Influence of boundary conditions and confinement on nonlocal effects in flows of wormlike micellar systems

In this paper we report on the influence of different geometric and boundary constraints on nonlocal (spatially inhomogeneous) effects in wormlike micellar systems. In a previous paper, nonlocal effects were observable by measuring the local rheological flow curves of micelles flowing in a microchannel under different pressure drops, which appeared to differ from the flow curve measured using conventional rheometry. Here we show that both the confinement and the boundary conditions can influence those nonlocal effects. The role of the nature of the surface is analyzed in detail using a simple scalar model that incorporates inhomogeneities, which captures the flow behavior in both wide and confined geometries. This leads to an estimate for the nonlocal "diffusion" coefficient (i.e., the shear curvature viscosity) which corresponds to a characteristic length from 1 to 10 microm.

Coarse-grained simulations of flow-induced nucleation in semicrystalline polymers

We perform kinetic Monte Carlo simulations of flow-induced nucleation in polymer melts with an algorithm that is tractable even at low undercooling. The configuration of the noncrystallized chains under flow is computed with a recent nonlinear tube model. Our simulations predict both enhanced nucleation and the growth of shish-like elongated nuclei for sufficiently fast flows. The simulations predict several experimental phenomena and theoretically justify a previously empirical result for the flow-enhanced nucleation rate. The simulations are highly pertinent to both the fundamental understanding and process modeling of flow-induced crystallization in polymer melts.

Two-dimensional perturbations in a scalar model for shear banding

We present an analytical study of a toy model for shear banding, without normal stresses, which uses a piecewise linear approximation to the flow curve (shear stress as a function of shear rate). This model exhibits multiple stationary states, one of which is linearly stable against general two-dimensional perturbations. This is in contrast to analogous results for the Johnson-Segalman model, which includes normal stresses, and which has been reported to be linearly unstable for general two-dimensional perturbations. This strongly suggests that the linear instabilities found in the Johnson-Segalman can be attributed to normal stress effects.

Nonmonotonic models are not necessary to obtain shear banding phenomena in entangled polymer solutions

Recent experiments on entangled polymer solutions may indicate a constitutive instability, and have led some to question the validity of existing constitutive models. We use a modern constitutive model, the Rolie-Poly model plus a solvent viscosity, and show that (i) this simple class of models captures instability, (ii) shear banding phenomena is observable for weakly stable fluids in flow geometries with sufficiently inhomogeneous total stress, and (iii) transient phenomena exhibit inhomogeneities similar to shear banding, even for weakly stable fluids.

Manipulation and charge determination of proteins in photopatterned solid supported bilayers

This work demonstrates the use of deep UV micropatterned chlorotrimethylsilane (TMS) monolayers to support lipid membranes on SiO(2) surfaces. After immersing such a patterned surface into a solution containing small unilamellar vesicles of egg PC, supported bilayer lipid membranes were formed on the hydrophilic, photolyzed regions and lipid monolayer over the hydrophobic, non-photolyzed regions. A barrier between the lipid monolayer and bilayer regions served to stop charged lipids migrating between the two. This allows the system to be used to separate charged lipids or proteins by electrophoresis. Either oppositely charged fluorescence labeled lipids [Texas Red DHPE (negative charge) and D291 (positive charge)] or lipids with different charge numbers [Texas Red DHPE (one negative charge) and NBD PS (two negative charges)] can be separated. We have also studied the migration of streptavidin attached to a biotinylated lipid. Negatively charged streptavidin responds to the applied electric field by moving in the direction of electroosmotic flow, i.e. towards the negative electrode. However the direction of streptavidin movement can be controlled by altering the difference in zeta potential between that of the streptavidin (zeta(1)) and the lipid membrane (zeta(2)). If zeta(1) > zeta(2), streptavidin moves to the negative electrode, while if zeta(1) < zeta(2), streptavidin moves to the positive electrode. This balance was manipulated by adding positively charged lipid DOTAP to the membrane. After measuring the average drift velocity of streptavidin as a function of DOTAP concentration, the point where zeta(1) approximately zeta(2) was found. At this point zeta(1) was calculated to be -9.8 mV which is in good agreement with the value of -13 mV from force measurements and corresponds to a charge of -2e per streptavidin, thus demonstrating the applicability of this method for determining protein charge.

