Deformation Of Elastic Membrane Research Articles

Investigation on an underwater solar concentrating photovoltaic-membrane distillation (CPV-MD) integrated system

This paper presents an underwater solar concentrating photovoltaic-membrane distillation (CPV-MD) integrated system for regions of coastal cities and islands where land resources are insufficient and suffer from critical shortages in electricity and freshwater. A deformable solar concentrator that works underwater is innovatively designed and matched with the photovoltaic-membrane distillation module. Given its application scenario, the integrated system is designed without metallic components to prevent seawater corrosion. The concentrator's optical characteristics are revealed via optical simulations. The results illustrate that the concentrator bears optimal optical performance when its elastic membrane's deformation ratio α is 0.25 and height ratio γ is 0.35. An experimental setup with a solar cell radius of 50 mm is developed and tested in actual weather to reveal its electricity and freshwater yield performance. It is found that the integrated system exhibits similar performance under the light incident angle of 0°and 10°. Additionally, for the experiment with average solar radiation of 514 W/m2, the integrated system's output power varies between 1.53 W and 1.0 W, with an average electrical efficiency of 3.16 %. The accumulated freshwater yield is 67.8 g, with an average water yield efficiency of 28.5 %. This work may provide a new perspective on underwater solar energy utilization.

Wrapping of a vesicle nanoparticle with variable bending stiffness by membrane

Cellular uptake of nanoparticle (NP) is an important biological process involving mechanically and structurally heterogeneous environments, such as biophysical heterogeneity of single extracellular vesicles and biomechanical heterogeneity of small viral capsids. Despite of these heterogeneous environments, poor understanding of membrane interacting with vesicle NP of non-uniform mechanical properties still exists. To address this issue, combining the continuum Canham–Helfrich theory of membrane and the stochastic Markov method on state transition, we establish a theoretical model of the wrapping of a NP with any variable bending stiffness. As NPs are hypothesized with two typical types of non-uniform bending stiffness distributions (Gaussian-like and piecewise), through both minimum energy and stochastic dynamic approaches, it is identified that the membrane tends to encapsulate the NP with a sealing near soft region of NP. Because complete wrapping of NP with a sealing near its stiff region requires large elastic deformation of membrane. In addition, during cellular uptake, rotation phenomenon of the NP with variable bending stiffness is found, which is reminiscent of previous observations on homogeneous NP as reported in literature. These predictions are verified by relevant Monte Carlo simulations. Our findings are of interest to not only the fundamental understanding of cellular uptake but also the applications in the design of nanocarriers for drug delivery.

Membrane Deformation Modulated by Hydration and Cholesterol Unveiled by Solid-State 2H NMR Spectroscopy

Phospholipid membranes are biological liquid crystals in which intermolecular interactions at mesoscopic length scales play key roles in the emergence of membrane physical properties like structure and rigidity. Such interactions modulated by membrane hydration [1] and cholesterol [2] have been investigated using solid-state 2H NMR spectroscopy. The average structure is manifested by the lineshapes through principal values of static or residual coupling tensors due to quadrupolar interactions. The residual quadrupolar couplings (RQCs) yield segmental order parameters for the individual acyl segments (i), providing average membrane properties such as bilayer thickness, area/lipid, and spontaneous curvature [3]. We show that membrane dehydration and increased cholesterol content result in greater RQCs, indicative of membrane thickening. Elastic membrane deformations are exhibited as collective order-director fluctuations (ODF) contributing to the nuclear magnetic relaxation. At mesoscopic length scales the thermal fluctuations connect to membrane mechanical properties via the fluctuation-dissipation theorem. Model-free interpretation of the functional dependence of spin-lattice relaxation rates, R1Z, on segmental order parameters (square-law) reveals emergent material properties in the liquid-crystalline state. The R1Z relaxation dispersion and temperature dependence of square-law plots indicate a nematic-like membrane hydrocarbon core. Solid-state 2H NMR relaxation studies demonstrate that both dehydration and increased cholesterol content in the membrane lead to decreased slopes of square-law plots, indicating an increase in membrane bending rigidity, consistent with neutron spin-echo (NSE) measurements. Analogous 2H NMR studies with various membrane lipid compositions and peptide-reconstituted membranes have addressed lipid-mediated cell signaling and lipid-protein interactions. Molecular dynamics simulations provide further insights on the correspondence of the solid-state NMR and NSE results. [1] K.J. Mallikarjunaiah et al. (2019) Phys. Chem. Chem. Phys. 21, 18422. [2] S. Chakraborty et al. (2020) Proc. Natl. Acad. Sci. 117, 21896. [3] Mallikarjunaiah et al. (2011) Biophys. J. 100, 98.

