Dynamics and Instabilities of Collapsed Polymers in Shear Flow

Dynamics of a polyelectrolyte in simple shear flow

The configurational dynamics of a polyelectrolyte (PE), subjected to a simple shear flow, is studied using Brownian dynamics (BD) and Dissipative Particle Dynamics (DPD) simulations of a bead-spring model with explicit counterions. We explore the effect of counterion condensation on the tumbling and extension of PEs by varying the shear rates for a range of values of the electrostatic coupling parameter A (which is defined as the ratio of the Bjerrum length to the size of the monomer). In all cases, the power spectrum of Rs(t) (which characterizes the projected length of the PE in the flow direction as a function of time) exhibits a power law decay at high frequencies, similar to that for a dumbbell in shear flow. For lower values of A (A ~ 2), the tumbling of the PE is periodic and is always associated with folding and stretching, which is in contrast to the oscillatory transition between the extended and globular states seen at higher values of A (A ~ 15). We observe that for A ~ 2 the tumbling frequency decreases and the average tumbling time increases with hydrodynamic interaction (HI). For A > 15, we observe a critical shear rate γ[combining dot]c below which there is considerable counterion condensation and the PE remains in the globular state with a structure akin to that of a neutral polymer in poor solvent. The γ[combining dot]c and the behavior of the PE above the critical shear rate are dependent on the HI. For a given shear rate, when there is considerable condensed counterion fluctuation, the PE extends as a whole and then collapses by the formation of folds with no observable periodicity in tumbling. When the condensed counterion fluctuations are suppressed, the polymer exhibits periodic tumbling. Simulation artifacts resulting from the implicit nature of the solvent and that due to boundary conditions are discussed by comparing the BD results with that obtained from the DPD simulations incorporating Ewald summation for electrostatics.

The unfolded von Willebrand factor response in bloodstream: the self-association perspective

von Willebrand factor (vWF) is a multimeric glycoprotein essential for hemostasis after vascular injury, which modulates platelet-surface and platelet–platelet interactions by linking platelet receptors to the extracellular matrix and to each other. The crucial role of vWF in platelet function is particularly apparent when hemodynamic conditions create blood flow with high shear stress. Through multiple functional domains, vWF mediates the attachment of platelets to exposed tissues, where immobilized vWF is able to support a homotypic and/or heterotypic self-association. The self-association of vWF is also supported by a rapidly expanding reservoir of novel evidences that the thiol/disulfide exchange regulates vWF multimer size in the blood circulation. Moreover, in addition to proteolysis and reduction of ADAMTS13 (a disintegrin and metalloproteinase with a thrombospondin type 1 motif, member 13), the regulation of vWF multimer size and self-association may depend on a disulfide bond reductase activity ascribed to thrombospondin-1 (TSP-1). Along with the classical signaling pathways in activated platelets, evidence is emerging that lipid rafts also play important roles in various phases of hemostasis and thrombosis and facilitate the interaction between the key signaling molecules. Developments in these areas will refine our understanding of the role played by vWF self-association in physiological hemostasis and pathological thrombosis.

Computational fluid dynamics (CFD) insights into agitation stress methods in biopharmaceutical development

Agitation of small amounts of liquid is performed routinely in biopharmaceutical process, formulation, and packaging development. Protein degradation commonly results from agitation, but the specific stress responsible or degradation mechanism is usually not well understood. Characterization of the agitation stress methods is critical to identifying protein degradation mechanisms or specific sensitivities. In this study, computational fluid dynamics (CFD) was used to model agitation of 1 mL of fluid by four types of common laboratory agitation instruments, including a rotator, orbital shaker, magnetic stirrer and vortex mixer. Fluid stresses in the bulk liquid and near interfaces were identified, quantified and compared. The vortex mixer provides the most intense stresses overall, while the stir bar system presented locally intense shear proximal to the hydrophobic stir bar surface. The rotator provides gentler fluid stresses, but the air-water interfacial area and surface stresses are relatively high given its low rotational frequency. The orbital shaker provides intermediate-level stresses but with the advantage of a large stable platform for consistent vial-to-vial homogeneity. Selection of experimental agitation methods with targeted types and intensities of stresses can facilitate better understanding of protein degradation mechanisms and predictability for "real world" applications.