Mechanical unfolding revisited through a simple but realistic model

Single-molecule experiments and their application to probe the mechanical resistance and related properties of proteins provide a new dimension in our knowledge of these important and complex biological molecules. Single-molecule techniques may not have yet overridden solution experiments as a method of choice to characterize biophysical and biological properties of proteins, but have stimulated a debate and contributed considerably to bridge theory and experiment. Here we demonstrate this latter contribution by illustrating the reach of some theoretical findings using a solvable but nontrivial molecular model whose properties are analogous to those of the corresponding experimental systems. In particular, we show the relationship between the thermodynamic and the mechanical properties of a protein. The simulations presented here also illustrate how forced and spontaneous unfolding occur through different pathways and that folding and unfolding rates at equilibrium cannot in general be obtained from forced unfolding experiments or simulations. We also study the relationship between the energy surface and the mechanical resistance of a protein and show how a simple analysis of the native state can predict much of the mechanical properties of a protein.

Free energy for protein folding from nonequilibrium simulations using the Jarzynski equality

The equilibrium free energy difference between two long-lived molecular species or "conformational states" of a protein (or any other molecule) can in principle be estimated by measuring the work needed to shuttle the system between them, independent of the irreversibility of the process. This is the meaning of the Jarzynski equality (JE), which we test in this paper by performing simulations that unfold a protein by pulling two atoms apart. Pulling is performed fast relative to the relaxation time of the molecule and is thus far from equilibrium. Choosing a simple protein model for which we can independently compute its equilibrium properties, we show that the free energy can be exactly and effectively estimated from nonequilibrium simulations. To do so, one must carefully and correctly determine the ensemble of states that are pulled, which is more important the farther from equilibrium one performs simulations; this highlights a potential problem in using the JE to extract the free energy from forced unfolding experiments. The results presented here also demonstrate that the free energy difference between the native and denatured states of a protein measured in solution is not always equal to the free energy profile that can be estimated from forced unfolding simulations (or experiments) using the JE.

Validation of the Jarzynski relation for a system with strong thermal coupling: an isothermal ideal gas model

We revisit the paradigm of an ideal gas under isothermal conditions. A moving piston performs work on an ideal gas in a container that is strongly coupled to a heat reservoir. The thermal coupling is modeled by stochastic scattering at the boundaries. In contrast to recent studies of an adiabatic ideal gas with a piston [R.C. Lua and A.Y. Grosberg, J. Phys. Chem. B 109, 6805 (2005); I. Bena, Europhys. Lett. 71, 879 (2005)], the container and piston stay in contact with the heat bath during the work process. Under this condition the heat reservoir as well as the system depend on the work parameter lambda and microscopic reversibility is broken for a moving piston. Our model is thus not included in the class of systems for which the nonequilibrium work theorem has been derived rigorously either by Hamiltonian [C. Jarzynski, J. Stat. Mech. (2004) P09005] or stochastic methods [G.E. Crooks, J. Stat. Phys. 90, 1481 (1998)]. Nevertheless the validity of the nonequilibrium work theorem is confirmed both numerically for a wide range of parameter values and analytically in the limit of a very fast moving piston, i.e., in the far nonequilibrium regime.

Internal protein dynamics shifts the distance to the mechanical transition state

Mechanical unfolding of polyproteins by force spectroscopy provides valuable insight into their free energy landscapes. Most experiments of the unfolding process have been fit to two-state and/or one dimensional models, with the details of the protein and its dynamics often subsumed into a zero-force unfolding rate and a distance x{u}{1D} to the transition state. We consider the entire phase space of a model protein under a constant force, and show that x{u}{1D} contains a sizeable contribution from exploring the full multidimensional energy landscape. This effect is greater for proteins with many degrees of freedom that are affected by force; and surprisingly, we predict that externally attached flexible linkers also contribute to the measured unfolding characteristics.

Vorticity banding during the lamellar-to-onion transition in a lyotropic surfactant solution in shear flow

We report on the rheology of a lyotropic lamellar surfactant solution (SDS/dodecane/pentanol/ water), and identify a discontinuous transition between two shear thinning regimes which correspond to the low-stress lamellar phase and the more viscous shear-induced multilamellar vesicle, or "onion" phase. We study in detail the flow curve, stress as a function of shear rate, during the transition region, and present evidence that the region consists of a shear-banded phase where the material has macroscopically separated into bands of lamellae and onions stacked in the vorticity direction. We infer very slow and irregular transformations from lamellae to onions as the stress is increased through the two-phase region, and identify distinct events consistent with the nucleation of small fractions of onions that coexist with sheared lamellae.

