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The aim of this study was to investigate whether it is possible to prevent oolemma lysis after Piezo-assisted intracytoplasmic sperm injection (Piezo-ICSI) caused by abnormal membrane rupture. A total of 489 mature oocytes were obtained from 85 patients who underwent Piezo-ICSI in an infertility clinic. Inseminated oocytes were classified into the following two groups: normal rupture and abnormal rupture, and a portion of abnormally ruptured oocytes was randomly exposed to 7% PVP solution. Normal fertilization rate, degeneration rate, proportion of high-quality embryos on day 3, blastocyst formation, and morphologically high-quality blastocysts were compared. Abnormal rupture was defined as cytoplasmic membrane rupture before piezo pulse driving. Among the abnormal rupture groups, the normal fertilization and degeneration rates were compared between the high-stretched (ruptured at ≥ 50% during oocyte membrane stretching) and low-stretched (< 50% position) oocytes. The degeneration rate was significantly higher in abnormally ruptured oocytes than in normally ruptures oocytes (14.3% vs 1.3%, p < 0.001), and there was no significant difference in embryonic development after fertilization. PVP treatment immediately after oolemma rupture significantly decreased the degeneration rate (6.0% vs 19.7%, p = 0.031) and increased the normal fertilization rate. Similarly, there were no significant differences in the developmental potential. Furthermore, pregnancy outcome data showed no significant differences in pregnancy and live birth rates. The degeneration rate was reduced by treating low-stretched oocytes with PVP. Exposure to polyvinylpyrrolidone (PVP) immediately after abnormal membrane rupture represents an effective strategy to prevent oocyte degeneration. This is the first study to propose a strategy for the prevention of oocyte degeneration in Piezo-ICSI. These findings are expected to reduce the oocyte degeneration rate and increase normal fertilization rate as well as assist patients who can only acquire oocytes with weak plasma membranes. [ABSTRACT FROM AUTHOR]

We have studied the process of electroporation of bilayer lipid membranes (BLMs) made of dioleoylphosphatidylcholine (DOPC). We obtained experimental data on the average lifetime of the membrane as a function of applied transmembrane voltage in the range of 200–375 mV. The analysis of the obtained data showed that the dependence is nonmonotonic and cannot be described in terms of the classical theory of electroporation. These results are consistent with modern models of the process of formation of through conductive pores in a membrane. The above models imply a complex pore energy profile and its dependence on a membrane tension and an external electric field. Thus, we have shown that the classical theory of electroporation does not satisfy the experimentally observed dependencies of the average membrane lifetime on the applied potential difference and requires further refinement. [ABSTRACT FROM AUTHOR]

Antimicrobial activity of some amphipathic peptides is associated with the formation of through pores in bacterial membranes. Antimicrobial peptides (AMPs) specifically bind to the plasma membrane by incorporating their hydrophobic regions into the outer lipid monolayer. The membrane is inevitably deformed. Many AMPs form so-called toroidal pores, the edge of which is partially lined with peptide molecules. The edge of the pore is characterized by significant deformations. In this work, we calculated the energy of the pore edge, with amphipathic peptides located on the pore equator, as well as the energy of deformations induced by AMP in a planar lipid bilayer. It was shown that for certain physicochemical and geometric characteristics of the AMP molecule the energy of the pore, on the equator of which two or more peptide molecules are located, can be lower than the energy of deformations induced in the planar bilayer by the same number of peptide molecules. Thus, two AMP molecules can, in principle, form a through pore in the membrane, although this is possible only in a fairly narrow range of physicochemical and geometric characteristics of the peptides. [ABSTRACT FROM AUTHOR]

Osmotic pressure can break the fluid balance between intracellular and extracellular solutions. In hypo-osmotic solution, water molecules, which transfer into the cell and burst, are driven by the concentration difference of solute across the semi-permeable membrane. The complicated dynamic processes of intermittent bursts have been previously observed. However, the underlying physical mechanism has yet to be thoroughly explored and analyzed. Here, the intermittent release of inclusion in giant unilamellar vesicles was investigated quantitatively, applying the combination of experimental and theoretical methods in the hypo-osmotic medium. Experimentally, we adopted a highly sensitive electron multiplying charge-coupled device to acquire intermittent dynamic images. Notably, the component of the vesicle phospholipids affected the stretch velocity, and the prepared solution of vesicles adjusted the release time. Theoretically, we chose equations and numerical simulations to quantify the dynamic process in phases and explored the influences of physical parameters such as bilayer permeability and solution viscosity on the process. It was concluded that the time taken to achieve the balance of giant unilamellar vesicles was highly dependent on the molecular structure of the lipid. The pore lifetime was strongly related to the internal solution environment of giant unilamellar vesicles. The vesicles prepared in viscous solution were able to visualize long-lived pores. Furthermore, the line tension was measured quantitatively by the release velocity of inclusion, which was of the same order of magnitude as the theoretical simulation. In all, the experimental values well matched the theoretical values. Our investigation clarified the physical regulatory mechanism of intermittent pore formation and inclusion release, which provides an important reference for the development of novel technologies such as gene therapy based on transmembrane transport as well as controlled drug delivery based on liposomes. [ABSTRACT FROM AUTHOR]

The paper investigates the formation and stability of the surface nanobubbles with regard to the line tension at the triple phase boundary; the pinning effect, when the bubble stands on the surface and the triple phase boundary does not move; and the Kelvin equation. It is shown that the negative line tension can cause a spontaneous nanobubble formation at the small diameter of the phase boundary curve and the small contact angle. [ABSTRACT FROM AUTHOR]