Giant nonmonotonic stretching response of a self-associating polymer in shear flow

Self-associating polymers are ubiquitous in synthetic and biological systems. Here, we use a combination of simulation and theory to show that these polymers exhibit a counterintuitive strong nonmonotonic stretching response in shear flow. Furthermore, we demonstrate that this behavior can be tuned by controlling the barrier for dissociation of the bonds and develop a quantitative and predictive theory based on conformational transitions to explain the observed behavior. Our results can be important in understanding previous experimental and theoretical observations and further aid in the development of novel smart materials.

Dynamics of collapsed polymers under the simultaneous influence of elongational and shear flows

Collapsed polymers in solution represent an oft-overlooked area of polymer physics, however recent studies of biopolymers in the bloodstream have suggested that the physics of polymer globules are not only relevant but could potentially lead to powerful new ways to manipulate single molecules using fluid flows. In the present article, we investigate the behavior of a collapsed polymer globule under the influence of linear combinations of shear and elongational flows. We generalize the theory of globule-stretch transitions that has been developed for the specific case of simple shear and elongational flows to account for behavior in arbitrary flow fields. In particular, we find that the behavior of a globule in flow is well represented by a two-state model wherein the critical parameters are the transition probabilities to go from a collapsed to a stretched state P(g-s) and vice versa P(s-g). The collapsed globule to stretch transition is described using a nucleation protrusion mechanism, and the reverse transition is described using either a tumbling or a relaxation mechanism. The magnitudes of P(g-s) and P(s-g) govern the state in which the polymer resides; for P(g-s) ≈ 0 and P(s-g) ≈ 1 the polymer is always collapsed, for P(g-s) ≈ 0 and P(s-g) ≈ 0 the polymer is stuck in either the collapsed or stretched state, for P(g-s) ≈ 1 and P(s-g) ≈ 0 the polymer is always stretched, and for P(g-s) ≈ 1 and P(s-g) ≈ 1 the polymer undergoes tumbling behavior. These transition probabilities are functions of the flow geometry, and we demonstrate that our theory quantitatively predicts globular polymer conformation in the case of mixed two-dimensional flows, regardless of orientation and representation, by comparing theoretical results to Brownian dynamics simulations. Generalization of the theory to arbitrary three-dimensional flows is discussed as is the incorporation of this theory into rheological equations.

Dynamics of polymers in flowing colloidal suspensions

Using hydrodynamic simulations we examine the behavior of single polymers in a confined colloidal suspension under flow. We study the conformations of both, collapsed and noncollapsed polymers. Our results show that the presence of the colloids has a pronounced effect on the unfolding and refolding cycles of collapsed polymers, but does not have a large effect for noncollapsed polymers. Further inspection of the conformations reveals that the strong flow around the colloids and the direct physical compressions exerted on a globular polymer diffusing in between colloidal shear bands largely facilitate the initiation and unraveling of the globular chains. These results are important for rheological studies of (bio)polymer-(bio)colloid mixtures.

Hydrodynamic effects in proteins

Experimental and numerical results pertaining to flow-induced effects in proteins are reviewed. Special emphasis is placed on shear-induced unfolding and on the role of solvent mediated hydrodynamic interactions in the conformational transitions in proteins.

Rheo-NMR studies of an enzymatic reaction: evidence of a shear-stable macromolecular system

Understanding the effects of shear forces on biopolymers is key to understanding how biological systems function. Although currently there is good agreement between theoretical predictions and experimental measurements of the behavior of DNA and large multimeric proteins under shear flow, applying the same arguments to globular proteins leads to the prediction that they should only exhibit shear-induced conformational changes at extremely large shear rates. Nevertheless, contradictory experimental evidence continues to appear, and the effect of shear on these biopolymers remains contentious. Here, a custom-built rheo-NMR cell was used to investigate whether shear flow modifies enzyme action compared with that observed quiescently. Specifically, (1)H NMR was used to follow the kinetics of the liberation of methanol from the methylesterified polysaccharide pectin by pectinmethylesterase enzymes. Two different demethylesterifying enzymes, known to have different action patterns, were used. In all experiments performed, Couette flows with shear rates of up to 1570 s(-1) did not generate detectable differences in the rate of methanol liberation compared to unsheared samples. This study provides evidence for a shear-stable macromolecular system consisting of a largely beta-sheet protein and a polysaccharide, in line with current theoretical predictions, but in contrast to some other experimental work on other proteins.

