Table of contents

In the early 1980s Goran Lindblom and Ake Wieslander, and then Sol Gruner, independently suggested that stored stresses in biological membranes had a regulatory effect on the biological activity of proteins that interacted with the membrane. Interestingly, the evidence for this came from biological observation in the case of Lindblom and Wieslander, and physical in the case of Gruner. The work that has subsequently grown from these seeds has continued to flourish in the multidisciplinary soil that lies between physics, chemistry, biochemistry and cell biology, and in this collection of work we have exemplars of where the progeny of these early ideas have flourished. The papers contain both review, opinion and recent research on biomembranes and span physical measurement of simplified model systems, theory and computational modelling of biomembranes from atomistic to continuum, and the measurement and modelling of the interaction between membrane and protein with specific regard to how protein behaviour is modulated by the membrane.

Over the last decade it has become increasingly evident that the biological membrane is more than a simple partitioner of cellular space. It interacts with its surroundings in elegant and surprising ways and is an integral part of the cell's machinery for controlling biochemical dynamics. As life scientists uncover and describe more of the membrane machinery it is becoming increasingly clear that our underlying understanding of membrane behaviour and the application of new tools to measure phenomena that are currently only qualitatively understood will be critical to our ability to understand how the complex molecular machinery at the cell membrane works. I believe that this is a significant and intriguing challenge for the community of physical scientists and this collection of articles is a window onto the science that lies ahead.

The non-local interfacial Hamiltonian for short-ranged models of wetting phenomena proposed by Parry and co-authors is discussed in the context of the history of wetting transitions.

The static structure factor S(q) is measured for a set of deionized latex dispersions with different numbers of ionizable surface groups per particle and similar diameters. For a given volume fraction, the height of the main peak of S(q), which is a direct measure of the spatial ordering of latex particles, does not increase monotonically with the number of ionizable groups. This behaviour cannot be described using the classical renormalization scheme based on the cell model. We analyse our experimental data using a renormalization model based on the jellium approximation, which predicts the weakening of the spatial order for moderate and large particle charges.

We study the phase behaviour of hard spheres confined between two parallel hard plates using extensive computer simulations. We determine the full equilibrium phase diagram for arbitrary densities and plate separations from one to five hard-sphere diameters using free energy calculations. We find a first-order fluid–solid transition, which corresponds to either capillary freezing or melting depending on the plate separation. The coexisting solid phase consists of crystalline layers with either triangular () or square () symmetry. Increasing the plate separation, we find a sequence of crystal structures from , where n is the number of crystal layers, in agreement with experiments on colloids. At high densities, the transition between square to triangular phases is interrupted by intermediate structures, e.g., prism, buckled, and rhombic phases.

There exist several important in vivo examples, where a DNA chain is compacted on interacting with nanoscale objects such as proteins, thereby forming complexes with a well defined molecular architecture. One of the well known manifestations of such a natural organization of a semi-flexible DNA chain on nanoscale objects is hierarchical DNA molecule assembly into a chromosome, which is mediated by cationic histone proteins at the first stages of compaction. The biological importance of this and other natural nanostructural organizations of the DNA molecule has inspired many theoretical and numerical studies to gain physical insight into this problem. On the other hand, the experimental model systems containing DNA and nanoobjects, which are important to extend our knowledge beyond natural systems, were almost unavailable until the last decade. Accelerating progress in nanoscale chemistry and materials science has brought about various nanoscale three-dimensional structures such as dendrimers, nanoparticles, and nanotubes, and thus has provided a basis for the next important step in creating novel DNA-containing nanostructures, modelling of natural DNA compaction, and verification of accumulated theoretical predictions on the interaction between DNA and nanoscale templates. This review is written to highlight this early stage of nano-inspired progress and it is focused on physico-chemical and biophysical experimental investigations as well as theoretical and numerical studies dedicated to the compaction of DNA on nanoscale three-dimensional templates.

We derive a non-local effective interfacial Hamiltonian model for short-ranged wetting phenomena using a Green's function method. The Hamiltonian is characterized by a binding potential functional and is accurate to exponentially small order in the radii of curvature of the interface and the bounding wall. The functional has an elegant diagrammatic representation in terms of planar graphs which represent different classes of tube-like fluctuations connecting the interface and wall. For the particular cases of planar, spherical and cylindrical interfacial (and wall) configurations, the binding potential functional can be evaluated exactly. More generally, the non-local functional naturally explains the origin of the effective position-dependent stiffness coefficient in the small-gradient limit.