Unsaturated and saturated phospholipids tend to laterally segregate, especially in the presence of cholesterol. Small molecules such as neurotransmitters, toxins, drugs etc. possibly modulate this lateral segregation. The small aromatic neurotransmitter serotonin (5-HT) has been found to bind to membranes. We studied the lipid structure and packing of a ternary membrane mixture consisting of palmitoyl-oleoyl-phosphatidylcholine, palmitoyl-sphingomyelin, and cholesterol at a molar ratio of 4/4/2 in the absence and in the presence of 5-HT, using a combination of solid-state 2H NMR, atomic force microscopy, and atomistic molecular dynamics (MD) simulations. Both NMR and MD report formation of a liquid ordered (L o ) and a liquid disordered (L d ) phase coexistence with small domains. Lipid exchange between the domains was fast such that single component 2H NMR spectra are detected over a wide temperature range. A drastic restructuring of the domains was induced when 5-HT is added to the membranes at a 9 mol% concentration relative to the lipids. 2H NMR spectra of all components of the mixture showed two prominent contributions indicative of molecules of the same kind residing both in the disordered and the ordered phase. Compared to the data in the absence of 5-HT, the lipid chain order in the disordered phase was further decreased in the presence of 5-HT. Likewise, addition of serotonin increased lipid chain order within the ordered phase. These characteristic lipid chain order changes were confirmed by MD simulations. The 5-HT-induced larger difference in lipid chain order results in more pronounced differences in the hydrophobic thickness of the individual membrane domains. The correspondingly enlarged hydrophobic mismatch between ordered and disordered phases is assumed to increase the line tension at the domain boundary, which drives the system into formation of larger size domains. These results not only demonstrate that small membrane binding molecules such as neurotransmitters have a profound impact on essential membrane properties. It also suggests a mechanism by which the interaction of small molecules with membranes can influence the function of membrane proteins and non-cognate receptors. Altered membrane properties may modify lateral sorting of membrane protein, membrane protein conformation, and thus influence their function as suspected for neurotransmitters, local anesthetics, and other small drug molecules. [ABSTRACT FROM AUTHOR]

Line tension is calculated for a simple model of a surface nanobubble formed on a smooth hydrophobic substrate. It is shown that, with an increase in the contact angle at a certain critical value, the surface tension changes sign from positive to negative. This means that the surface tension stretches the nanobubble, increasing its radius of curvature and thereby stabilizing it. [ABSTRACT FROM AUTHOR]

We study the geometry of a stable drop of incompressible liquid constrained to lie in a spherical container. The energy functional is comprised of the surface tension, the wetting energy and the line tension. It is shown that the only stable equilibrium drops having the topology of a disc are flat discs and spherical caps. Sharp conditions for the stability of equilibrium spherical caps and flat discs are given. [ABSTRACT FROM AUTHOR]

Three-dimensional crack growth initiation is examined under the assumption that the crack front remains smooth. Two important modeling issues, specific to three-dimensional rather than two-dimensional cracks, are addressed. First, it is established that, at each point along the crack front, the velocity and configurational force are two-dimensional vectors, lying in the local normal plane. This allows one to generalize any two-dimensional crack growth criterion to three dimensions. Second, a simple mesoscopic model to account for along-the-front non-locality is proposed. This model eliminates pathological growth patterns ubiquitous to basic models applied to three-dimensional cracks. Further, the model is straightforward to use as it relies on standard fracture properties only. [ABSTRACT FROM AUTHOR]

The large plasticity, dynamics and adaptability of biological membranes allow different modes of intrinsic and inducible permeability. These phenomena are of physiological importance for a number of natural functions related to cell death and can also be manipulated artificially for practical purposes like gene transfer, drug delivery, prevention of infections or anticancer therapy. For these advances to develop in a controllable and specific way, we need a sufficient understanding of the membrane permeability phenomena. Since the formulation of early concepts of pore formation, there has been an enormous effort to describe membrane permeability by using theory, simulations and experiments. A major breakthrough has come recently through theoretical developments that allow building continuous trajectories of pore formation both in the absence and presence of stress conditions. The new model provides a coherent quantitative view of membrane permeabilization, useful to test the impact of known lipid properties, make predictions and postulate specific pore intermediates that can be studied by simulations. For example, this theory predicts unprecedented dependencies of the line tension on the pore radius and on applied lateral tension which explain previous puzzling results. In parallel, important concepts have also come from molecular dynamics simulations, of which the role of water for membrane permeabilization is of special interest. These advances open new challenges and perspectives for future progress in the study of membrane permeability, as experiments and simulations will need to test the theoretical predictions, while theory achieves new refinements that provide a physical ground for observations. [ABSTRACT FROM AUTHOR]

It is believed that separation of lipid matrix of biological membranes into ordered and disordered phases plays an important role in the lateral distribution of proteins and transduction of cellular signals through the plasma membrane. In model lipid membranes with symmetric composition of monolayers, such phase separation always leads to formation of bilayer domains. However, the lipid composition of outer and inner monolayers of plasma membranes of cells is different, i.e., these membranes are asymmetric. The mechanism of coupling of monolayer domains into bilayer structures in cells still remains unexplained. The ordered lipid domain is thicker than the surrounding membrane; as a result, elastic deformations occur at their boundary. Minimization of the elastic part of the boundary energy contributes to the coupling of monolayer domains in opposite monolayers. However, this driving force is not enough to ensure that domains will come into register: at a certain fraction of the membrane area occupied by the domains, the elastic energy can reach the minimum in antisymmetric configurations (the ordered domain in the upper monolayer is opposed by disordered monolayer of the surrounding membrane). As an alternative factor of the coupling, we considered curvature thermal fluctuations of the membrane shape. Our theoretical analysis of elastic deformations in a lipid bilayer that is asymmetric in monolayer composition shows that more rigid lipid domains tend to distribute into the region with lower curvature of the monolayer; these regions naturally coincide in opposite monolayers. Thus, the coupling of ordered domains in different monolayers is provided by their greater bending stiffness as compared to the surrounding membrane. At the same time, greater ordering leads to lateral condensation, i.e., to the decrease of the average area per lipid molecule. The difference in area per lipid molecule in the coexisting membrane phases, on the contrary, tends to separate bilayer domains into their monolayer components. To quantify the coupling energy of ordered domains, it is necessary to take both of these effects into account. [ABSTRACT FROM AUTHOR]

