Microscopic interactions and emerging elasticity in model soft particulate gels

We discuss a class of models for particulate gels in which the particle contacts are described by an effective interaction combining a two-body attraction and a three-body angular repulsion. Using molecular dynamics, we show how varying the model parameters allows us to sample, for a given gelation protocol, a variety of gel morphologies. For a specific set of the model parameters, we identify the local elastic structures that get interlocked in the gel network. Using the analytical expression of their elastic energy from the microscopic interactions, we can estimate their contribution to the emergent elasticity of the gel and gain new insight into its origin.

Fluctuating viscoelasticity based on a finite number of dumbbells

Two alternative routes are taken to derive, on the basis of the dynamics of a finite number of dumbbells, viscoelasticity in terms of a conformation tensor with fluctuations. The first route is a direct approach using stochastic calculus only, and it serves as a benchmark for the second route, which is guided by thermodynamic principles. In the latter, the Helmholtz free energy and a generalized relaxation tensor play a key role. It is shown that the results of the two routes agree only if a finite-size contribution to the Helmholtz free energy of the conformation tensor is taken into account. Using statistical mechanics, this finite-size contribution is derived explicitly in this paper for a large class of models; this contribution is non-zero whenever the number of dumbbells in the volume of observation is finite. It is noted that the generalized relaxation tensor for the conformation tensor does not need any finite-size correction.

Particle Formation Mechanisms in the Nanoprecipitation of Polystyrene

Numerous precipitation methods for creating nanoparticle dispersions that are based on mixing a solution with a miscible nonsolvent have been developed. Here, we show that for polymer particles, the formation is highly dependent on the rate of mixing. We also demonstrate the importance of the glass transition of the polymers on particle formation. A simple model of droplet formation during mixing provides a satisfactory description of the observed dependence of particle size on polymer molecular weight, concentration, solvent ratio, and mixing conditions.

Roles of Interleaflet Coupling and Hydrophobic Mismatch in Lipid Membrane Phase-Separation Kinetics

Characterizing the nanoscale dynamic organization within lipid bilayer membranes is central to our understanding of cell membranes at a molecular level. We investigate phase separation and communication across leaflets in ternary lipid bilayers, including saturated lipids with between 12 and 20 carbons per tail. Coarse-grained molecular dynamics simulations reveal a novel two-step kinetics due to hydrophobic mismatch, in which the initial response of the apposed leaflets upon quenching is to increase local asymmetry (antiregistration), followed by dominance of symmetry (registration) as the bilayer equilibrates. Antiregistration can become thermodynamically preferred if domain size is restricted below ∼20 nm, with implications for the symmetry of rafts and nanoclusters in cell membranes, which have similar reported sizes. We relate our findings to theory derived from a semimicroscopic model in which the leaflets experience a “direct” area-dependent coupling, and an “indirect” coupling that arises from hydrophobic mismatch and is most important at domain boundaries. Registered phases differ in composition from antiregistered phases, consistent with a direct coupling between the leaflets. Increased hydrophobic mismatch purifies the phases, suggesting that it contributes to the molecule-level lipid immiscibility. Our results demonstrate an interplay of competing interleaflet couplings that affect phase compositions and kinetics, and lead to a length scale that can influence lateral and transverse bilayer organization within cells.

The physics of stratum corneum lipid membranes

The stratum corneum (SC), the outermost layer of skin, comprises rigid corneocytes (keratin-filled dead cells) in a specialized lipid matrix. The continuous lipid matrix provides the main barrier against uncontrolled water loss and invasion of external pathogens. Unlike all other biological lipid membranes (such as intracellular organelles and plasma membranes), molecules in the SC lipid matrix show small hydrophilic groups and large variability in the length of the alkyl tails and in the numbers and positions of groups that are capable of forming hydrogen bonds. Molecular simulations provide a route for systematically probing the effects of each of these differences separately. In this article, we present the results from atomistic molecular dynamics of selected lipid bilayers and multi-layers to probe the effect of these polydispersities. We address the nature of the tail packing in the gel-like phase, the hydrogen bond network among head groups, the bending moduli expected for leaflets comprising SC lipids and the conformation of very long ceramide lipids in multi-bilayer lipid assemblies.This article is part of the themed issue 'Soft interfacial materials: from fundamentals to formulation'.

Registered and antiregistered phase separation of mixed amphiphilic bilayers

We derive a mean-field free energy for the phase behavior of coupled bilayer leaflets, which is implicated in cellular processes and important to the design of artificial membranes. Our model accounts for amphiphile-level structural features, particularly hydrophobic mismatch, which promotes antiregistration, in competition with the direct transmidplane coupling usually studied, which promotes registration. We show that the phase diagram of coupled leaflets allows multiple metastable coexistences, and we illustrate the kinetic implications of this with a detailed study of a bilayer of equimolar overall composition. For approximate parameters estimated to apply to phospholipids, equilibrium coexistence is typically registered, but metastable antiregistered phases can be kinetically favored by hydrophobic mismatch. Thus, a bilayer in the spinodal region can require nucleation to equilibrate, in a novel manifestation of Ostwald's rule of stages. Our results provide a framework for understanding disparate existing observations in the literature, elucidating a subtle competition of couplings and a key role for phase-transition kinetics in bilayer phase behavior.

