Predicting Steady Shear Rheology of Condensed-Phase Monomolecular Films at the Air-Water Interface.

Predicting the non-Newtonian shear response of soft interfaces in biophysical systems and engineered products has been compromised by the use of linear (Newtonian) constitutive equations. We present a generalized constitutive equation, with tractable material properties, governing the response of Newtonian and non-Newtonian interfaces subjected to a wide range of steady shear. With experiments spanning six decades of shear rate, we capture and unify divergent reports of shear-thinning behavior of monomolecular films of the lipid dipalmitoylphosphatidylcholine, the primary constituent of mammalian cell walls and lung surfactant, at near-physiological packing densities.

Surface shear viscosity as a macroscopic probe of amyloid fibril formation at a fluid interface.

Amyloidogenesis of proteins is of wide interest because amyloid structures are associated with many diseases, including Alzheimer's and type II diabetes. Dozens of different proteins of various sizes are known to form amyloid fibrils. While there are numerous studies on the fibrillization of insulin induced by various perturbations, shearing at fluid interfaces has not received as much attention. Here, we present a study of human insulin fibrillization at room temperature using a deep-channel surface viscometer. The hydrodynamics of the bulk flow equilibrates in just over a minute, but the proteins at the air-water interface exhibit a very slow development during which the surface (excess) shear viscosity deduced from a Newtonian surface model increases slightly over a period of a day and a half. Then, there is a very rapid increase in the surface shear viscosity to effectively unbounded levels as the interface becomes immobilized. Atomic force microscopy shows that fibrils appear at the interface after it becomes immobilized. Fibrillization in the bulk does not occur until much later. This has been verified by concurrent atomic force microscopy and circular dichroism spectroscopy of samples from the bulk. The immobilized interface has zero in-plane shear rate, however due to the bulk flow, there is an increase in the strength of the normal component of the shear rate at the interface, implicating this component of shear in the fibrillization process ultimately resulting in a thick weave of fibrils on the interface. Real-time detection of fibrillization via interfacial rheology may find utility in other studies of proteins at sheared interfaces.

Shear-induced amyloid fibrillization: the role of inertia.

Agitation of protein is known to induce deleterious effects on protein stability and structure, with extreme agitation sometimes resulting in complete aggregation into amyloid fibrils. Many mechanisms have been proposed to explain how protein becomes unstable when subjected to flow, including alignment of protein species, shear-induced unfolding, simple mixing, or fragmentation of existing fibrils to create new seeds. Here a shearing flow was imposed on a solution of monomeric human insulin via a rotating Couette device with a small hydrophobic fluid interface. The results indicate that even very low levels of shear are capable of accelerating amyloid fibril formation. Simulations of the flow suggest that the shear enhances fibrillization kinetics when flow inertia is non-negligible and the resulting meridional circulation allows for advection of bulk protein to the hydrophobic interface.

Flow-induced 2D protein crystallization: characterization of the coupled interfacial and bulk flows.

Two-dimensional crystallization of the protein streptavidin, crystallizing below a biotinylated lipid film spread on a quiescent air-water interface is a well studied phenomenon. More recently, 2D crystallization induced by a shearing interfacial flow has been observed at film surface pressures significantly lower than those required in a quiescent system. Here, we quantify the interfacial and bulk flow associated with 2D protein crystallization through numerical modeling of the flow along with a Newtonian surface model. Experiments were conducted over a wide range of conditions resulting in a state diagram delineating the flow strength required to induce crystals for various surface pressures. Through measurements of the velocity profile at the air-water interface, we found that even in the cases where crystals are formed, the macroscopic flow at the interface is well described by the Newtonian model. However, the results show that even in the absence of any protein in the system, the viscous response of the biotinylated lipid film is complicated and strongly dependent on the strength of the flow. This observation suggests that the insoluble lipid film plays a key role in flow-induced 2D protein crystallization.

Performance of a microscope with an embedded oscillating pinned-contact liquid lens.

