Blood clot formation under flow: the importance of factor XI depends strongly on platelet count

Integrating biomarkers for hemostatic disorders into computational models of blood clot formation: A systematic review

In the pursuit of personalized medicine, there is a growing demand for computational models with parameters that are easily obtainable to accelerate the development of potential solutions. Blood tests, owing to their affordability, accessibility, and routine use in healthcare, offer valuable biomarkers for assessing hemostatic balance in thrombotic and bleeding disorders. Incorporating these biomarkers into computational models of blood coagulation is crucial for creating patient-specific models, which allow for the analysis of the influence of these biomarkers on clot formation. This systematic review aims to examine how clinically relevant biomarkers are integrated into computational models of blood clot formation, thereby advancing discussions on integration methodologies, identifying current gaps, and recommending future research directions. A systematic review was conducted following the PRISMA protocol, focusing on ten clinically significant biomarkers associated with hemostatic disorders: D-dimer, fibrinogen, Von Willebrand factor, factor Ⅷ, P-selectin, prothrombin time (PT), activated partial thromboplastin time (APTT), antithrombin Ⅲ, protein C, and protein S. By utilizing this set of biomarkers, this review underscores their integration into computational models and emphasizes their integration in the context of venous thromboembolism and hemophilia. Eligibility criteria included mathematical models of thrombin generation, blood clotting, or fibrin formation under flow, incorporating at least one of these biomarkers. A total of 53 articles were included in this review. Results indicate that commonly used biomarkers such as D-dimer, PT, and APTT are rarely and superficially integrated into computational blood coagulation models. Additionally, the kinetic parameters governing the dynamics of blood clot formation demonstrated significant variability across studies, with discrepancies of up to 1, 000-fold. This review highlights a critical gap in the availability of computational models based on phenomenological or first-principles approaches that effectively incorporate affordable and routinely used clinical test results for predicting blood coagulation. This hinders the development of practical tools for clinical application, as current mathematical models often fail to consider precise, patient-specific values. This limitation is especially pronounced in patients with conditions such as hemophilia, protein C and S deficiencies, or antithrombin deficiency. Addressing these challenges by developing patient-specific models that account for kinetic variability is crucial for advancing personalized medicine in the field of hemostasis.

The foundation for investigating factor XI as a target for inhibition in human cardiovascular disease

Anticoagulant therapy is a mainstay in the management of patients with cardiovascular disease and related conditions characterized by a heightened risk for thrombosis. Acute coronary syndrome, chronic coronary syndrome, ischemic stroke, and atrial fibrillation are the most common. In addition to their proclivity for thrombosis, each of these four conditions is also characterized by local and systemic inflammation, endothelial/endocardial injury and dysfunction, oxidative stress, impaired tissue-level reparative capabilities, and immune dysregulation that plays a critical role in linking molecular events, environmental triggers, and phenotypic expressions. Knowing that cardiovascular disease and thrombosis are complex and dynamic, can the scientific community identify a common pathway or specific point of interface susceptible to pharmacological inhibition or alteration that is likely to be safe and effective? The contact factors of coagulation may represent the proverbial "sweet spot" and are worthy of investigation. The following review provides a summary of the fundamental biochemistry of factor XI, its biological activity in thrombosis, inflammation, and angiogenesis, new targeting drugs, and a pragmatic approach to managing hemostatic requirements in clinical trials and possibly day-to-day patient care in the future.

A new look at TFPI inhibition of factor X activation

Blood coagulation is a vital physiological process involving a complex network of biochemical reactions, which converge to form a blood clot that repairs vascular injury. This process unfolds in three phases: initiation, amplification, and propagation, ultimately leading to thrombin formation. Coagulation begins when tissue factor (TF) is exposed on an injured vessel's wall. The first step is when activated factor VII (VIIa) in the plasma binds to TF, forming complex TF:VIIa, which activates factor X. Activated factor X (Xa) is necessary for coagulation, so the regulation of its activation is crucial. Tissue Factor Pathway Inhibitor (TFPI) is a critical regulator of the initiation phase as it inhibits the activation of factor X. While previous studies have proposed two pathways-direct and indirect binding-for TFPI's inhibitory role, the specific biochemical reactions and their rates remain ambiguous. Many existing mathematical models only assume an indirect pathway, which may be less effective under physiological flow conditions. In this study, we revisit datasets from two experiments focused on activated factor X formation in the presence of TFPI. We employ an adaptive Metropolis method for parameter estimation to reinvestigate a previously proposed biochemical scheme and corresponding rates for both inhibition pathways. Our findings show that both pathways are essential to replicate the static experimental results. Previous studies have suggested that flow itself makes a significant contribution to the inhibition of factor X activation. We added flow to this model with our estimated parameters to determine the contribution of the two inhibition pathways under these conditions. We found that direct binding of TFPI is necessary for inhibition under flow. The indirect pathway has a weaker inhibitory effect due to removal of solution phase inhibitory complexes by flow.

Mathematical modeling identifies clotting factor combinations that modify thrombin generation in normal and factor VIII-, IX-, or XI-deficient blood

Background

In healthy individuals, plasma levels of clotting proteins naturally vary within a range of 50% to 150% of their mean values. We do not know how these variations modify thrombin generation.

Objectives

To assess the impact of protein level variations on simulated thrombin generation in normal and factor (F)VIII-, FIX-, or FXI-deficient blood.

Methods

We used a mathematical model of flow-mediated coagulation to simulate thrombin generation with all possible combinations of clotting protein variations within the normal range and for various tissue factor levels. We selected, analyzed, and ranked combinations that enhanced thrombin generation compared with baseline.

Results

Protein variations most strongly affected thrombin generation at intermediate tissue factor levels. Low tissue factor levels prevented coagulation initiation, while high tissue factor levels always triggered thrombin generation. At intermediate levels, we identified protein variations that substantially modified thrombin generation. Low-normal FV shortened lag times and increased thrombin generation, whereas high-normal FV lengthened lag times and reduced thrombin generation. With severe FVIII and FIX deficiencies, low-normal tissue factor pathway inhibitor α and antithrombin amplified the effect of low-normal FV. For moderate FVIII and FIX deficiencies, high-normal tissue factor pathway inhibitor α and antithrombin enhanced the impact of high-normal FV in reducing thrombin production. In normal and FXI-deficient blood, high-normal FVIII and FIX significantly boosted thrombin generation.

Conclusion

Our mathematical model predicted how variations in clotting protein levels, within the normal range, could contribute to the variability of bleeding phenotypes observed with clotting factor deficiencies. Our study generated experimentally testable hypotheses that could aid in developing new therapies toward normal hemostasis.

