Internal tension in a collapsed polymer under shear flow and the connection to enzymatic cleavage of von Willebrand factor

Mechanical forces control the valency of the malaria adhesin VAR2CSA by exposing cryptic glycan binding sites

Plasmodium falciparum (Pf) is responsible for the most lethal form of malaria. VAR2CSA is an adhesin protein expressed by this parasite at the membrane of infected erythrocytes for attachment to the placenta, leading to pregnancy-associated malaria. VAR2CSA is a large 355 kDa multidomain protein composed of nine extracellular domains, a transmembrane helix, and an intracellular domain. VAR2CSA binds to Chondroitin Sulphate A (CSA) of the proteoglycan matrix of the placenta. Shear flow, as the one occurring in blood, has been shown to enhance the (VAR2CSA-mediated) adhesion of Pf-infected erythrocytes on the CSA-matrix. However, the underlying molecular mechanism governing this enhancement has remained elusive. Here, we address this question by using equilibrium, force-probe, and docking-based molecular dynamics simulations. We subjected the VAR2CSA protein-CSA sugar complex to a force mimicking the tensile force exerted on this system due to the shear of the flowing blood. We show that upon this force exertion, VAR2CSA undergoes a large opening conformational transition before the CSA sugar chain dissociates from its main binding site. This preferential order of events is caused by the orientation of the molecule during elongation, as well as the strong electrostatic attraction of the sugar to the main protein binding site. Upon opening, two additional cryptic CSA binding sites get exposed and a functional dodecameric CSA molecule can be stably accommodated at these force-exposed positions. Thus, our results suggest that mechanical forces increase the avidity of VAR2CSA by turning it from a monovalent to a multivalent state. We propose this to be the molecular cause of the observed shear-enhanced adherence. Mechanical control of the valency of VAR2CSA is an intriguing hypothesis that can be tested experimentally and which is of relevance for the understanding of the malaria infection and for the development of anti placental-malaria vaccines targeting VAR2CSA.

Predicting reaction behavior of tethered polymers in shear flow

Kinetics of force-mediated chemical reactions of end-tethered polymers with varying chain length N in varying shear rate flow γ̇ are explored via coarse-grained Brownian dynamics simulations. At fixed γ̇, force F along a polymer increases linearly with N as previously predicted; however, contrary to existing theory, the F(N) slope increases for N above a transition length that exhibits minimal dependence on γ̇. Force profiles are used in a stochastic model of a force-mediated reaction to compute the time for x percent of a polymer population to experience a reaction, tx. Observations are insensitive to the selected value of x in that tx data for varying N and γ̇ can be consistently collapsed onto a single curve via appropriate scaling, with one master curve for systems below the transition N (small N) and another for those above (large N). Different force scaling for small and large N results in orders of magnitude difference in force-mediated reaction kinetics as represented by the population response time. Data presented illustrate the possibility of designing mechano-reactive polymer populations with highly controlled response to flow across a range in γ̇.

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.

Recent Advances and Emerging Challenges in the Molecular Modeling of Mechanobiological Processes

Many biological processes result from the effect of mechanical forces on macromolecular structures and on their interactions. In particular, the cell shape, motion, and differentiation directly depend on mechanical stimuli from the extracellular matrix or from neighboring cells. The development of experimental techniques that can measure and characterize the tiny forces acting at the cellular scale and down to the single-molecule, biomolecular level has enabled access to unprecedented details about the involved mechanisms. However, because the experimental observables often do not provide a direct atomistic picture of the corresponding phenomena, particle-based simulations performed at various scales are instrumental in complementing these experiments and in providing a molecular interpretation. Here, we will review the recent key achievements in the field, and we will highlight and discuss the many technical challenges these simulations are facing, as well as suggest future directions for improvement.

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.

Exposure of Von Willebrand Factor Cleavage Site in A1A2A3-Fragment under Extreme Hydrodynamic Shear

Von Willebrand Factor (vWf) is a giant multimeric extracellular blood plasma involved in hemostasis. In this work we present multi-scale simulations of its three-domains fragment A1A2A3. These three domains are essential for the functional regulation of vWf. Namely the A2 domain hosts the site where the protease ADAMTS13 cleavages the multimeric vWf allowing for its length control that prevents thrombotic conditions. The exposure of the cleavage site follows the elongation/unfolding of the domain that is caused by an increased shear stress in blood. By deploying Lattice Boltzmann molecular dynamics simulations based on the OPEP coarse-grained model for proteins, we investigated at molecular level the unfolding of the A2 domain under the action of a perturbing shear flow. We described the structural steps of this unfolding that mainly concerns the β-strand structures of the domain, and we compared the process occurring under shear with that produced by the action of a directional pulling force, a typical condition of single molecule experiments. We observe, that under the action of shear flow, the competition among the elongational and rotational components of the fluid field leads to a complex behaviour of the domain, where elongated structures can be followed by partially collapsed melted globule structures with a very different degree of exposure of the cleavage site. Our simulations pose the base for the development of a multi-scale in-silico description of vWf dynamics and functionality in physiological conditions, including high resolution details for molecular relevant events, e.g., the binding to platelets and collagen during coagulation or thrombosis.