Elastic Membrane Deformations Determine Interaction of Gramicidin a Dimers, Monomers, and Pairs thereby Modulating the Lifetime of the Conducting State

Gramicidin A is a 15-mer antimicrobial peptide produced by Bacillus brevis. In a bilayer lipid membrane, two gramicidin A monomers located in opposite monolayers can form an ion channel due to head-to-head transmembrane dimerization. To form a dimer, gramicidin A monomers first have to stand one on top of another, forming axially symmetric structure called the “pair”. We demonstrated that three key gramicidin A structures: monomer, pair, and dimer, cause elastic deformations of the membrane. We calculated the energy of deformations in the framework of a continuum theory of elasticity of liquid crystals adapted to lipid membranes. On the way from isolated monomers to the conducting dimer, the pair corresponds to the top of the energy barrier. Thus, the energy barrier of dimerization is determined by the energies of the pair and two monomers; the energy barrier of dimer dissociation is determined by the energies of the pair and the dimer. We obtained dependences of the membrane elastic energy on the distance between two monomers, two dimers, dimer and pair, dimer and monomer, pair and monomer. Two dimers were shown to strongly attract each other, while the dimer and the pair repel at short distances (< 2 nm) and attract at larger distances (> 2 nm). From the energy profiles it follows that the lifetime of the conducting state should increase about 1000-fold if two dimers are located close to each other, which is the case for the so-called tandem (linked) gramicidin channels. Monomers were shown to be strongly attracted by dimers; highly concentrated monomers, in turn, modulate the energy of the dimer. We predict exponential growth of the conducting state lifetime with monomer concentration, when exceeding a critical one.

Tunable fluidic lenses with high dioptric power

We report a complete theoretical model and supporting experimental results on the fabrication and characterization of macroscopic adaptive fluidic lenses with high dioptric power, tunable focal distance, and aperture shape. The lens is 17 mm wide and is made of an elastic polydimethylsiloxane (PDMS) polymer, which can adaptively restore accommodation distance within several cm according to the fluidic volume mechanically pumped in. Moreover, the lens can provide for magnification in the range of +25 diopter to +100 diopter with optical aberrations within a fraction of a wavelength, and overall lens weight of less than 2 g. The agreement between the non-linear theoretical model describing the elastic membrane deformation and the experimental results is apparent. We stress that these features make the proposed lenses appropriate for the low vision segment, as well as for applications in video magnifiers, camera zooms, telescope and microscopes objectives, and other machine vision applications where large magnification is required.

Mechanical behaviour of short membranous liquid-filled cylinders under axial loadings

The mechanical behaviour of membranous liquid-filled cylinders is important in many industrial and biomedical applications, such as in modelling the incudostapedial joint in the middle ear. Although membranous liquid-filled containers with various geometries have been investigated under different loading conditions, no study on the mechanical behaviour of membranous circular tubes under tension-compression testing has been published. In this work, we use the theory of large deformations of elastic membranes to develop an analytical model for a liquid-filled circular tube under an axial load, neglecting the effect of gravity. We use the Mooney–Rivlin strain-energy function and numerically calculate solutions for short to moderate tube lengths. A finite-element model of the tube is also developed and the simulation results are compared with the solution from the analytical model. The finite-element model is then used for the case of a tube with an elliptical cross-section. We observe a nonlinear behaviour in the force-displacement curve of the tubes when close to the zero-force configuration. Furthermore, the tube can go through instabilities when the force changes sign. The unstable region grows if some liquid is removed from the membranous container, causing the straight walls to become convex, and also if the tube length is increased. The tube becomes stiffer and the nonlinear behaviour becomes less significant when the tube cross-section is changed from circular to elliptical. The results may provide insight into experimental observations of the mechanical behaviour of the incudostapedial joint.