Single molecule studies of dynamic platelet interactions with endothelial cells

A biotechnological platform consisting of two-color 3D super-resolution readout and a microfluidic system was developed to investigate platelet interaction with a layer of perfused endothelial cells under flow conditions. Platelet activation has been confirmed via CD62P clustering on the membrane and mitochondrial morphology of ECs at the single cell level were examined using 3D two-color single-molecule localization microscopy and classified applying machine learning. To compare binding of activated platelets to intact or stressed ECs, a femtosecond laser was used to induced damage to single ECs within the perfused endothelial layer. We observed that activated platelets bound to the perfused ECs layer preferentially in the proximity to single stressed ECs. Platelets activated under flow were ∼6 times larger compared to activated ones under static conditions. The CD62P expression indicated more CD62P proteins on membrane of dynamically activated platelets, with a tendency to higher densities at the platelet/EC interface. Platelets activated under static conditions showed a less pronounced CD62P top/bottom asymmetry. The clustering of CD62P in the platelet membrane differs depending on the activation conditions. Our results confirm that nanoscopic analysis using two-color 3D super-resolution technology can be used to assess platelet interaction with a stressed endothelium under dynamic conditions.

An adjoint-based method for the computation of gradients in coagulation schemes

An adjoint-based methodology is proposed to compute the gradient of the outcomes of mathematical models for the coagulation cascade. The method is first exposed and validated by considering a simple, analytically tractable case involving only 3 species. Its potential is further illustrated by considering a detailed model for the extrinsic pathway involving 34 chemical species interacting through 45 chemical reactions and for which the gradient of Endogeneous Thrombin Potential, clotting time, maximum rate and peak value of thrombin with respect to the initial concentrations and reactions rates are computed. It is shown that the method produces gradients estimates that are fully consistent with the finite differences approximation used so far in the literature, but at a much lower computational cost.

A model of fluid-structure and biochemical interactions for applications to subclinical leaflet thrombosis

Subclinical leaflet thrombosis (SLT) is a potentially serious complication of aortic valve replacement with a bioprosthetic valve in which blood clots form on the replacement valve. SLT is associated with increased risk of transient ischemic attacks and strokes and can progress to clinical leaflet thrombosis. SLT following aortic valve replacement also may be related to subsequent structural valve deterioration, which can impair the durability of the valve replacement. Because of the difficulty in clinical imaging of SLT, models are needed to determine the mechanisms of SLT and could eventually predict which patients will develop SLT. To this end, we develop methods to simulate leaflet thrombosis that combine fluid-structure interaction and a simplified thrombosis model that allows for deposition along the moving leaflets. Additionally, this model can be adapted to model deposition or absorption along other moving boundaries. We present convergence results and quantify the model's ability to realize changes in valve opening and pressures. These new approaches are an important advancement in our tools for modeling thrombosis because they incorporate both adhesion to the surface of the moving leaflets and feedback to the fluid-structure interaction.

Biomechanical activation of blood platelets via adhesion to von Willebrand factor studied with mesoscopic simulations

Platelet adhesion and activation are essential initial processes of arterial and microvascular hemostasis, where high hydrodynamic forces from the bloodflow impede coagulation. The process relies on von Willebrand factor (VWF)-a linear multimeric protein of blood plasma plays a pivotal role in mechanochemical regulation of shear-induced platelet aggregation (SIPA). Adhesive interactions between VWF and glycoprotein receptors GPIb are crucial for platelet recruitment under high shear stress in fluid. Recent advances in experimental studies revealed that mechanical tension on the extracellular part of GPIb may trigger a cascade of biochemical reactions in platelets leading to activation of integrins [Formula: see text] (also known as GPIIb/IIIa) and strengthening of the adhesion. The present paper is aimed at investigation of this process by three-dimensional computer simulations of platelet adhesion to surface-grafted VWF multimers in pressure-driven flow of platelet-rich plasma. The simulations demonstrate that GPIb-mediated mechanotransduction is a feasible way of platelet activation and stabilization of platelet aggregates under high shear stress. Quantitative understanding of mechanochemical processes involved in SIPA would potentially promote the discovery of new anti-platelet medication and the development of multiscale numerical models of platelet thrombosis and hemostasis.

Inhibition of platelet-surface-bound proteins during coagulation under flow I: TFPI

Blood coagulation is a self-repair process regulated by activated platelet surfaces, clotting factors, and inhibitors. Tissue factor pathway inhibitor (TFPI) is one such inhibitor, well known for its inhibitory action on the active enzyme complex comprising tissue factor (TF) and activated clotting factor VII. This complex forms when TF embedded in the blood vessel wall is exposed by injury and initiates coagulation. A different role for TFPI, independent of TF:VIIa, has recently been discovered whereby TFPI binds a partially cleaved form of clotting factor V (FV-h) and impedes thrombin generation on activated platelet surfaces. We hypothesized that this TF-independent inhibitory mechanism on platelet surfaces would be a more effective platform for TFPI than the TF-dependent one. We examined the effects of this mechanism on thrombin generation by including the relevant biochemical reactions into our previously validated mathematical model. Additionally, we included the ability of TFPI to bind directly to and inhibit platelet-bound FXa. The new model was sensitive to TFPI levels and, under some conditions, TFPI could completely shut down thrombin generation. This sensitivity was due entirely to the surface-mediated inhibitory reactions. The addition of the new TFPI reactions increased the threshold level of TF needed to elicit a strong thrombin response under flow, but the concentration of thrombin achieved, if there was a response, was unchanged. Interestingly, we found that direct binding of TFPI to platelet-bound FXa had a greater anticoagulant effect than did TFPI binding to FV-h alone, but that the greatest effects occurred if both reactions were at play. The model includes activated platelets' release of FV species, and we explored the impact of varying the FV/FV-h composition of the releasate. We found that reducing the zymogen FV fraction of this pool, and thus increasing the fraction that is FV-h, led to acceleration of thrombin generation.

Inhibition of platelet-surface-bound proteins during coagulation under flow II: Antithrombin and heparin

Blood coagulation is a self-repair process regulated by activated platelet surfaces, clotting factors, and inhibitors. Antithrombin (AT) is one such inhibitor that impedes coagulation by targeting and inactivating several key coagulation enzymes. The effect of AT is greatly enhanced in the presence of heparin, a common anticoagulant drug. When heparin binds to AT, it either bridges with the target enzyme or induces allosteric changes in AT leading to more favorable binding with the target enzyme. AT inhibition of fluid-phase enzymes caused little suppression of thrombin generation in our previous mathematical models of blood coagulation under flow. This is because in that model, flow itself was a greater inhibitor of the fluid-phase enzymes than AT. From clinical observations, it is clear that AT and heparin should have strong inhibitory effects on thrombin generation, and thus we hypothesized that AT could be inhibiting enzymes bound to activated platelet surfaces that are not subject to being washed away by flow. We extended our mathematical model to include the relevant reactions of AT inhibition at the activated platelet surfaces as well as those for unfractionated heparin and a low molecular weight heparin. Our results show that AT alone is only an effective inhibitor at low tissue factor densities, but in the presence of heparin, it can greatly alter, and in some cases shut down, thrombin generation. Additionally, we studied each target enzyme separately and found that inactivation of no single enzyme could substantially suppress thrombin generation.

