Dynamics and Instabilities of Collapsed Polymers in Shear Flow

Stability and deformation of biomolecular condensates under the action of shear flow

Biomolecular condensates play a key role in cytoplasmic compartmentalization and cell functioning. Despite extensive research on the physico-chemical, thermodynamic, or crowding aspects of the formation and stabilization of the condensates, one less studied feature is the role of external perturbative fluid flow. In fact, in living cells, shear stress may arise from streaming or active transport processes. Here, we investigate how biomolecular condensates are deformed under different types of shear flows. We first model Couette flow perturbations via two-way coupling between the condensate dynamics and fluid flow by deploying Lattice Boltzmann Molecular Dynamics. We then show that a simplified approach where the shear flow acts as a static perturbation (one-way coupling) reproduces the main features of the condensate deformation and dynamics as a function of the shear rate. With this approach, which can be easily implemented in molecular dynamics simulations, we analyze the behavior of biomolecular condensates described through residue-based coarse-grained models, including intrinsically disordered proteins and protein/RNA mixtures. At lower shear rates, the fluid triggers the deformation of the condensate (spherical to oblated object), while at higher shear rates, it becomes extremely deformed (oblated or elongated object). At very high shear rates, the condensates are fragmented. We also compare how condensates of different sizes and composition respond to shear perturbation, and how their internal structure is altered by external flow. Finally, we consider the Poiseuille flow that realistically models the behavior in microfluidic devices in order to suggest potential experimental designs for investigating fluid perturbations in vitro.

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.

Enhanced Pulley Effect for Translocation: The Interplay of Electrostatic and Hydrodynamic Forces

Solid-state nanopore sensors remain a promising solution to the rising global demand for genome sequencing. These single-molecule sensing technologies require single-file translocation for high resolution and accurate detection. In a previous publication, we discovered a hairpin unraveling mechanism, namely, the pulley effect, in a pressure-driven translocation system. In this paper, we further investigate the pulley effect in the presence of pressure-driven fluid flow and an opposing force provided by an electrostatic field as an approach to increase single-file capture probability. A hydrodynamic flow is used to move the polymer forward, and two oppositely charged electrostatic square loops are used to create an opposing force. By optimizing the balance between forces, we show that the single-file capture can be amplified from about 50% to almost 95%. The force location, force strength, and flow rate are used as the optimizing variables.

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

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

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.

Statistical Dynamics of Flow-Driven Globular Polymers

The response of collapsed polymers to the effects of linear mixed flow is studied theoretically in this paper using a model of a self-interacting finitely extensible Gaussian chain that evolves stochastically in the presence of random thermal fluctuations and an external fluid velocity gradient. The interactions that produce compact chain configurations are described by a harmonic pair potential of strength κ that acts between nonbonded sites on the chain backbone. Several chain properties are calculated analytically from this model as a function of κ for elongational and shear flows, including the dependence of the chain's steady-state mean-square end-to-end distance on the Weissenberg number of the flow, the time-dependence of the chain's relaxation to equilibrium from a steady-state of given chain extension, and the nature of the force-extension curves that are obtained from the free energy change between unperturbed and flow-stretched states of the chain. For both elongational and shear flows (but to different degrees), it is found that the greater the value of κ (and the more compact the chain), the more difficult it is, in general, for the imposed flow to induce a transition between compact and extended states, in broad agreement with available data from numerical simulations. For the relaxation process, the differences between the two flow types are more marked. The characteristic decay time for relaxation from a state prepared by elongational flow is essentially independent of κ, whereas in the case of a state prepared by shear flow, it is distinctly κ-dependent, the relaxation becoming faster at larger κ.

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.