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.

Prediction of Sub-Monomer A2 Domain Dynamics of the von Willebrand Factor by Machine Learning Algorithm and Coarse-Grained Molecular Dynamics Simulation

We develop a machine learning tool useful for predicting the instantaneous dynamical state of sub-monomer features within long linear polymer chains, as well as extracting the dominant macromolecular motions associated with sub-monomer behaviors of interest. We employ the tool to better understand and predict sub-monomer A2 domain unfolding dynamics occurring amidst the dominant large-scale macromolecular motions of the biopolymer von Willebrand Factor (vWF) immersed in flow. Results of coarse-grained Molecular Dynamics (MD) simulations of non-grafted vWF multimers subject to a shearing flow were used as input variables to a Random Forest Algorithm (RFA). Twenty unique features characterizing macromolecular conformation information of vWF multimers were used for training the RFA. The corresponding responses classify instantaneous A2 domain state as either folded or unfolded, and were directly taken from coarse-grained MD simulations. Three separate RFAs were trained using feature/response data of varying resolution, which provided deep insights into the highly correlated macromolecular dynamics occurring in concert with A2 domain unfolding events. The algorithm is used to analyze results of simulation, but has been developed for use with experimental data as well.

Coarse-Grain Modeling of Shear-Induced Binding between von Willebrand Factor and Collagen

Von Willebrand factor (VWF) is a large multimeric protein that aids in blood clotting. Near injury sites, hydrodynamic force from increased blood flow elongates VWF, exposing binding sites for platelets and collagen. To investigate VWF binding to collagen that is exposed on injured arterial surfaces, Brownian dynamics simulations are performed with a coarse-grain molecular model. Accounting for hydrodynamic interactions in the presence of a stationary surface, shear flow conditions are modeled. Binding between beads in coarse-grain VWF and collagen sites on the surface is described via reversible ligand-receptor-type bond formation, which is governed via Bell model kinetics. For conditions in which binding is energetically favored, the model predicts a high probability for binding at low shear conditions; this is counter to experimental observations but in agreement with what prior modeling studies have revealed. To address this discrepancy, an additional binding criterion that depends on the conformation of a submonomer feature in the model local to a given VWF binding site is implemented. The modified model predicts shear-induced binding, in very good agreement with experimental observations; this is true even for conditions in which binding is significantly favored energetically. Biological implications of the model modification are discussed in terms of mechanisms of VWF activity.

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.

Internal Tensile Force and A2 Domain Unfolding of von Willebrand Factor Multimers in Shear Flow

Using Brownian molecular dynamics simulations, we examine the internal dynamics and biomechanical response of von Willebrand factor (vWF) multimers subject to shear flow. The coarse grain multimer description employed here is based on a monomer model in which the A2 domain of vWF is explicitly represented by a nonlinear elastic spring whose mechanical response was fit to experimental force/extension data from vWF monomers. This permits examination of the dynamic behavior of hydrodynamic forces acting on A2 domains as a function of shear rate and multimer length, as well as position of an A2 domain along the multimer contour. Force/position data reveal that collapsed multimers exhibit a force distribution with two peaks, one near each end of the chain; unraveled multimers, however, show a single peak in A2 domain force near the center of multimers. Guided further by experimental data, significant excursions of force acting on a domain are associated with an increasing probability for A2 domain unfolding. Our results suggest that the threshold shear rate required to induce A2 domain unfolding is inversely proportional to multimer length. By examining data for the duration and location of significant force excursions, convincing evidence is advanced that unfolding of A2 domains, and therefore scission of vWF multimers by the size-regulating blood enzyme ADAMTS13, happen preferentially near the center of unraveled multimers.

Hydrodynamic Shear Effects on Grafted and Non-Grafted Collapsed Polymers

We study collapsed homo-polymeric molecules under linear shear flow conditions using hydrodynamic Brownian dynamics simulations. Tensile force profiles and the shear-rate-dependent globular-coil transition for grafted and non-grafted chains are investigated to shine light on the different unfolding mechanisms. The scaling of the critical shear rate, at which the globular-coil transition takes place, with the monomer number is inverse for the grafted and non-grafted scenarios. This implicates that for the grafted scenario, larger chains have a decreased critical shear rate, while for the non-grafted scenario higher shear rates are needed in order to unfold larger chains. Protrusions govern the unfolding transition of non-grafted polymers, while for grafted polymers, the maximal tension appears at the grafted end.