Association of FXI activity with thrombo-inflammation, extracellular matrix, lipid metabolism and apoptosis in venous thrombosis

Animal experiments and early phase human trials suggest that inhibition of factor XIa (FXIa) safely prevents venous thromboembolism (VTE), and specific murine models of sepsis have shown potential efficacy in alleviating cytokine storm. These latter findings support the role of FXI beyond coagulation. Here, we combine targeted proteomics, machine learning and bioinformatics, to discover associations between FXI activity (FXI:C) and the plasma protein profile of patients with VTE. FXI:C was measured with a modified activated partial prothrombin time (APTT) clotting time assay. Proximity extension assay-based protein profiling was performed on plasma collected from subjects from the Genotyping and Molecular Phenotyping of Venous Thromboembolism (GMP-VTE) Project, collected during an acute VTE event (n = 549) and 12-months after (n = 187). Among 444 proteins investigated, N = 21 and N = 66 were associated with FXI:C during the acute VTE event and at 12 months follow-up, respectively. Seven proteins were identified as FXI:C-associated at both time points. These FXI-related proteins were enriched in immune pathways related to causes of thrombo-inflammation, extracellular matrix interaction, lipid metabolism, and apoptosis. The results of this study offer important new avenues for future research into the multiple properties of FXI, which are of high clinical interest given the current development of FXI inhibitors.

Sensitivity analysis of a reduced model of thrombosis under flow: Roles of Factor IX, Factor XI, and γ'-Fibrin

A highly reduced extrinsic pathway coagulation model (8 ODEs) under flow considered a thin 15-micron platelet layer where transport limitations were largely negligible (except for fibrinogen) and where cofactors (FVIIa, FV, FVIII) were not rate-limiting. By including thrombin feedback activation of FXI and the antithrombin-I activities of fibrin, the model accurately simulated measured fibrin formation and thrombin fluxes. Using this reduced model, we conducted 10,000 Monte Carlo (MC) simulations for ±50% variation of 5 plasma zymogens and 2 fibrin binding sites for thrombin. A sensitivity analysis of zymogen concentrations indicated that FIX activity most influenced thrombin generation, a result expected from hemophilia A and B. Averaging all MC simulations confirmed both the mean and standard deviation of measured fibrin generation on 1 tissue factor (TF) molecule per μm2. Across all simulations, free thrombin in the layer ranged from 20 to 300 nM (mean: 50 nM). The top 2% of simulations that produced maximal fibrin were dominated by conditions with low antithrombin-I activity (decreased weak and strong sites) and high FIX concentration. In contrast, the bottom 2% of simulations that produced minimal fibrin were dominated by low FIX and FX. The percent reduction of fibrin by an ideal FXIa inhibitor (FXI = 0) ranged from 71% fibrin reduction in the top 2% of MC simulations to only 34% fibrin reduction in the bottom 2% of MC simulations. Thus, the antithrombotic potency of FXIa inhibitors may vary depending on normal ranges of zymogen concentrations. This reduced model allowed efficient multivariable sensitivity analysis.

Remote Spatiotemporal Control of a Magnetic and Electroconductive Hydrogel Network via Magnetic Fields for Soft Electronic Applications

Multifunctional hydrogels are a class of materials offering new opportunities for interfacing living organisms with machines due to their mechanical compliance, biocompatibility, and capacity to be triggered by external stimuli. Here, we report a dual magnetic- and electric-stimuli-responsive hydrogel with the capacity to be disassembled and reassembled up to three times through reversible cross-links. This allows its use as an electronic device (e.g., temperature sensor) in the cross-linked state and spatiotemporal control through narrow channels in the disassembled state via the application of magnetic fields, followed by reassembly. The hydrogel consists of an interpenetrated polymer network of alginate (Alg) and poly(3,4-ethylenedioxythiophene) (PEDOT), which imparts mechanical and electrical properties, respectively. In addition, the incorporation of magnetite nanoparticles (Fe₃O₄ NPs) endows the hydrogel with magnetic properties. After structural, (electro)chemical, and physical characterization, we successfully performed dynamic and continuous transport of the hydrogel through disassembly, transporting the polymer-Fe₃O₄ NP aggregates toward a target using magnetic fields and its final reassembly to recover the multifunctional hydrogel in the cross-linked state. We also successfully tested the PEDOT/Alg/Fe₃O₄ NP hydrogel for temperature sensing and magnetic hyperthermia after various disassembly/re-cross-linking cycles. The present methodology can pave the way to a new generation of soft electronic devices with the capacity to be remotely transported.

The Art and Science of Building a Computational Model to Understand Hemostasis

Computational models of various facets of hemostasis and thrombosis have increased substantially in the last decade. These models have the potential to make predictions that can uncover new mechanisms within the complex dynamics of thrombus formation. However, these predictions are only as good as the data and assumptions they are built upon, and therefore model building requires intimate coupling with experiments. The objective of this article is to guide the reader through how a computational model is built and how it can inform and be refined by experiments. This is accomplished by answering six questions facing the model builder: (1) Why make a model? (2) What kind of model should be built? (3) How is the model built? (4) Is the model a “good” model? (5) Do we believe the model? (6) Is the model useful? These questions are answered in the context of a model of thrombus formation that has been successfully applied to understanding the interplay between blood flow, platelet deposition, and coagulation and in identifying potential modifiers of thrombin generation in hemophilia A.

A MATHEMATICAL MODEL OF PLATELET AGGREGATION IN AN EXTRAVASCULAR INJURY UNDER FLOW

We present the first mathematical model of flow-mediated primary hemostasis in an extravascular injury which can track the process from initial deposition to occlusion. The model consists of a system of ordinary differential equations (ODEs) that describe platelet aggregation (adhesion and cohesion), soluble-agonist-dependent platelet activation, and the flow of blood through the injury. The formation of platelet aggregates increases resistance to flow through the injury, which is modeled using the Stokes-Brinkman equations. Data from analogous experimental (microfluidic flow) and partial differential equation models informed parameter values used in the ODE model description of platelet adhesion, cohesion, and activation. This model predicts injury occlusion under a range of flow and platelet activation conditions. Simulations testing the effects of shear and activation rates resulted in delayed occlusion and aggregate heterogeneity. These results validate our hypothesis that flow-mediated dilution of activating chemical adenosine diphosphate hinders aggregate development. This novel modeling framework can be extended to include more mechanisms of platelet activation as well as the addition of the biochemical reactions of coagulation, resulting in a computationally efficient high throughput screening tool of primary and secondary hemostasis.

Computationally Driven Discovery in Coagulation

Bleeding frequency and severity within clinical categories of hemophilia A are highly variable and the origin of this variation is unknown. Solving this mystery in coagulation requires the generation and analysis of large data sets comprised of experimental outputs or patient samples, both of which are subject to limited availability. In this review, we describe how a computationally driven approach bypasses such limitations by generating large synthetic patient data sets. These data sets were created with a mechanistic mathematical model, by varying the model inputs, clotting factor, and inhibitor concentrations, within normal physiological ranges. Specific mathematical metrics were chosen from the model output, used as a surrogate measure for bleeding severity, and statistically analyzed for further exploration and hypothesis generation. We highlight results from our recent study that employed this computationally driven approach to identify FV (factor V) as a key modifier of thrombin generation in mild to moderate hemophilia A, which was confirmed with complementary experimental assays. The mathematical model was used further to propose a potential mechanism for these observations whereby thrombin generation is rescued in FVIII-deficient plasma due to reduced substrate competition between FV and FVIII for FXa (activated factor X).

