Shear-stress-induced conformational changes of von Willebrand factor in a water-glycerol mixture observed with single molecule microscopy

Molecular mechanisms of catch bonds and their implications for platelet hemostasis

Adhesive molecular bonds between blood cells are essential for thrombosis and hemostasis as they provide means for platelet adhesion, aggregation, and signaling in flowing blood. According to the nowadays conventional definition, a "catch" bond is a type of non-covalent bio-molecular bridge, whose dissociation lifetime counter-intuitively increases with applied tensile force. Following recent experimental findings, such receptor-ligand protein bonds are vital to the blood cells involved in the prevention of bleeding (hemostatic response) and infection (immunity). In this review, we examine the up-to-date experimental discoveries and theoretical insights about catch bonds between the blood cells, their biomechanical principles at the molecular level, and their role in platelet thrombosis and hemostasis.

Receptor-Ligand Binding: Effect of Mechanical Factors

Gaining insight into the in situ receptor-ligand binding is pivotal for revealing the molecular mechanisms underlying the physiological and pathological processes and will contribute to drug discovery and biomedical application. An important issue involved is how the receptor-ligand binding responds to mechanical stimuli. This review aims to provide an overview of the current understanding of the effect of several representative mechanical factors, such as tension, shear stress, stretch, compression, and substrate stiffness on receptor-ligand binding, wherein the biomedical implications are focused. In addition, we highlight the importance of synergistic development of experimental and computational methods for fully understanding the in situ receptor-ligand binding, and further studies should focus on the coupling effects of these mechanical factors.

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.

Effect of pulsatility on shear-induced extensional behavior of Von Willebrand factor

BACKGROUND

Patients with continuous flow ventricular assist devices (CF-VADs) are at high risk for non-surgical bleeding, speculated to associate with the loss of pulsatility following CF-VAD placement. It has been hypothesized that continuous shear stress causes elongation and increased enzymatic degradation of von Willebrand Factor (vWF), a key player in thrombus formation at sites of vascular damage. However, the role of loss of pulsatility on the unravelling behavior of vWF has not been widely explored.

METHODS

vWF molecules were immobilized on the surface of microfluidic devices and subjected to various pulsatile flow profiles, including continuous flow and pulsatile flow of different magnitudes, dQ/dt (i.e., first derivative of flow rate) of pulsatility and pulse frequencies to mimic in vivo shear flow environments with and without CF-VAD support. VWF elongation was observed using total internal reflection fluorescence (TIRF) microscopy. Besides, the vWF level is measured from the patients' blood sample before and after CF-VAD implantation from a clinical perspective. To our knowledge, this work is the first in providing direct, visual observation of single vWF molecule extension under controlled-pulsatile shear flow.

RESULTS

Unravelling of vWF (total sample size n ~ 200 molecules) is significantly reduced under pulsatile flow (p < 0.01) compared to continuous flow. An increase in the magnitude of pulsatility further reduces unravelling lengths, while lower frequency of pulsatility (20 vs. 60 pulses per min) does not have a major effect on the maximum or minimum unravelling lengths. Evaluation of CF-VAD patient blood samples (n = 13) demonstrates that vWF levels decreased by ~40% following CF-VAD placement (p < 0.01), which correlates to single-molecule observations from a clinical point of view.

CONCLUSIONS

Pulsatile flow reduces unfolding of vWF compared to continuous flow and a lower pulse frequency of 20 pulses/minute yielded comparable vWF unfolding to 60 pulses/minute. These findings could shed light on non-surgical bleeding associated with the loss of pulsatility following CF-VAD placement.