Cross-slip is a thermally activated process by which a screw dislocation changes its slip plane. Understanding and modelling the activation barrier of the cross-slip process as a free-energy barrier that depends on the stress conditions at the vicinity of the dislocation is crucial. In this work, we employ the line-tension model for the cross-slip of screw dislocations in face-centred cubic (FCC) metals in order to calculate the energy barrier when both Escaig stresses are applied on the primary and cross-slip planes and Schmid stress is applied on the cross-slip plane. We propose a closed-form expression for the activation energy for cross-slip in a large range of stresses, without any fitting parameters. The results of the proposed model are in good agreement with previous numerical results and atomistic simulations. We also show that, when Schmid stress is applied on the cross-slip plane, the energy barrier is decreased, and in particular, cross-slip can occur even when the Escaig stress in the primary plane is smaller than that on the cross-slip plane. The proposed closed-form expression for the activation energy can be easily implemented in dislocation dynamics simulations, owing to its simplicity and universality. This will allow cross-slip to be more accurately related to macroscopic plasticity. [ABSTRACT FROM AUTHOR]

The resistance of a dislocation to bowing under stress governs the strength of the gamut of metallic material systems. This resistance is commonly referred to as the dislocation line tension (Γ) and is employed ubiquitously within continuum scale models of metal plasticity. Despite its significance, a unifying model for the line tension of a bowing dislocation segment, which has been analytically derived and independently reproduces simulation results, remains lacking. Here, we report a model for Γ of a curved, semicircular bowing dislocation segment. Upon applying our model to the operative stress of a Frank–Read dislocation source, we predict a prelogarithmic scaling of the Frank–Read source strength in agreement with existing simulation results. Moreover, in the limit of infinitesimal bowout we predict a prelogarithmic line tension factor which also agrees with theoretical analyses. Our model provides insight into the evolution of an arbitrarily oriented, stressed dislocation segment without resorting to numerical methods. [ABSTRACT FROM AUTHOR]

A generalized Young’s equation, which takes into account two corrections to the line tension by the curvature dependence of the liquid-vapor surface tension and by the contact angle dependence of the intrinsic line tension, is derived from the thermodynamic free-energy minimization. The correction from the curvature dependence can be qualitatively estimated using Tolman’s formula. The correction from the contact angle dependence can be estimated for nanometer-scale droplets for which the analytical formula for the intrinsic line tension determined from the van der Waals interaction is available. The two corrections to the apparent line tension of this van der Waals nano-droplets are as small as nN, and lead to either a positive or a negative apparent line tension. The gravitational line tension for millimeter-scale droplets by the gravitational acceleration is also considered. The gravitational line tension is of the order of N so that the correction from the curvature dependence can be neglected. Yet, the contact angle dependence is so large that the apparent line tension becomes always negative though the intrinsic line tension without the correction is always positive. These two examples demonstrate clear distinction between the theoretically calculated intrinsic line tension and the experimentally determined apparent line tension which includes these two corrections. Naive comparison of the experimentally determined and the theoretically calculated line tension is not always possible. [ABSTRACT FROM AUTHOR]

Plastic deformation, at all strain rates, is accommodated by the collective motion of crystalline defects known as dislocations. Here, we extend an analysis for the energetic stability of a straight dislocation, the so-called line tension (Γ), to steady-state moving dislocations within elastically anisotropic media. Upon simplification to isotropy, our model reduces to an explicit analytical form yielding insight into the behaviour of Γ with increasing velocity. We find that at the first shear wave speed within an isotropic solid, the screw dislocation line tension diverges positively indicating infinite stability. The edge dislocation line tension, on the other hand, changes sign at approximately of the first shear wave speed, and subsequently diverges negatively indicating that the straight configuration is energetically unstable. In anisotropic crystals, the dependence of Γ on the dislocation velocity is significantly more complex; at velocities approaching the first shear wave speed within the plane of the crystal defined by the dislocation line, Γ tends to diverge, with the sign of the divergence strongly dependent on both the elastic properties of the crystal and the orientation of the dislocation line. We interpret our analyses within the context of recent molecular dynamics simulations of the motion of dislocations near the first shear wave speed. Both the simulations and our analyses are indicative of instabilities of nominally edge dislocations within fcc crystals approaching the first shear wave speed. We apply our analyses towards predicting the behaviour of dislocations within bcc crystals in the vicinity of the first shear wave speed. [ABSTRACT FROM AUTHOR]

Cross-slip is a dislocation mechanism by which screw dislocations can change their glide plane. This thermally activated mechanism is an important mechanism in plasticity and understanding the energy barrier for cross-slip is essential to construct reliable cross-slip rules in dislocation models. In this work, we employ a line tension model for cross-slip of screw dislocations in face-centred cubic (FCC) metals in order to calculate the energy barrier under Escaig stresses. The analysis shows that the activation energy is proportional to the stacking fault energy, the unstressed dissociation width and a typical length for cross-slip along the dislocation line. Linearisation of the interaction forces between the partial dislocations yields that this typical length is related to the dislocation length that bows towards constriction during cross-slip. We show that the application of Escaig stresses on both the primary and the cross-slip planes varies the typical length for cross-slip and we propose a stress-dependent closed form expression for the activation energy for cross-slip in a large range of stresses. This analysis results in a stress-dependent activation volume, corresponding to the typical volume surrounding the stressed dislocation at constriction. The expression proposed here is shown to be in agreement with previous models, and to capture qualitatively the essentials found in atomistic simulations. The activation energy function can be easily implemented in dislocation dynamics simulations, owing to its simplicity and universality. [ABSTRACT FROM PUBLISHER]