Influence of Injection Application on the Sol-Gel Phase Transition Conditions of Polysaccharide-Based Hydrogels

Polysaccharide matrices formed via thermoinduced sol-gel phase transition are promising systems used as drug carriers and minimally invasiveness scaffolds in tissue engineering. The strong shear field generated during injection may lead to changes in the conformation of polymer molecules and, consequently, affect the gelation conditions that have not been studied so far. Chitosan (CS) and hydroxypropyl cellulose (HPC) sols were injected through injection needles (14 G-25 G) or sheared directly in the rheometer measuring system. Then the sol-gel phase transition conditions were determined at 37 °C using rheometric, turbidimetric, and rheo-optical techniques. It was found that the use of low, respecting injection, shear rates accelerate the gelation, its increase extends the gelation time; applying the highest shear rates may significantly slow down (HPC) or accelerate gelation (CS) depending on thixotropic properties. From a practical point of view, the conducted research indicates that the use of thin needles without preliminary tests may lead to an extension of the gelation time and consequently the spilling of the polymeric carrier before gelation. Finally, an interpretation of the influence of an intensive shear field on the conformation of the molecules on a molecular scale was proposed.

Multivalent polymers can control phase boundary, dynamics, and organization of liquid-liquid phase separation

Multivalent polymers are a key structural component of many biocondensates. When interacting with their cognate binding proteins, multivalent polymers such as RNA and modular proteins have been shown to influence the liquid-liquid phase separation (LLPS) boundary to both control condensate formation and to influence condensate dynamics after phase separation. Much is still unknown about the function and formation of these condensed droplets, but changes in their dynamics or phase separation are associated with neurodegenerative diseases such as amyotrophic lateral sclerosis (ALS) and Alzheimer's Disease. Therefore, investigation into how the structure of multivalent polymers relates to changes in biocondensate formation and maturation is essential to understanding and treating these diseases. Here, we use a coarse-grain, Brownian Dynamics simulation with reactive binding that mimics specific interactions in order to investigate the difference between non-specific and specific multivalent binding polymers. We show that non-specific binding interactions can lead to much larger changes in droplet formation at lower protein-polymer interaction energies than their specific, valence-limited counterparts. We also demonstrate the effects of solvent conditions and polymer length on phase separation, and we present how modulating binding energy to the polymer can change the organization of a droplet in a three component system of polymer, binding protein, and solvent. Finally, we compare the effects of surface tension and polymer binding on the condensed phase dynamics, and show that both lower protein solubilities and higher attraction/affinity of the protein to the polymer result in slower droplet dynamics. This research will help to better understand experimental systems and provides additional insight into how multivalent polymers can control LLPS.

A Continuum Model for the Unfolding of von Willebrand Factor

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

Emergent slow dynamics of collapsed polymers flowing through porous media

Using hydrodynamic simulations, we study the single polymers flowing through model porous media (close-packed colloidal crystal). In good solvent or high flow rates, the polymer transport is similar to gel electrophoresis, with size-dependent sieving for L_{c}/L≲1 and size-independent biased reptation for L_{c}/L≳1 (L_{c} is the polymer contour length and L is the diameter of colloids forming the porous media). Importantly, in bad solvent and low flow rates, the polymers show an extra window of size-dependent velocity for 1≲L_{c}/L≲2, where the polymer transport is controlled by a globule-stretch transition at pore throats, and the transport velocity is much slower than reptation.

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.

Mechanical Forces Impacting Cleavage of Von Willebrand Factor in Laminar and Turbulent Blood Flow

Von Willebrand factor (VWF) is a large multimeric hemostatic protein. VWF is critical in arresting platelets in regions of high shear stress found in blood circulation. Excessive cleavage of VWF that leads to reduced VWF multimer size in plasma can cause acquired von Willebrand syndrome, which is a bleeding disorder found in some heart valve diseases and in patients receiving mechanical circulatory support. It has been proposed that hemodynamics (blood flow) found in these environments ultimately leads to VWF cleavage. In the context of experiments reported in the literature, scission theory, developed for polymers, is applied here to provide insight into flow that can produce strong extensional forces on VWF that leads to domain unfolding and exposure of a cryptic site for cleavage through a metalloproteinase. Based on theoretical tensile forces, laminar flow only enables VWF cleavage when shear rate is large enough (>2800 s−1) or when VWF is exposed to constant shear stress for nonphysiological exposure times (>20 min). Predicted forces increase in turbulence, increasing the chance for VWF cleavage. These findings can be used when designing blood-contacting medical devices by providing hemodynamic limits to these devices that can otherwise lead to acquired von Willebrand syndrome.