Interaction of amphipathic peptides mediated by elastic membrane deformations

Amphipathic alpha-helical peptides are perspective antimicrobial drugs. These peptides are partially embedded into the membrane to a shallow depth so that the longitudinal axis of the helix is parallel to the plane of the membrane or deviates from it by a small angle. In the framework of theory of elasticity of liquid crystals, adapted to lipid membranes, we calculated the energy of deformations occurring near the peptides partially embedded into the membrane. The energy of deformations is minimal when two peptides are parallel to each other and stay at a distance of about 5 nm. This configuration is stable with respect to small parallel displacements of the peptides and with respect to small variation of the angle between their axes both in the plane of the membrane and in the perpendicular direction. As a result of deformation the average thickness of the membrane decreases. The distribution of the elastic energy density has a maximum in the middle between the peptides. This region is the most likely place for formation of the through pores in the membrane. Since the equilibrium distance between the peptides is relatively large, it is assumed that the originally appearing pore should be purely lipidic.

Lipid Perturbation by Membrane Proteins and the Lipophobic Effect

Understanding how membrane proteins interact with their environment is fundamental to the understanding how the fold and interact with each other. We report coarse grain molecular dynamics simulations on a series of membrane proteins in a membrane environment and describe how the lipids are perturbed by the presence of proteins. We analyze these perturbations in terms of elastic membrane deformations and local lipid protein interactions. However these two factors are insufficient to describe the variety of effects that we observe and the changes caused by membranes proteins to the structure and dynamics of their lipid environment. Other factors that change the conformation available to lipid molecules are evident and are able to modify lipid structure far from the protein surface, and thus mediate long-range interactions between membrane proteins. We suggest that these multiple modifications to lipid behaviour are responsible, at the molecular level, for the lipophobic effect we have proposed to account for our observations of membrane protein organization.

Equibiaxial Mechano-Elastic Strain on Osteblasts: Theoretical Considerations

This study outlines a theoretical model that governs how the transmission of mechano-stimulation affects the proliferation of osteoblast-like (MC3T3-E1) bone cells attached to a deformable silasticnano-bioactive membrane. The nano-bioactive silastic membrane was functionalized by exposure to ultraviolet oven (UV Ozone) treatment regimes, coated with an extra-cellular matrix (ECM) protein, which is fibronectin (FN) and then seeded with MC3T3-E1 cells. The proliferation of MC3T3-E1 cells were evaluated after the cells were plated on the functionalized FN-coated nano-bioactive membrane surfaces and subjected to a 2 hour mechano-stimulation comprising of the application of a 2% dynamic equi-biaxial strain at 1 Hz frequency cycle. Elevation of the phalloidin-stained cellular actin cytoskeleton was observed, indicating the occurrence of mechanical transduction of the applied strains through the cell integrin receptors which culminated in the reorganization of the cellular cytoskeleton. The classical theory of elastic membrane deformation, therefore, rightly predicts mechano-transduction between the bioengineered nano-bioactive membrane surfaces and the applied mechanical force strains, via the integrin receptors, to the MC3T3-E1 cells, leading to enhanced cellular proliferation.

Lipid perturbation by membrane proteins and the lipophobic effect

Understanding how membrane proteins interact with their environment is fundamental to the understanding of their structure, function and interactions. We have performed coarse-grained molecular dynamics simulations on a series of membrane proteins in a membrane environment to examine the perturbations of the lipids by the presence of protein. We analyze these perturbations in terms of elastic membrane deformations and local lipid protein interactions. However these two factors are insufficient to describe the variety of effects that we observe and the changes caused by membranes proteins to the structure and dynamics of their lipid environment. Other factors that change the conformation available to lipid molecules are evident and are able to modify lipid structure far from the protein surface, and thus mediate long-range interactions between membrane proteins. We suggest that these multiple modifications to lipid behavior are responsible, at the molecular level, for the lipophobic effect we have proposed to account for our observations of membrane protein organization.