It has been shown recently that lyotropic systems are convenient for studies of faceting, growth or anisotropic surface melting of crystals. All these phenomena imply the active contribution of surface steps and bulk dislocations. We show here that steps can be observed in situ and in real time by means of a new method combining hygroscopy with phase contrast. First results raise interesting issues about the consequences of bicontinuous topology on the structure and dynamical behaviour of steps and dislocations.

The short-range order in liquid binary Al-rich alloys (Al–Fe, Al–Ti) was studied by x-ray diffraction. The measurements were performed using a novel containerless technique which combines aerodynamic levitation with inductive heating. The average structure factors, S(Q), have been determined for various temperatures and compositions in the stable liquid state. From S(Q), the pair correlation functions, g(r), have been calculated. The first interatomic distance is nearly temperature-independent, whereas the first-shell coordination number decreases with increasing temperature for all the alloys investigated. For the Al–Fe alloys, room-temperature scanning electron microscropy (SEM) studies show the formation of a microstructure, namely the existence of Al₁₃Fe₄ inclusions in the Al matrix.

The rotational dynamics of the spin probe cholestane dissolved in a narrow distribution poly(n-butyl acrylate) sample has been investigated via electron spin resonance (ESR) spectroscopy. The measurements were carried out in a wide temperature range: different dynamic regions have been recognized, and the coupling of the probe dynamics to the α and secondary relaxations has been revealed. In particular, the coupling with the structural relaxation is ruled by two fractionary Vogel–Fulcher laws (VF). The crossover from one VF region to the other occurs at the temperature T_C = 1.17T_g, signalling the onset of the cooperativity in the dynamics and confirming a behaviour previously observed in ESR studies carried out on polymeric glass-formers. Furthermore, in this work we discuss the activated regime at the highest temperatures and show that the activation energy does not depend on the length of the polymer main- and side-chains, while its onset temperature linearly depends on the chain length.

During the past two decades the drainage behaviour and temporal evolution of aqueous foams has been subjected to intensive research activities. For the in situ monitoring of liquid metallic foams, it is not possible to use the established drainage observation methods employed for aqueous foams. The generally high melting point and conductivity as well as the opaque nature of these systems require the use of high temperature furnaces in combination with radiography techniques based on x-rays or neutrons. Due to these experimental difficulties, the data from a direct in situ observation of the material redistribution in liquid metallic foams has not been tested quantitatively with numerical solutions from any of the existing drainage models. In two recent studies the density profiles of solidified aluminium foam columns at different stages of the ageing process have been compared with corresponding numerical solutions of the Plateau channel-dominated drainage equation. However, due to the stochastic nature of the foam structure and its development, it was not possible to achieve a reliable quantitative comparison. In our paper we will show a direct quantitative comparison between experimental observations performed by means of x-ray radioscopy and numerical solutions of an adapted version of the channel-dominated drainage equation. Our results indicate that this theory can in principle be used to predict the temporal evolution during the ageing of metallic foams. By incorporating coalescence effects into the numerical description it can be shown that the material redistribution strongly depends upon the rate at which the pore structure evolves. This is in good agreement with our experimental observations.

We probed the topologies imposed on configuration hyperspace by the potential energy function—the shapes of the constant potential energy manifolds—for the glassy state of monatomic Lennard-Jones matter, by following trajectories of constant potential energy. A prominent characteristic of this model matter is well-defined regions of confinement (pockets) in configuration hyperspace. We found that there are constant potential energy hyperspace paths (tubes) between such pockets, applying even to paths linking glassy regions to crystalline regions of configuration hyperspace. Also, we found that glass and crystal pockets are interspersed. For monatomic Lennard-Jones matter at least, the transition from glass to crystal therefore does not have to involve the traversing of a potential energy barrier, as is usually assumed.

We combine a density functional theory (DFT) treatment of capillary evaporation in a cylindrical pore with the morphometric approach in order to study the formation and breaking of bubbles in a hydrophobically lined part of a cone. The morphometric approach, in which the grand potential of a system is described in four geometrical terms with corresponding thermodynamical coefficients, allows extrapolation or scaling from macroscopic system sizes to nanoscales. Since only a small number of fluid particles are involved in bubble formation, it is a pseudo phase transition, and the system is subjected to fluctuations between states with and without a bubble. Fluctuations are not included in a DFT treatment, which makes it possible to explore both states of the system in great detail, in contrast to computer simulations, in which averages might be obscured by fluctuations.