Polymer Stiffness Regulates Multivalent Binding and Liquid-Liquid Phase Separation

Multivalent binding is essential to many biological processes because it builds high-affinity bonds by using several weak binding interactions simultaneously. Multivalent polymers have shown promise as inhibitors of toxins and other pathogens, and they are important components in the formation of biocondensates. Explaining how structural features of these polymers change their binding and subsequent control of phase separation is critical to designing better pathogen inhibitors and also to understanding diseases associated with membraneless organelles. In this work, we will examine the binding of a multivalent polymer to a small target. This scenario could represent a polymeric inhibitor binding to a toxic protein or RNA binding to an RNA-binding protein in the case of liquid-liquid phase separation. We use simulation and theory to show that flexible random-coil polymers bind more strongly than stiff rod-like polymers and that flexible polymers nucleate condensed phases at lower binding energies than their rigid analogs. We hope these results will provide insight into the rational design of polymeric inhibitors and improve our understanding of phase separation in cells and membraneless organelles.

Hydrodynamic interactions in topologically linked ring polymers

Despite decades of interdisciplinary research on topologically linked ring polymers, their dynamics remain largely unstudied. These systems represent a major scientific challenge as they are often subject to both topological and hydrodynamic interactions (HI), which render dynamical solutions either mathematically intractable or computationally prohibitive. Here we circumvent these limitations by preaveraging the HI of linked rings. We show that the symmetry of ring polymers leads to a hydrodynamic decoupling of ring dynamics. This decoupling is valid even for nonideal polymers and nonequilibrium conditions. Physically, our findings suggest that the effects of topology and HI are nearly independent and do not act cooperatively to influence polymer dynamics. We use this result to develop highly efficient Brownian dynamics algorithms that offer enormous performance improvements over conventional methods and apply these algorithms to simulate catenated ring polymers at equilibrium, confirming the independence of topological effects and HI. The methods developed here can be used to study and simulate large systems of linked rings with HI, including kinetoplast DNA, Olympic gels, and poly[n]catenanes.

Influence of Binding Site Affinity Patterns on Binding of Multivalent Polymers

Using inspiration from biology, we can leverage multivalent binding interactions to enhance weak, monovalent binding between molecules. While most previous studies have focused on multivalent binders with uniform binding sites, new synthetic polymers might find it desirable to have multiple binding moieties along the chain. Here, we probe how patterning of heterogeneous binding sites along a polymer chain controls the binding affinity of a polymer using a reactive Brownian dynamics scheme. Unlike monovalent binders that are pattern-agnostic, we find that divalent binding is dependent on both the polymer pattern and binding target concentration. For dilute targets, blocky polymers provide high local concentrations of high-affinity sites, but at high target concentrations, competition for binding sites makes alternating polymers the strongest binders. Subsequently, we show that random copolymers are robust to target concentration fluctuations. These results will assist in the rational design of multivalent polymer therapeutics and materials.

