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.

Replica-averaging: An algorithm to study mechano-reactive processes for polymers under flow conditions.

A new method based on quasi-independent parallel simulation approach, replica-averaging, has been developed to study the influence of flow on mechanical force-mediated polymer processes, such as denaturation and breaking of bonds. This method considerably mitigates the unphysical prediction of force-mediated events inherent in Brownian dynamics (BD) polymer chain simulations that employ instantaneous force profile-based criteria to identify the occurrence of such events. This inaccuracy in predicting force-mediated event kinetics is due to high fluctuations of the instantaneous force profile around the average force. Replica-averaging reduces such high fluctuation effects by computing a force profile that faithfully represents the average force profile of the polymer chain conformation, which is then used to predict reactive events. For transient conformation conditions, the replica-averaged method more accurately predicts the mechano-reactive kinetics than the time-averaged method typically employed to reduce the unphysical prediction of force-mediated events in BD simulations. Furthermore, the influence of the proposed replica-averaging method parameters on the accuracy of predicting the true average force profile along the polymer is discussed.

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.

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.

A mechano-reactive coarse-grained model of the blood-clotting agent von Willebrand factor.

The von Willebrand Factor (vWF) is a large blood glycoprotein that aids in hemostasis. Within each vWF monomer, the A2 domain hosts a cleavage site for enzyme ADAMTS13, which regulates the size of vWF multimers. This cleavage site can only be exposed when an A2 domain unfolds, and the unfolding reaction energy landscape is highly sensitive to the force conditions on the domain. Based on previous optical tweezer experimental results, we advance here a new activated A2 monomer model (AA2MM) for coarse-grained modeling of vWF that accurately represents the force-based probabilistic change between the unfolded/refolded states. A system of springs is employed to mimic the complex mechanical response of vWF monomers subject to pulling forces. AA2MM was validated by comparing monomer scale simulation results to data from prior pulling experiments on vWF monomer fragments. The model was further validated by comparing multimer scale Brownian dynamics simulation results to experiments using microfluidic chamber microscopy to visualize tethered vWF proteins subject to flow. The A2 domain unfolding reaction was studied in bulk flow simulations (pure shear and elongation flow), giving evidence that elongational flow drives the vWF size regulation process in blood. The mechanoreactive, coarse-grained AA2MM accurately describes the complex mechanical coupling between human blood flow conditions and vWF protein reactivity.

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.

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.

Long-ranged Protein-glycan Interactions Stabilize von Willebrand Factor A2 Domain from Mechanical Unfolding.

von Willebrand Factor (vWF) is a large multimeric protein that binds to platelets and collagen in blood clotting. vWF A2 domain hosts a proteolytic site for ADAMTS13 (A Disintegrin and Metalloprotease with a ThromboSpondin type 1 motif, member 13) to regulate the size of vWF multimers. This regulation process is highly sensitive to force conditions and protein-glycan interactions as the process occurs in flowing blood. There are two sites on A2 domain (N1515 and N1574) bearing various N-linked glycan structures. In this study, we used molecular dynamics (MD) simulation to study the force-induced unfolding of A2 domain with and without a single N-linked glycan type on each site. The sequential pullout of ß-strands was used to represent a characteristic unfolding sequence of A2. This unfolding sequence varied due to protein-glycan interactions. The force-extension and total energy-extension profiles also show differences in magnitude but similar characteristic shapes between the systems with and without glycans. Systems with N-linked glycans encountered higher energy barriers for full unfolding and even for unfolding up to the point of ADAMTS13 cleavage site exposure. Interestingly, there is not much difference observed for A2 domain structure itself with and without glycans from standard MD simulations, suggesting roles of N-glycans in A2 unfolding through long-ranged protein-glycan interactions.

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.

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.

Self-pinning of a nanosuspension droplet: Molecular dynamics simulations.