A mathematical model to quantify the effects of platelet count, shear rate, and injury size on the initiation of blood coagulation under venous flow conditions

Platelets upregulate the generation of thrombin and reinforce the fibrin clot which increases the incidence risk of venous thromboembolism (VTE). However, the role of platelets in the pathogenesis of venous cardiovascular diseases remains hard to quantify. An experimentally validated model of thrombin generation dynamics is formulated. The model predicts that a high platelet count increases the peak value of generated thrombin as well as the endogenous thrombin potential (ETP) as reported in experimental data. To investigate the effects of platelets density, shear rate, and wound size on the initiation of blood coagulation, we calibrate a previously developed model of venous thrombus formation and implement it in 3D using a novel cell-centered finite-volume solver. We conduct numerical simulations to reproduce in vitro experiments of blood coagulation in microfluidic capillaries. Then, we derive a reduced one-equation model of thrombin distribution from the previous model under simplifying hypotheses and we use it to determine the conditions of clotting initiation on the platelet count, the shear rate, and the plasma composition. The initiation of clotting also exhibits a threshold response to the size of the wounded region in good agreement with the reported experimental findings.

A mathematical model of coagulation under flow identifies factor V as a modifier of thrombin generation in hemophilia A

BACKGROUND

The variability in bleeding patterns among individuals with hemophilia A, who have similar factor VIII (FVIII) levels, is significant and the origins are unknown.

OBJECTIVE

To use a previously validated mathematical model of flow-mediated coagulation as a screening tool to identify parameters that are most likely to enhance thrombin generation in the context of FVIII deficiency.

METHODS

We performed a global sensitivity analysis (GSA) on our mathematical model to identify potential modifiers of thrombin generation. Candidates from the GSA were confirmed by calibrated automated thrombography (CAT) and flow assays on collagen-tissue factor (TF) surfaces at a shear rate of 100 per second.

RESULTS

Simulations identified low-normal factor V (FV) (50%) as the strongest modifier, with additional thrombin enhancement when combined with high-normal prothrombin (150%). Low-normal FV levels or partial FV inhibition (60% activity) augmented thrombin generation in FVIII-inhibited or FVIII-deficient plasma in CAT. Partial FV inhibition (60%) boosted fibrin deposition in flow assays performed with whole blood from individuals with mild and moderate FVIII deficiencies. These effects were amplified by high-normal prothrombin levels in both experimental models.

CONCLUSIONS

These results show that low-normal FV levels can enhance thrombin generation in hemophilia A. Further explorations with the mathematical model suggest a potential mechanism: lowering FV reduces competition between FV and FVIII for factor Xa (FXa) on activated platelet surfaces (APS), which enhances FVIII activation and rescues thrombin generation in FVIII-deficient blood.

Effects of hydrophobicity, tethering and size on flow-induced activation of von Willebrand factor multimers

Von Willebrand factor (VWF) is a multimeric protein of blood plasma that mediates platelet adhesion to injury under strong hemodynamic flows in arterias and microvasvulature. We present a 3D coarse-grained computer model of VWF multimers in flowing viscous fluid that explicitely grasps the dynamics, the conformational changes and the hydrodynamics-induced activation of adhesivity of these protein concatamers to GPIb receptor of blood platelets. The model is based on the fluctuating Lattice Boltzmann method for modelling the hydrodynamics in the simulation box and the Lagrangian particle dynamics coupled to the fluid by a viscous drag force. The model has been validated by the comparison with the experimental data found in literature. We studied the effect of hydrophobic interactions on the conformational dynamics of VWF multimers. The simulations suggest that the contour length is an important parameter that controls the functionality of VWF multimers in blood. We also demonstrate that tethering to the surface of a vessel wall promoted the flow-induced activation of VWF, while those multimers that remain untethered and move freely in the blood plasma require a stronger shearing to get activated.

A Mathematical Model of Bivalent Binding Suggests Physical Trapping of Thrombin within Fibrin Fibers

Thrombin is an enzyme that plays many important roles in the blood clotting process; it activates platelets, cleaves coagulation proteins within feedback loops, and cleaves fibrinogen into fibrin, which polymerizes into fibers to form a stabilizing gel matrix in and around growing clots. Thrombin also binds to the formed fibrin matrix, but this interaction is not well understood. Thrombin-fibrin binding is often described as two independent, single-step binding events, one high-affinity and one low-affinity. However, kinetic schemes describing these single-step binding events do not explain experimentally-observed residency times of fibrin-bound thrombin. In this work, we study a bivalent, sequential-step binding scheme as an alternative to the high-affinity event and, in addition to the low-affinity one. We developed mathematical models for the single- and sequential-step schemes consisting of reaction-diffusion equations to compare to each other and to experimental data. We then used Bayesian inference, in the form of Markov chain Monte Carlo, to learn model parameter distributions from previously published experimental data. For the model to best fit the data, we made an additional assumption that thrombin was irreversibly sequestered; we hypothesized that this could be due to thrombin becoming physically trapped within fibrin fibers as they formed. We further estimated that ∼30% of thrombin in the experiments to which we compare our model output became physically trapped. The notion of physically trapped thrombin may provide new insights into conflicting observations regarding the speed of fibrinolysis. Finally, we show that our new model can be used to further probe scenarios dealing with thrombin allostery.

Assessing the impact of product inhibition in a chromogenic assay

Chromogenic substrates (CS) are synthetic substrates used to monitor the activity of a target enzyme. It has been reported that some CSs display competitive product inhibition with their target enzyme. Thus, in assays where enzyme activity is continuously monitored over long periods of time, the product inhibition may significantly interfere with the reactions being monitored. Despite this knowledge, it is rare for CSs to be directly incorporated into mathematical models that simulate these assays. This devalues the predictive power of the models. In this study, we examined the interactions between a single enzyme, coagulation factor Xa, and its chromogenic substrate. We developed, and experimentally validated, a mathematical model of a chromogenic assay for factor Xa that explicitly included product inhibition from the CS. We employed Bayesian inference, in the form of Markov-Chain Monte Carlo, to estimate the strength of the product inhibition and other sources of uncertainty such as pipetting error and kinetic rate constants. Our model, together with carefully calibrated biochemistry experiments, allowed for full characterization of the strength and impact of product inhibition in the assay. The effect of CS product inhibition in more complex reaction mixtures was further explored using mathematical models.

Intrinsic Coagulation Pathway, History of Headache, and Risk of Ischemic Stroke

Background and Purpose—

Hypercoagulable states in migraine patients may play a role in the pathophysiology underlying the association between migraine and ischemic stroke. This study aims to provide more insight into the potential association of headache, ischemic stroke, and the intrinsic coagulation pathway.