Mixing of a mAb Formulation in a New Magnetically Coupled Single-Use Mixing System: Key Learnings of Preliminary Experimental and Computational Evaluation

MilliporeSigma recently introduced a new magnetically coupled single-use mixing system (Mobius® Power MIX) for more efficient mixing of buffers and media in biopharmaceutical applications. Experimental and computational fluid dynamics (CFD) assessments were performed on the Power MIX 100 system to understand product quality impact, shear, and mixing efficiency. It was interesting to note slightly higher submicron (0.4-1 μm) and subvisible (1-54 μm) particle formation at the lower mixing speed (50 RPM) compared to higher mixing speeds (100/200 RPM). Mixing speed and time showed negligible impact on the other product quality attributes tested, including protein concentration, turbidity, general appearance, purity, and soluble aggregates. The CFD simulations provided useful information with respect to the impact of batch size (20-100 L), viscosity (2-50 cP), and impeller speed (100-300 RPM) on mixing time (mixing time ranged from 10 to 365 s) and shear (maximum shear rate was found to be localized around the impeller and it was about 30,260 s^-1, whereas the average shear rate ranged from 4 to 36 s^-1). Statistical analysis of the CFD results showed that natural-log transformation and quadratic fitting were found to be suitable statistical models to predict mixing time and shear within the design space of the parameters assessed in the present study.

Computational Insights into Avidity of Polymeric Multivalent Binders

Multivalent binding interactions are commonly found throughout biology to enhance weak monovalent binding such as between glycoligands and protein receptors. Designing multivalent polymers to bind to viruses and toxic proteins is a promising avenue for inhibiting their attachment and subsequent infection of cells. Several studies have focused on oligomeric multivalent inhibitors and how changing parameters such as ligand shape, size, linker length, and flexibility affect binding. However, experimental studies of how larger structural parameters of multivalent polymers, such as degree of polymerization, affect binding avidity to targets have mixed results, with some finding an improvement with longer polymers and some finding no effect. Here, we use Brownian dynamics simulations to provide a theoretical understanding of how the degree of polymerization affects the binding avidity of multivalent polymers. We show that longer polymers increase binding avidity to multivalent targets but reach a limit in binding avidity at high degrees of polymerization. We also show that when interacting with multiple targets simultaneously, longer polymers are able to use intertarget interactions to promote clustering and improve binding efficiency. We expect our results to narrow the design space for optimizing the structure and effectiveness of multivalent inhibitors as well as be useful to understand biological design strategies for multivalent binding.

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.

Ring polymer dynamics and tumbling-stretch transitions in planar mixed flows

The properties of dilute polymer solutions are governed by the conformational dynamics of individual polymers which can be perturbed in the presence of an applied flow. Much of our understanding of dilute solutions comes from studying how flows manipulate the molecular features of polymer chains out of equilibrium, primarily focusing on linear polymer chains. Recently there has been an emerging interest in the dynamics of nonlinear architectures, particularly ring polymers, which exhibit surprising out-of-equilibrium dynamics in dilute solutions. In particular, it has been observed that hydrodynamics can couple to topology in planar elongational and shear flows, driving molecular expansion in the nonflow direction that is not observed for linear chains. In this paper, we extend our understanding of dilute ring polymer dynamics to mixed flows, which represent flow profiles intermediate between simple shear or planar elongation. We map the conformational behaviors at a number of flow geometries and strengths, demonstrating transitions between coiled, tumbling, and stretched regimes. Indeed, these observations are consistent with how linear chains respond to mixed flows. For both linear and ring polymers, we observe a marked first-order-like transition between tumbling and stretched polymers that we attribute to a dynamic energy barrier between the two states. This manifests as bimodal extension distributions in a narrow range of flow strengths and geometries, with the primary difference between rings and linear chains being the presence of molecular expansion in the vorticity direction.

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.

Unfolding of a diblock chain and its anomalous diffusion induced by active particles

We study the structural and dynamical behavior of an A-B diblock chain in the bath of active Brownian particles (ABPs) by Brownian dynamics simulations in two dimensions. We are interested in the situation that the effective interaction between the A segments is attractive, while that between the B segments is repulsive. Therefore, in thermal (nonactive) equilibrium, the A block "folds" into a compact globule, while the B block is in the expanded coil state. Interestingly, we find that the A block could "unfold" sequentially like unknitting a sweater, driven by the surrounding ABPs when the propelling strength on them is beyond a certain value. This threshold value decreases and then levels off as the length of the B block increases. We also find a simple power-law relation between the unfolding time of the A block and the self-propelling strength and an exponential relation between the unfolding time and the length of the B block. Finally, we probe the translational and rotational diffusion of the chain and find that both of them show "super-diffusivity" in a large time window, especially when the self-propelling strength is small and the A block is in the folded state. Such super-diffusivity is due to the strong asymmetric distribution of ABPs around the chain. Our work provides new insights into the behavior of a polymer chain in the environment of active objects.