Lipid organization and the morphology of solid-like domains in phase-separating binary lipid membranes

In multi-component lipid membranes, phase separation can lead to the formation of domains. The morphology of fluid-like domains has been rationalized in terms of membrane elasticity and line tension. We show that the morphology of solid-like domains is governed by different physics, and instead reflects the molecular ordering of the lipids. An understanding of this link opens new possibilities for the rational design of patterned membranes.

Nonlinear dynamics of an interface between shear bands

We study numerically the nonlinear dynamics of a shear banding interface in two-dimensional planar shear flow, within the nonlocal Johnson-Segalman model. Consistent with a recent linear stability analysis, we find that an initially flat interface is unstable with respect to small undulations for a sufficiently small ratio of the interfacial width l to cell length L(x). The instability saturates in finite amplitude interfacial fluctuations. For decreasing l/L(x) these undergo a nonequilibrium transition from simple traveling interfacial waves with constant average wall stress, to periodically rippling waves with a periodic stress response. When multiple shear bands are present we find erratic interfacial dynamics and a stress response suggesting low dimensional chaos.

Effect of hydrophobic mismatch on phase behavior of lipid membranes

We investigate the competing effects of hydrophobic mismatch and chain stretching on the morphology and evolution of domains in lipid membranes via Monte Carlo techniques. We model the membrane as a binary mixture of particles that differ in their preferred lengths, with the shorter particles mimicking unsaturated nonraft lipids and the longer particles mimicking saturated raft lipids. We find that phase separation can be induced upon increasing either the ratio J/kappa of the hydrophobic surface tension J to the compressibility modulus kappa. J/kappa determines the decay length for thickness changes. When this decay length is larger than the system size the membrane remains mixed. Furthermore, increasing the thickness relaxation time can induce transient phase separation.

Mechanical resistance of proteins explained using simple molecular models

Recent experiments have demonstrated that proteins unfold when two atoms are mechanically pulled apart, and that this process is different to when heated or when a chemical denaturant is added to the solution. Experiments have also shown that the response of proteins to external forces is very diverse, some of them being "hard," and others "soft." Mechanical resistance originates from the presence of barriers on the energy landscape; together, experiment and simulation have demonstrated that unfolding occurs through alternative pathways when different pairs of atoms undergo mechanical extension. Here we use simulation to probe the mechanical resistance of six structurally diverse proteins when pulled in different directions. For this, we use two very different models: a detailed, transferable one, and a coarse-grained, structure-based one. The coarse-grained model gives results that are surprisingly similar to the detailed one and qualitatively agree with experiment; i.e., the mechanical resistance of different proteins or of a single protein pulled in different directions can be predicted by simulation. The results demonstrate the importance of pulling direction relative to the local topology in determining mechanical stability, and rationalize the effect of the location of importation/degradation tags on the rates of mitochondrial import or protein degradation in vivo.

Budding and domain shape transformations in mixed lipid films and bilayer membranes

We study the stability and shapes of domains with spontaneous curvature in fluid films and membranes, embedded in a surrounding membrane with zero spontaneous curvature. These domains can result from the inclusion of an impurity in a fluid membrane or from phase separation within the membrane. We show that for small but finite line and surface tensions and for finite spontaneous curvatures, an equilibrium phase of protruding circular domains is obtained at low impurity concentrations. At higher concentrations, we predict a transition from circular domains, or caplets, to stripes. In both cases, we calculate the shapes of these domains within the Monge representation for the membrane shape. With increasing line tension, we show numerically that there is a budding transformation from stable protruding circular domains to spherical buds. We calculate the full phase diagram and demonstrate two triple points of, respectively, bud-flat-caplet and flat-stripe-caplet coexistence.