Targeting shear gradient activated von Willebrand factor by the novel single-chain antibody A1 reduces occlusive thrombus formation in vitro

Intraluminal thrombus formation precipitates conditions such as acute myocardial infarction and disturbs local blood flow resulting in areas of rapidly changing blood flow velocities and steep gradients of blood shear rate. Shear rate gradients are known to be pro-thrombotic with an important role for the shear-sensitive plasma protein von Willebrand factor (VWF). Here, we developed a single-chain antibody (scFv) that targets a shear gradient specific conformation of VWF to specifically inhibit platelet adhesion at sites of SRGs but not in areas of constant shear. Microfluidic flow channels with stenotic segments were used to create shear rate gradients during blood perfusion. VWF-GPIbα interactions were increased at sites of shear rate gradients compared to constant shear rate of matched magnitude. The scFv-A1 specifically reduced VWF-GPIbα binding and thrombus formation at sites of SRGs but did not block platelet deposition and aggregation under constant shear rate in upstream sections of the channels. Significantly, the scFv A1 attenuated platelet aggregation only in the later stages of thrombus formation. In the absence of shear, direct binding of scFv-A1 to VWF could not be detected and scFV-A1 did not inhibit ristocetin induced platelet agglutination. We have exploited the pro-aggregatory effects of SRGs on VWF dependent platelet aggregation and developed the shear-gradient sensitive scFv-A1 antibody that inhibits platelet aggregation exclusively at sites of shear rate gradients. The lack of VWF inhibition in non-stenosed vessel segments places scFV-A1 in an entirely new class of anti-platelet therapy for selective blockade of pathological thrombus formation while maintaining normal haemostasis.

Von Willebrand Factor Facilitates Intravascular Dissemination of Microsporidia Encephalitozoon hellem

Microsporidia are a group of spore-forming, fungus-related pathogens that can infect both invertebrates and vertebrates including humans. The primary infection site is usually digestive tract, but systemic infections occur as well and cause damages to organs such as lung, brain, and liver. The systemic spread of microsporidia may be intravascular, requiring attachment and colonization in the presence of shear stress. Von Willebrand Factor (VWF) is a large multimeric intravascular protein and the key attachment sites for platelets and coagulation factors. Here in this study, we investigated the interactions between VWF and microsporidia Encephalitozoon hellem (E. hellem), and the modulating effects on E. hellem after VWF binding. Microfluidic assays showed that E. hellem binds to ultra-large VWF strings under shear stress. In vitro germination assay and infection assay proved that E. hellem significantly increased the rates of germination and infection, and these effects would be reversed by VWF blocking antibody. Mass spectrometry analysis further revealed that VWF-incubation altered various aspects of E. hellem including metabolic activity, levels of structural molecules, and protein maturation. Our findings demonstrated that VWF can bind microsporidia in circulation, and modulate its pathogenicity, including promoting germination and infection rate. VWF facilitates microsporidia intravascular spreading and systemic infection.

Predicting pathological von Willebrand factor unraveling in elongational flow

The globular-to-unraveled conformation transition of von Willebrand factor (vWF), a large polymeric glycoprotein in human blood plasma, is a crucial step in the process of clotting at sites of vascular injury. However, unraveling of vWF multimers in uninjured vasculature can lead to pathology (i.e., thrombus formation or degradation of vWF proteins by enzyme ADAMTS13, making them nonfunctional). To identify blood flow conditions that might induce pathological unraveling of vWF multimers, here we have computed the globular-to-unraveled transition rate of vWF multimers subjected to varying strain rate elongational flow by employing an enhanced sampling technique, the weighted ensemble method. Weighted ensemble sampling was employed instead of standard brute-force simulations because pathological blood flow conditions can induce undesired vWF unraveling on timescales potentially inaccessible to standard simulation methods. Results here indicate that brief but periodic exposure of vWF to the elongational flow of strain rate greater than or equal to 2500 s^-1 represents a source of possible pathology caused by the undesired unraveling of vWF multimers.