Methods—

We included patients from the RATIO study (Risk of Arterial Thrombosis in Relation to Oral Contraceptives), a Dutch population-based case-control study including young women (age <50) with ischemic stroke and healthy controls. We defined a headache group based on a questionnaire on headache history. Intrinsic coagulation proteins were measured through both antigen levels (FXII, FXI, prekallikrein, HK [high molecular weight kininogen]) and protein activation, determined by measuring activated protein complex with C1esterase-inhibitor (FXIIa-C1-INH, FXIa-C1-INH, Kallikrein-C1-INH) or antitrypsin-inhibitor (FXIa-AT-INH). We calculated adjusted odds ratios and performed an interaction analysis assessing the increase in stroke risk associated with high levels of intrinsic coagulation and history of headache.

Results—

We included 113 ischemic stroke cases and 598 healthy controls. In total, 134 (19%) patients had a history of headache, of whom 38 were cases and 96 controls. The combination of headache and high intrinsic coagulation protein levels (all but FXII antigen level and both FXIa-inhibitors) was associated with an increase in ischemic stroke risk higher than was expected based on their individual effects (adjusted odds ratio FXI antigen level alone: 1.7, 95% CI, 1.0–2.9; adjusted odds ratio headache alone: 2.0, 95% CI, 1.1−3.7; combination: 5.2, 95% CI, 2.3−11.6)

Conclusions—

Headache and high intrinsic coagulation protein levels may biologically interact, increasing risk for ischemic stroke.

Review of quantitative systems pharmacological modeling in thrombosis

Hemostasis and thrombosis are often thought as two sides of the same clotting mechanism whereas hemostasis is a natural protective mechanism to prevent bleeding and thrombosis is a blood clot abnormally formulated inside a blood vessel, blocking the normal blood flow. The evidence to date suggests that at least arterial thrombosis results from the same critical pathways of hemostasis. Analysis of these complex processes and pathways using quantitative systems pharmacological model-based approach can facilitate the delineation of the causal pathways that lead to the emergence of thrombosis. In this paper, we provide an overview of the main molecular and physiological mechanisms associated with hemostasis and thrombosis, and review the models and quantitative system pharmacological modeling approaches that are relevant in characterizing the interplay among the multiple factors and pathways of thrombosis. An emphasis is given to computational models for drug development. Future trends are discussed.

Coated platelets introduce significant delay in onset of peak thrombin production: Theoretical predictions

Platelets play a crucial role in the initiation, progress, termination as well as regulation of blood coagulation. Recent studies have confirmed that not all but only a small percentage of thrombin-activated platelets ("coated" platelets) exhibit procoagulant properties (namely the expression of phosphatidylserine binding sites) required for the acceleration and progress of coagulation. A mechanistic model is developed for in vitro coagulation whose key features are distinct equations for coated platelets, thrombin dose-dependence for coated platelets, and competitive binding of coagulation factors to platelet membrane. Model predictions show significant delay in the onset of peak Va production, and peak thrombin production when dose-dependence is incorporated instead of a fixed theoretical maximum percentage of coated platelets. Further, peak thrombin concentration is significantly overestimated when either fractional presence of coated platelets is ignored (by 299.4%) or when dose-dependence on thrombin is ignored (by 24.7%).

A local and global sensitivity analysis of a mathematical model of coagulation and platelet deposition under flow

The hemostatic response involves blood coagulation and platelet aggregation to stop blood loss from an injured blood vessel. The complexity of these processes make it difficult to intuit the overall hemostatic response without quantitative methods. Mathematical models aim to address this challenge but are often accompanied by numerous parameters choices and thus need to be analyzed for sensitivity to such choices. Here we use local and global sensitivity analyses to study a model of coagulation and platelet deposition under flow. To relate with clinical assays, we measured the sensitivity of three specific thrombin metrics: lag time, maximum relative rate of generation, and final concentration after 20 minutes. In addition, we varied parameters of three different classes: plasma protein levels, kinetic rate constants, and platelet characteristics. In terms of an overall ranking of the model’s sensitivities, we found that the local and global methods provided similar information. Our local analysis, in agreement with previous findings, shows that varying parameters within 50-150% of baseline values, in a one-at-a-time (OAT) fashion, always leads to significant thrombin generation in 20 minutes. Our global analysis gave a different and novel result highlighting groups of parameters, still varying within the normal 50-150%, that produced little or no thrombin in 20 minutes. Variations in either plasma levels or platelet characteristics, using either OAT or simultaneous variations, always led to strong thrombin production and overall, relatively low output variance. Simultaneous variation in kinetics rate constants or in a subset of all three parameter classes led to the highest overall output variance, incorporating instances with little to no thrombin production. The global analysis revealed multiple parameter interactions in the lag time and final concentration leading to relatively high variance; high variance was also observed in the thrombin generation rate, but parameters attributed to that variance acted independently and additively.

Establishing the Transient Mass Balance of Thrombosis: From Tissue Factor to Thrombin to Fibrin Under Venous Flow

Supplemental Digital Content is available in the text.

Objective—

We investigated the coregulation of thrombin and fibrin as blood flows over a procoagulant surface.

Approach and Results—

Using microfluidic perfusion of factor XIIa-inhibited human whole blood (200 s⁻¹ wall shear rate) over a 250-μm long patch of collagen/TF (tissue factor; ≈1 molecule per μm²) and immunoassays of the effluent for F1.2 (prothrombin fragment 1.2), TAT (thrombin–antithrombin complex), and D-dimer (post–end point plasmin digest), we sought to establish the transient mass balance for clotting under venous flow. F1.2 (but almost no free thrombin detected via TAT assay) continually eluted from clots when fibrin was allowed to form. Low-dose fluorescein-Phe-Pro-Arg-chloromethylketone stained fibrin-bound thrombin—a staining ablated by anti–γ′-fibrinogen or the fibrin inhibitor glypro-arg-pro but highly resistant to 7-minute buffer rinse, demonstrating tight binding of thrombin to γ′-fibrin. With fibrin polymerizing for 500 seconds, 92 000 thrombin molecules and 203 000 clot-associated fibrin monomer equivalents were generated per TF molecule (or per μm²). Fibrin reached 15 mg/mL in the pore space (porosity ≈0.5) of a 15-μm-thick thrombus core by 500 seconds and 30 mg/mL by 800 seconds. For a known rate of ≈60 FPA (fibrinopeptide-A) per thrombin per second, each thrombin molecule generated only 3 fibrin monomer equivalents during 500 seconds, indicating an intraclot thrombin half-life of ≈70 ms, much shorter than its diffusional escape time (≈10 seconds). By 800 seconds, gly-pro-arg-pro allowed 4-fold more F1.2 generation, consistent with gly-pro-arg-pro ablating fibrin’s antithrombin-I activity and facilitating thrombin-mediated FXIa activation.

Conclusions—

Under flow, fibrinogen continually penetrates the clot, and γ′-fibrin regulates thrombin.