Results are presented from molecular dynamics simulations of Pb(l) nanodroplets containing dispersed Cu nanoparticles (NPs) and spreading on solid surfaces. Three-dimensional simulations are employed throughout, but droplet spreading and pinning are reduced to two-dimensional processes by modeling cylindrical NPs in cylindrical droplets; NPs have radius R_{NP}≅3nm while droplets have initial R_{0}≅42nm. At low particle loading explored here, NPs in sufficient proximity to the initial solid-droplet interface are drawn into advancing contact lines; entrained NPs eventually bind with the underlying substrate. For relatively low advancing contact angle θ_{adv}, self-pinning on entrained NPs occurs; for higher θ_{adv}, depinning is observed. Self-pinning and depinning cases are compared and forces on NPs at the contact line are computed during a depinning event. Though significant flow in the droplet occurs in close proximity to the particle during depinning, resultant forces are relatively low. Instead, forces due to liquid atoms confined between the particles and substrate dominate the forces on NPs; that is, for the NP size studied here, forces are interface dominated. For pinning cases, a precursor wetting film advances ahead of the pinned contact line but at a significantly slower rate than for a pure droplet. This is because the precursor film is a bilayer of liquid atoms on the substrate surface but it is instead a monolayer film as it crosses over pinning particles; thus, mass delivery to the bilayer structure is impeded.

Thin film compressive stresses due to adatom insertion into grain boundaries.

Atomic simulations of the growth of polycrystalline Ni demonstrate that deposited atoms incorporate into the film at boundaries, resulting in compressive stress generation. Incorporated atoms can also leave the boundaries and thus relieve compressive stress. This leads to a complex interplay between growth stress, adatom incorporation, and surface structure. A simple, theoretical model that accounts for grain size effects is proposed and is in good agreement with simulation results.

Liquid nanodroplets spreading on chemically patterned surfaces.

Controlling the spatial distribution of liquid droplets on surfaces via surface energy patterning can be used to deliver material to specified regions via selective liquid/solid wetting. Although studies of the equilibrium shape of liquid droplets on heterogeneous substrates exist, much less is known about the corresponding wetting kinetics. Here we present large-scale atomistic simulations of liquid nanodroplets spreading on chemically patterned surfaces. Results are presented for lines of polymer liquid (droplets) on substrates consisting of alternating strips of wetting (equilibrium contact angle theta0 = 0 degrees) and nonwetting (theta0 approximately 90 degrees) material. Droplet spreading is compared for different wavelength lambda of the pattern and strength of surface interaction on the wetting strips. For small lambda, droplets partially spread on both the wetting and nonwetting regions of the substrate to attain a finite contact angle less than 90 degrees. In this case, the extent of spreading depends on the interaction strength in the wetting regions. A transition is observed such that, for large lambda, the droplet spreads only on the wetting region of the substrate by pulling material from nonwetting regions. In most cases, a precursor film spreads on the wetting portion of the substrate at a rate strongly dependent on the width of the wetting region.

Tribological properties of alkylsilane self-assembled monolayers.

In this study, we perform molecular dynamics simulations of adhesive contact and friction between alkylsilane Si(OH)(3)(CX(2))(10)CX(3) and alkoxylsilane Si(OH)(2)(CX(2))(10)CX(3) (where X = H or F) self-assembled monolayers (SAMs) on an amorphous silica substrate. The alkylsilane SAMs are primarily hydrogen-bonded or physisorbed to the surface. The alkoxylsilane SAMs are covalently bonded or chemisorbed to the surface. Previously, we studied the chemisorbed systems. In this work, we study the physisorbed systems and compare the tribological properties with the chemisorbed systems. Furthermore, we examine how water at the interface of the SAMs and substrate affects the tribological properties of the physisorbed systems. When less than a third of a monolayer is present, very little difference in the microscopic friction coefficient mu or shear stresses is observed. For increasing amounts of water, the values of mu and the shear stresses decrease; this effect is somewhat more pronounced for fluorocarbon alkylsilane SAMs than for the hydrocarbon SAMs. The observed decrease in friction is a consequence of a slip plane that occurs in the water as the amount of water is increased. We studied the frictional behavior using relative shear velocities ranging from v = 2 cm/s to 2 m/s. Similar to previously reported results for alkoxylsilane SAMs, the values of the measured stress and mu for the alkylsilane SAM systems decrease monotonically with v.

Surface wetting of liquid nanodroplets: droplet-size effects.