Effects of Shear Stress on Production of FVIII and vWF in a Cell-Based Therapeutic for Hemophilia A

Microfluidic technology enables recapitulation of organ-level physiology to answer pertinent questions regarding biological systems that otherwise would remain unanswered. We have previously reported on the development of a novel product consisting of human placental cells (PLC) engineered to overexpress a therapeutic factor VIII (FVIII) transgene, mcoET3 (PLC-mcoET3), to treat Hemophilia A (HA). Here, microfluidic devices were manufactured to model the physiological shear stress in liver sinusoids, where infused PLC-mcoET3 are thought to lodge after administration, to help us predict the therapeutic outcome of this novel biological strategy. In addition to the therapeutic transgene, PLC-mcoET3 also constitutively produce endogenous FVIII and von Willebrand factor (vWF), which plays a critical role in FVIII function, immunogenicity, stability, and clearance. While vWF is known to respond to flow by changing conformation, whether and how shear stress affects the production and secretion of vWF and FVIII has not been explored. We demonstrated that exposure of PLC-mcoET3 to physiological levels of shear stress present within the liver sinusoids significantly reduced mRNA levels and secreted FVIII and vWF when compared to static conditions. In contrast, mRNA for the vector-encoded mcoET3 was unaltered by flow. To determine the mechanism responsible for the observed decrease in FVIII and vWF mRNA, PCR arrays were performed to evaluate expression of genes involved in shear mechanosensing pathways. We found that flow conditions led to a significant increase in KLF2, which induces miRNAs that negatively regulate expression of FVIII and vWF, providing a mechanistic explanation for the reduced expression of these proteins in PLC under conditions of flow. In conclusion, microfluidic technology allowed us to unmask novel pathways by which endogenous FVIII and vWF are affected by shear stress, while demonstrating that expression of the therapeutic mcoET3 gene will be maintained in the gene-modified PLCs upon transplantation, irrespective of whether they engraft within sites that expose them to conditions of shear stress.

Intradimer forces and their implication for conformations of von Willebrand factor multimers

The largest blood glycoprotein von Willebrand factor (VWF) responds to hydrodynamic stresses in the bloodstream with abrupt conformation changes, thus increasing its adhesivity to platelets and collagen. Arterial and microvascular hemostasis relies on mechanical and physicochemical properties of this macromolecule. Recently, it was discovered that the mechanical properties of VWF are controlled by multiple pH-dependent interactions with opposite trends within dimeric subunits. In this work, computer simulations reveal the effect of these intradimer forces on the conformation of VWF multimers in various hydrodynamic conditions. A coarse-grained computer model of VWF has been proposed and parameterized to give a good agreement with experimental data. The simulations suggest that strong attraction between VWF D4 domains increases the resistance to elongation under shear stress, whereas even intermediate attraction between VWF C domains contributes to VWF compaction in nonsheared fluid. It is hypothesized that the detailed subdimer dynamics of VWF concatamers may be one of the biophysical regulators of initial hemostasis and arterial thrombosis.

Excessively activated plasminogen in human plasma cleaves VWF multimers and reduces collagen-binding activity

Plasmin (Pm) is a serine protease that can dissolve fibrin clots. Several possible functions of Pm in blood other than fibrinolysis have been proposed. To explore the effects of Pm on primary haemostasis, we evaluated the cleavage of von Willebrand factor multimers (VWFMs) in human plasma by streptokinase (SK)-activated plasminogen (Pg) and the binding ability of the digested VWFMs to collagen. SK-activated Pg and ADAMTS13 (a VWF-cleaving enzyme) in human plasma cleaved VWFMs in conformation-dependent manners through dialysis to the urea-containing buffer. However, VWFMs in human plasma under vortex-based shear stress were cleaved by SK-activated Pg but not by ADAMTS13. These results suggested that the VWFM-cleavage sites in human plasma are exposed to some extent by vortex-based shear stress for Pm but not for ADAMTS13. Additionally, we revealed that cleavage by SK-activated Pg reduced VWFMs’ binding ability to collagen, and VWFMs in human plasma were cleaved by Pm at several sites. These results suggest that SK-activated Pg degrades VWFMs, reduces their binding abilities to collagen and affects primary haemostasis. Because excessive Pg activation can degrade fibrinogen/fibrin, we propose that SK-activated Pg in blood may cause impaired primary and secondary haemostasis.

