Shear-Induced Extensional Response Behaviors of Tethered von Willebrand Factor

Abstract

We perform single-molecule flow experiments using confocal microscopy and a microfluidic device for shear rates up to 20,000 s⁻¹ and present results for the shear-induced unraveling and elongation of tethered von Willebrand factor (VWF) multimers. Further, we employ companion Brownian dynamics simulations to help explain details of our experimental observations using a parameterized coarse-grained model of VWF. We show that global conformational changes of tethered VWF can be accurately captured using a relatively simple mechanical model. Good agreement is found between experimental results and computational predictions for the threshold shear rate of extension, existence of nonhomogenous fluorescence distributions along unraveled multimer contours, and large variations in extensional response behaviors. Brownian dynamics simulations reveal the strong influence of varying chain length, tethering point location, and number of tethering locations on the underlying unraveling response. Through a complex molecule like VWF that naturally adopts a wide distribution of molecular size and has multiple binding sites within each molecule, this work demonstrates the power of tandem experiment and simulation for understanding flow-induced changes in biomechanical state and global conformation of macromolecules.

Significance

We advance experimental data for the shear-induced extensional response of the individual blood-clotting factor, von Willebrand factor (VWF), using a microfluidic device and fluorescence microscopy. Further, we use the results from tandem Brownian dynamics simulations of an experimentally parameterized coarse-grained VWF model to help explain some of our central observations from experiment. This work elucidates further details of the flow-induced biomechanical response behaviors of tethered VWF and demonstrates the power and capabilities of increasingly complex coarse-grained models employed in tandem with experiment.

Introduction

Functionality for some biologically relevant molecules is strongly dependent upon changes in their biomechanical state. These changes can manifest in, for example, polymeric conformation or the internal stress distribution and occur in response to the sensation of stimuli, such as chemical signaling or mechanical stimulation (1, 2, 3, 4, 5). In particular, flow plays an important role in the regulation of biomechanical state and functionality for a number of biomolecules and their assemblies (6, 7, 8, 9, 10). Conventional studies have focused on the bulk rheological properties of solutions or gels, whereas recent research aims at elucidating the dynamics of individual biomolecules under flow using both experimental and computational approaches. Flow-induced conformational changes of λDNA are a benchmark example (11, 12, 13, 14, 15, 16). Examination of single λDNA molecules opened the door to many new flow experiments, new physical principles governing the dynamics, and the development of mathematical and molecular modeling techniques for understanding these principles (17). Another well-studied example is a clotting factor called von Willebrand factor (VWF) that has attracted much attention as the “Jedi knight of the bloodstream” because of its hydrodynamic force-sensing capabilities that promote hemostasis (18). Dynamics of VWF interactions with collagen and platelets receptor have been investigated in response to external forces (19, 20, 21).

VWF is a plasma protein that initiates platelet plug formation in response to vascular damage (22, 23). VWF functionality is flow-regulated (24, 25, 26). Under normal circulation conditions, VWF exists in a compact globular conformation (24, 27). However, VWF senses elevated hydrodynamic force at the site of vascular damage and responds by unraveling (28, 29, 30, 31, 32). VWF is essentially inert under typical blood flow conditions, but its functionality is activated upon changes in biomechanical state on multiple length scales in response to sufficient hydrodynamic force. Unraveling, on a macromolecular level, reveals previously hidden active sites that are otherwise deeply buried within the globule (18, 30, 31). Further biomechanical changes on a submonomer level activate functionalities such as A1 domain-platelet binding (30) and A2 domain scission (28, 29, 33, 34, 35, 36, 37, 38, 39). VWF binds to the platelet receptor GPIbα in the A1 domain, which has been shown to be regulated by internal A1 domain tension and autoinhibited by force-dependent structural changes arising from an A2 domain association (30, 40, 41, 42, 43). A1-GPIbα interaction has also shown to trigger platelet integrin signaling and activation (44, 45). VWF functionality also manifests in A3-collagen binding (34). In the event of vascular damage, VWF is able to bind with exposed collagen at the A3 domain and become tethered to the vessel wall. Tethering can also occur if ultralarge VWF remains anchored during secretion into the vasculature.