Three Weaknesses for Three Perturbations: Comparing Protein Unfolding Under Shear, Force, and Thermal Stresses

The perturbation of a protein conformation by a physiological fluid flow is crucial in various biological processes including blood clotting and bacterial adhesion to human tissues. Investigating such mechanisms by computer simulations is thus of great interest, but it requires development of ad hoc strategies to mimic the complex hydrodynamic interactions acting on the protein from the surrounding flow. In this study, we apply the Lattice Boltzmann Molecular Dynamics (LBMD) technique built on the implicit solvent coarse-grained model for protein Optimized Potential for Efficient peptide structure Prediction (OPEP) and a mesoscopic representation of the fluid solvent, to simulate the unfolding of a small globular cold-shock protein in shear flow and to compare it to the unfolding mechanisms caused either by mechanical or thermal perturbations. We show that each perturbation probes a specific weakness of the protein and causes the disruption of the native fold along different unfolding pathways. Notably, the shear flow and the thermal unfolding exhibit very similar pathways, while because of the directionality of the perturbation, the unfolding under force is quite different. For force and thermal disruption of the native state, the coarse-grained simulations are compared to all-atom simulations in explicit solvent, showing an excellent agreement in the explored unfolding mechanisms. These findings encourage the use of LBMD based on the OPEP model to investigate how a flow can affect the function of larger proteins, for example, in catch-bond systems.

Polymer margination in uniform shear flows

We address the issue of polymer margination (migration towards surfaces) in uniform shear flows through extensive LBMD (lattice-Boltzmann molecular dynamics) simulations. In particular we consider the effect of monomer size, a on the chain's overall margination tendency for chains of length N = 16, 32 monomers in flows at multiple shear rates [small gamma, Greek, dot above]. We observed higher margination of chains with larger radii monomers in comparison to smaller radii monomer chains of the same length N. We quantify this effect by considering various measures such as the distribution of the maximum extent of the chain into the channel bulk, zm, distribution of its center of mass in the direction normal to the surface, zc and the distributions of the chain's radius of gyration in directions parallel and perpendicular to the surface i.e. Rx, Ry and Rz respectively.

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.

Flow-induced adhesion of shear-activated polymers to a substrate

Adhesion of polymers and proteins to substrates plays a crucial role in many technological applications and biological processes. A prominent example is the von Willebrand factor (VWF) protein, which is essential in blood clotting as it mediates adhesion of blood platelets to the site of injury at high shear rates. VWF is activated by flow and is able to bind efficiently to damaged vessel walls even under extreme flow-stress conditions; however, its adhesion is reversible when the flow strength is significantly reduced or the flow is ceased. Motivated by the properties and behavior of VWF in flow, we investigate adhesion of shear-activated polymers to a planar wall in flow and whether the adhesion is reversible under flow stasis. The main ingredients of the polymer model are cohesive inter-monomer interactions, a catch bond with the adhesive surface, and the shear activation/deactivation of polymer adhesion correlated with its stretching in flow. The cohesive interactions within the polymer maintain a globular conformation under low shear stresses and allow polymer stretching if a critical shear rate is exceeded, which is directly associated with its activation for adhesion. Our results show that polymer adhesion at high shear rates is significantly stabilized by catch bonds, while at the same time they also permit polymer dissociation from a surface at low or no flow stresses. In addition, the activation/deactivation mechanism for adhesion plays a crucial role in the reversibility of its adhesion. These observations help us better understand the adhesive behavior of VWF in flow and interpret its adhesion malfunctioning in VWF-related diseases.