Microfluidic devices for studying coagulation biology

The ability to study the behavior of cells, proteins, and cell-cell or cell-protein interactions under dynamic forces such as shear stress under fluid flow, provides a more accurate understanding of the physiopathology of hemostasis. This review touches upon the traditional methods for studying blood coagulation and platelet aggregation and provides an overview on cellular and protein response to shear stress. We also elaborate on the biological aspects of how cells recognize mechanical forces and convert them into biochemical signals that can drive various signaling pathways. We give a detailed description of the various types of microfluidic devices that are employed to study the complex processes of platelet aggregation and blood coagulation under flow conditions as well as to investigate endothelial shear-response. We also highlight works mimicking artificial vessels as platforms to study the mechanisms of coagulation, and finish our review by describing anticipated clinical uses of microfluidics devices and their standardization.

In Vitro Thrombogenicity Testing of Biomaterials

The short- and long-term thrombogenicity of implant materials is still unpredictable, which is a significant challenge for the treatment of cardiovascular diseases. A knowledge-based approach for implementing biofunctions in materials requires a detailed understanding of the medical device in the biological system. In particular, the interplay between material and blood components/cells as well as standardized and commonly acknowledged in vitro test methods allowing a reproducible categorization of the material thrombogenicity requires further attention. Here, the status of in vitro thrombogenicity testing methods for biomaterials is reviewed, particularly taking in view the preparation of test materials and references, the selection and characterization of donors and blood samples, the prerequisites for reproducible approaches and applied test systems. Recent joint approaches in finding common standards for a reproducible testing are summarized and perspectives for a more disease oriented in vitro thrombogenicity testing are discussed.

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.

Shear-Induced Extensional Response Behaviors of Tethered von Willebrand Factor

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.

Correlating Conformational Dynamics with the Von Willebrand Factor Reductase Activity of Factor H Using Single Molecule Force Measurements

Activation of proteins often involves conformational transitions, and these switches are often difficult to characterize in multidomain proteins. Full-length factor H (FH), consisting of 20 small consensus repeat domains (150 kD), is a complement control protein that regulates the activity of the alternative complement pathway. Different preparations of FH can also reduce the disulfide bonds linking large Von Willebrand factor (VWF) multimers into smaller, less adhesive forms. In contrast, commercially available purified FH (pFH) has little or no VWF reductase activity unless the pFH is chemically modified by either ethylenediaminetetraacetic acid (EDTA) or urea. We used atomic force microscopy single molecule force measurements to investigate different forms of FH, including recombinant FH and pFH, in the presence or absence of EDTA and urea, and to correlate the conformational changes to its activities. We found that the FH conformation depends on the method used for sample preparation, which affects the VWF reductase activity of FH.

Characterizing the HeartMate II Left Ventricular Assist Device Outflow Using Particle Image Velocimetry

Ventricular assist devices (VADs) are implanted in patients with a diseased ventricle to maintain peripheral perfusion as a bridge-to-transplant or as destination therapy. However, some patients with continuous flow VADs (e.g., HeartMate II (HMII)) have experienced gastrointestinal (GI) bleeding, in part caused by the proteolytic cleavage or mechanical destruction of von Willebrand factor (vWF), a clotting glycoprotein. in vitro studies were performed to measure the flow located within the HMII outlet cannula under both steady and physiological conditions using particle image velocimetry (PIV). Under steady flow, a mock flow loop was used with the HMII producing a flow rate of 3.2 L/min. The physiological experiment included a pulsatile pump operated at 105 BPM with a ventricle filling volume of 50 mL and in conjunction with the HMII producing a total flow rate of 5.0 L/min. Velocity fields, Reynolds normal stresses (RNSs), and Reynolds shear stresses (RSSs) were analyzed to quantify the outlet flow's potential contribution to vWF degradation. Under both flow conditions, the HMII generated principal Reynolds stresses that are, at times, orders of magnitude higher than those needed to unfurl vWF, potentially impacting its physiological function. Under steady flow, principal RNSs were calculated to be approximately 500 Pa in the outlet cannula. Elevated Reynolds stresses were observed throughout every phase of the cardiac cycle under physiological flow with principal RNSs approaching 1500 Pa during peak systole. Prolonged exposure to these conditions may lead to acquired von Willebrand syndrome (AvWS), which is accompanied by uncontrollable bleeding episodes.

