Predicting pathological von Willebrand factor unraveling in elongational flow

A continuum model for the elongation and orientation of Von Willebrand factor with applications in arterial flow

The blood protein Von Willebrand factor (VWF) is critical in facilitating arterial thrombosis. At pathologically high shear rates, the protein unfolds and binds to the arterial wall, enabling the rapid deposition of platelets from the blood. We present a novel continuum model for VWF dynamics in flow based on a modified viscoelastic fluid model that incorporates a single constitutive relation to describe the propensity of VWF to unfold as a function of the scalar shear rate. Using experimental data of VWF unfolding in pure shear flow, we fix the parameters for VWF's unfolding propensity and the maximum VWF length, so that the protein is half unfolded at a shear rate of approximately 5000 s - 1 . We then use the theoretical model to predict VWF's behaviour in two complex flows where experimental data are challenging to obtain: pure elongational flow and stenotic arterial flow. In pure elongational flow, our model predicts that VWF is 50% unfolded at approximately 2000 s - 1 , matching the established hypothesis that VWF unfolds at lower shear rates in elongational flow than in shear flow. We demonstrate the sensitivity of this elongational flow prediction to the value of maximum VWF length used in the model, which varies significantly across experimental studies, predicting that VWF can unfold between 2000 and 3200 s - 1 depending on the selected value. Finally, we examine VWF dynamics in a range of idealised arterial stenoses, predicting the relative extension of VWF in elongational flow structures in the centre of the artery compared to high shear regions near the arterial walls.

The interplay between adsorption and aggregation of von Willebrand factor chains in shear flows

Von Willebrand factor (VWF) is a giant extracellular glycoprotein that carries out a key adhesive function during primary hemostasis. Upon vascular injury and triggered by the shear of flowing blood, VWF establishes specific interactions with several molecular partners in order to anchor platelets to collagen on the exposed subendothelial surface. VWF also interacts with itself to form aggregates that, adsorbed on the surface, provide more anchor sites for the platelets. However, the interplay between elongation and subsequent exposure of cryptic binding sites, self-association, and adsorption on the surface remained unclear for VWF. In particular, the role of shear flow in these three processes is not well understood. In this study, we address these questions by using Brownian dynamics simulations at a coarse-grained level of resolution. We considered a system consisting of multiple VWF-like self-interacting chains that also interact with a surface under a shear flow. By a systematic analysis, we reveal that chain-chain and chain-surface interactions coexist nontrivially to modulate the spontaneous adsorption of VWF and the posterior immobilization of secondary tethered chains. Accordingly, these interactions tune VWF's extension and its propensity to form shear-assisted functional adsorbed aggregates. Our data highlight the collective behavior VWF self-interacting chains have when bound to the surface, distinct from that of isolated or flowing chains. Furthermore, we show that the extension and the exposure to solvent have a similar dependence on shear flow, at a VWF-monomer level of resolution. Overall, our results highlight the complex interplay that exists between adsorption, cohesion, and shear forces and their relevance for the adhesive hemostatic function of VWF.

Image-based flow simulation of platelet aggregates under different shear rates

Hemodynamics is crucial for the activation and aggregation of platelets in response to flow-induced shear. In this paper, a novel image-based computational model simulating blood flow through and around platelet aggregates is presented. The microstructure of aggregates was captured by two different modalities of microscopy images of in vitro whole blood perfusion experiments in microfluidic chambers coated with collagen. One set of images captured the geometry of the aggregate outline, while the other employed platelet labelling to infer the internal density. The platelet aggregates were modelled as a porous medium, the permeability of which was calculated with the Kozeny-Carman equation. The computational model was subsequently applied to study hemodynamics inside and around the platelet aggregates. The blood flow velocity, shear stress and kinetic force exerted on the aggregates were investigated and compared under 800 s-1, 1600 s-1 and 4000 s-1 wall shear rates. The advection-diffusion balance of agonist transport inside the platelet aggregates was also evaluated by local Péclet number. The findings show that the transport of agonists is not only affected by the shear rate but also significantly influenced by the microstructure of the aggregates. Moreover, large kinetic forces were found at the transition zone from shell to core of the aggregates, which could contribute to identifying the boundary between the shell and the core. The shear rate and the rate of elongation flow were investigated as well. The results imply that the emerging shapes of aggregates are highly correlated to the shear rate and the rate of elongation. The framework provides a way to incorporate the internal microstructure of the aggregates into the computational model and yields a better understanding of the hemodynamics and physiology of platelet aggregates, hence laying the foundation for predicting aggregation and deformation under different flow conditions.