The pressure-induced structural evolutions of CaSiO₃–MgSiO₃ glasses have been examined by means of molecular dynamics simulation. Our calculations revealed that Si coordination remained unchanged up to 15 GPa, while modifier cations caused significant changes in the short-range order structure. In the present study, we conclude that the main compression mechanisms for CaSiO₃–MgSiO₃ glasses are: (1) the Si–O–Si angle reduction, (2) the coordination increase of Ca and Mg cations, and (3) the compaction in the medium-range scale. Furthermore, small changes in the Qⁿ distribution suggest pressure-induced disproportionation reactions. Similar pressure responses between CaSiO₃–MgSiO₃ glasses may imply that the structural changes of SiO₄ framework units are more significant than those of interstitial cations, Ca and Mg.

In recent years it has become evident that many biological functions and processes are associated with the adoption by cellular membranes of complex geometries, at least locally. In this paper, we initially discuss the range of self-assembled structures that lipids, the building blocks of biological membranes, may form, focusing specifically on the inverse lyotropic phases of negative interfacial mean curvature. We describe the roles of curvature elasticity and packing frustration in controlling the stability of these inverse phases, and the experimental determination of the spontaneous curvature and the curvature elastic parameters. We discuss how the lyotropic phase behaviour can be tuned by the addition of compounds such as long-chain alkanes, which can relieve packing frustration. The latter section of the paper elaborates further on the structure, geometric properties, and stability of the inverse bicontinuous cubic phases.

A detailed understanding of the mixing properties of membranes to which detergents are added is mandatory for improving the application and interpretation of detergent based protein or lipid extraction assays. For Triton X-100 (TX-100), a nonionic detergent frequently used in the process of solubilizing and purifying membrane proteins and lipids, we present here a detailed study of the mixing properties of binary and ternary lipid mixtures by means of high-sensitivity isothermal titration calorimetry (ITC). To this end the partitioning thermodynamics of TX-100 molecules from the aqueous phase to lipid bilayers composed of various mixtures of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), egg-sphingomyelin (SM), and cholesterol (cho) are characterized. Composition-dependent partition coefficients K are analysed within the frame of a thermodynamic model developed to describe nonideal mixing in multicomponent lipid/detergent systems. The results imply that POPC, fluid SM, and TX-100 mix almost ideally (nonideality parameters |ρ_α/β|<RT). However, favourable SM/cho (ρ_SM/cho≤−6RT) and unfavourable PC/cho interactions (ρ_PC/cho = 2RT) may under certain conditions cause POPC/TX-100-enriched domains to segregate from SM/cho-enriched ones. TX-100/cho contacts are unfavourable (ρ_cho/TX = 4RT), so the system tends to avoid them. That means, addition of TX-100 promotes the separation of SM/cho-rich from PC/TX-100-rich domains. It appears that cho/detergent interactions are crucial governing the abundance and composition of detergent-resistant membrane patches.

Lipids bearing net electric charges in their hydrophilic headgroups are ubiquitous in biological membranes. Recently, the interest in cationic lipids has surged because of their potential as non-viral transfection vectors. In order to utilize cationic lipids in transfer of nucleic acids and to elucidate the role of charged lipids in cellular membranes in general, their complex interactions within the membrane and with the molecules in the surrounding media need to be thoroughly characterized. Yet, even interactions between monovalent counter-ions and charged lipids are inadequately understood. We studied the interactions of the cationic gemini surfactant (2R,3R)-2,3-dimethoxy-1,4- bis(N-hexadecyl-N,N-dimethylammonium)butane dibromide (RR-1) with chloride, bromide, fluoride, and iodide as counter-ions by differential scanning calorimetry and Langmuir balance. Chloride interacts avidly with RR-1, efficiently condensing the monolayer, decreasing the collapse pressure, and elevating the main transition temperature. With bromide and iodide clearly different behaviour was observed, indicating specific interactions between RR-1 and these counter-ions. Moreover, with fluoride as a counter-ion and in pure water identical results were obtained, demonstrating inefficient electrostatic screening of the headgroups of RR-1 and suggesting fluoride being depleted on the surface of RR-1 membranes.