Space and Time Resolved Detection of Platelet Activation and von Willebrand Factor Conformational Changes in Deep Suspensions

Tracking cells and proteins' phenotypic changes in deep suspensions is critical for the direct imaging of blood-related phenomena in in vitro replica of cardiovascular systems and blood-handling devices. This paper introduces fluorescence imaging techniques for space and time resolved detection of platelet activation, von Willebrand factor (VWF) conformational changes, and VWF-platelet interaction in deep suspensions. Labeled VWF, platelets, and VWF-platelet strands are suspended in deep cuvettes, illuminated, and imaged with a high-sensitivity EM-CCD camera, allowing detection using an exposure time of 1 ms. In-house postprocessing algorithms identify and track the moving signals. Recombinant VWF-eGFP (rVWF-eGFP) and VWF labeled with an FITC-conjugated polyclonal antibody are employed. Anti-P-Selectin FITC-conjugated antibodies and the calcium-sensitive probe Indo-1 are used to detect activated platelets. A positive correlation between the mean number of platelets detected per image and the percentage of activated platelets determined through flow cytometry is obtained, validating the technique. An increase in the number of rVWF-eGFP signals upon exposure to shear stress demonstrates the technique's ability to detect breakup of self-aggregates. VWF globular and unfolded conformations and self-aggregation are also observed. The ability to track the size and shape of VWF-platelet strands in space and time provides means to detect pro- and antithrombotic processes.

Flow-induced elongation of von Willebrand factor precedes tension-dependent activation

Von Willebrand factor, an ultralarge concatemeric blood protein, must bind to platelet GPIbα during bleeding to mediate hemostasis, but not in the normal circulation to avoid thrombosis. Von Willebrand factor is proposed to be mechanically activated by flow, but the mechanism remains unclear. Using microfluidics with single-molecule imaging, we simultaneously monitored reversible Von Willebrand factor extension and binding to GPIbα under flow. We show that Von Willebrand factor is activated through a two-step conformational transition: first, elongation from compact to linear form, and subsequently, a tension-dependent local transition to a state with high affinity for GPIbα. High-affinity sites develop only in upstream regions of VWF where tension exceeds ~21 pN and depend upon electrostatic interactions. Re-compaction of Von Willebrand factor is accelerated by intramolecular interactions and increases GPIbα dissociation rate. This mechanism enables VWF to be locally activated by hydrodynamic force in hemorrhage and rapidly deactivated downstream, providing a paradigm for hierarchical mechano-regulation of receptor–ligand binding.

Von Willebrand factor (VWF) is a blood protein involved in clotting and is proposed to be activated by flow, but the mechanism is unknown. Here the authors show that VWF is first converted from a compact to linear form by flow, and is subsequently activated to bind GPIbα in a tension-dependent manner.

Role of fluid shear stress in regulating VWF structure, function and related blood disorders