Previous authors have used single-molecule experiments and simulations to examine the flow-induced dynamics and functionality of tethered and free-flowing VWF, which helped elucidate molecular-level behaviors crucial to VWF biology and physics (19, 21). Atomic force microscopy (AFM) has been used to capture in situ variations in the three-dimensional structure of VWF under shearing (26, 46). However, the temporal resolution of AFM is insufficient for capturing the highly dynamic behavior of VWF in flow. Furthermore, the AFM probe could potentially interfere with observations of shear-induced conformational changes. Microfluidic channels combined with fluorescence microscopy have enabled visualization of shear-induced VWF unraveling. Significant elongations were observed above a critical shear rate of 5000 s⁻¹ for free-flowing VWF in the bulk (47). Other authors observed extended conformations of nongrafted VWF in the bulk above the threshold shear stress of approximately 2.0–2.5 Pa (48). This corresponds to shear rates of approximately 20,000–25,000 s⁻¹ for a fluid viscosity of 100 mPa∙s, which is 100 times larger than the viscosity of water at room temperature. Recently, in their seminal work, Fu et al. observed shear-induced elongation and activation and subsequent VWF-GPIbα binding of surface-bound VWF in shearing flows (30).

The optical imaging techniques typically employed for single-molecule visualization have limited spatial and temporal resolutions, which challenges their use for probing submonomer VWF dynamics. Nonetheless, subtle domain-level conformational changes at length scales below 10 nm have been captured using small-angle neutron scattering and fluorescence microscopy at shear rates <3000 s⁻¹ for VWF in the bulk (25). In addition, Arya et al. used optical tweezers to characterize the interactions between VWF and GPIbα (19, 21). Despite these in-depth studies, many domain-level details of the underlying flow-induced biomechanical responses of VWF remain unknown.

A variety of molecular dynamics simulations and modeling techniques have been used to study polymers in flow. Using coarse-grained models, numerous authors have characterized internal force distributions, adhesion and cleavage rates, critical shear rates, and conformational changes exhibited by tethered and nongrafted VWF subject to various flow and chain conditions (49, 50, 51, 52, 53, 54, 55, 56, 57, 58). Prior authors examined long linear polymers using a coarse-grained model to reveal the mechanism responsible for the initiation of macromolecular unraveling in bulk-flowing polymers, which they described in a protrusion nucleation theory (59, 60, 61). Recently, a more finely resolved model was employed to reveal submonomer VWF dynamics that helped provide a mechanistic explanation for the mechanically regulated autoinhibition of VWF-platelet binding (40). Those authors identified that cleavage of an unusual disulfide bond in the A2 domain modifies its structure and molecular stresses in a long-range allosteric manner, which induces A1-A2 domain binding and blocks the GPIbα binding site in the A1 domain.

Our group has previously introduced an experimentally parameterized and coarse-grained model of VWF. In those works, we performed Brownian dynamics (BD) simulations of VWF in shear flows to examine the internal dynamics experienced by nongrafted multimers and their shear-dependent rates of adhesion to a model surface (49, 50, 51). The dynamical behaviors of tethered and free-flowing polymers differ greatly (62), and in this study, we turn our attention to the biomechanical response behaviors of tethered VWF in shear flows. We advance experimental data for the shear-induced elongation of surface-bound VWF in a microfluidic device using fluorescence microscopy. We compare our data with previously reported values for the threshold shear rate of extension and discuss new, to our knowledge, observations of the extensional response behavior. Lastly, we employ BD simulations to examine VWF multimers bound to a model surface and probe various molecular sizes, shear rates, and VWF-surface tethering conditions to offer further explanation for our shear-induced extension observations. By combining an experimentally parameterized coarse-grained model with microfluidic-based experiments, this work demonstrates how one could gain in-depth understanding of flow-induced global conformational changes of macromolecules.

Materials and Methods

VWF labeling and purification

The VWF multimer sample is derived from human plasma (Millipore, Burlington, MA), and the molecular weight (MW) has a wide distribution as confirmed by Western blot. A sulfo-N-hydroxysuccinimide-LC-Biotinylation kit (Thermo Fisher Scientific, Waltham, MA) and an Alexa 488 5-sulfodichlorophenol Ester kit (Thermo Fisher Scientific) were applied to tag VWF with biotin and fluorophore molecules. The excitation peak wavelength of the fluorophore is 490 nm, and the emission band is 470–690 nm with a peak of 525 nm, according to the manufacturer’s data sheet. Both the fluorophore and biotin were covalently conjugated to amine groups on VWF, which is typically present in protein through the side chain of lysine (K) residues. Alexa 488 sulfodichlorophenol ester produces carboxamide bonds with VWF. N-Hydroxysuccinimide esters of biotin react with primary amino groups of VWF and form covalent amide bonds. Labeled VWF was purified by Slide-A-Lyzer MINI Dialysis Device Floats (Thermo Fisher Scientific). Biotinylation was confirmed by dot blot.