Modeling thrombosis in silico: Frontiers, challenges, unresolved problems and milestones

Hemostasis is a complex physiological mechanism that functions to maintain vascular integrity under any conditions. Its primary components are blood platelets and a coagulation network that interact to form the hemostatic plug, a combination of cell aggregate and gelatinous fibrin clot that stops bleeding upon vascular injury. Disorders of hemostasis result in bleeding or thrombosis, and are the major immediate cause of mortality and morbidity in the world. Regulation of hemostasis and thrombosis is immensely complex, as it depends on blood cell adhesion and mechanics, hydrodynamics and mass transport of various species, huge signal transduction networks in platelets, as well as spatiotemporal regulation of the blood coagulation network. Mathematical and computational modeling has been increasingly used to gain insight into this complexity over the last 30 years, but the limitations of the existing models remain profound. Here we review state-of-the-art-methods for computational modeling of thrombosis with the specific focus on the analysis of unresolved challenges. They include: a) fundamental issues related to physics of platelet aggregates and fibrin gels; b) computational challenges and limitations for solution of the models that combine cell adhesion, hydrodynamics and chemistry; c) biological mysteries and unknown parameters of processes; d) biophysical complexities of the spatiotemporal networks' regulation. Both relatively classical approaches and innovative computational techniques for their solution are considered; the subjects discussed with relation to thrombosis modeling include coarse-graining, continuum versus particle-based modeling, multiscale models, hybrid models, parameter estimation and others. Fundamental understanding gained from theoretical models are highlighted and a description of future prospects in the field and the nearest possible aims are given.

Mathematical Techniques for Understanding Platelet Regulation and the Development of New Pharmacological Approaches

Mathematical and computational modeling is currently in the process of becoming an accepted tool in the arsenal of methods utilized for the investigation of complex biological systems. For some problems in the field, like cellular metabolic regulation, neural impulse propagation, or cell cycle, progress is already unthinkable without use of such methods. Mathematical models of platelet signaling, function, and metabolism during the last years have not only been steadily increasing in their number, but have also been providing more in-depth insights, generating hypotheses, and allowing predictions to be made leading to new experimental designs and data. Here we describe the basic approaches to platelet mathematical model development and validation, highlighting the challenges involved. We then review the current theoretical models in the literature and how these are being utilized to increase our understanding of these complex cells.

A Mathematical Model of Venous Thrombosis Initiation

We present a mathematical model for the initiation of venous thrombosis (VT) due to slow flow and the consequent activation of the endothelial cells (ECs) lining the vein, in the absence of overt mechanical disruption of the EC layer. It includes all reactions of the tissue factor (TF) pathway of coagulation through fibrin formation, incorporates the accumulation of blood cells on activated ECs, accounts for the flow-mediated delivery and removal of coagulation proteins and blood cells from the locus of the reactions, and accounts for the activity of major inhibitors including heparan-sulfate-accelerated antithrombin and activated protein C. The model reveals that the occurrence of robust thrombin generation (a thrombin burst) depends in a threshold manner on the density of TF on the activated ECs and on the concentration of thrombomodulin and the degree of heparan-sulfate accelerated antithrombin activity on those cells. Small changes in any of these in appropriate narrow ranges switches the response between "no burst" and "burst." The model predicts synergies among the inhibitors, both in terms of each inhibitor's multiple targets, and in terms of interactions between the different inhibitors. The model strongly suggests that the rate and extent of accumulation of activated monocytes, platelets, and MPs that can support the coagulation reactions has a powerful influence on whether a thrombin burst occurs and the thrombin response when it does. The slow rate of accumulation of cells supporting coagulation is one reason that the progress of VT is so much slower than that of arterial thrombosis initiated by subendothelial exposure.

Systems Analysis of Thrombus Formation

The systems analysis of thrombosis seeks to quantitatively predict blood function in a given vascular wall and hemodynamic context. Relevant to both venous and arterial thrombosis, a Blood Systems Biology approach should provide metrics for rate and molecular mechanisms of clot growth, thrombotic risk, pharmacological response, and utility of new therapeutic targets. As a rapidly created multicellular aggregate with a polymerized fibrin matrix, blood clots result from hundreds of unique reactions within and around platelets propagating in space and time under hemodynamic conditions. Coronary artery thrombosis is dominated by atherosclerotic plaque rupture, complex pulsatile flows through stenotic regions producing high wall shear stresses, and plaque-derived tissue factor driving thrombin production. In contrast, venous thrombosis is dominated by stasis or depressed flows, endothelial inflammation, white blood cell-derived tissue factor, and ample red blood cell incorporation. By imaging vessels, patient-specific assessment using computational fluid dynamics provides an estimate of local hemodynamics and fractional flow reserve. High-dimensional ex vivo phenotyping of platelet and coagulation can now power multiscale computer simulations at the subcellular to cellular to whole vessel scale of heart attacks or strokes. In addition, an integrated systems biology approach can rank safety and efficacy metrics of various pharmacological interventions or clinical trial designs.

Multi-Constituent Simulation of Thrombus Deposition

In this paper, we present a spatio-temporal mathematical model for simulating the formation and growth of a thrombus. Blood is treated as a multi-constituent mixture comprised of a linear fluid phase and a thrombus (solid) phase. The transport and reactions of 10 chemical and biological species are incorporated using a system of coupled convection-reaction-diffusion (CRD) equations to represent three processes in thrombus formation: initiation, propagation and stabilization. Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: in vivo thrombus growth in an injured blood vessel and in vitro thrombus deposition in micro-channels (1.5 mm × 1.6 mm × 0.1 mm) with small crevices (125 μm × 75 μm and 125 μm × 137 μm). For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally. Based on the success with these two benchmark problems, which have very different flow conditions and biological environments, we believe that the current model will provide useful insight into the genesis of thrombosis in blood-wetted devices, and provide a tool for the design of less thrombogenic devices.

Localization of Short-Chain Polyphosphate Enhances its Ability to Clot Flowing Blood Plasma

Short-chain polyphosphate (polyP) is released from platelets upon platelet activation, but it is not clear if it contributes to thrombosis. PolyP has increased propensity to clot blood with increased polymer length and when localized onto particles, but it is unknown whether spatial localization of short-chain polyP can accelerate clotting of flowing blood. Here, numerical simulations predicted the effect of localization of polyP on clotting under flow, and this was tested in vitro using microfluidics. Synthetic polyP was more effective at triggering clotting of flowing blood plasma when localized on a surface than when solubilized in solution or when localized as nanoparticles, accelerating clotting at 10-200 fold lower concentrations, particularly at low to sub-physiological shear rates typical of where thrombosis occurs in large veins or valves. Thus, sub-micromolar concentrations of short-chain polyP can accelerate clotting of flowing blood plasma under flow at low to sub-physiological shear rates. However, a physiological mechanism for the localization of polyP to platelet or vascular surfaces remains unknown.

Synergy Between Tissue Factor and Exogenous Factor XIa in Initiating Coagulation

OBJECTIVE

Recent evidence suggests involvement of coagulation factor XIa (FXIa) in thrombotic event development. This study was conducted to explore possible synergies between tissue factor (TF) and exogenous FXIa (E-FXIa) in thrombin generation.