We study the distension-induced gradient capillarity in membrane bud formation. The budding process is assumed to be primarily driven by diffusion of transmembrane proteins and acting line tensions on the protein-concentrated interface. The proposed model, based on the Helfrich-type potential, is designed to accommodate inhomogeneous elastic responses of the membrane, non-uniform protein distributions over the membrane surface and, more importantly, the thickness distensions induced by bud formations in the membrane. The latter are employed via the augmented energy potential of bulk incompressibility in a weakened manner. By computing the variations of the proposed membrane energy potential, we obtained the corresponding equilibrium equation (membrane shape equation) describing the morphological transitions of the lipid membrane undergoing bud formation and the associated thickness distensions. The effects of lipid distension on the shape equation and the necessary adjustments to the accompanying boundary conditions are also derived in detail. The resulting shape equation is solved numerically for the parametric representation of the surface which has one-to-one-correspondence with the membrane surface under consideration. The proposed model successfully predicts the bud formation phenomenon on a flat lipid membrane and the associated thickness distensions of the membrane and demonstrates a smooth transition from one phase to the other (including necking domains). It is also found that the final deformed configuration is energetically favorable and therefore is stable. Finally, we show that the inhomogeneous thickness deformation on the membrane in response to transmembrane protein diffusion makes a significant contribution to the budding and necking processes of the membrane. [ABSTRACT FROM AUTHOR]

We study the formation of membrane budding in model lipid bilayers with the budding assumed to be driven by means of diffusion of trans-membrane proteins over a composite membrane surface. The theoretical model for the lipid membrane incorporates a modified Helfrich-type formulation as a special case. In addition, a spontaneous curvature is introduced into the model in order to accommodate the effect of the non-uniformly distributed proteins in the bending response of the membrane. Furthermore, we discuss the effects of line tension on the budding of the membrane, and the necessary adjustments to the boundary conditions. The resulting shape equation is solved numerically for the parametric representation of the surface, which has one to one correspondence to the membrane surface in consideration. Our numerical results successfully predict the vesicle formation phenomenon on a flat lipid membrane surface, since the present analysis is not restricted to the conventional Monge representation often adopted to the problems of this kind for the obvious computational simplicity, despite its limited capability to describe the deformed configuration of membranes. In addition, we show that line tension at the interface of the protein-concentrated domain makes a significant contribution to the bud formation of membranes. [ABSTRACT FROM AUTHOR]

The functional mechanisms of local anesthetics (LAs) have not yet been fully explained, despite their importance in modern medicine. Recently, an indirect interaction between channel proteins and LAs was proposed as follows: LAs alter the physical properties of lipid membranes, thus affecting the channel proteins. To examine this hypothesis, we investigated changes in thermal stability in lipid membranes consisting of dioleoylphosphocholine, dipalmitoylphosphocholine, and cholesterol by adding the LAs, lidocaine and tetracaine. The miscibility temperature of liquid-ordered (Lo) and liquid-disordered (Ld) phase separation was lowered, whereas that of phase separation between solid-ordered (So) and Ld phases was unchanged by LAs. Furthermore, we measured the line tension at the Lo/Ld interface from domain boundary fluctuation and found that it was significantly decreased by LAs. Finally, differential scanning calorimetry (DSC) revealed a change in the lipid main transition temperature on the addition of LAs. Based on the DSC measurements, we considered that LAs are partitioned into two coexisting phases. [ABSTRACT FROM AUTHOR]

Theoretical model of a through pore formation in lipid bilayer membrane under applied lateral tension was developed. In the framework of elastic theory of liquid crystals adapted to lipid membranes, we calculated a continuous trajectory from intact bilayer through a hydrophobic defect to a through pore. It was shown that the major energetic characteristic of membrane stability with respect to the pore formation, i. e., line tension, depends both on the pore radius and on the value of the applied lateral tension. This leads to a non-monotonous dependence of the average waiting time of the pore formation on the lateral tension: at low tensions the waiting time was large, then there was a local minimum, after which the average waiting time was increasing again. For membranes formed from stearoyl oleoyl phosphatidylcholine, the local minimum corresponded to the lateral tension of 7 mN/m; the calculated value of the edge line tension of a large pore was 16.5 pN. These results are consistent with available experimental data. [ABSTRACT FROM AUTHOR]

We have developed a new device called the dynamic cell, whereby the twist angle and cell thickness of a liquid crystal cell can be dynamically varied. For a twist angle larger than 90°, there occurs a breaking of anchoring at a certain threshold cell thickness. This structural transition converts the super-twisted state to a normal twisted state by flipping the surface director by 180°. A disclination loop separates the normal twisted region from the super-twisted region. By controlling the twist and thickness, we can stabilize this loop and calculate its line tension. [ABSTRACT FROM AUTHOR]