Microfluidic device fabrication

The microfluidic device used in experiment is illustrated in Fig. 1 A. The channel pattern, illustrated in Fig. 1 B, was created on a silicon wafer using standard photolithography techniques. Applying the wafer as a mold, a 10:1 mixture of polydimethylsiloxane (PDMS) precursor and curing agent (Dow Corning, Midland, MI) was incubated at 60°C overnight to cure fully. An inlet and outlet were drilled through the solidified PDMS layer, which was then sealed onto a #1.5 glass coverslip (Corning, Corning, NY) by O₂ plasma. The channel measured 50 μm in height and 8 mm in length and varied in width from 0.1 to 1.0 nm. Fluorescent imaging of tethered VWF occurred in the constricted region of the microfluidic channel, illustrated in Fig. 1 A, where the shear rate is the greatest.

Figure 1.

(A) A photograph of the PDMS microfluidic channel used for flow experiments (filled with dye for illustration). (B) A microchannel schematic (dimensions measured in mm) is given. (C) Confocal microscopy was used to image VWF multimers tethered on the microfluidic device surface. The top schematic illustrates flow through the constricted region of the microchannel, where fluorescent imaging was conducted. Bottom schematics illustrate shear-induced extension of one tethered VWF multimer, which depends on the shearing strength. To see this figure in color, go online.

Surface modification and VWF immobilization

After device fabrication, the glass surface was coated with streptavidin to immobilize biotinylated VWF molecules. First, the microfluidic channel was incubated with 10 μg/mL biotinylated bovine serum albumin (Sigma-Aldrich, St. Louis, MO) for 2 hours. Then, a commercial blocking solution (Candor, Wangen, Germany) was injected into the channel and incubated for 30 min. Afterwards, 10 μg/mL streptavidin (Sigma-Aldrich) was applied for a 10-min incubation before the channel was washed by 15 μL washing buffer (Perkin Elmer, Waltham, MA). Subsequently, the solution of VWF multimers labeled with biotin and fluorophore was slowly injected into the channel and incubated for 5 min. After VWF immobilization, free D-biotin (Sigma-Aldrich) was injected into the device and incubated for another 10 min to block unreacted streptavidin binding sites. All incubations occurred at room temperature. Standard phosphate-buffered saline solution (Thermo Fisher Scientific) was used to dissolve and dilute the reagents to desired concentrations.

Flow experiments and image acquisition

The top schematic in Fig. 1 C illustrates flow through the constricted region of the microfluidic device where imaging occurred, and the bottom schematics depict the shear-dependent elongation of tethered VWF multimers. A syringe pump was used to attain eight shear rates herein considered that ranged from 0 to 20,000 s⁻¹. Shear rates were calculated based on corresponding flow rates and by assuming a steady laminar flow through a channel of rectangular cross section. The flushing buffer was based on phosphate-buffered saline and contained 0.02% Tween 20 (Fisher Scientific, NH), 0.1 mM free biotin, and 0.5 mg/mL bovine serum albumin (Sigma-Aldrich). A fluorescence confocal microscope captured single-molecule unraveling events at one frame per second. Image analysis was conducted to obtain conformation and elongational lengths. Normalized extension (E) is defined for each shear rate as the elongational length (L) minus the initial length (L_o), divided by the difference of the maximal (L_max) and initial lengths of the same molecule,$E=(L-L_0)/(L_{max}-L_0)$. Initial and maximal lengths are given by measurements of each molecule at shear rates 0 and 20,000 s⁻¹, respectively (with exceptions addressed in text).

Coarse-grained VWF monomer model

Our VWF model represents a single monomer by a system of two beads connected by a finitely extensible nonlinear elastic (FENE) spring. A bead radius of a = 15 nm was selected to accurately represent length scales inherent to the molecular architecture. The connecting FENE spring is explicitly used to model the A2 domain, which has a spring constant, H = 0.12 pN/nm, and maximal extensible length, Q_max = 51.5 nm, that were parameterized by fitting experimental A2 force-extension data (33). The overall length of a model VWF monomer at equilibrium is 61.0 nm, which includes a 1.0 nm FENE spring equilibrium length and agrees with experimentally reported values ranging from 60 to 70 nm (18, 31). Adjacent monomers are connected by stiff harmonic springs that represent disulfide bonds. Simulations were performed for VWF multimers composed of 20, 40, and 80 monomers (N = 40, 80, and 160 beads, respectively). These lengths are within the physiological range (18) and agree with multimer length estimates for VWF multimers observed experimentally in this work. Further model details and parameter values are given in the Supporting Materials and Methods and our previous works (49, 50, 51).