The spreading of liquid nanodroplets of different initial radii R0 is studied using molecular dynamics simulation. Results for two distinct systems, Pb on Cu(111), which is nonwetting, and a coarse-grained polymer model, which wets the surface, are presented for Pb droplets ranging in size from approximately 55,000 to 220,000 atoms and polymer droplets ranging in size from approximately 200,000 to 780 000 monomers. In both cases, a precursor foot precedes the spreading of the main droplet. This precursor foot spreads as r(2)(f)(t) = 2D(eff)t with an effective diffusion constant that exhibits a droplet-size dependence D(eff) approximately R(1/2)(0). The radius of the main droplet r(b)(t) approximately R(4/5)(0) is in agreement with kinetic models for the cylindrical geometry studied.

Diverse spreading behavior of binary polymer nanodroplets.

Molecular dynamics simulations are used to study the spreading of binary polymer nanodroplets in a cylindrical geometry. The polymers, described by the bead-spring model, spread on a flat surface with a surface-coupled Langevin thermostat to mimic the effects of a corrugated surface. Each droplet consists of chains of length 10 or 100 monomers with approximately 350,000 monomers total. The qualitative features of the spreading dynamics are presented for differences in chain length, surface interaction strength, and composition. When the components of the droplet differ only in the surface interaction strength, the more strongly wetting component forms a monolayer film on the surface even when both materials are above or below the wetting transition. In the case where the only difference is the polymer chain length, the monolayer film beneath the droplet is composed of an equal amount of short chain and long chain monomers even when one component (the shorter chain length) is above the wetting transition and the other is not. The fraction of short and long chains in the precursor foot depends on whether both the short and the long chains are in the wetting regime. Diluting the concentration of the strongly wetting component in a mixture with a weakly wetting component decreases the rate of diffusion of the wetting material from the bulk to the surface and limits the spreading rate of the precursor foot, but the bulk spreading rate actually increases when both components are present. This may be due to the strongly wetting material pushing out the weakly wetting material as it moves toward the precursor foot.

Spreading dynamics of polymer nanodroplets in cylindrical geometries.

The spreading of one- and two-component polymer nanodroplets is studied using molecular dynamics simulation in a cylindrical geometry. The droplets consist of polymer chains of length 10, 40, and 100 monomers per chain described by the bead-spring model spreading on a flat surface with a surface-coupled Langevin thermostat. Each droplet contains approximately 350,000 monomers. The dynamics of the individual components of each droplet is analyzed and compared to the dynamics of single-component droplets for the spreading rates of the precursor foot and bulk droplet, the time evolution of the contact angle, and the velocity distribution inside the droplet. We derive spreading models for the cylindrical geometry analogous to the kinetic and hydrodynamic models previously developed for the spherical geometry, and show that hydrodynamic behavior is observed at earlier times for the cylindrical geometry. The contact radius is predicted to scale as r(t) approximately t1/5 from the kinetic model and r (t) approximately t1/7 for the hydrodynamic model in the cylindrical geometry.

Precursor film controlled wetting of Pb on Cu.

Wetting in a system where the kinetics of drop spreading are controlled by the rate of formation of a precursor film is modeled for the first time at the atomistic scale. Molecular dynamics simulations of Pb(l) wetting Cu(111) and Cu(100) show that a precursor film of atomic thickness evolves and spreads diffusively. This precursor film spreads significantly faster on Cu(111) than on Cu(100). For Cu(100), the kinetics of drop spreading are dramatically decreased by slow advancement of the precursor film. Slow precursor film kinetics on Cu(100) are partly due to the formation of a surface alloy at the solid-liquid interface which does not occur on Cu(111).

Spreading dynamics of polymer nanodroplets.

The spreading of polymer droplets is studied using molecular dynamics simulations. To study the dynamics of both the precursor foot and the bulk droplet, large hemispherical drops of 200 000 monomers are simulated using a bead-spring model for polymers of chain length 10, 20, and 40 monomers per chain. We compare spreading on flat and atomistic surfaces, chain length effects, and different applications of the Langevin and dissipative particle dynamics thermostats. We find diffusive behavior for the precursor foot and good agreement with the molecular kinetic model of droplet spreading using both flat and atomistic surfaces. Despite the large system size and long simulation time relative to previous simulations, we find that even larger systems are required to observe hydrodynamic behavior in the hemispherical spreading droplet.