A Finsler geometric surface model is studied as a coarse-grained model for membranes of three components, such as zwitterionic phospholipid (DOPC), lipid (DPPC) and an organic molecule (cholesterol). To understand the phase separation of liquid-ordered (DPPC rich) Lo and liquid-disordered (DOPC rich) Ld, we introduce a binary variable σ(= ±1) into the triangulated surface model. We numerically determine that two circular and stripe domains appear on the surface. The dependence of the morphological change on the area fraction of Lo is consistent with existing experimental results. This provides us with a clear understanding of the origin of the line tension energy, which has been used to understand these morphological changes in three-component membranes. In addition to these two circular and stripe domains, a raft-like domain and budding domain are also observed, and the several corresponding phase diagrams are obtained. [ABSTRACT FROM AUTHOR]

Spherical and cylindrical water droplets on silicon surface are studied to tune the silicon–oxygen interaction. We use molecular dynamics simulations to estimate the contact angle of two different shaped droplets. We found that the cylindrical droplets are independent of the line tension as their three phases curvature is equal zero. Additionally, we compare an analytical model, taking into account or not the Tolman length and we show that for spherical small size droplets, this length is important to be included, in contrast to cylindrical droplets in which the influence of the Tolman length is negligible. We demonstrate that the usual convenient way to exclude linear tension in the general case can give wrong results. Here, we consider cylindrical droplets, since their contact angle does not depend on the droplet size in the range of few to 10ths of nanometres. The droplets are stabilised due to the periodic boundary conditions. This allows us to propose a new parameterisation for nanoscale droplets, which is independent the size of the droplets or its shape, minimising at the same time the calculation procedure. With the proposed methodology, we can extract the epsilon parameter of the interaction potential between a liquid and a solid from the nanoscaled molecular simulation with only as input the macrosized experimental wetting angle for a given temperature. [ABSTRACT FROM PUBLISHER]

The line tension, which characterizes the excess free energy per unit length of the boundary between different lipid membrane domains, is one of the factors that determines domain size and dynamics. Consequently, experimental methods and corresponding modeling studies related to the line tension continue to attract significant interest. Considering a planar binary lipid layer with two domains consisting of neutral and anionic lipids, one with a higher and one with a lower average surface charge density, we calculate the electrostatic contribution to the line tension at the domain boundary using mean-field electrostatics. The influence of lipid mobility in each phase is studied through solutions of the Poisson-Boltzmann equation for different sets of boundary conditions that include the limiting cases of fixing the local surface charge density or surface potential, and the intermediate case of allowing the lipids to migrate subject to a demixing entropy penalty. In addition to our numerical results, we derive simple analytic expressions for the electrostatic contribution to the line tension in the linearized Debye-Hückel limit. We find the electrostatic contribution to the line tension to be negative with magnitudes on the order of piconewton close to physiological conditions. Because this is comparable to experimentally reported values of the total line tension, we conclude that electrostatic interactions generally provide an important contribution to the total line tension between differently charged domains in lipid bilayers. [ABSTRACT FROM AUTHOR]

Wetting of droplets on homogeneous and spherical concave rough surfaces is investigated based on thermodynamics. In this study, neglecting the droplet gravity and the thickness of the precursor film of the liquid-vapor interface, the three-phase system is divided into six parts using Gibbs concept of dividing surface. The system Helmholtz free energy is established based on thermodynamics. Supposing the temperature and chemical potential to be constant, a new generalized Young's equation of the equilibrium contact angle for a spherical droplet on a spherical concave rough surfaces is obtained including the line tension effects. Under certain conditions, this generalized Young's equation is the same as the Rusanov's equation. [ABSTRACT FROM AUTHOR]

Many water-soluble cationic porphyrins are known to be prospective chemotherapeutics and photosensitizers for cancer treatment and diagnosis. The physicochemical properties of porphyrins, in particular their interactions with membranes, are important determining factors of their biological activity. The influence of cationic meso-tetra-[4- N-(2′-hydroxyethyl) pyridyl] porphyrin (H2TOEtPyP) on the stability and conductivity of bilayer lipid membranes (BLMs) was studied. H2TOEtPyP4 porphyrin was shown to decrease the stability of BLMs made of a mixture of DOPS and DPPE (1:1) in an electric field because of a reduction of line tension of spontaneously formed pore edges in the BLM. The presence of cationic porphyrin was found to reduce BLM surface tension. This effect was enhanced with increasing porphyrin concentration. H2TOEtPyP4 increased the probability of spontaneous pore formation. Further investigating the cyclic current-voltage characteristics of BLMs allowed determining the electrical capacity and conductivity of BLMs in the presence of H2TOEtPyP4 porphyrin. It was shown that in the presence of cationic porphyrin the electrical capacity as well as conductivity of the BLM increases. [ABSTRACT FROM AUTHOR]

We review a few simulation methods and results related to the structure and non-equilibrium dynamics in the coexistence region of immiscible symmetric binary fluids, in bulk as well as under confinement, with special emphasis on the latter. Monte Carlo methods to estimate interfacial tensions for flat and curved interfaces have been discussed. The latter, combined with a thermodynamic integration technique, provides contact angles for coexisting fluids attached to the wall. For such three-phase coexistence, results for the line tension are also presented. For the kinetics of phase separation, various mechanisms and corresponding theoretical expectations have been discussed. A comparative picture between the domain growth in bulk and confinement (including thin-film and semi-infinite geometry) has been presented from molecular dynamics simulations. Applications of finite-size scaling technique have been discussed in both equilibrium and non-equilibrium contexts. [ABSTRACT FROM PUBLISHER]

Theoretical model of structure of through pore in lipid bilayer is developed. We assumed that hydrophobic void can appear between monolayers of the membrane. The void is supposed to be filled by organic solvent or low-polarity impurities, which are usually present in artificial and cell membranes. The pore edge was divided to three regions: two monolayer and one bilayer, which surfaces were assumed continuously conjugated. The line tension of the edge was calculated in the framework of theory of elasticity of liquid crystals adapted to lipid membranes. The energy of boundary of hydrocarbon lipid chains with the void was also taken into account. We calculated the pore edge line tension for different volumes of the void. It appeared that at low surface tension at the void's boundary the line tension decreases for increasing void volume. For zero volume the obtained line tension value is 6.8 pN, which is in accordance with available experimental data. [ABSTRACT FROM AUTHOR]