BD simulations

BD simulations began with a 20-chain ensemble of noninteracting VWF multimers, each with a unique initial compact globular conformation that was previously equilibrated. The Langevin equation is used to describe the motion of the bead ensemble in the inertia-free limit. Hydrodynamic interactions are captured using the Rotne-Prager-Yamakawa tensor, with the modifications outlined by Hoda and Larson to account for the presence of the model surface (63). The Brownian square-root tensor is computed by Cholesky decomposition of the diffusion tensor. Data collection occurred once every 2500 time steps, where the time step selected was Δt = 15.35 × 10⁻⁴ μs. Simulations continued until an ensemble average quasisteady elongational length was achieved, which depended on shear rate and typically converged well below a duration of 10⁶ time steps (except for shear rates near the threshold value for extension). Further simulation details and description of the governing equations are given in the Supporting Materials and Methods and our previous works (49, 50, 51).

Results and Discussion

Reversible unraveling of VWF in shear flows

Circulating VWF exhibits a wide range of sizes, from dimer units (520 kDa) to large multimers containing up to 40–200 monomers (18). Western blot results indicated that our VWF sample had a wide MW distribution starting at approximately 1000 kDa (∼4-mer), although determination of the larger multimer MWs is difficult because of the lack of standards. Dot blot results indicated that VWF was successfully labeled with biotin and capable of tethering to streptavidin-coated surfaces. A casein-based coating was applied inside the microfluidic channel to minimize nonspecific binding. The concentration of each reagent was optimized so that multiple molecules were visible in each frame under the microscope while significant spacing was present to prevent interference from neighboring molecules. Flowing in free biotin after VWF incubation blocked streptavidin not bound to a VWF chain, which prevented additional binding during elongation and ensured reversible VWF unraveling. Without any flow, we observed fluorescently labeled VWF multimers appearing as dots on the channel surface with diameters ranging from 0.5 to 1.5 μm, which is comparable to previously reported sizes (30, 47, 48). In control experiments without streptavidin coating, few fluorescent dots were observed in the channel, confirming that the fluorescent signals observed were individually tethered molecules.

Under physiological conditions, circulating VWF does not bind GPIb-IX-V or to the blood vessel wall, which is lined by endothelial cells. Only when shear is high—for example, at the bleeding site—will VWF be activated by flow and unravel from coil to string. Unraveled VWF binds to the matrix protein collagen and mediates platelet plug formation (64). Instead of using collagen or model cells that express GPIb-IX-V to immobilize VWF molecules, we applied avidin-biotin binding, the strongest known noncovalent receptor-ligand pair (65, 66), because it allows immobilization of VWF with one or few strong anchorage points not easily breakable by shear. This also allows VWF to unravel and relax reversibly. The type of immobilization chemistry is not expected to change the biomechanical behavior of the untethered portion of the VWF multimer. Also, the number of interaction sites between each biotinylated VWF and an avidin coating can be controlled through the level of biotinylation and density of surface avidin, as well as blocking redundant avidin on the surface with free biotin; by doing so, the untethered portion of VWF, upon unraveling, does not develop additional interactions with the substrate.

In streptavidin-coated channels, we further inspected the mechanical behavior of single immobilized VWF molecules under flow. Cycles of elongation followed by relaxation were achieved by turning the flow on and off using a syringe pump. Experiments were first performed at a single shear rate with multiple elongation cycles (Fig. S3). The averaged elongation was consistent over multiple cycles of flow, whereas there is a ∼15% variation in length after the molecule reaches the maximal length. A relaxation time above 10 s was found to be sufficient for the molecule to relax back to its original length at the end of each flow cycle. A single molecule was then examined at eight shear rates that increased stepwise from 0 up to 20,000 s⁻¹. The molecules were exposed to each shear condition for 15 s, controlled by a syringe pump, and flow was stopped for another 15 s to allow their relaxation after each shear exposure.

Typical single-chain unraveling dynamics are discussed for the example VWF multimer depicted in Fig. 2 A (Video S1). Image analysis at each shear rate yields multimer length in the flow direction, which is plotted as a function of shear rate in Fig. 2 C. For this example chain, the globular diameter measured at 0 shearing is 1.2 μm, and the maximal observed length is 4.0 μm at the highest shear rate tested of 20,000 s⁻¹. Normalized extension, also illustrated in Fig. 2 C, initially increases rapidly but slows down around the shear rate of 5000 s⁻¹, where the molecule reaches 80% of the longest observed length. Comparable simulation results are depicted by the snapshots in Fig. 2 B for a 40-mer chain (N = 80 beads) that is tethered to a model surface at one terminal bead. Simulation data for elongation and normalized extension in Fig. 2 C are average results for a 20-chain ensemble possessing identical length and tethering conditions as the multimer depicted in Fig. 2 B. Average normalized extension exceeds 70% of the maximal observed length at 5000 s⁻¹, which compares with the value of 80% for its experimental counterpart. Elongation and normalized extension curves for experiment and simulation in Fig. 2 C share similar features and shape. This agreement, at least qualitatively, suggests that our simulations capture the flow-induced extensional response behavior observed in experiment for increasing shear rate.

Figure 2.