A liquid drop with pinned contact lines in a through-hole behaves as a natural oscillator with low dissipation, while serving as a biconvex lens with a variable focal distance. By embedding such an oscillating liquid lens into a microscope and analyzing it, we show that the object distance of the system can rapidly scan a range of over 1 mm, while maintaining a resolving power comparable to that of the base microscope configuration. Using this scanning object plane enabled by the liquid lens, we show how moving microscopic objects can be observed in three spatial dimensions and time.

Removal versus fragmentation of amyloid-forming precursors via membrane filtration.

The presence of even minute amounts of protein aggregates in solution can significantly alter the kinetics of amyloid formation. Removal of such pre-existing aggregates is critical for reproducible analysis of amyloid formation. Here we examine the effects of membrane filtration on insulin fibrillization. We find that filtration of insulin with large pore membranes (≥ 100 nm) generally slows fibril formation relative to unfiltered solutions by removing pre-aggregated protein. Unexpectedly, filtration with small pore membranes (< 100 nm) showed no beneficial effect and, in some cases, accelerated insulin fibril formation. This effect may be due to fragmentation of pre-existing aggregates during filtration through small pore membranes, which can increase the number of amyloid-forming precursors. These findings reveal the complexity of removing protein aggregates via filtration and suggest optimal filtration protocols for conducting fibril formation analysis of insulin and similar amyloidogenic proteins.

Optical performance of an oscillating, pinned-contact double droplet liquid lens.

Liquid droplets can produce spherical interfaces that are smooth down to the molecular scale due to surface tension. For typical gas/liquid systems, spherical droplets occur on the millimeter and smaller scales. By coupling two droplets, with contact lines pinned at each edge of a cylindrical hole through a plate, a biconvex lens is created. Using a sinusoidal external pressure, this double droplet system (DDS) can be readily forced to oscillate at resonance. The resulting change in the curvatures of the droplets produces a time-varying focal length. Such an oscillating DDS was introduced in 2008 [Nat. Photonics 2, 610 (2008)]. Here we provide a more comprehensive description of the system's optical performance, showing the effects of liquid volume and driving pressure amplitude on the back focal distance, radii of curvature, object distance, and image sharpness.

Effects of Shear Rate and Protein Concentration on Amyloidogenesis via Interfacial Shear.

The influence of hydrodynamics on protein fibrillization kinetics is relevant to biophysics, biochemical reactors, medicine, and disease. This investigation focused on the effects of interfacial shear on the fibrillization kinetics of insulin. Human insulin served as a model protein for studying shear-induced fibrillization with relevance to amyloid diseases such as Alzheimer's, Parkinson's, prions, and type 2 diabetes. Insulin solutions at different protein concentrations were subjected to shear flows with prescribed interfacial angular velocities using a knife-edge (surface) viscometer (KEV) operating in a laminar axisymmetric flow regime where inertia is significant. Fibrillization kinetics were quantified using intrinsic fibrillization rate and times (onset, half, and end) determined through spectroscopic measurement of monomer extinction curves and fitting to a sigmoidal function. Additionally, the occurrence of gelation was determined through macroscopic imaging and transient fibril microstructure was captured using fluorescence microscopy. The results showed that increasing interfacial shear rate produced a monotonic increase in intrinsic fibrillization rate and a monotonic decrease in fibrillization time. Protein concentration did not significantly impact the intrinsic fibrillization rate or times; however, a minimum fibril concentration for gelation was found. Protein microstructure showed increasing aggregation and plaque/cluster formation with time.

Growth of microorganisms in an interfacially driven space bioreactor analog.

Fluid bioreactors in microgravity environments may utilize alternative methods of containment and mixing. The ring-sheared drop (RSD) is a containerless mixing device which functions in microgravity using surface tension for containment and mixes through interfacially-driven flow. To assess the feasibility of using interfacially driven flow devices, such as the RSD, as bioreactors, Escherichia coli growth and recombinant protein expression were analyzed in a ground-based analog of the RSD called the knife edge surface viscometer (KEV). Results demonstrated that the KEV can facilitate the growth of E. coli and that growth rate increases logarithmically with increasing knife edge rotation rate, similar to the standard growth method on Earth (orbital shaker). Furthermore, the KEV was shown to be viable for supporting recombinant protein expression in E. coli at levels comparable to those achieved using standard growth methods.