Research on giant vesicles is becoming increasingly popular. Giant vesicles provide model biomembrane systems for systematic measurements of mechanical and rheological properties of bilayers as a function of membrane composition and temperature, as well as hydrodynamic interactions. Membrane response to external factors (for example electric fields, ions and amphiphilic molecules) can be directly visualized under the microscope. In this paper we review our current understanding of lipid bilayers as obtained from studies on giant unilamellar vesicles. Because research on giant vesicles increasingly attracts the interest of scientists from various backgrounds, we also try to provide a concise introduction for newcomers in the field. Finally, we summarize some recent developments on curvature effects induced by polymers, domain formation in membranes and shape transitions induced by electric fields.

Shape equations allow the understanding of complex conformations of membranes of cells and cell organelles. We describe the theoretical approaches used to describe the elastic behaviour of lipid membranes, review the sets of equations proposed previously to analyse membrane mechanical equilibrium and discuss their limitations. We further present a derivation of generalized shape equations, which are not limited by any assumptions about the membrane structure and shape. These equations represent a tool for the analysis of complex shapes of cell membranes.

Biological membranes are examples of 'smart' materials whose properties and behaviour emerge from the propagation across many scales of the molecular characteristics of their constituents. Artificial smart materials, such as drug delivery vehicles and biosensors, often rely on modifying naturally occurring soft matter, such as polymers and lipid vesicles, so that they possess useful behaviour. However, the complexity of natural membranes, both in their static properties, exemplified in their phase behaviour, and in their dynamic properties, as in the kinetics of their formation and interactions, hinders their rational modification. Mesoscopic simulations, such as dissipative particle dynamics (DPD), allow in silico experiments to be easily and cheaply performed on complex, soft materials requiring as input only the molecular structure of the constituents at a coarse-grained level. They can therefore act as a guide to experimenters prior to performing costly assays. Additionally, mesoscopic simulations provide the only currently feasible window on the length- and timescales relevant to important biophysical processes such as vesicle fusion. We review here the development of computational models of bilayer membranes, and in particular the use of mesoscopic simulations to follow the molecular rearrangements that occur during membrane fusion.

We have reparameterized the dihedral parameters in a commonly used united-atom lipid force field so that they can be used with the all-atom OPLS force field for proteins implemented in the molecular dynamics simulation software GROMACS. Simulations with this new combination give stable trajectories and sensible behaviour of both lipids and protein. We have calculated the free energy of transfer of amino acid side chains between water and 'lipid-cyclohexane', made of lipid force field methylene groups, as a hydrophobic mimic of the membrane interior, for both the OPLS-AA and a modified OPLS-AA force field which gives better hydration free energies under simulation conditions close to those preferred for the lipid force field. The average error is 4.3 kJ mol⁻¹ for water–'lipid-cyclohexane' compared to 3.2 kJ mol⁻¹ for OPLS-AA cyclohexane and 2.4 kJ mol⁻¹ for the modified OPLS-AA water–'lipid-cyclohexane'. We have also investigated the effect of different methods to combine parameters between the united-atom lipid force field and the united-atom protein force field ffgmx. In a widely used combination, the strength of interactions between hydrocarbon lipid tails and proteins is significantly overestimated, causing a decrease in the area per lipid and an increase in lipid ordering. Using straight combination rules improves the results. Combined, we suggest that using OPLS-AA together with the united-atom lipid force field implemented in GROMACS is a reasonable approach to membrane protein simulations. We also suggest that using partial volume information and free energies of transfer may help to improve the parameterization of lipid–protein interactions and point out the need for accurate experimental data to validate and improve force field descriptions of such interactions.

Lipid bilayers are elastic bodies with properties that can be manipulated/controlled by the adsorption of amphipathic molecules. The resulting changes in bilayer elasticity have been shown to regulate integral membrane protein function. To further understand the amphiphile-induced modulation of bilayer material properties (thickness, intrinsic monolayer curvature and elastic moduli), we examined how an enantiomeric pair of viral anti-fusion peptides (AFPs)—Z–Gly–D-Phe and Z–Gly–Phe, where Z denotes a benzyloxycarbonyl group, as well as Z–Phe–Tyr and Z–D-Phe–Phe–Gly—alters the function of enantiomeric pairs of gramicidin channels of different lengths in planar bilayers. For both short and long channels, the channel lifetimes and appearance frequencies increase as linear functions of the aqueous AFP concentration, with no apparent effect on the single-channel conductance. These changes in channel function do not depend on the chirality of the channels or the AFPs. At pH 7.0, the relative changes in channel lifetimes do not vary when the channel length is varied, indicating that these compounds exert their effects primarily by causing a positive-going change in the intrinsic monolayer curvature. At pH 4.0, the AFPs are more potent than at pH 7.0 and have greater effects on the shorter channels, indicating that these compounds now change the bilayer elastic moduli. When AFPs of different anti-fusion potencies are compared, the rank order of the anti-fusion activity and the channel-modifying activity is similar, but the relative changes in anti-fusion potency are larger than the changes in channel-modifying activity. We conclude that gramicidin channels are useful as molecular force transducers to probe the influence of small amphiphiles upon lipid bilayer material properties.