Shear-induced elongations of a single surface-bound VWF multimer under increasing shear rate are illustrated from top to bottom by (A) experimental fluorescence microscopy images and (B) BD simulation snapshots. Shear flows act in the positive x-direction. Elongational length and normalized extension are illustrated in (C) as a function of shear rate for the molecule depicted in (A) and the average behavior of 20 model VWF chains with the same characteristics (i.e., size and tethering conditions) as that illustrated in (B). The model VWF chain illustrated in (B) is composed of 40 monomers (N = 80 beads) and is wall-bound at the terminal bead indicated by an arrow. A single VWF monomer is represented by two beads, one darker and the other lighter shaded, connected by an FENE spring, and adjacent monomers are connected by harmonic springs. Shear rates corresponding to images in both (A) and (B) are $\dot{\gamma }$ = 0, 500, 1000, 2000, 5000, 10,000, 15,000, and 20,000 s⁻¹. To see this figure in color, go online.

It should be noted that the quiescent molecular diameter between experimental measurements and simulation differs significantly (Fig. 2, A and B at 0 s⁻¹). This difference could be partially accounted for by the lateral resolution of the confocal fluorescent microscope of ∼400 nm. Fluorescence species smaller than the resolution length would appear larger. However, because the lateral resolution is finer than the observed VWF diameters, we believe a second factor contributes more significantly to the large quiescent diameter, which is image smearing due to molecular Brownian motion during the exposure time of 1 s. Simulations reveal that for the case of a single terminally bound bead, the thermal motion of the polymer chain about the tether location causes the observed diameter to appear ∼3–4 times larger than the physical diameter on timescales associated with the image acquisition or exposure time. This effect has greater influence on shorter rather than longer chains, which is what we expect because the coefficient of diffusion for a generally spherical and collapsed multimer is inversely proportional to its globular radius. Diffusive effects are also mediated by the number and location of wall-bound beads. Using the simulated smearing factors of 3–4 to rescale the quiescent VWF diameter in the experiments, we found close agreements between the confocal and simulation results.

Despite the smearing effect at zero flow conditions, it has little influence on length measurements at high shear rates. This is because hydrodynamic effects dominate the dynamics of VWF, as opposed to thermal molecular motion, and we hence suspect that unraveled chains exhibit decreased configurational fluctuations—i.e., image smearing. This is corroborated by comparing the signal/noise ratio for the steady-state elongational lengths (Fig. S2), which clearly illustrates that flow-induced conformational changes dwarf those due to thermal fluctuations at high shear rates. As a result, the length measurement from simulation and experiments compare well at high shear (Fig. 2, inset).

Fluorescence microscopy images of different molecules demonstrated variable “fluorescent banding,” or distinct high-intensity fluorescence regions along unraveled chain contours. Some examples of this phenomenon are illustrated in Fig. 3 A. Assuming a uniform fluorophore labeling on the molecule surface in the coiled state, the banding suggests, at least qualitatively, that local monomer density varies in the flow direction, and consequently so may the potential for VWF activation. Previous authors observed similar behavior and analyzed the fluorescence intensity distribution to estimate the average extension per VWF monomer (30). An inhomogeneous extension distribution, hydrodynamic shielding, or topological constraints associated with these intensity regions may change local physiological properties such as internal stress distribution that may also alter VWF binding affinity toward platelets (30). We observed high-intensity regions at both termini and at locations in between, although banding in central regions appeared to occur more often for long elongations at high shear rates.

Figure 3.

(A) Fluorescence microscopy images show the presence of high-intensity fluorescence regions along the contour of tethered VWF multimers that have unraveled because of fluid shearing for five different example images. (B) Simulation snapshots show variation in local molecular density along chain contours. Snapshots depict quasisteady elongations for various chain length (N) and tethering conditions (tether point (TP)), tabulated in (B). Arrows indicate tether locations. To see this figure in color, go online.

The simulation snapshots illustrated in Fig. 3 B are used to discuss the presence of high-intensity fluorescent regions observed in experiment. Snapshots depict the shear-induced unraveling response of VWF for various chain lengths and tethering conditions. Snapshots illustrate steady-state elongational lengths, which converged after a short, transient unraveling period. Upon application of flow, an initially compact globule rotates about its tether point in an attempt to align in the flow direction. Unraveling begins from the tether point location past a threshold shear rate and propagates down the chain contour. For constant shear rates near the threshold value, steady-state extension is achieved before complete macromolecular unraveling because hydrodynamic force lacks the strength required to entirely unravel the chain. In this case, a stable globule forms at the free end of the multimer, illustrated in Fig. 3 B (i–iv). This may account for the high-intensity fluorescent regions observed experimentally at the free end of the tethered multimers.