APPROACH AND RESULTS

In thrombin generation assays, for increasing concentrations of E-FXIa with low, but not with high TF concentrations, peak thrombin significantly increased whereas lag time and time to peak significantly decreased. Similar dependencies of lag times and rates of thrombin generation were found in mathematical model simulations. In both in vitro and in silico experiments that included E-FXIa, thrombin bursts were seen for TF levels much lower than those required without E-FXIa. For in silico thrombin bursts initiated by the synergistic action of TF and E-FXIa, the mechanisms leading to the burst differed substantially from those for bursts initiated by high TF alone. For the synergistic case, sustained activation of platelet-bound FIX by E-FXIa, along with the feedback-enhanced activation of platelet-bound FVIIIa and FXa, was needed to elicit a thrombin burst. Furthermore, the initiation of thrombin bursts by high TF levels relied on different platelet FIX/FIXa binding sites than those involved in bursts initiated by low TF levels with E-FXIa.

CONCLUSIONS

Low concentrations of TF and exogenous FXIa, each too low to elicit a burst in thrombin production alone, act synergistically when in combination to cause substantial thrombin production. The observation about FIX/FIXa binding sites may have therapeutic implications.

Dynamics of Thrombin Generation and Flux from Clots during Whole Human Blood Flow over Collagen/Tissue Factor Surfaces

Coagulation kinetics are well established for purified blood proteases or human plasma clotting isotropically. However, less is known about thrombin generation kinetics and transport within blood clots formed under hemodynamic flow. Using microfluidic perfusion (wall shear rate, 200 s^-1) of corn trypsin inhibitor-treated whole blood over a 250-μm long patch of type I fibrillar collagen/lipidated tissue factor (TF; ∼1 TF molecule/μm²), we measured thrombin released from clots using thrombin-antithrombin immunoassay. The majority (>85%) of generated thrombin was captured by intrathrombus fibrin as thrombin-antithrombin was largely undetectable in the effluent unless Gly-Pro-Arg-Pro (GPRP) was added to block fibrin polymerization. With GPRP present, the flux of thrombin increased to ∼0.5 × 10^-12 nmol/μm²-s over the first 500 s of perfusion and then further increased by ∼2-3-fold over the next 300 s. The increased thrombin flux after 500 s was blocked by anti-FXIa antibody (O1A6), consistent with thrombin-feedback activation of FXI. Over the first 500 s, ∼92,000 molecules of thrombin were generated per surface TF molecule for the 250-μm-long coating. A single layer of platelets (obtained with α_IIbβ₃ antagonism preventing continued platelet deposition) was largely sufficient for thrombin production. Also, the overall thrombin-generating potential of a 1000-μm-long coating became less efficient on a per μm² basis, likely due to distal boundary layer depletion of platelets. Overall, thrombin is robustly generated within clots by the extrinsic pathway followed by late-stage FXIa contributions, with fibrin localizing thrombin via its antithrombin-I activity as a potentially self-limiting hemostatic mechanism.

Transport physics and biorheology in the setting of hemostasis and thrombosis

The biophysics of blood flow can dictate the function of molecules and cells in the vasculature with consequent effects on hemostasis, thrombosis, embolism, and fibrinolysis. Flow and transport dynamics are distinct for (i) hemostasis vs. thrombosis and (ii) venous vs. arterial episodes. Intraclot transport changes dramatically the moment hemostasis is achieved or the moment a thrombus becomes fully occlusive. With platelet concentrations that are 50- to 200-fold greater than platelet-rich plasma, clots formed under flow have a different composition and structure compared with blood clotted statically in a tube. The platelet-rich, core/shell architecture is a prominent feature of self-limiting hemostatic clots formed under flow. Importantly, a critical threshold concentration of surface tissue factor is required for fibrin generation under flow. Once initiated by wall-derived tissue factor, thrombin generation and its spatial propagation within a clot can be modulated by γ'-fibrinogen incorporated into fibrin, engageability of activated factor (FIXa)/activated FVIIIa tenase within the clot, platelet-derived polyphosphate, transclot permeation, and reduction of porosity via platelet retraction. Fibrin imparts tremendous strength to a thrombus to resist embolism up to wall shear stresses of 2400 dyne cm(-2) . Extreme flows, as found in severe vessel stenosis or in mechanical assist devices, can cause von Willebrand factor self-association into massive fibers along with shear-induced platelet activation. Pathological von Willebrand factor fibers are A Disintegrin And Metalloprotease with ThromboSpondin-1 domain 13 resistant but are a substrate for fibrin generation due to FXIIa capture. Recently, microfluidic technologies have enhanced the ability to interrogate blood in the context of stenotic flows, acquired von Willebrand disease, hemophilia, traumatic bleeding, and drug action.

Regulation of Early Steps of GPVI Signal Transduction by Phosphatases: A Systems Biology Approach

We present a data-driven mathematical model of a key initiating step in platelet activation, a central process in the prevention of bleeding following Injury. In vascular disease, this process is activated inappropriately and causes thrombosis, heart attacks and stroke. The collagen receptor GPVI is the primary trigger for platelet activation at sites of injury. Understanding the complex molecular mechanisms initiated by this receptor is important for development of more effective antithrombotic medicines. In this work we developed a series of nonlinear ordinary differential equation models that are direct representations of biological hypotheses surrounding the initial steps in GPVI-stimulated signal transduction. At each stage model simulations were compared to our own quantitative, high-temporal experimental data that guides further experimental design, data collection and model refinement. Much is known about the linear forward reactions within platelet signalling pathways but knowledge of the roles of putative reverse reactions are poorly understood. An initial model, that includes a simple constitutively active phosphatase, was unable to explain experimental data. Model revisions, incorporating a complex pathway of interactions (and specifically the phosphatase TULA-2), provided a good description of the experimental data both based on observations of phosphorylation in samples from one donor and in those of a wider population. Our model was used to investigate the levels of proteins involved in regulating the pathway and the effect of low GPVI levels that have been associated with disease. Results indicate a clear separation in healthy and GPVI deficient states in respect of the signalling cascade dynamics associated with Syk tyrosine phosphorylation and activation. Our approach reveals the central importance of this negative feedback pathway that results in the temporal regulation of a specific class of protein tyrosine phosphatases in controlling the rate, and therefore extent, of GPVI-stimulated platelet activation.

Prediction of Molecular Interaction between Platelet Glycoprotein Ibα and von Willebrand Factor using Molecular Dynamics Simulations

AIM

The molecular mechanism of the unique interaction between platelet membrane glycoprotein Ibα (GPIbα) and von Willebrand Factor (VWF), necessary for platelet adhesion under high shear stress, is yet to be clarified.

METHODS

The molecular dynamics simulation using NAMD (Nanoscale Molecular Dynamics) package with the CHARMM 22 (Chemistry at Harvard Macromolecular Mechanics) force field were used to predict dynamic structural changes occurring in the binding site of A1 domain of VWF and N terminus domain of GPIbα under water soluble condition.

RESULTS

The mean distance between the mass center of A1 domain of VWF and GPIbα in the stable form was predicted as 27.3 Å. The potential of mean force between the A1 domain of VWF and GPIbα were calculated in conditions of various distances of the mass center between them. All the calculated values were fitted to the Morse potential energy function curve. The maximum adhesive force between A1 domain of VWF and GPIbα was predicted as 62.3 pN by differentiating the potential of mean force with respect to the molecular distance.