Conformation of von Willebrand factor in shear flow revealed with stroboscopic single-molecule imaging

von Willebrand factor (VWF) is a multimeric blood protein that acts as a mechanical probe, responding to changes in flow to initiate platelet plug formation. Previously, our laboratory tests had shown that using single-molecule imaging that shear stress can extend surface-tethered VWF, but paradoxically, we found that the required shear stress was higher than reported for free-in-flow VWF, an observation inconsistent with basic physical principles. To resolve this inconsistency critical to VWF's molecular mechanism, we measured free-VWF extension in shear flow using pulsed laser stroboscopic imaging of single molecules. Here, laser pulses of different durations are used to capture multiple images of the same molecule within each frame, enabling accurate length measurements in the presence of motion blur. At high shear stresses, we observed a mean shift in VWF extension of <200 nm, much shorter than the multiple-micron extensions previously reported with no evidence for the predicted sharp globule-stretch conformational transition. Modeling VWF with a Brownian dynamics simulation, our results were consistent with VWF behaving as an uncollapsed polymer rather than the theorized compact ball. The muted response of free VWF to high shear rates implies that the tension experienced by free VWF in physiological shear flow is lower than indicated by previous reports and that tethering to platelets or the vessel wall is required to mechanically activate VWF adhesive function for primary hemostasis.

Uncertainty quantification of a thrombosis model considering the clotting assay PFA-100®

Mathematical models of thrombosis are currently used to study clinical scenarios of pathological thrombus formation. As these models become more complex to predict thrombus formation dynamics high computational cost must be alleviated and inherent uncertainties must be assessed. Evaluating model uncertainties allows to increase the confidence in model predictions and identify avenues of improvement for both thrombosis modeling and anti-platelet therapies. In this work, an uncertainty quantification analysis of a multi-constituent thrombosis model is performed considering a common assay for platelet function (PFA-100®). The analysis is facilitated thanks to time-evolving polynomial chaos expansions used as a parametric surrogate for the full thrombosis model considering two quantities of interest; namely, thrombus volume and occlusion percentage. The surrogate is thoroughly validated and provides a straightforward access to a global sensitivity analysis via computation of Sobol' coefficients. Six out of 15 parameters linked to thrombus consitution, vWF activity, and platelet adhesion dynamics were found to be most influential in the simulation variability considering only individual effects; while parameter interactions are highlighted when considering the total Sobol' indices. The influential parameters are related to thrombus constitution, vWF activity, and platelet to platelet adhesion dynamics. The surrogate model allowed to predict realistic PFA-100® closure times of 300,000 virtual cases that followed the trends observed in clinical data. The current methodology could be used including common anti-platelet therapies to identify scenarios that preserve the hematological balance.

Engineered Molecular Therapeutics Targeting Fibrin and the Coagulation System: a Biophysical Perspective

The coagulation cascade represents a sophisticated and highly choreographed series of molecular events taking place in the blood with important clinical implications. One key player in coagulation is fibrinogen, a highly abundant soluble blood protein that is processed by thrombin proteases at wound sites, triggering self-assembly of an insoluble protein hydrogel known as a fibrin clot. By forming the key protein component of blood clots, fibrin acts as a structural biomaterial with biophysical properties well suited to its role inhibiting fluid flow and maintaining hemostasis. Based on its clinical importance, fibrin is being investigated as a potentially valuable molecular target in the development of coagulation therapies. In this topical review, we summarize our current understanding of the coagulation cascade from a molecular, structural and biophysical perspective. We highlight single-molecule studies on proteins involved in blood coagulation and report on the current state of the art in directed evolution and molecular engineering of fibrin-targeted proteins and polymers for modulating coagulation. This biophysical overview will help acclimatize newcomers to the field and catalyze interdisciplinary work in biomolecular engineering toward the development of new therapies targeting fibrin and the coagulation system.