Transbilayer Registration of Liquid-Ordered Domains: No Interactions at the Membrane Midplane Required

The mechanism responsible for the registration of liquid-ordered (Lo) domains in the two membrane leaflets is a matter of debate. As an alternative to the thus far enigmatic interactions at the membrane midplane, we propose that minimization of the line tension around the thicker Lo bilayer drives registration. Based on the continuum elasticity theory, we demonstrate that the thickness mismatch at the Lo/Ld boundary results in elastic deformations of lipid molecules. The deformations require a minimum of energy FD when the domain boundaries are shifted relative to each other by several nanometers1. Accumulation of lipids or peptides with non-zero spontaneous curvature in the thin rim around the domains further sharply decreases FD, thus explaining the line activity of monosialoganglioside GM1. In addition to FD, the mutual attraction of stiffed membrane regions must contribute to domain registration2. Since energy FU is required to prevent membranes from undulating, maximizing the membrane area that is free to undulate by aligning the stiff Lo domains from opposing leaflets minimizes FU. Thus, domain registration minimizes FU and FD explaining why (i) transbilayer coupling can occur without interaction at the membrane midplane and (ii) registration does not require specific lipids in Lo domains.The work was supported by the Russian Foundation for Basic Research (15-54-15006) and by the Austrian Science Fund (I12267).1) Galimzyanov, Molotkovsky, Bozdaganyan, Cohen, Pohl, Akimov. Elastic Membrane Deformations Govern Interleaflet Coupling of Lipid-Ordered Domains. Phys.Rev.Lett. 115:088101, 2015.2) Horner, Antonenko, Pohl. Coupled diffusion of peripherally bound peptides along the outer and inner membrane leaflets. Biophys.J. 96:2689-2695, 2009.

Elastic Membrane Deformations Govern Interleaflet Coupling of Lipid-Ordered Domains.

The mechanism responsible for domain registration in two membrane leaflets has thus far remained enigmatic. Using continuum elasticity theory, we show that minimum line tension is achieved along the rim between thicker (ordered) and thinner (disordered) domains by shifting the rims in opposing leaflets by a few nanometers relative to each other. Increasing surface tension yields an increase in line tension, resulting in larger domains. Because domain registration is driven by lipid deformation energy, it does not require special lipid components or interactions at the membrane midplane.

Intra-Membrane Surface Flow in Response to Protein Induced Spontaneous Curvature

Lipid bilayers are unique in their biophysical properties. They are fluid in-plane and solid in bending. While traditional models use the Helfrich approach to model the elastic deformations of the bilayer membrane, these approaches only provide insight into the equilibrium configurations of the elastic deformations of the membrane. But many membrane deformations are dynamic and occur in response to protein binding. To capture these effects, it is important to model the viscoelastic properties of the lipid bilayer rather than the elastic bending alone. We have recently developed a model that accounts for the elastic bending behavior of the membrane and captures the flow of lipids on the surface of the membrane in response to a driving force.One important component in membrane deformations is the binding of proteins to the membrane surface. We use the viscous-elastic model of the bilayer membrane to capture the dynamics of membrane shape change in response to protein binding. The binding of proteins to the membrane is modeled as a kinetic process, and the surface density of the protein is assumed to be proportional to the spontaneous curvature of the membrane in that region. Numerical simulations show that binding of proteins changes the shape of the membrane and induces lipid flow from the boundaries. to allow for the increase in surface area of the membrane. Additionally, the surface pressure field evolves from a homogeneous distribution to an inhomogeneous distribution. Together,these results capture the dynamics of lipid flow and surface evolution in response to protein binding.

