Bonded straight and helical flagellar filaments form ultra-low-density glasses.

We study how the three-dimensional shape of rigid filaments determines the microscopic dynamics and macroscopic rheology of entangled semidilute Brownian suspensions. To control the filament shape we use bacterial flagella, which are microns-long helical or straight filaments assembled from flagellin monomers. We compare the dynamics of straight rods, helical filaments, and shape-diblock copolymers composed of seamlessly joined straight and helical segments. Caged by their neighbors, straight rods preferentially diffuse along their long axis, but exhibit significantly suppressed rotational diffusion. Entangled helical filaments escape their confining tube by corkscrewing through the dense obstacles created by other filaments. By comparison, the adjoining segments of the rod-helix shape-diblocks suppress both the translation and the corkscrewing dynamics. Consequently, the shape-diblock filaments become permanently jammed at exceedingly low densities. We also measure the rheological properties of semidilute suspensions and relate their mechanical properties to the microscopic dynamics of constituent filaments. In particular, rheology shows that an entangled suspension of shape rod-helix copolymers forms a low-density glass whose elastic modulus can be estimated by accounting for how shear deformations reduce the entropic degrees of freedom of constrained filaments. Our results demonstrate that the three-dimensional shape of rigid filaments can be used to design rheological properties of semidilute fibrous suspensions.

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.

Effects of Passive Phospholipid Flip-Flop and Asymmetric External Fields on Bilayer Phase Equilibria.

Compositional asymmetry between the leaflets of bilayer membranes modifies their phase behavior and is thought to influence other important features such as mechanical properties and protein activity. We address here how phase behavior is affected by passive phospholipid flip-flop, such that the compositional asymmetry is not fixed. We predict transitions from "pre-flip-flop" behavior to a restricted set of phase equilibria that can persist in the presence of passive flip-flop. Surprisingly, such states are not necessarily symmetric. We further account for external symmetry breaking, such as a preferential substrate interaction, and show how this can stabilize strongly asymmetric equilibrium states. Our theory explains several experimental observations of flip-flop-mediated changes in phase behavior and shows how domain formation and compositional asymmetry can be controlled in concert, by manipulating passive flip-flop rates and applying external fields.

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.

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 ß-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 ß-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.

Critical point fluctuations in supported lipid membranes.

In this paper, we demonstrate that it is possible to observe many aspects of critical phenomena in supported lipid bilayers using atomic force microscopy (AFM) with the aid of stable and precise temperature control. The regions of criticality were determined by accurately measuring and calculating phase diagrams for the 2 phase L(d)-L(o) region, and tracking how it moves with temperature, then increasing the sampling density around the estimated critical regions. Compositional fluctuations were observed above the critical temperature (T(c)) and characterised using a spatial correlation function. From this analysis, the phase transition was found to be most closely described by the 2D Ising model, showing it is a critical transition. Below T(c) roughening of the domain boundaries occurred due to the reduction in line tension close to the critical point. Smaller scale density fluctuations were also detected just below T(c). At T(c), we believe we have observed fluctuations on length scales greater than 10 microm. The region of critically fluctuating 10-100 nm nanodomains has been found to extend a considerable distance above T(c) to temperatures within the biological range, and seem to be an ideal candidate for the actual structure of lipid rafts in cell membranes. Although evidence for this idea has recently emerged, this is the first direct evidence for nanoscale domains in the critical region.

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.

Concentrating membrane proteins using asymmetric traps and AC electric fields.

Membrane proteins are key components of the plasma membrane and are responsible for control of chemical ionic gradients, metabolite and nutrient transfer, and signal transduction between the interior of cells and the external environment. Of the genes in the human genome, 30% code for membrane proteins (Krogh et al. J. Mol. Biol.2001, 305, 567). Furthermore, many FDA-approved drugs target such proteins (Overington et al. Nat. Rev. Drug Discovery 2006, 5, 993). However, the structure-function relationships of these are notably sparse because of difficulties in their purification and handling outside of their membranous environment. Methods that permit the manipulation of membrane components while they are still in the membrane would find widespread application in separation, purification, and eventual structure-function determination of these species (Poo et al. Nature 1977, 265, 602). Here we show that asymmetrically patterned supported lipid bilayers in combination with AC electric fields can lead to efficient manipulation of charged components. We demonstrate the concentration and trapping of such components through the use of a "nested trap" and show that this method is capable of yielding an approximately 30-fold increase in the average protein concentration. Upon removal of the field, the material remains trapped for several hours as a result of topographically restricted diffusion. Our results indicate that this method can be used for concentrating and trapping charged membrane components while they are still within their membranous environment. We anticipate that our approach could find widespread application in the manipulation and study of membrane proteins.

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.

Kinetic Monte Carlo simulations of flow-induced nucleation in polymer melts.

We derive a kinetic Monte Carlo algorithm to simulate flow-induced nucleation in polymer melts. The crystallisation kinetics are modified by both stretching and orientation of the amorphous chains under flow, which is modelled by a recent non-linear tube theory. Rotation of the crystallites under flow is modelled by a simultaneous Brownian dynamics simulation. Our kinetic Monte Carlo approach is highly efficient at simulating nucleation and is tractable even at low under-cooling. The simulations predict enhanced nucleation under both transient and steady state shear. Furthermore the model predicts the growth of shish-like elongated nuclei for sufficiently fast flows, which grow by a purely kinetic mechanism.

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.