Distribution and history of extensional stresses on vWF surrogate molecules in turbulent flow

The configuration of proteins is critical for their biochemical behavior. Mechanical stresses that act on them can affect their behavior leading to the development of decease. The von Willebrand factor (vWF) protein circulating with the blood loses its efficacy when it undergoes non-physiological hemodynamic stresses. While often overlooked, extensional stresses can affect the structure of vWF at much lower stress levels than shear stresses. The statistical distribution of extensional stress as it applies on models of the vWF molecule within turbulent flow was examined here. The stress on the molecules of the protein was calculated with computations that utilized a Lagrangian approach for the determination of the molecule trajectories in the flow filed. The history of the stresses on the proteins was also calculated. Two different flow fields were considered as models of typical flows in cardiovascular mechanical devises, one was a Poiseuille flow and the other was a Poiseuille–Couette flow field. The data showed that the distribution of stresses is important for the design of blood flow devices because the average stress can be below the critical value for protein damage, but tails of the distribution can be outside the critical stress regime.

Flow-regulated nucleation protrusion theory for collapsed polymers

The globular-stretch transition of a collapsed polymer in low strain rate elongational flow is studied using polymeric protrusion kinetics scaling laws and numerical simulation. Results demonstrate the influence of fluid flow on the occurrence probability of long-length thermally nucleated polymeric protrusions, which regulate collapsed polymer unfolding in low strain rate flows. Further, we estimate that the globular-stretch transition rate (k_{s}) in low strain rate (∈[over ̇]) elongational flows varies as k_{s}∼e^{-α∈[over ̇]^{-1}}. Results here reveal that the existing approach of neglecting the effects of fluid flow on thermally nucleated protrusions distribution is not valid for analyzing polymer unfolding behavior in low strain rate flows. Neglecting such an effect overestimates the constant α in the scaling law of transition rate (k_{s}∼e^{-α∈[over ̇]^{-1}}) by a factor of 2.

A Continuum Model for the Unfolding of von Willebrand Factor

von Willebrand Factor is a mechano-sensitive protein circulating in blood that mediates platelet adhesion to subendothelial collagen and platelet aggregation at high shear rates. Its hemostatic function and thrombogenic effect, as well as susceptibility to enzymatic cleavage, are regulated by a conformational change from a collapsed globular state to a stretched state. Therefore, it is essential to account for the conformation of the vWF multimers when modeling vWF-mediated thrombosis or vWF degradation. We introduce a continuum model of vWF unfolding that is developed within the framework of our multi-constituent model of platelet-mediated thrombosis. The model considers two interconvertible vWF species corresponding to the collapsed and stretched conformational states. vWF unfolding takes place via two regimes: tumbling in simple shear and strong unfolding in flows with dominant extensional component. These two regimes were demonstrated in a Couette flow between parallel plates and an extensional flow in a cross-slot geometry. The vWF unfolding model was then verified in several microfluidic systems designed for inducing high-shear vWF-mediated thrombosis and screening for von Willebrand Disease. The model predicted high concentration of stretched vWF in key regions where occlusive thrombosis was observed experimentally. Strong unfolding caused by the extensional flow was limited to the center axis or middle plane of the channels, whereas vWF unfolding near the channel walls relied upon the shear tumbling mechanism. The continuum model of vWF unfolding presented in this work can be employed in numerical simulations of vWF-mediated thrombosis or vWF degradation in complex geometries. However, extending the model to 3-D arbitrary flows and turbulent flows will pose considerable challenges.