Molecular Mechanism of Protein Unfolding under Shear: A Lattice Boltzmann Molecular Dynamics Study

Proteins are marginally stable soft-matter entities that can be disrupted using a variety of perturbative stresses, including thermal, chemical, or mechanical ones. Fluid under extreme flow conditions is a possible route to probe the weakness of biomolecules and collect information on the molecular cohesive interactions that secure their stability. Moreover, in many cases, physiological flow triggers the functional response of specialized proteins as occurring in blood coagulation or cell adhesion. We deploy the Lattice Boltzmann molecular dynamics technique based on the coarse-grained model for protein OPEP to study the mechanism of protein unfolding under Couette flow. Our simulations provide a clear view of how structural elements of the proteins are affected by shear, and for the simple study case, the β-hairpin, we exploited the analogy to pulling experiments to quantify the mechanical forces acting on the protein under shear.

Margination and stretching of von Willebrand factor in the blood stream enable adhesion

The protein von Willebrand factor (VWF) is essential in primary hemostasis, as it mediates platelet adhesion to vessel walls. VWF retains its compact (globule-like) shape in equilibrium due to internal molecular associations, but is able to stretch when a high enough shear stress is applied. Even though the shear-flow sensitivity of VWF conformation is well accepted, the behavior of VWF under realistic blood flow conditions remains poorly understood. We perform mesoscopic numerical simulations together with microfluidic experiments in order to characterize VWF behavior in blood flow for a wide range of flow-rate and hematocrit conditions. In particular, our results demonstrate that the compact shape of VWF is important for its migration (or margination) toward vessel walls and that VWF stretches primarily in a near-wall region in blood flow making its adhesion possible. Our results show that VWF is a highly optimized protein in terms of its size and internal associations which are necessary to achieve its vital function. A better understanding of the relevant mechanisms for VWF behavior in microcirculation provides a further step toward the elucidation of the role of mutations in various VWF-related diseases.

Modeling the cleavage of von Willebrand factor by ADAMTS13 protease in shear flow

Von Willebrand factor (VWF) is a key protein in hemostasis as it mediates adhesion of blood platelets to a site of vascular injury. A proper distribution of VWF lengths is important for normal functioning of hemostatic processes, because a diminished number of long VWF chains may significantly limit blood clotting and lead to bleeding, while an abundant number of long VWFs may result in undesired thrombotic events. VWF size distribution is controlled by ADAMTS13 protease, which can cleave VWF chains beyond a critical shear rate when the chains are stretched enough such that cleavage sites become accessible. To better understand the cleavage process, we model VWF cleavage in shear flow using mesoscopic hydrodynamic simulations. Two cleavage models are proposed, a geometrical model based on the degree of local stretching of VWF, and a tension-force model based on instantaneous tension force within VWF bonds. Both models capture the susceptibility of VWF to cleavage at high shear rates; however, the geometrical model appears to be much more robust than the force model. Our simulations show that VWF susceptibility to cleavage in shear flow becomes a universal function of shear rate, independent of VWF length for long enough chains. Furthermore, VWF is cleaved with a higher probability close to its ends in comparison to cleaving in the middle, which results into longer circulation lifetimes of VWF multimers. Simulations of dynamic cleavage of VWF show an exponential distribution of chain lengths, consistently with available in vitro experiments. The proposed cleavage models can be used in realistic simulations of hemostatic processes in blood flow.