The line tension for a Lennard–Jones (LJ) fluid on a (9, 3) solid of varying strength was calculated using Monte Carlo simulations. A new perturbation method was used to determine the interfacial tension between liquid–vapour, solid–liquid and solid–vapour phases for this system to determine the Young's equation contact angle. Cylindrical and spherical nanodroplets were simulated for comparison. The contact angles from the cylindrical drops and Young's equation agree very well over the range of surface strengths and cylindrical drop sizes, except on a very weak surface. Tolman length effects were not observable for cylindrical drops. This shows that quite small systems can reproduce macroscopic contact angles. For spherical droplets, a deviation between the contact angle of spherical droplets and Young's equation was evident, but decreased with increasing interaction strengths to be negligible for contact angles less than 90°. Linear fitting of the contact angle data for varying droplet sizes showed no clear effect by line tension on contact angle. All calculated line tension values have a magnitude less than 4 × 10− 12J/m with both negative and positive signs. The best estimate of line tension for this system of LJ droplets was 1 × 10− 13J/m, which is smaller than the reported estimations in the literature, and is too small to be conclusively positive or negative in value. [ABSTRACT FROM AUTHOR]

Membrane integrity is crucial for maintaining the intricate signaling and chemically-isolated intracellular environment of neurons; disruption risks deleterious effects, such as unregulated ionic flux, neuronal apoptosis, and oxidative radical damage as observed in spinal cord injury and traumatic brain injury. This paper, in addition to a discussion of the current understanding of cellular tactics to seal membranes, describes two major factors involved in membrane repair. These are line tension, the hydrophobic attractive force between two lipid free-edges, and membrane tension, the rigidity of the lipid bilayer with respect to the tethered cortical cytoskeleton. Ca, a major mechanistic trigger for repair processes, increases following flux through a membrane injury site, and activates phospholipase enzymes, calpain-mediated cortical cytoskeletal proteolysis, protein kinase cascades, and lipid bilayer microdomain modification. The membrane tension appears to be largely modulated through vesicle dynamics, cytoskeletal organization, membrane curvature, and phospholipase manipulation. Dehydration of the phospholipid gap edge and modification of membrane packaging, as in temperature variation, experimentally impact line tension. Due to the time-sensitive nature of axonal sealing, increasing the efficacy of axolemmal sealing through therapeutic modification would be of great clinical value, to deter secondary neurodegenerative effects. Better therapeutic enhancement of membrane sealing requires a complete understanding of its intricate underlying neuronal mechanism. [ABSTRACT FROM AUTHOR]

Using Gibbs’ method of dividing surfaces, the contact angle of a drop on a flat homogeneous rough non-deformable solid substrate is investigated. For this system, a new generalized Young’s equation for the contact angle, including the influences of line tension and which valid for any dividing surface between liquid phase and vapor phase is derived. Under some assumptions, this generalized Young’s equation reduces to the Wenzel’s equation or Rosanov’s equation valid for the surface of tension. [ABSTRACT FROM PUBLISHER]

In this work, some implications of a recent model for the mechanical behavior of biological membranes (Deseri et al. in Continuum Mech Thermodyn 20(5):255-273, ) are exploited by means of a prototypical one-dimensional problem. We show that the knowledge of the membrane stretching elasticity permits to establish a precise connection among surface tension, bending rigidities and line tension during phase transition phenomena. For a specific choice of the stretching energy density, we evaluate these quantities in a membrane with coexistent fluid phases, showing a satisfactory comparison with the available experimental measurements. Finally, we determine the thickness profile inside the boundary layer where the order-disorder transition is observed. [ABSTRACT FROM AUTHOR]

Due to its complexity, line tension is usually neglected or indirectly estimated in studying heterogeneous nucleation. In this work, we try to provide a direct and quantitative description of it. Within a three-dimensional density functional framework, the total excess free energy and individual energies at different two-phase interfaces are calculated during the droplet or bubble nucleation in binary fluids, and the line tension and contact angle are determined simultaneously. Meanwhile, the contact angle can also be measured directly from the spatial configuration of droplet or bubble. Comparing the calculated and measured contact angles, one can see that a good agreement is achieved for bubble and droplet at solvophilic and solvophobic walls. It is shown that line tension provides a considerable modification of contact angle prediction that is of great importance in engineering applications. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4390-4398, 2013 [ABSTRACT FROM AUTHOR]

Virus budding is a complex, multistep process in which viral proteins make specific alterations in membrane curvature. Many different viral proteins can deform the membrane and form a budding virion, but very few can mediate membrane scission to complete the budding process. As a result, enveloped viruses have developed numerous ways of facilitating membrane scission, including hijacking host cellular scission machinery and expressing their own scission proteins. These proteins mediate scission in very different ways, though the biophysical mechanics underlying their actions may be similar. In this review, we explore the mechanisms of membrane scission and the ways in which enveloped viruses use these systems to mediate the release of budding virions. [ABSTRACT FROM AUTHOR]