Von Willebrand factor (VWF) is the largest glycoprotein in blood. It plays a crucial role in primary hemostasis via its binding interaction with platelet and endothelial cell surface receptors, other blood proteins and extra-cellular matrix components. This protein is found as a series of repeat units that are disulfide bonded to form multimeric structures. Once in blood, the protein multimer distribution is dynamically regulated by fluid shear stress which has two opposing effects: it promotes the aggregation or self-association of multiple VWF units, and it simultaneously reduces multimer size by facilitating the force-dependent cleavage of the protein by various proteases, most notably ADAMTS13 (a disintegrin and metalloprotease with thrombospondin type repeats, motif 1 type 13). In addition to these effects, fluid shear also controls the solution and substrate-immobilized structure of VWF, the nature of contact between blood platelets and substrates, and the biomechanics of the GpIbα–VWF bond. These features together regulate different physiological and pathological processes including normal hemostasis, arterial and venous thrombosis, von Willebrand disease, thrombotic thrombocytopenic purpura and acquired von Willebrand syndrome. This article discusses current knowledge of VWF structure–function relationships with emphasis on the effects of hydrodynamic shear, including rapid methods to estimate the nature and magnitude of these forces in selected conditions. It shows that observations made by many investigators using solution and substrate-based shearing devices can be reconciled upon considering the physical size of VWF and the applied mechanical force in these different geometries.

Platelet activation risk index as a prognostic thrombosis indicator

Platelet activation in blood flow under high, overcritical shear rates is initiated by Von Willebrand factor. Despite the large amount of experimental data that have been obtained, the value of the critical shear rate, above which von Willebrand factor starts to activate platelets, is still controversial. Here, we recommend a theoretical approach to elucidate how the critical blood shear rate is dependent on von Willebrand factor size. We derived a diagram of platelet activation according to the shear rate and von Willebrand factor multimer size. We succeeded in deriving an explicit formula for the dependence of the critical shear rate on von Willebrand factor molecule size. The platelet activation risk index was introduced. This index is dependent on the flow conditions, number of monomers in von Willebrand factor, and platelet sensitivity. Probable medical applications of the platelet activation risk index as a universal prognostic index are discussed.

Simple microfluidic stagnation point flow geometries

A geometrically simple flow cell is proposed to generate different types of stagnation flows, using a separation flow and small variations of the geometric parameters. Flows with high local deformation rates can be changed from purely rotational, over simple shear flow, to extensional flow in a region surrounding a stagnation point. Computational fluid dynamic calculations are used to analyse how variations of the geometrical parameters affect the flow field. These numerical calculations are compared to the experimentally obtained streamlines of different designs, which have been determined by high speed confocal microscopy. As the flow type is dictated predominantly by the geometrical parameters, such simple separating flow devices may alleviate the requirements for flow control, while offering good stability for a wide variety of flow types.

Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules

We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems.

STABILITY OF A CYLINDRICAL SOLUTE-SOLVENT INTERFACE: EFFECT OF GEOMETRY, ELECTROSTATICS, AND HYDRODYNAMICS

The solute-solvent interface that separates biological molecules from their surrounding aqueous solvent characterizes the conformation and dynamics of such molecules. In this work, we construct a solvent fluid dielectric boundary model for the solvation of charged molecules and apply it to study the stability of a model cylindrical solute-solvent interface. The motion of the solute-solvent interface is defined to be the same as that of solvent fluid at the interface. The solvent fluid is assumed to be incompressible and is described by the Stokes equation. The solute is modeled simply by the ideal-gas law. All the viscous force, hydrostatic pressure, solute-solvent van der Waals interaction, surface tension, and electrostatic force are balanced at the solute-solvent interface. We model the electrostatics by Poisson's equation in which the solute-solvent interface is treated as a dielectric boundary that separates the low-dielectric solute from the high-dielectric solvent. For a cylindrical geometry, we find multiple cylindrically shaped equilibrium interfaces that describe polymodal (e.g., dry and wet) states of hydration of an underlying molecular system. These steady-state solutions exhibit bifurcation behavior with respect to the charge density. For their linearized systems, we use the projection method to solve the fluid equation and find the dispersion relation. Our asymptotic analysis shows that, for large wavenumbers, the decay rate is proportional to wavenumber with the proportionality half of the ratio of surface tension to solvent viscosity, indicating that the solvent viscosity does affect the stability of a solute-solvent interface. Consequences of our analysis in the context of biomolecular interactions are discussed.