Micromechanical model for isolated polymer-colloid clusters under tension

Binary polymer-colloid (PC) composites form the majority of biological load-bearing materials. Due to the abundance of the polymer and particles, and their simple aggregation process, PC clusters are used broadly by nature to create biomaterials with a variety of functions. However, our understanding of the mechanical features of the clusters and their load transfer mechanism is limited. Our main focus in this paper is the elastic behavior of close-packed PC clusters formed in the presence of polymer linkers. Therefore, a micromechanical model is proposed to predict the constitutive behavior of isolated polymer-colloid clusters under tension. The mechanical response of a cluster is considered to be governed by a backbone chain, which is the stress path that transfers most of the applied load. The developed model can reproduce the mean behavior of the clusters and is not dependent on their local geometry. The model utilizes four geometrical parameters for defining six shape descriptor functions which can affect the geometrical change of the clusters in the course of deformation. The predictions of the model are benchmarked against an extensive set of simulations by coarse-grained-Brownian dynamics, where clusters with different shapes and sizes were considered. The model exhibits good agreement with these simulations, which, besides its relative simplicity, makes the model an excellent add-on module for implementation into multiscale models of nanocomposites.

Swelling of Collagen-Hyaluronic Acid Co-Gels: An In Vitro Residual Stress Model

Tissue-equivalents (TEs), simple model tissues with tunable properties, have been used to explore many features of biological soft tissues. Absent in most formulations however, is the residual stress that arises due to interactions among components with different unloaded levels of stress, which has an important functional role in many biological tissues. To create a pre-stressed model system, co-gels were fabricated from a combination of hyaluronic acid (HA) and reconstituted Type-I collagen (Col). When placed in solutions of varying osmolarity, HA-Col co-gels swell as the HA imbibes water, which in turn stretches (and stresses) the collagen network. In this way, co-gels with residual stress (i.e., collagen fibers in tension and HA in compression) were fabricated. When the three gel types tested here were immersed in hypotonic solutions, pure HA gels swelled the most, followed by HA-Col co-gels; no swelling was observed in pure collagen gels. The greatest swelling rates and swelling ratios occurred in the lowest salt concentration solutions. Tension on the collagen component of HA-Col co-gels was calculated from a stress balance and increased nonlinearly as swelling increased. The swelling experiment results were in good agreement with the stress predicted by a fibril network + non-fibrillar interstitial matrix computational model.

Cooperation within von Willebrand factors enhances adsorption mechanism

von Willebrand factor (VWF) is a naturally collapsed protein that participates in primary haemostasis and coagulation events. The clotting process is triggered by the adsorption and conformational changes of the plasma VWFs localized to the collagen fibres found near the site of injury. We develop coarse-grained models to simulate the adsorption dynamics of VWF flowing near the adhesive collagen fibres at different shear rates and investigate the effect of factors such as interaction and cooperativity of VWFs on the success of adsorption events. The adsorption probability of a flowing VWF confined to the receptor field is enhanced when it encounters an adhered VWF in proximity to the collagen receptors. This enhancement is observed within a wide range of shear rates and is mostly controlled by the attractive van der Waals interactions rather than the hydrodynamic interactions among VWF monomers. The cooperativity between the VWFs acts as an effective mechanism for enhancing VWF adsorption to the collagen fibres. Additionally, this implies that the adsorption of such molecules is nonlinearly dependent on the density of flowing VWFs. These findings are important for studies of primary haemostasis as well as general adsorption dynamics processes in polymer physics.

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

By means of Brownian hydrodynamics simulations we show that the tension distribution along the contour of a single collapsed polymer in shear flow is inhomogeneous and above a threshold shear rate exhibits a double-peak structure when hydrodynamic interactions are taken into account. We argue that the tension maxima close to the termini of the polymer chain reflect the presence of polymeric protrusions. We establish the connection to shear-induced globule unfolding and determine the scaling behavior of the maximal tensile forces and the average protrusion length as a function of shear rate, globule size, and cohesive strength. A quasi-equilibrium theory is employed in order to describe the simulation results. Our results are used to explain experimental data for the shear-sensitive enzymatic degradation of von Willebrand factor.