Mechanical Model of Cell Membrane Penetration by Vertical Nanowires

For many therapeutic and scientific applications, direct access into a cell's interior is the key for delivering various biomolecules to alter cell behavior or for intracellular assays. However, the lipid membrane presents a challenging barrier that prevents biomolecular species from entering the cytosol.The recent discovery of cell viability despite penetration by vertical nanowires (NW) has opened new avenues for direct intracellular access. Cells are found to be impaled onto small diameter nanowires without application of any external force. Vertical NW arrays have been reported to serve as a universal and efficient platform for introducing RNA, DNA, proteins and peptides into a broad range of cell types.However, the cell membrane penetration mechanism by vertical nanowires is still unknown. Several recent experiments have shown that the penetration efficiency is greatly reduced with increasing NW diameter. Understanding the penetration mechanism is the key to optimizing the design of nanowires and developing advanced devices based on this technique.In this work a mechanical model is developed to predict cell membrane penetration by vertical nanowires. The tension and strain on cell membranes due to indentation by nanowire are calculated using a model of axisymmetric deformation of elastic membrane indented by a probe with a hemispherical tip. The critical membrane rupture conditions are determined under different failure criteria, either tension or strain. The effects of NW radius, NW aspect ratio and cell membrane stiffness on penetration are investigated based on the mechanical model. Our results provide a practical guide to designing nanowires for applications in cell membrane penetration.

Stabilization of bilayer structure of raft due to elastic deformations of membrane

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.

Two-row radial gas-static bearing with lubricant-outflow regulator

The high pliability of gas-static bearings limits their applicability in spindles of metal-cutting machines. Two methods of reducing the pliability (sometimes to zero or negative values) are known: 1) the use of input units that compensate the lubricant flow rate [1, 2]; 2) the use of units that compensate the motion of elements separated by a gas layer [3, 4]. Such gas-static bearings, operating at negative pliability, may be used to compensate the positive pliability of elastic elements in the metal-cutting machine, so as to improve machining. We know that bearings with active compensation of the lubricant flow rate are characterized by high energy consumption, unstable static properties, and inability to ensure negative pliability at moderate and high loads [1]. Bearings with active motion compensation are largely free of these problems but are structurally more complex. This is true especially of radial bearings [4]. In the present work, we consider a new method of reducing the pliability, in which lubricant-outflow regulators are employed. The resulting radial gas-static bearings are relatively simple in design (Fig. 1). The bearing consists of housing 1 , shaft 2 (subject to external load f ), and two symmetric (relative to the bearing’s central plane) rigid annular elements 3 , connected hermetically to housing 1 by means of elastic elements (membranes) 4. A double gas-choking system in the pressure lines ensures stability of the bearing [5]. The gas (at pressure p in ) is sent in the pressure line through choking annular slots 6 to intermediate flow cavity 7 at pressure p r ; then to thin lubricant gaps 5 (thickness h r ), formed by housing 1 and elastic membranes 4 ; and to intermediate damping annular slots 8 . Overcoming the resistance of these slots, the gas falls at pressure p f into thin supporting gas layer 9 (thickness h ) and passes from the bearing to the surroundings at pressure p a through a gap of thickness h f . Under the action of load f , shaft 2 shifts its position, and the hydraulic drag at the lubricant layers h , h r , and h f changes. In the loaded section, p r and p f increase; in the unloaded section, they decrease. In reaction, forces act on element 3 and membrane 4 in the region of the gaps h r and h f and they are displaced in the opposite direction to the load, as follows from an analysis of the pressure distribution at the working surfaces of element 3 and membrane 4 . Consequently, there is greater increase in hydraulic drag and hence in gas pressure in the loaded end region of the supporting layer and greater decrease in these factors in the unloaded region. This ensures active regulation of lubricant outflow. The integral reaction of the forces at element 3 and membrane 4 is balanced by the drag associated with elastic deformation of membrane 4 . The continuity of the gas flow through the pressure line, which ensures active pressure redistribution, leads to smaller eccentricity e of the shaft and the bearing housing and hence to smaller pliability ∂ e / ∂ f . The bearing pliability will decrease with increase in radial pliability of the membrane and hence greater eccentricity of the annular elements 3 and the bearing housing. In investigating the static characteristics, we assume that the axes of the housing and the mobile elements are parallel. Dimensionless variables are employed in the calculations. Linear dimensions are referred to the shaft radius r 0 ; pressures to p in ; forces to π p in ; mass flow rates of the gas to / µ RT ; and gaps and eccentricities of the mobile elements to h 0 . Here h 0 is the thickness h of the supporting gas layer when the elements are coaxial (with no load f ); µ is the lubricant viscosity; R , T are, respectively, the universal gas constant and the absolute temperature of the lubricant. We consider the r0

