velocity and lysis occurring only at the front. For adding complexity, such as clot heterogeneity or complex flow conditions, we propose a 3-dimensional mesoscopic numerical model of blood flow and fibrinolysis, which validates the analytical model's results. Such a numerical model could help us better understand the spatial evolution of the thrombi breakdown, extract the most relevant physiological parameters to lysis efficiency, and possibly explain the failure of the clinical treatment. These findings suggest that even though real-world fibrinolysis is a complex biological process, a simplified model can recover the main features of lysis evolution.

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.

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.