A methodology for the determination of the solid-fluid contact angle, to be employed within molecular dynamics (MD) simulations, is developed and systematically applied. The calculation of the contact angle of a fluid drop on a given surface, averaged over an equilibrated MD trajectory, is divided in three main steps: (i) the determination of the fluid molecules that constitute the interface, (ii) the treatment of the interfacial molecules as a point cloud data set to define a geometric surface, using surface meshing techniques to compute the surface normals from the mesh, (iii) the collection and averaging of the interface normals collected from the post-processing of the MD trajectory. The average vector thus found is used to calculate the Cassie contact angle (i.e., the arccosine of the averaged normal z-component). As an example we explore the effect of the size of a drop of water on the observed solid-fluid contact angle. A single coarsegrained bead representing two water molecules and parameterized using the SAFT-γ Mie equation of state (EoS) is employed, meanwhile the solid surfaces are mimicked using integrated potentials. The contact angle is seen to be a strong function of the system size for small nano-droplets. The thermodynamic limit, corresponding to the infinite size (macroscopic) drop is only truly recovered when using an excess of half a million water coarse-grained beads and/or a drop radius of over 26 nm. [ABSTRACT FROM AUTHOR]

Water droplets on bare silicon surfaces are studied to examine the wetting behaviour as a function of the surface energy and to parameterise water–silicon interactions in order to recover the hydrophobic behaviour measured by experiments. Two different wetting regimes characterised by a critical interaction strength value are observed. At a threshold value of the water–silicon interaction parameter, water molecules start penetrating into the first layer of silicon surface under thermally vibrating walls, resulting in two distinct wetting behaviours. Fixed (cold) silicon walls do not exhibit the two different wetting characteristics. Size effects are studied for nano-scale droplets, and line tension influence is observed depending on the surface wettability. Decrease in the droplet size increases the contact angle values for the low wetting cases, while contact angles decrease for smaller droplets on the high wetting surfaces. Considering the line tension effects and droplet size, ϵSi–Ofor water–silicon interactions to recover the hydrophobic behaviour of silicon surfaces is estimated to be 12.5% of the value predicted using the Lorentz–Berthelot mixing rule. [ABSTRACT FROM AUTHOR]

The paper proposes a general framework allowing the analysis of wetting problems in the situation when interfacial tensions depend on external fields. An equation predicting apparent contact angles of sessile droplets deposited on rough surfaces in the presence of external fields is derived. The problem of wetting is discussed in the framework of the variational approach. Derivation of a general equation generalizing the Cassie and Wenzel approaches is presented. The effects related to the line tension which are important for nano-structured surfaces are considered. [ABSTRACT FROM AUTHOR]

A harbor is a sheltered part of a body of water deep enough to provide anchorage and refuge for ships and a place where commercial or other activities can develop. Is of great importance for the moored vessels to evaluate the oscillation period - depending on vessel displacement, number, type and position of the mooring lines. The resonance between the natural oscillation of the vessel in cargo or bunkering operations and the waves, stationary or not, with unexpected and high surge displacement, can lead to pollution or even greater accidents if chemical or LPG - LNG operations are involved. The purpose of the present paper is to evaluate the changes in surge natural oscillations period of moored vessels for different scenarios. [ABSTRACT FROM AUTHOR]

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Bilayer thickness in membrane domains enriched with sphingomielin and cholesterol (known as 'rafts') is bigger than thickness of neighboring membrane. Monolayers need to deform to compensate the thicknesses difference in the vicinity of the raft boundary. Line tension of the boundary of rafts associated with elastic deformations originating from the compensation of the thickness mismatch is calculated in the frame-work of the elasticity theory. In the calculations deformations of splay, tilt and lateral stretching/compression are considered. It is assumed that raft consists of two monolayer domains situated in the different membrane monolayers; it is also assumed that the boundaries of domains can shift in the lateral direction with respect to relative to each other. Dependence of the boundary energy of raft on the value of the relative shift of the boundaries is calculated. It is shown that the boundary energy is minimal when shift is equal to 4.5 nm. Dependence of the optimal shift on the mismatch of the monolayer thicknesses of raft and surrounding membrane as well as membrane shape in the vicinity of boundary are calculated. The calculated values of line tension are in a good agreement with available experimental data. Taking into account deformation of stretching/compression increases the accuracy of calculations by 30%; this exceeds the uncertainty of the line tension measurements by modern techniques. [ABSTRACT FROM AUTHOR]

Two-phase lipid membrane is modeled with lipids of different bending rigidity of hydrophobic tails: domains consist of 'rigid' lipid liquid condensed phase and are surrounded by the 'flexible' lipid liquid expanded phase. Within the framework of the earlier proposed model of flexible strings, entropic contribution not including mismatch energy is calculated analytically. 'Entropic' line tension is found to be weakly dependent on the domain radius. According to the model, it is shown that merely 'entropic mismatch' is not enough for the domain formation. In the paper it is assumed that lipids at the boundary, on the average, have larger area than the ones in the volume. This leads to an increase of energy of boundary lipids. Cases of lipids with nearly the same bending rigidities and with strongly different ones are considered. Free energy is calculated using Taylor expansion on the difference of area of lipids at the domain's boundary and in the volume. Based on the calculated boundary energy domain stability in the finite system is estimated. [ABSTRACT FROM AUTHOR]

Line tension of the boundary of specific domains (rafts) rich in sphingomyelin was calculated. The line tension was calculated based on macroscopic theory of elasticity under assumption that the bilayer in raft is thicker than in the surrounding membrane. The calculations took into account the possibility of lateral shift of the domain boundaries located in different monolayers of the membrane. The line tension was associated with the energy of elastic deformations appearing in the vicinity of the boundary in order to compensate for the difference in the thickness of the monolayers. Spatial distribution of deformations and the line tension was calculated by minimization of elastic free energy of the system. Dependence of the line tension on the distance between the domains boundaries located in different monolayers was obtained. It was shown that the line tension is minimal if the distance is about 4 nm. Thus, membrane deformations stabilize the bilayer structure of rafts observed experimentally. The calculated value of line tension is about 0.6 pN for the difference between the monolayer thickness of raft and surrounding membrane of about 0.5 nm, which is in agreement with the experimental data available. [ABSTRACT FROM AUTHOR]