Multi-physics system modeling of a pneumatic micro actuator

We present a first step in the conception of a micro pressure source. It consists in three main parts: (i) a heating resistance built on a dielectric membrane, (ii) air encapsulated at atmospheric pressure and (iii) an elastomer membrane with high elastic properties. A PDMS-based material is chosen as the membrane material for its elastic properties. When the actuation is required, air is heated to increase its pressure; the gain in pressure produces the deformation of the elastic membrane. Physical models have been developed for each step of operation: the heating of the resistance, the air pressurization and the elastic membrane deformation. An important model feature is the coupling of air pressurization with membrane deformation. This paper presents each individual model that has been correlated with experimental results. Then, all the models are implemented into one system model used to predict the actuator performance as a function of input electrical signal.

On finite deformations of elastic membranes

The established theory of the Finite Deformations of Elastic Membranes is based on the assumption that the considered membrane is deformed under the action of edge tractions and pressures applied on its two faces. It is further tacitly assumed that the pressures are small. Though the assumption of small pressure-difference is reasonable, the pressure themselves need not be small. Neither the surface tractions need be normal to the corresponding surfaces. In this paper the equations of Finite Elasticity are used for the derivation of a generalized Membrane Theory. No assumptions are made about the surface tractions. A small non-dimensional parameter ϵ = h/L is introduced in the three-dimensional equations, where 2 h is the variable thickness of the membrane and L a characteristic length. The zero and first-order equations are obtained. From the zero-order equations it follows that the pressures applied on the faces of the membrane are equal to the zero-order and the shear tractions equal and opposite to the same order. From the first-order equations it is deduced that the pressure difference is small. It is also proved that for zero shear tractions and small pressures the equations derived here reduce to the usual equations of the non-linear Membrane Theory.

Relaxed energy densities for small deformations of membranes

The theory of plane stress for infinitesimal deformations of elastic membranes commonly yields solutions that are unstable with respect to out-of-plane perturbations. This can be remedied by replacing the elastic strain energy by a certain relaxed energy density. This procedure yields tension field theory when it is appropriate. Minimum energy and minimum complementary energy theorems, based on the relaxed energy density, are proved.

Joined dissimilar orthotropic elastic cylindrical membranes under internal pressure and longitudinal tension

AbstractFollowing work in an earlier paper, the theory of finite deformation of elastic membranes is applied to the problem of two initially-circular semi-infinite cylindrical membranes of the same radius but of different material, joined longitudinally at a cross-section. The body is inflated by constant interior pressure and is also extended longitudinally. The exact solution found for an arbitrary material is now specialised to the orthotropic case, and the results are interpreted for forms of the strain-energy function introduced by Vaishnav and by How and Clarke in connection with the study of arteries. Also considered in this context is the similar problem where two semi-infinite cylindrical membranes of the same material are separated by a cuff of different material. Numerical solutions are obtained for various pressures and longitudinal extensions. It is shown that discontinuities in the circumferential stress at the joint can be reduced by suitable choice of certain coefficients in the expression defining the strain-energy function. The results obtained here thus solve the problem of static internal pressure loading in extended dissimilar thin orthotropic tubes, and may also be useful in the preliminary study of surgical implants in arteries.