Nucleation of symmetric domains in the coupled leaflets of a bilayer

We study the kinetics governing the attainment of inter-leaflet domain symmetry in a phase-separating amphiphilic bilayer. "Indirect" inter-leaflet coupling via hydrophobic mismatch can induce an instability towards a metastable pattern of locally asymmetric domains upon quenching from high temperature. This necessitates a nucleation step to form the conventional symmetric domains, which are favoured by a "direct" inter-leaflet coupling. We model the energetics for a symmetric domain to nucleate from the metastable state, and find that an interplay between hydrophobic mismatch and thickness stretching/compression causes the effective hydrophobic mismatch, and thus line tension, to depend on domain size. This leads to strong departure from classical nucleation theory. We speculate on implications for cell membrane rafts or clusters, whose size may be of similar magnitude to estimated critical radii for domain symmetry.

Perspectives on the viscoelasticity and flow behavior of entangled linear and branched polymers

We briefly review the recent advances in the rheology of entangled polymers and identify emerging research trends and outstanding challenges, especially with respect to branched polymers. Emphasis is placed on the role of well-characterized model systems, as well as the synergy of synthesis-characterization, rheometry and modeling/simulations. The theoretical framework for understanding the observed linear and nonlinear rheological phenomena is the tube model, which is critically assessed in view of its successes and shortcomings, and alternative approaches are briefly discussed. Finally, intriguing experimental findings and controversial issues that merit consistent explanation, such as shear banding instabilities, multiple stress overshoots in transient simple shear and enhanced steady-state elongational viscosity in polymer solutions, are discussed, and future directions such as branch point dynamics and anisotropic monomeric friction are outlined.

Kinetics of symmetry and asymmetry in a phase-separating bilayer membrane

We simulate a phase-separating bilayer in which the leaflets experience a direct coupling favoring local compositional symmetry ("registered" bilayer phases), and an indirect coupling due to hydrophobic mismatch that favors strong local asymmetry ("antiregistered" bilayer phases). For wide ranges of overall leaflet compositions, multiple competing states are possible. For estimated physical parameters, a quenched bilayer may first evolve toward a metastable state more asymmetric than if the leaflets were uncorrelated; subsequently, it must nucleate to reach its equilibrium, more symmetric, state. These phase-transition kinetics exhibit characteristic signatures through which fundamental and opposing interleaflet interactions may be probed. We emphasize how bilayer phase diagrams with a separate axis for each leaflet can account for overall and local symmetry or asymmetry, and capture a range of observations in the experiment and simulation literature.

Adsorption at liquid interfaces induces amyloid fibril bending and ring formation

Protein fibril accumulation at interfaces is an important step in many physiological processes and neurodegenerative diseases as well as in designing materials. Here we show, using β-lactoglobulin fibrils as a model, that semiflexible fibrils exposed to a surface do not possess the Gaussian distribution of curvatures characteristic for wormlike chains, but instead exhibit a spontaneous curvature, which can even lead to ring-like conformations. The long-lived presence of such rings is confirmed by atomic force microscopy, cryogenic scanning electron microscopy, and passive probe particle tracking at air- and oil-water interfaces. We reason that this spontaneous curvature is governed by structural characteristics on the molecular level and is to be expected when a chiral and polar fibril is placed in an inhomogeneous environment such as an interface. By testing β-lactoglobulin fibrils with varying average thicknesses, we conclude that fibril thickness plays a determining role in the propensity to form rings.

Fast cholesterol flip-flop and lack of swelling in skin lipid multilayers

Atomistic simulations were performed on hydrated model lipid multilayers that are representative of the lipid matrix in the outer skin (stratum corneum). We find that cholesterol transfers easily between adjacent leaflets belonging to the same bilayer via fast orientational diffusion (tumbling) in the inter-leaflet disordered region, while at the same time there is a large free energy cost against swelling. This fast flip-flop may play an important role in accommodating the variety of curvatures that would be required in the three dimensional arrangement of the lipid multilayers in skin, and for enabling mechanical or hydration induced strains without large curvature elastic costs.