For an understanding of interfacial phenomena of fluids on the nanoscale a detailed knowledge of the excess free energies of fluids due to walls is required, as well as of the interfacial tension between coexisting fluid phases. A description of simulation approaches to solve this task is given for a suitable model binary (A + B) fluid. Sampling the order parameter distribution of the system without walls, the curvature dependent and flat interfacial tensions of coexisting 'bulk' phases is extracted. In a thin film geometry, the difference in wall free energies is found via a new thermodynamic integration method. Thus the contact angle θ of macroscopic droplets is estimated from Young's equation, for varying interactions between the fluid particles and the walls, which compares well with direct observations of inclined interfaces in ultrathin slit pores. Studying two-phase situations where a wall-attached droplet exists in the slit pore in thermal equilibrium, the excess free energy due to the droplet is found as a function of the droplet size, which is compatible with the classical theory for heterogeneous nucleation, if a line tension correction to the contact angle is made. For θ = 90○ an alternative method for extracting the line tension is also presented. [ABSTRACT FROM AUTHOR]

Thousands of plant and animal species have been observed to have superhydrophobic surfaces that lead to various novel behaviors. These observations have inspired attempts to create artificial superhydrophobic surfaces, given that such surfaces have multitudinous applications. Superhydrophobicity is an enhanced effect of surface roughness and there are known relationships that correlate surface roughness and superhydrophobicity, based on the underlying physics. However, while these examples demonstrate the level of roughness they tell us little about the independence of this effect in terms of its scale. Thus, they are not capable of explaining why such naturally occurring surfaces commonly have micron-submicron sizes. Here we report on the discovery of a new relation, its physical basis and its experimental verification. The results reveal that scaling-down roughness into the micro-submicron range is a unique and elegant strategy to not only achieve superhydrophobicity but also to increase its stability against environmental disturbances. This new relation takes into account the previously overlooked but key fact that the accumulated line energy arising from the numerous solid-water-air intersections that can be distributed over the apparent contact area, when air packets are trapped at small scales on the surface, can dramatically increase as the roughness scale shrinks. This term can in fact become the dominant contributor to the surface energy and so becomes crucial for accomplishing superhydrophobicity. These findings guide fabrication of stable super water-repellant surfaces. [ABSTRACT FROM AUTHOR]

We study the Γ-convergence of the following functional ( p > 2) where Ω is an open bounded set of $${\mathbb{R}^3}$$ and W and V are two non-negative continuous functions vanishing at α, β and α′, β′, respectively. In the previous functional, we fix a = 2 − p and u is a scalar density function, Tu denotes its trace on ∂Ω, d( x, ∂Ω) stands for the distance function to the boundary ∂Ω. We show that the singular limit of the energies $${F_{\varepsilon}}$$ leads to a coupled problem of bulk and surface phase transitions. [ABSTRACT FROM AUTHOR]

Lipid bilayer model membranes that contain a single lipid species can undergo transitions between ordered and disordered phases, and membranes that contain a mixture of lipid species can undergo phase separations. Studies of these transformations are of interest for what they can tell us about the interaction energies of lipid molecules of different species and conformations. Nanoscopic phases (<200 nm) can provide a model for membrane rafts, specialized membrane domains enriched in cholesterol and sphingomyelin, which are believed to have essential biological functions in cell membranes. Crucial questions are whether lipid nanodomains can exist in stable equilibrium in membranes and what is the distribution of their sizes and lifetimes in membranes of different composition. Theoretical methods have supplied much information on these questions, but better experimental methods are needed to detect and characterize nanodomains under normal membrane conditions. This review summarizes linkages between theoretical and experimental studies of phase separation in lipid bilayer model membranes. [ABSTRACT FROM AUTHOR]

Abstract: Membranes with simple lipid composition exhibit complex phase behavior. Ordered and disordered liquid phases can coexist in cholesterol-containing membranes with lipid compositions resembling biological membranes and at physiological temperatures. Research during the last years suggests that these lipid domains play a role in the organization of biological membranes. Understanding the principles that govern the formation and stability of lipid domains is of great importance to build a model that properly describes membrane structure and function. In this review, we describe the current knowledge of the chemical and physical basis of lipid domains and its application to biological membranes. [Copyright &y& Elsevier]

Let Ω be an open bounded set of ℝ3 and let W and V be two non-negative continuous functions vanishing at α, β and α', β', respectively. We analyze the asymptotic behavior as ε → 0, in terms of Γ-convergence, of the following functional: $$ F_{\varepsilon}(u):=\varepsilon^{p-2} \int_{\Omega}|Du|^{p}dx+\frac{1} {\varepsilon^{\frac{p-2}{p-1}}}\int_{\Omega} W(u)dx+\frac{1}{\varepsilon} \int_{\partial\Omega} V(Tu)d\mathcal{H}^{2},\quad p > 2, $$ where u is a scalar density function and Tu denotes its trace on ∂Ω. We show that the singular limit of the energies Fε leads to a coupled problem of bulk and surface phase transitions. [ABSTRACT FROM AUTHOR]

Prompted by recent works on line tension effects upon the stability of liquid droplets laid on a rigid substrate, we prove existence and stability of equilibrium configurations when the substrate is either planar or spherical. For positive line tension our argument involves only set symmetrization, while for negative line tension a stability criterion is proposed which makes variational problems well-posed in the framework of sets with finite perimeter. Several applications illustrate the role of the criterion in providing a natural cutoff length that selects destabilizing modes. [ABSTRACT FROM AUTHOR]