Simulated microgravity in the ring-sheared drop.

The ring-sheared drop is a module for the International Space Station to study sheared fluid interfaces and their influence on amyloid fibril formation. A 2.54-cm diameter drop is constrained by a stationary sharp-edged ring at some latitude and sheared by the rotation of another ring in the other hemisphere. Shearing motion is conveyed primarily by the action of surface shear viscosity. Here, we simulate microgravity in the laboratory using a density-matched liquid surrounding the drop. Upon shearing, the drop's deformation away from spherical is found to be a result of viscous and inertial forces balanced against the capillary force. We also present evidence that the deformation increases with increasing surface shear viscosity.

Three-dimensional modes in a periodically driven elongated cavity.

Three-dimensional instability modes of the periodic flow in a rectangular cavity driven by the harmonic sliding oscillation of its floor are explored experimentally. Theory for a cavity with infinite span predicts two synchronous modes and a quasiperiodic traveling-wave mode as primary transitions from two-dimensional to three-dimensional flow for different combinations of floor oscillation amplitude and frequency. Previously, only one of the two synchronous modes had been found experimentally. Here, we provide experimental details of both synchronous modes and a quasiperiodic mode. All three modes appear in the parameter regimes predicted by the theory; however, in the finite-span experiments, the traveling wave nature of the quasiperiodic mode is replaced by a nonpropagating mode with spatial features similar to those of the traveling mode.

Comparison of Human and Bovine Insulin Amyloidogenesis under Uniform Shear.

A diverse range of proteins can assemble into amyloid fibrils, a process that generally results in a loss of function and an increase in toxicity. The occurrence and rate of conversion is strongly dependent on several factors including molecular structure and exposure to hydrodynamic forces. To investigate the origins of shear-induced enhancement in the rate of fibrillization, a stable rotating Couette flow was used to evaluate the kinetics of amyloid formation under uniform shear for two similar insulin species (human and bovine) that demonstrate unique fibrillization kinetics. The presence of shear-induced nuclei predicted by previous studies is supported by observations of a lag between the consumption of soluble insulin and the precipitation of amyloid aggregates. The apparent fibrillization rate generally increases with shear. However, a two-parameter kinetic model revealed that the nucleation rate has a maximum value at intermediate shear rates. The fibril elongation rate increases monotonically with shear and is similar for both insulin variants, suggesting that increased elongation rates are related to mixing. Differences between human and bovine insulin kinetics under shear are attributable to the nucleation step.

Influence of coexisting phases on the surface dilatational viscosity of Langmuir monolayers.

Monolayer hydrodynamics are usually described in terms of a Newtonian constitutive relationship. However, this macroscopic view fails to account for small-scale coexisting phase domains, which are generally present in the monolayer and appear to have profound macroscopic effects. Here, we provide direct evidence of these effects, consisting of Brewster angle microscopy images of the monolayer, space- and time-resolved interfacial velocity measurements, and comparisons with predictions based on the Navier-Stokes equations together with the classic model for a Newtonian interface.

Non-newtonian behavior of an insoluble monolayer: effects of inertia.

Interfacial velocity measurements were performed in an optical annular channel, consisting of stationary inner and outer cylinders, a floor rotating at a constant rate, and a flat free surface on which an insoluble monolayer was initially spread. Measurements for essentially inviscid monolayers and some viscous monolayers on water show good agreement with numerical predictions for a Newtonian interface (Boussinesq-Scriven surface model) coupled to a bulk flow described by the Navier-Stokes equations. Here, we consider in detail a viscous monolayer, namely hemicyanine, and find that above a certain concentration, the monolayer does not behave Newtonian at a Reynolds number of about 250. We show that the discrepancies between the measurements and predicted Newtonian behavior are not due to compositional effects (i.e., nonuniform monolayer distribution), Reynolds number (i.e., inertia and/or secondary flows), or surface dilatational viscosity (which does not play any role in the parameter regime investigated). We show prima facie evidence that the observed shear thinning nature of the velocity profile is associated with a phase transition at C approximately 0.9 mg/m(2) at low Reynolds numbers. At large Reynolds numbers (Re=8500), hemicyanine is found to flow like a viscous Newtonian monolayer on the air/water interface, with viscosity dependent only on the local concentration.