Similarly, high-intensity regions were observed in experiments at upstream tether point locations. Simulation results, depicted in Fig. 3 B (i, v), suggest these may result from VWF-surface tethering at interior contour locations. In this case, two VWF strands extend from the tether point location, and their relative lengths depend on the binding location along the chain contour. Depending on flow and tether point conditions, simulations revealed the shorter of two chain fragments can congregate around the tether point location, which may explain the high-intensity regions observed experimentally there. High-intensity regions were also observed experimentally at interior contour locations for some unraveled chains, although tethering point conditions can, in part, account for these observations, illustrated in Fig. 3 B (iii–v). This is under further investigation and will be addressed in a later study.

Shear-induced VWF unraveling

Reversible unraveling was recorded for 70 VWF molecules at various shear rates up to 20,000 s⁻¹. The corresponding elongational lengths are illustrated in Fig. 4 A, which increase with shear rate. At 0 shearing, most of the coiled VWF molecules adopted globular conformations with diameters between 1.0 and 1.5 μm. Most chains reach maximal lengths between 2.0 and 4.0 μm at the highest shear rate considered of 20,000 s⁻¹, with the shortest and longest extensions being approximately 1.8 and 5.8 μm, respectively. The contour length of a single VWF monomer is approximately 60–70 nm (18, 31). This suggests the observed VWF multimers range from ∼25 to 95 monomers in length, assuming multimers that are terminally tethered and fully extended at 20,000 s⁻¹. This range agrees well with the VWF size distribution present in plasma (32).

Figure 4.

Experimental unraveling results for 70 tethered VWF molecules for the eight shear rates herein considered: $\dot{\gamma }$ = 0, 500, 1000, 2000, 5000, 10,000, and 20,000 s⁻¹. (A) Raw elongational lengths are shown. (B) Box-and-whisker representation of raw elongation lengths are shown. Boxes indicate the central 50% of data, wherein lines show median values and whiskers indicate the lowest and highest observed values not considered as outliers. Data represented by crossed symbols, +, are data points considered to be statistical outliers based on the box-and-whisker representation (see text). (C) Normalized extension is shown. (D) Ensemble average normalized extension as a function of shear rate is shown. The inset illustrates the same data in a linear-log plot, but only for the five smallest shear rates considered (<5000 s⁻¹). The shaded region represents one standard deviation (SD) in experimental variation.

Fig. 4 B presents the same data in a box-and-whisker plot. Boxes indicate the central 50% of data, wherein lines show median values and whiskers indicate the lowest and highest observed values not considered as outliers. Data represented by crossed symbols are statistical outliers based on the box-and-whisker representation; they have length values more than 1.5 times the interquartile range away from the top or bottom of the box. The outliers we observed generally have much longer extension than the majority of the molecules and likely represent ultrahigh MW multimers.

The underlying shear-induced extensional response can be compared among the 70 molecules of various lengths by normalizing elongation data, illustrated in Fig. 4 C. A few multimers attain their maximal lengths below the highest shear rate of 20,000 s⁻¹; in these cases, the maximal length was taken from the corresponding shear rates depicted in Fig. 4 C, leading to a drop of normalized extension at greater shear rates.

The average normalized extension as a function of shear rate is illustrated in Fig. 4 D and is obtained by averaging the 70 curves in Fig. 4 C. Ensemble average multimer extension steeply increases up to 5000 s⁻¹, where it reaches ∼60% of the maximal value. The inset highlights the lower range of shear response in a linear-log plot between the shear rates 0 and 5000 s⁻¹. Average extension data in this shear rate range was heuristically fitted to$E=c_1\log \left(\dot{\gamma }\right)+c_2$, and the threshold shear rate associated with the onset of extension was determined to be 400 s⁻¹ by extrapolating to zero extension. Fu et al. examined a range of molecular sizes and shear stresses and reported elongation of tethered VWF multimers occurred at the threshold shear stress of 1.5 Pa, which corresponds to a shear rate of 1500 s⁻¹ for the fluid viscosity employed of 1 cP (30). The single longest elongational length they observed under shearing was 6.5 μm. These differences may be caused by different sample sources. The VWF sample used in Fu and colleagues’ work is recombinant human VWF expressed in Chinese hamster ovary (CHO) cells and further purified by an ion exchange column (30). The VWF used in our study is purified from human plasma by gel filtration chromatography according to the manufacturer’s data sheet. VWF made from different species could have different post-translational modifications. In particular, glycosylation has shown to affect VWF structure and function (67, 68, 69). As a result, VWF molecules in our experiments could potentially display different mechanical properties compared to VWF made from CHO cells.