Fluid Mechanics of Blood Clot Formation

Intravascular blood clots form in an environment in which hydrodynamic forces dominate and in which fluid-mediated transport is the primary means of moving material. The clotting system has evolved to exploit fluid dynamic mechanisms and to overcome fluid dynamic challenges to ensure that clots that preserve vascular integrity can form over the wide range of flow conditions found in the circulation. Fluid-mediated interactions between the many large deformable red blood cells and the few small rigid platelets lead to high platelet concentrations near vessel walls where platelets contribute to clotting. Receptor-ligand pairs with diverse kinetic and mechanical characteristics work synergistically to arrest rapidly flowing cells on an injured vessel. Variations in hydrodynamic stresses switch on and off the function of key clotting polymers. Protein transport to, from, and within a developing clot determines whether and how fast it grows. We review ongoing experimental and modeling research to understand these and related phenomena.

Von Willlebrand adhesion to surfaces at high shear rates is controlled by long-lived bonds

Von Willebrand factor (vWF) adsorbs and immobilizes platelets at sites of injury under high-shear-rate conditions. It has been recently demonstrated that single vWF molecules only adsorb significantly to collagen above a threshold shear, and here we explain such counterintuitive behavior using a coarse-grained simulation and a phenomenological theory. We find that shear-induced adsorption only occurs if the vWF-surface bonds are slip-resistant such that force-induced unbinding is suppressed, which occurs in many biological bonds (i.e., catch bonds). Our results quantitatively match experimental observations and may be important to understand the activation and mechanical regulation of vWF activity during blood clotting.

Unfolding of collapsed polymers in shear flow: effects of colloid banding structures in confining channels

Using hydrodynamic simulations, we demonstrate that confined colloidal suspensions can greatly enhance the unfolding of collapsed single polymers in flow. When colloids come in direct contact with the polymers due to the flow, the collapsed chains become flattened or elongated on the surface of the colloids, increasing the probability of forming large chain protrusions that the flow can pull out to unfold the polymers. This phenomenon may be suppressed if the colloid size is commensurate with the confining channels, where the colloids form well-defined banding structures. Here, we analyze the colloid banding structures in detail and their relation to the chain unfolding. We find that for colloid volume fractions up to 30%, the confined colloids form simple cubic (sc), hexagonal (hex), or a mixture of sc + hex structures. By directly changing the heights of the confining channels, we show that the collapsed polymers unfold the most in the mixed sc + hex structures. The diffuse (not well-defined) bands in the mixed sc + hex structures provide the highest collision probability for the colloids and the polymers, thus enhancing unfolding the most. Without colloidal suspensions, we show that the confining channels alone do not have an observable effect on the unfolding of collapsed polymers. The well-defined colloid bands also suppress the unfolding of noncollapsed polymers. In fact, the average size for noncollapsed chains is even smaller in the well-defined bands than in a channel without any colloids. The appearance of well-defined bands in this case also indicates that lift forces experienced by the polymers in confinement are negligible compared to those exerted by the colloidal band structures. Our results may be important for understanding the dynamics of mixed colloid polymer solutions.

Shear-induced dynamics of polymeric globules at adsorbing homogeneous and inhomogeneous surfaces

The dynamics and adsorption behavior of a single collapsed homopolymer on a surface in shear flow is investigated by means of Brownian hydrodynamics simulations. We study different homogeneous and inhomogeneous surface models and determine dynamic state diagrams as a function of the cohesive strength, the adhesive strength, and the shear rate. We find distinct dynamical adsorbed states that are classified into rolling and slipping states, globular and coil-like states, as well as isotropic and prolate states. We identify two different cyclic processes based on trajectories of the polymer stretching and the polymer separation from the surface. For adsorption on an inhomogeneous surface consisting of discrete binding sites, we observe stick-roll motion for highly corrugated surface potentials. Although the resulting high surface friction leads to low drift velocities and reduced hydrodynamic lift forces on such inhomogeneous surfaces, a shear-induced adsorption is not found in the presence of full hydrodynamic interactions. A hydrodynamically stagnant surface model is introduced for which shear-induced adsorption is observed in the absence of hydrodynamic interactions.