Hydrodynamics of a bounded vertical film with nonlinear surface properties.

The drainage of a thin liquid film with an insoluble monolayer down a vertical wall is studied. Lubrication theory is used to develop a model where the film is pinned at the top with a given thickness and the film drains into a bath at the bottom. A nonlinear equation of state is used for the surface tension and the surface viscosity is a nonlinear function of the surfactant concentration; these are appropriate for some aqueous systems. The three partial differential equations are solved via discretization in space and then the resulting differential algebraic system is solved. Results are described for a wide range of parameters, and the conditions under which the free surface is immobilized are discussed.

Electromagnetic liquid pistons for capillarity-based pumping.

The small scales associated with lab-on-a-chip technologies lend themselves well to capillarity-dominated phenomena. We demonstrate a new capillarity-dominated system where two adjoining ferrofluid droplets can behave as an electronically-controlled oscillator or switch by an appropriate balance of magnetic, capillary, and inertial forces. Their oscillatory motion can be exploited to displace a surrounding liquid (akin to an axial piston pump), forming electromagnetic "liquid pistons." Such ferrofluid pistons can pump a precise volume of liquid via finely tunable amplitudes (cf. pump stroke) or resonant frequencies (cf. pump speed) with no solid moving parts for long-term operation without wear in a small device. Furthermore, the rapid propagation of electromagnetic fields and the favorable scaling of capillary forces with size permit micron sized devices with very fast operating speeds (∼kHz). The pumping dynamics and performance of these liquid pistons is explored, with experimental measurements showing good agreement with a spherical cap model. While these liquid pistons may find numerous applications in micro- and mesoscale fluidic devices (e.g., remotely activated drug delivery), here we demonstrate the use of these liquid pistons in capillarity-dominated systems for chip-level, fast-acting adaptive liquid lenses with nearly perfect spherical interfaces.

Protein crystallization at the air/water interface induced by shearing bulk flow.

We have observed 2D protein crystallization under conditions where in the absence of flow, crystallization fails to occur. Even under conditions where crystallization does occur in quiescent systems, we have found that flow can accelerate the crystallization process. By interrogating the flow responsible for this enhanced crystallization, we have correlated the enhancement with large shear in the plane of the interface. Some possible mechanisms for why interfacial shear can enhance the crystallization process are proposed.

Effects of shearing flow with inertia on monolayer mesoscale structure.

In an experimental flow system capable of imparting a well-controlled shear-rate distribution with inertia to a monolayer consisting of coexisting phases, we have studied the resulting phase morphology and domain fragmentation. These evolve on distinct time scales: the viscous time associated with the viscosity in the bulk and the Marangoni stress and the fragmentation/relaxation time associated with the phase morphology. A relationship between the microstructure (line tension) and macroflow (shear rate) determining the meso length scale of the coexisting phase domains has been deduced from dimensional analysis and was found to correlate well with the quantitative experimental observations.

Flow-induced patterning of Langmuir monolayers.

Insoluble monolayers on water have been patterned at the macroscopic scale (i.e., at the centimeter scale of the flow apparatus) as well as the mesoscopic scale (i.e., down to the micron scale resolvable via optical microscopy). The macroscopic patterning at the air/water interface results from a hydrodynamic instability leading to a steadily precessing flow pattern. The velocity field is measured, and the associated shear stress at the interface is shown to be locally amplified by the flow pattern. The resulting hydrodynamic effects on two different monolayer systems are explored: (1) the pattern in a model monolayer consisting of micron-size, surface-bound particles is visualized to show that the particles are concentrated into isolated regions of converging flow with high shear, and (2) Brewster angle microscopy of a Langmuir monolayer (vitamin K1) shows not only that the monolayer is patterned at the macroscopic scale but also that the localized high-shear flow further patterns the monolayer at the mesoscale.