Elongational flow induces the unfolding of von Willebrand factor at physiological flow rates

The unfolding of von Willebrand Factor (vWF), one of the largest multimeric proteins in our body, has been shown to be a crucial step in the process of blood clotting. Here we show that elongational flows, which appear during vasoconstriction or stenosis, are the primary activation mechanisms of vWF, and unfold the multimeric protein at flow rates that are two orders-of -magnitude below those corresponding to pure shear. The findings presented here complement the current understanding of blood clotting from the molecular to the physiological level, and provide new physical insights into the connection between clotting anomalies, such as Heyde's syndrome and stenosis. These findings also represent a new paradigm in the function and activation of vWF.

Single flexible and semiflexible polymers at high shear: non-monotonic and non-universal stretching response

Using Brownian hydrodynamic simulation techniques, we study single polymers in shear. We investigate the effects of hydrodynamic interactions, excluded volume, chain extensibility, chain length and semiflexibility. The well-known stretching behavior with increasing shear rate [Formula: see text] is only observed for low shear [Formula: see text] < [Formula: see text] , where [Formula: see text] is the shear rate at maximum polymer extension. For intermediate shear rates [Formula: see text] < [Formula: see text] < [Formula: see text] the radius of gyration decreases with increasing shear with minimum chain extension at [Formula: see text] . For even higher shear [Formula: see text] < [Formula: see text] the chain exhibits again shear stretching. This non-monotonic stretching behavior is obtained in the presence of excluded-volume and hydrodynamic interactions for sufficiently long and inextensible flexible polymers, while it is completely absent for Gaussian extensible chains. We establish the heuristic scaling laws [Formula: see text] approximately N (-1.4) and [Formula: see text] approximately N (0.7) as a function of chain length N , which implies that the regime of shear-induced chain compression widens with increasing chain length. These scaling laws also imply that the chain response at high shear rates is not a universal function of the Weissenberg number Wi = [Formula: see text] [Formula: see text] anymore, where [Formula: see text] is the equilibrium relaxation time. For semiflexible polymers a similar non-monotonic stretching response is obtained. By extrapolating the simulation results to lengths corresponding to experimentally studied DNA molecules, we find that the shear rate [Formula: see text] to reach the compression regime is experimentally realizable.

Response of a concentrated monoclonal antibody formulation to high shear

There is concern that shear could cause protein unfolding or aggregation during commercial biopharmaceutical production. In this work we exposed two concentrated immunoglobulin-G1 (IgG1) monoclonal antibody (mAb, at >100 mg/mL) formulations to shear rates between 20,000 and 250,000 s(-1) for between 5 min and 30 ms using a parallel-plate and capillary rheometer, respectively. The maximum shear and force exposures were far in excess of those expected during normal processing operations (20,000 s(-1) and 0.06 pN, respectively). We used multiple characterization techniques to determine if there was any detectable aggregation. We found that shear alone did not cause aggregation, but that prolonged exposure to shear in the stainless steel parallel-plate rheometer caused a very minor reversible aggregation (<0.3%). Additionally, shear did not alter aggregate populations in formulations containing 17% preformed heat-induced aggregates of a mAb. We calculate that the forces applied to a protein by production shear exposures (<0.06 pN) are small when compared with the 140 pN force expected at the air-water interface or the 20-150 pN forces required to mechanically unfold proteins described in the atomic force microscope (AFM) literature. Therefore, we suggest that in many cases, air-bubble entrainment, adsorption to solid surfaces (with possible shear synergy), contamination by particulates, or pump cavitation stresses could be much more important causes of aggregation than shear exposure during production.