CONCLUSIONS

The molecular dynamics simulation is useful for predicting the dynamic structure changes of protein bonds involved in platelet adhesion and for predicting the adhesive forces generated between their interactions.

FXIa and platelet polyphosphate as therapeutic targets during human blood clotting on collagen/tissue factor surfaces under flow

Factor XIIa (FXIIa) and factor XIa (FXIa) contribute to thrombosis in animal models, whereas platelet-derived polyphosphate (polyP) may potentiate contact or thrombin-feedback pathways. The significance of these mediators in human blood under thrombotic flow conditions on tissue factor (TF) -bearing surfaces remains inadequately resolved. Human blood (corn trypsin inhibitor treated [4 μg/mL]) was tested by microfluidic assay for clotting on collagen/TF at TF surface concentration ([TF]wall) from ∼0.1 to 2 molecules per μm(2). Anti-FXI antibodies (14E11 and O1A6) or polyP-binding protein (PPXbd) were used to block FXIIa-dependent FXI activation, FXIa-dependent factor IX (FIX) activation, or platelet-derived polyP, respectively. Fibrin formation was sensitive to 14E11 at 0 to 0.1 molecules per µm(2) and sensitive to O1A6 at 0 to 0.2 molecules per µm(2). However, neither antibody reduced fibrin generation at ∼2 molecules per µm(2) when the extrinsic pathway became dominant. Interestingly, PPXbd reduced fibrin generation at low [TF]wall (0.1 molecules per µm(2)) but not at zero or high [TF]wall, suggesting a role for polyP distinct from FXIIa activation and requiring low extrinsic pathway participation. Regardless of [TF]wall, PPXbd enhanced fibrin sensitivity to tissue plasminogen activator and promoted clot retraction during fibrinolysis concomitant with an observed PPXbd-mediated reduction of fibrin fiber diameter. This is the first detection of endogenous polyP function in human blood under thrombotic flow conditions. When triggered by low [TF]wall, thrombosis may be druggable by contact pathway inhibition, although thrombolytic susceptibility may benefit from polyP antagonism regardless of [TF]wall.

Systems biology of coagulation

Accurate computer simulation of blood function can inform drug target selection, patient-specific dosing, clinical trial design, biomedical device design, as well as the scoring of patient-specific disease risk and severity. These large-scale simulations rely on hundreds of independently measured physical parameters and kinetic rate constants. However, the models can be validated against large-scale, patient-specific laboratory measurements. By validation with high-dimensional data, modeling becomes a powerful tool to predict clinically complex scenarios. Currently, it is possible to accurately predict the clotting rate of plasma or blood in a tube as it is activated with a dose of tissue factor, even as numerous coagulation factors are altered by exogenous attenuation or potentiation. Similarly, the dynamics of platelet activation, as indicated by calcium mobilization or inside-out signaling, can now be numerically simulated with accuracy in cases where platelets are exposed to combinations of agonists. Multiscale models have emerged to combine platelet function and coagulation kinetics into complete physics-based descriptions of thrombosis under flow. Blood flow controls platelet fluxes, delivery and removal of coagulation factors, adhesive bonding, and von Willebrand factor conformation. The field of blood systems biology has now reached a stage that anticipates the inclusion of contact, complement, and fibrinolytic pathways along with models of neutrophil and endothelial activation. Along with '-omics' data sets, such advanced models seek to predict the multifactorial range of healthy responses and diverse bleeding and clotting scenarios, ultimately to understand and improve patient outcomes.

Microfluidics and coagulation biology

The study of blood ex vivo can occur in closed or open systems, with or without flow. Microfluidic devices, which constrain fluids to a small (typically submillimeter) scale, facilitate analysis of platelet function, coagulation biology, cellular biorheology, adhesion dynamics, and pharmacology and, as a result, can be an invaluable tool for clinical diagnostics. An experimental session can accommodate hundreds to thousands of unique clotting, or thrombotic, events. Using microfluidics, thrombotic events can be studied on defined surfaces of biopolymers, matrix proteins, and tissue factor, under constant flow rate or constant pressure drop conditions. Distinct shear rates can be generated on a device using a single perfusion pump. Microfluidics facilitated both the determination of intraluminal thrombus permeability and the discovery that platelet contractility can be activated by a sudden decrease in flow. Microfluidic devices are ideal for multicolor imaging of platelets, fibrin, and phosphatidylserine and provide a human blood analog to mouse injury models. Overall, microfluidic advances offer many opportunities for research, drug testing under relevant hemodynamic conditions, and clinical diagnostics.

The influence of hindered transport on the development of platelet thrombi under flow

Vascular injury triggers two intertwined processes, platelet deposition and coagulation, and can lead to the formation of an intravascular clot (thrombus) that may grow to occlude the vessel. Formation of the thrombus involves complex biochemical, biophysical, and biomechanical interactions that are also dynamic and spatially-distributed, and occur on multiple spatial and temporal scales. We previously developed a spatial-temporal mathematical model of these interactions and looked at the interplay between physical factors (flow, transport to the clot, platelet distribution within the blood) and biochemical ones in determining the growth of the clot. Here, we extend this model to include reduction of the advection and diffusion of the coagulation proteins in regions of the clot with high platelet number density. The effect of this reduction, in conjunction with limitations on fluid and platelet transport through dense regions of the clot can be profound. We found that hindered transport leads to the formation of smaller and denser clots compared to the case with no protein hindrance. The limitation on protein transport confines the important activating complexes to small regions in the interior of the thrombus and greatly reduces the supply of substrates to these complexes. Ultimately, this decreases the rate and amount of thrombin production and leads to greatly slowed growth and smaller thrombus size. Our results suggest a possible physical mechanism for limiting thrombus growth.

Multiscale systems biology and physics of thrombosis under flow

Blood clotting under hemodynamic conditions involves numerous multiscale interactions from the molecular scale to macroscopic vessel and systemic circulation scales. Transmission of shear forces to platelet receptors such as GPIbα, P-selectin, α(2)β(1), and α(2b)β(3) controls adhesion dynamics. These forces also drive membrane tether formation, cellular deformation, and mechanosignaling in blood cells. Blood flow results in red blood cell (RBC) drift towards the center of the vessel along with a near-wall plasma layer enriched with platelets. RBC motions also dramatically enhance platelet dispersion. Trajectories of individual platelets near a thrombotic deposit dictate capture-activation-arrest dynamics as these newly arriving platelets are exposed to chemical gradients of ADP, thromboxane, and thrombin within a micron-scale boundary layer formed around the deposit. If shear forces are sufficiently elevated (>50 dyne/cm(2)), the largest polymers of von Willebrand Factor may elongate with concomitant shear-induced platelet activation. Finally, thrombin generation enhances platelet recruitment and clot strength via fibrin polymerization. By combination of coarse-graining, continuum, and stochastic algorithms, the numerical simulation of the growth rate, composition, and occlusive/embolic potential of a thrombus now spans multiscale phenomena. These simulations accommodate particular flow geometries, blood phenotype, pharmacological regimen, and reactive surfaces to help predict disease risk or response to therapy.