The shaded region in Fig. 4 D illustrates one SD in experimental variation for the average normalized extension. The variation in extensional behavior increases with shear rate until 5000 s⁻¹ and gradually decreases at higher shear rates. Discussed below, we show this variation is inherent to the system and a result of deterministic parameters that characterize the extensional response behavior. Because revealing these parameters is experimentally challenging, we have employed companion BD simulations to elucidate the details.

Influence of chain length and tether point

Using fluorescence microscopy, we observed large variation in the extensional response behavior exhibited by surface-immobilized VWF in shear flows. We have employed numerical simulations to study a few factors that may be contributors to this observation—chain length, tether point location, and multiple tethering point locations. Fig. 5 presents simulation results for the shear-induced normalized extension of model VWF multimers that are tethered to a model surface and subject to shearing flows.

Figure 5.

BD simulation results for the ensemble average normalized extension of tethered VWF multimers as a function of shear rate. Each simulation curve is an average result from a 20-chain ensemble. (A) Influence of chain length, for chains tethered at the first of N = 40, 80, and 160 beads, is shown. (B) Influence of TP location (measured by bead index) is shown for chains composed of 40 monomers (N = 80 beads) that are grafted to a model surface at one of four possible locations along the multimer contour. (C) Influence of multiple tethering point locations is shown for chains composed of N = 80 beads immobilized at two locations that are 0.225 μm apart in the flow direction. Curves correspond to the following 15 pairs of tethered bead combinations: {(1, 13), (1, 25), (1, 37), (1, 49), (1, 61), (1, 73), (13, 25), (13, 37), (13, 49), (13, 61), (13, 73), (25, 37), (25, 49), (25, 61), (25, 73)}. (D) Comparison of ensemble average normalized extension behavior between experiment and simulation is shown. The shaded region indicates one SD in experimental variation for the average normalized extension. Simulation results for varying (A) chain length and (B and C) tethering conditions are replotted in subfigure (D). Insets illustrate corresponding data in linear-log plots but for shear rates up to 5000 s⁻¹.

Fig. 5 A compares normalized extension for multimers composed of 20, 40, and 80 monomers (N = 40, 80, and 160 beads, respectively) that are tethered at the first (i.e., terminal) bead. The wall-bound bead was immobilized so the edge measured two bead diameters above the wall surface in the z-direction. For all chain lengths, extension sharply increases up to 5000 s⁻¹ and becomes more gradual with higher shearing. The inset depicts the same data in a linear-log plot for shear rates 0–5000 s⁻¹ and clearly illustrates that the extensional response behavior is dependent upon chain length. There is a nearly 40% difference in average normalized extension between chains that are 20 and 80 monomers in length (N = 40 and 160 beads, respectively) at the shear rate 2000 s⁻¹. Fu et al. also observed experimental variation in the extensional response behavior of tethered VWF in shear flows; however, their analysis indicated the normalized response was invariant to chain length. Our simulation results in Fig. 5 A indicate that the extensional response is larger for longer multimers because longer chains are subject to greater hydrodynamic forces that must be internally balanced. Further, Fig. 5 A indicates that the threshold shear rate for extension decreases with increasing chain length or MW. The longest chain length herein considered was composed of 80 monomers (N = 160 beads) and began unraveling at approximately 500 s⁻¹. Our results strongly suggest that the threshold shear rate for extension should decrease even further with increasing multimer lengths for terminally bound chains.

Knowledge of the tethering conditions cannot be easily obtained in experiments, and it is plausible that VWF-surface binding is possible anywhere along the multimer surface. We examined the influence of tether point location for VWF chains composed of 40 monomers (N = 80 beads). One out of four possible beads at different locations along the multimer contour was tethered to a model surface. Beads capable of tethering are indexed by 1, 13, 25, or 37 out of N = 80 beads total, which represent the full contour length and approximately one-sixth, one-third, and one-half of the total contour length, respectively. Fig. 5 B indicates that the extensional response is retarded as tethering location along the multimer contour tends toward the chain center. Further, the threshold shear rate for extension is approximately two to four times larger for interior tether point locations compared to terminally bound chains. This occurs because of topological constraints, hydrodynamic shielding effects between the two tethered chain fragments, and a reduction in the effective contour length realized by the flow (measured from the tether point location to the terminus of the longest strand).