Mechanically unfolding the small, topologically simple protein L

beta-sheet proteins are generally more able to resist mechanical deformation than alpha-helical proteins. Experiments measuring the mechanical resistance of beta-sheet proteins extended by their termini led to the hypothesis that parallel, directly hydrogen-bonded terminal beta-strands provide the greatest mechanical strength. Here we test this hypothesis by measuring the mechanical properties of protein L, a domain with a topology predicted to be mechanically strong, but with no known mechanical function. A pentamer of this small, topologically simple protein is resistant to mechanical deformation over a wide range of extension rates. Molecular dynamics simulations show the energy landscape for protein L is highly restricted for mechanical unfolding and that this protein unfolds by the shearing apart of two structural units in a mechanism similar to that proposed for ubiquitin, which belongs to the same structural class as protein L, but unfolds at a significantly higher force. These data suggest that the mechanism of mechanical unfolding is conserved in proteins within the same fold family and demonstrate that although the topology and presence of a hydrogen-bonded clamp are of central importance in determining mechanical strength, hydrophobic interactions also play an important role in modulating the mechanical resistance of these similar proteins.

The kinetics of phase separation in asymmetric membranes

Phase separation in a model asymmetric membrane is studied using Monte Carlo techniques. The membrane comprises two species of particles, which mimic different lipids in lipid bilayers and separately possess either zero or non-zero spontaneous curvatures. We study the influence of phase separation on membrane shape and the influence of the coupling of composition and height dynamics on phase separation and domain growth, via both the degree of shape asymmetry and relative kinetic coefficients for height relaxation.

Spatiotemporal oscillations and rheochaos in a simple model of shear banding

We study a simple model of shear banding in which the flow-induced phase is destabilized by coupling between flow and microstructure (wormlike micellar length). By varying the strength of instability and the applied shear rate, we find a rich variety of oscillatory and chaotic shear banded flows. At low shear and weak instability, the induced phase pulsates next to one wall of the flow cell. For stronger instability, high shear pulses ricochet across the cell. At high shear we see oscillating bands on either side of central defects. We discuss our results in the context of recent experiments.

Pulling geometry defines the mechanical resistance of a beta-sheet protein

Proteins show diverse responses when placed under mechanical stress. The molecular origins of their differing mechanical resistance are still unclear, although the orientation of secondary structural elements relative to the applied force vector is thought to have an important function. Here, by using a method of protein immobilization that allows force to be applied to the same all-beta protein, E2lip3, in two different directions, we show that the energy landscape for mechanical unfolding is markedly anisotropic. These results, in combination with molecular dynamics (MD) simulations, reveal that the unfolding pathway depends on the pulling geometry and is associated with unfolding forces that differ by an order of magnitude. Thus, the mechanical resistance of a protein is not dictated solely by amino acid sequence, topology or unfolding rate constant, but depends critically on the direction of the applied extension.

Kinetics of the shear banding instability in startup flows

Motivated by recent light scattering experiments on semidilute wormlike micelles, we study the early stages of the shear banding instability using the nonlocal Johnson-Segalman model with a "two-fluid" coupling of flow to micellar concentration. We perform a linear stability analysis for coupled fluctuations in shear rate gamma;, micellar strain W, and concentration phi about an initially homogeneous state. This resembles the Cahn-Hilliard (CH) analysis of fluid-fluid demixing (although we discuss important differences). First, assuming the initial state to lie on the intrinsic constitutive curve, we calculate the "spinodal" onset of instability in sweeps along this curve. We then consider start-up "quenches" into the unstable region. Here the instability in general occurs before the intrinsic constitutive curve can be attained, so we analyze the fluctuations with respect to the time-dependent start-up flow. We calculate the selected length and time scales at which inhomogeneity first emerges. When the coupling between flow and concentration is switched off, fluctuations in the "mechanical variables" gamma; and W are independent of those in phi, and are unstable when the intrinsic constitutive curve has negative slope; but no length scale is selected. Coupling to the concentration enhances this instability at short length scales, thereby selecting a length scale, consistent with the recent light scattering experiments. The spinodal region is then broadened by an extent that increases with proximity to an underlying (zero-shear) CH fluid-fluid (phi) demixing instability. Far from demixing, the broadening is slight and the instability is still mechanically dominated (by deltagamma; and deltaW) with only small deltaphi. Close to demixing, instability sets in at a very low shear rate, where it is dominated instead by deltaphi. In this way, the model captures a smooth crossover from shear banding instabilities that are perturbed by concentration coupling to demixing instabilities that are induced by shear.