The adsorption of proteins onto a lipid membrane depends on and thus reflects the energetics of the underlying substrate. This is particularly relevant for mixed membranes that contain lipid species with different affinities for the adsorbed proteins. In this case, there is an intricate interplay between lateral membrane organization and the number of adsorbed proteins. Most importantly, proteins often tend to enhance the propensity of the lipid mixture to form clusters, domains, or to macroscopically phase separate. Sigmoidal binding isotherms are the typical signature of the corresponding cooperativity in protein adsorption. We discuss the underlying thermodynamic basis, and compare various theoretical binding models for protein adsorption onto mixed membranes. We also present experimental data for the adsorption of the C2A protein motif and analyse to what extent these data reflect cooperative binding.

The self-assembly of microtubules and charged membranes has been studied, using x-ray diffraction and electron microscopy. Polyelectrolyte lipid complexes usually form structures templated by the lipid phase, when the polyelectrolyte curvature is much larger than the membrane spontaneous curvature. When the polyelectrolyte curvature approaches the membrane spontaneous curvature, as in microtubules, two types of new structures emerge. Depending on the conditions, vesicles either adsorb onto the microtubule, forming a 'beads on a rod' structure, or coat the microtubule, which now forms the template. Tubulin oligomers then coat the external lipid layer, forming a lipid protein nanotube. The tubulin oligomer coverage at the external layer is determined by the membrane charge density. The energy barrier between the beads on a rod and the lipid–protein nanotube states depends on the membrane bending rigidity and membrane charge density. By controlling the lipid/tubulin stoichiometry we can switch between lipid–protein nanotubes with open ends to lipid–protein nanotubes with closed end with lipid cups. This forms the basis for controlled drug encapsulation and release.

Biological membranes are complex environments, where membrane proteins are surrounded by a bilayer composed of many different types of lipid. The physical properties of the bilayer influence protein structure, folding and function, while specific interactions with lipid molecules can also contribute towards the biological activity of some membrane proteins. Improving understanding of these interactions has resulted in the development of synthetic lipid systems that allow the bilayer properties to be rationally manipulated in vitro to control protein behaviour.

A host of water-soluble enzymes are active at membrane surfaces and in association with membranes. Some of these enzymes are involved in signalling and in modification and remodelling of the membranes. A special class of enzymes, the phospholipases, and in particular secretory phospholipase A₂ (sPLA₂), are only activated at the interface between water and membrane surfaces, where they lead to a break-down of the lipid molecules into lysolipids and free fatty acids. The activation is critically dependent on the physical properties of the lipid-membrane substrate. A topical review is given of our current understanding of the physical mechanisms responsible for activation of sPLA₂ as derived from a range of different experimental and theoretical investigations.

Membrane protein function is generally regulated by the molecular composition of the host lipid bilayer. The underlying mechanisms have long remained enigmatic. Some cases involve specific molecular interactions, but very often lipids and other amphiphiles, which are adsorbed to lipid bilayers, regulate a number of structurally unrelated proteins in an apparently non-specific manner. It is well known that changes in the physical properties of a lipid bilayer (e.g., thickness or monolayer spontaneous curvature) can affect the function of an embedded protein. However, the role of such changes, in the general regulation of membrane protein function, is unclear. This is to a large extent due to lack of a generally accepted framework in which to understand the many observations. The present review summarizes studies which have demonstrated that the hydrophobic interactions between a membrane protein and the host lipid bilayer provide an energetic coupling, whereby protein function can be regulated by the bilayer elasticity. The feasibility of this 'hydrophobic coupling mechanism' has been demonstrated using the gramicidin channel, a model membrane protein, in planar lipid bilayers. Using voltage-dependent sodium channels, N-type calcium channels and GABA_A receptors, it has been shown that membrane protein function in living cells can be regulated by amphiphile induced changes in bilayer elasticity. Using the gramicidin channel as a molecular force transducer, a nanotechnology to measure the elastic properties experienced by an embedded protein has been developed. A theoretical and technological framework, to study the regulation of membrane protein function by lipid bilayer elasticity, has been established.