Similar to tether point location, it is plausible that multiple binding sites along the chain contour may immobilize VWF to a surface. We probed shear-induced elongations for 15 different wall-bound bead pair combinations for VWF multimers composed of 40 monomers (N = 80 beads). First, consider the case in which the two bound beads are in adjacent monomers; in this situation, the presence of multiple binding sites has little influence, and binding location along the multimer (as discussed above) is more significant. As the distance between the bound beads in the quiescent globular conformation increases, we postulate that the influence of multiple binding sites increases. Therefore, to maximize the influence of this effect, in these simulations, it was assumed that the two bound beads were a maximal possible distance apart in the quiescent globular conformation. That is, wall-bound beads were separated by 0.225 μm in the flow direction, which is near to the quiescent globular diameter for long multimers. Starting with bead 1, six additional beads were identified as eligible for binding: 13, 25, 37, 49, 61, and 73. Separate simulations were run with different combinations of two beads selected from this set of seven and subject to the separation distance requirement described above. Each pair of beads was immobilized so that their edges measured two bead diameters above the wall surface in the z-direction. After prescribing the locations of wall-bound beads, the remaining portions of the chain were allowed to equilibrate in quiescent flow to assume a physically relevant globular conformation as a starting state for the flow simulations. This procedure modeled the case as if the globule had naturally settled on the surface and become bound at the two prescribed bead locations. All starting conformations appeared to be similar to the molecule in Fig. 2 B at 0 shear rate. Curves in Fig. 5 C correspond to the following bead pair combinations: (1, 13), (1, 25), (1, 37), (1, 49), (1, 61), (1, 73), (13, 25), (13, 37), (13, 49), (13, 61), (13, 73), (25, 37), (25, 49), (25, 61), and (25, 73). Simulations with flow revealed that the threshold shear rate for extension and the magnitude of the elongational response are heavily influenced by the locations (along the multimer contour) of the multiple binding sites, illustrated in Fig. 5 C. Threshold shear rates for extension occur approximately between 500 and 2000 s⁻¹. Additionally, there is a nearly 50% difference between the smallest and largest normalized extensions observed at 5000 s⁻¹.

Fig. 5 D illustrates the ensemble average normalized extension as a function of shear rate for both experiment and simulation. The experimental data points and shaded region in Fig. 5 D illustrate normalized extension data and variation previously plotted in Fig. 4 D. The 22 simulation curves plotted in Fig. 5, A–C are superimposed on the experimental data in Fig. 5 D. The overlap of simulation curves and the shaded region from experiment suggests agreement in the observed and predicted unraveling response behavior. Simulation results capture the rapid increase in normalized extension up to 5000 s⁻¹ observed in experiments and the more gradual increase thereafter. Discussed earlier, variation in the extensional response behavior of tethered VWF in shear flows is attributed, at least in part, to changes in chain length, tether point location, and number of tethering location conditions. Changes in the number of tethering locations seems to introduce the most variation; however, all three variables alter the underlying biomechanical response of surface-bound VWF.

Conclusions

We advance data from single-molecule flow experiments for the reversible unraveling responses of tethered VWF multimers subject to shear flows up to 20,000 s⁻¹ using a microfluidic device and fluorescence microscopy. The observed flow-induced VWF elongation is in qualitative agreement with the previous reported result by Fu et al. (30). Shear-induced dynamics of the 70-molecule ensemble were compared by normalizing elongation data, which revealed large variations in the extensional responses of tethered VWF. This variation is explained using the results of companion BD simulations of an experimentally parameterized coarse-grained VWF model. Simulations revealed that the underlying biomechanical response of VWF is altered because of changes in chain length, tether point location, and number of tethering location conditions. We found that the threshold shear rate for extension decreases with increasing chain length and the magnitude of the normalized response at fixed shear rates is strongly dependent upon chain length and tethering conditions. Our simulation results suggest that the variation in normalized extension observed experimentally is inherent to the system because VWF naturally adopts a wide range of molecular sizes and, presumably, tethering conditions. We heuristically fitted shear-dependent normalized extension data from experiment and found the average threshold shear rate of extension for tethered VWF to be approximately 400 s⁻¹. Fluorescence microscopy images revealed nonhomogenous fluorescence distributions along unraveled multimer contours, which qualitatively suggests that the local molecular density varies in the flow direction. Our simulation results corroborate that these high-intensity fluorescent regions can manifest depending on the number and location of tethering points, as well as the shearing strength, which can cause portions of the chain to congregate together. This study demonstrates the efficacy of employing experiment and simulation in tandem to reveal the nature of flow-induced changes in biomechanical state for relevant biological molecules. We have shown that global conformational changes of tethered VWF can be predicted using a simple mechanical bead-spring model. Methods developed in this study are useful tools for examining flow-induced macromolecule conformation toward understanding their biological functions.

Author Contributions

All authors contributed to the design of this study. Y.W. and M.M. contributed equally to this work. Y.W. performed biological experiments and image analysis. M.M. performed molecular dynamics simulations, analysis of the simulation results, and some image analysis. Y.W. and M.M. equally contributed to the first draft. X.Z., E.W., A.O., and X.C. critically revised the manuscript and offered experimental/computational expertise.

Editor: Anatoly Kolomeisky.