Actin assembly at model-supported lipid bilayers

We report on the use of supported lipid bilayers to reveal dynamics of actin polymerization from a nonpolymerizing subphase via cationic phospholipids. Using varying fractions of charged lipid, lipid mobility, and buffer conditions, we show that dynamics at the nanoscale can be used to control the self-assembly of these structures. In the case of fluid-phase lipid bilayers, the actin adsorbs to form a uniform two-dimensional layer with complete surface coverage whereas gel-phase bilayers induce a network of randomly oriented actin filaments, of lower coverage. Reducing the pH increased the polymerization rate, the number of nucleation events, and the total coverage of actin. A model of the adsorption/diffusion process is developed to provide a description of the experimental data and shows that, in the case of fluid-phase bilayers, polymerization arises equally due to the adsorption and diffusion of surface-bound monomers and the addition of monomers directly from the solution phase. In contrast, in the case of gel-phase bilayers, polymerization is dominated by the addition of monomers from solution. In both cases, the filaments are stable for long times even when the G-actin is removed from the supernatant-making this a practical approach for creating stable lipid-actin systems via self-assembly.

Lamellar and inverse micellar structures of skin lipids: effect of templating

The outermost layer of skin comprises rigid nonviable cells (corneocytes) in a layered lipid matrix. Using atomistic simulations we find that the equilibrium phase of the skin lipids is inverse micellar. A model of the corneocyte is used to demonstrate that lamellar layering is induced by the patterned corneocyte wall. The inverse micellar phase is consistent with in vivo observations in regions where corneocyte walls are well separated (lacunar spaces) and in the inner layers of skin, and suggests a functional role in the lipid synthesis pathway in vivo.

Apparent fracture in polymeric fluids under step shear

Recent step strain experiments in well-entangled polymeric liquids demonstrated a bulk fracturelike phenomenon. We study this instability by using a modern version of the Doi-Edwards theory for entangled polymers, and we find close quantitative agreement with the experiments. The phenomenon occurs because the viscoelastic liquid is sheared into a rubbery state that possesses an elastic constitutive instability [G. Marrucci and N. Grizzuti, J. Rheol. 27, 433 (1983)]. The fracture is a transient manifestation of this instability, which relies on the amplification of spatially inhomogeneous fluctuations. This mechanism differs from the fracture in glassy materials and dense suspensions.

Quantification of the plasma clearance kinetics of a gadolinium-based contrast agent by photoinduced triplet harvesting

The use of gadolinium-based contrast agents (GBCA) is integral to the field of diagnostic magnetic resonance imaging (MRI). Pharmacokinetic evaluation of the plasma clearance of GBCA is required for all new agents or improved formulations, to address concerns over toxicity or unforeseen side effects. Current methods to measure GBCA in plasma lack either a rapid readout or the sensitivity to measure small samples or require extensive processing of plasma, all obstacles in the development and characterization of new GBCA. Here, we quantify the plasma concentration of a labeled analogue of a common clinical GBCA by ligand triplet harvesting and energy transfer. The nonemittive GBCA becomes a "dark donor" to a fluorescent detector molecule, with a lower limit of detection of 10(-7) M in unprocessed plasma. On a time scale of minutes, we determine the plasma clearance rate in the wild-type mouse, using time-resolved fluorescence on a standard laboratory plate reader.

Nanoscale mechanical probing of supported lipid bilayers with atomic force microscopy

We present theory and experiments for the force-distance curve F(z(0)) of an atomic force microscope (AFM) tip (radius R) indenting a supported fluid bilayer (thickness 2d). For realistic conditions the force is dominated by the area compressibility modulus κ(A) of the bilayer and, to an excellent approximation, given by F=πκ(A)Rz(0)(2)/(2d-z(0))(2). The experimental AFM force curves from coexisting liquid ordered and liquid disordered domains in three-component lipid bilayers are well described by our model, which provides κ(A) in agreement with literature values. The liquid ordered phase has a yieldlike response that we model as due to the breaking of hydrogen bonds.

Statistical mechanics far from equilibrium: prediction and test for a sheared system

We report the application of a far-from-equilibrium statistical-mechanical theory to a nontrivial system with Newtonian interactions in continuous boundary-driven flow. By numerically time stepping the force-balance equations of a one-dimensional model fluid we measure occupancies and transition rates in simulation. The high-shear-rate simulation data reproduce the predicted invariant quantities, thus supporting the theory that a class of nonequilibrium steady states of matter, namely, sheared complex fluids, is amenable to statistical treatment from first principles.

Undulation instability in a bilayer lipid membrane due to electric field interaction with lipid dipoles

Bilayer lipid membranes (BLMs) are an essential component of all biological systems, forming a functional barrier for cells and organelles from the surrounding environment. The lipid molecules that form membranes contain both permanent and induced dipoles, and an electric field can induce the formation of pores when the transverse field is sufficiently strong (electroporation). Here, a phenomenological free energy is constructed to model the response of a BLM to a transverse static electric field. The model contains a continuum description of the membrane dipoles and a coupling between the headgroup dipoles and the membrane tilt. The membrane is found to become unstable through buckling modes, which are weakly coupled to thickness fluctuations in the membrane. The thickness fluctuations, along with the increase in interfacial area produced by membrane buckling, increase the probability of localized membrane breakdown, which may lead to pore formation. The instability is found to depend strongly on the strength of the coupling between the dipolar headgroups and the membrane tilt as well as the degree of dipolar ordering in the membrane.

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.