Bilayer Bending Research Articles

Evaluation of bending modulus of lipid bilayers using undulation and orientation analysis.

In the current paper, phospholipid bilayers are modeled using coarse-grained molecular dynamics simulations with the MARTINI force field. The extracted molecular trajectories are analyzed using Fourier analysis of the undulations and orientation vectors to establish the differences between the two approaches for evaluating the bending modulus. The current work evaluates and extends the implementation of the Fourier analysis for molecular trajectories using a weighted horizon-based averaging approach. The effect of numerical parameters in the analysis of these trajectories is explored by conducting parametric studies. Computational modeling results are validated against experimentally characterized bending modulus of lipid membranes using a shape fluctuation analysis. The computational framework is then used to estimate the bending moduli for different types of lipids (phosphocholine, phosphoethanolamine, and phosphoglycerol). This work provides greater insight into the numerical aspects of evaluating the bilayer bending modulus, provides validation for the orientation analysis technique, and explores differences in bending moduli based on differences in the lipid nanostructures.

Rapid Accessible Fabrication and Engineering of Bilayered Hydrogels: Revisiting the Cross-Linking Effect on Superabsorbent Poly(acrylic acid).

Superabsorbent hydrogels are significant not only in materials science but also in industries and daily life, being used in diapers or soil conditioners as typical examples. The main feature of these materials is their capacity to hold considerable amount of water, which is strongly dependent on the cross-linking density. This study focuses on the preparation of hydrogels by reweighing the effect of cross-linking density on physical properties, which provides green fabrication of bilayered hydrogels that consist of homogeneous structural motifs but show programmed responses via sequential radical polymerization. In particular, when two hydrogel layers containing different cross-linking densities are joined together, an integrated linear bilayer shows heterogeneous deformation triggered by water. We monitor the linear hydrogel bilayer bending into a circle and engineer it by incorporating disperse dyes, changing colors as well as physical properties. In addition, we demonstrate an electric circuit switch using a patterned hydrogel. Anisotropic shape change of the polyelectrolyte switch closes an open circuit and lights a light-emitting diode in red. This proposed fabrication and engineering can be expanded to other superabsorbent systems and create smart responses in cross-linked systems for biomedical or environmental applications.

Depth-Dependent Physical Properties of Model Biological Lipid Bilayers

Lipid bilayers are thin, polar structures made up of two layers of lipid molecules. They are one of the constituents of the cellular plasma membrane, which forms a curved and continuous barrier around the cells and are responsible for exchange of molecules in and out of the cell. The type and composition of lipids that make up the many different types of bilayers can alter its various physical properties that change significantly with depth, such as the highly fluctuating lateral pressure profile. Studying the various depth-dependent properties can give important insights into membrane functionality and the way they modulate membrane proteins, which could be hard to investigate by experimental means. In this study, we use atomistic molecular dynamics simulations to quantify a number of bilayer properties in model bacterial, mammalian and cancer membranes that have heterogeneous lipid compositions. We examine some basic properties such as lipid area and volume, bilayer thickness and bending rigidity, as well as transmembrane profiles for electron density, lateral pressure and dipole potential. Our results show how individual lipids modulate physical properties of these heterogeneous bilayers, with potential implications on membrane function.

Graphene quantum dot–poly(vinylidene fluoride) composite for the preparation of asymmetric bilayer bending transducer

A newly developed asymmetric bilayer bending transducer composed of a graphene quantum dot (GQD)–poly(vinylidene fluoride) (PVDF) composite and a simple adhesive tape has been investigated. This bending transducer displays high actuation displacement (10.2 mm) and large electromechanical strain (0.3%) under relatively low electric field strength (20.8 MV m−1). The key to the high electromechanical performance lies in the unique GQD–PVDF interfacial structure and the high dielectric constant of GQD–PVDF (2350 at 1 Hz, 1% GQD weight percentage) caused by the interfacial polarization effect. The good electromechanical performance of our device shows bright prospect of GQD in smart materials field.

The effect of membrane softeners on rigidity of lipid vesicle bilayers: Derivation from vesicle size changes

Deformability is not just a fundamentally interesting vesicle characteristic; it is also the key determinant of vesicle ability to cross the skin barrier; i.e. skin penetrability. Development of bilayer vesicles for drug and vaccine delivery across the skin should hence involve optimization of this property, which is controllable by the concentration of bilayer softeners in or near the vesicle bilayers. To this end, we propose a simple method for quantifying the effect of bilayer softeners on deformability of bilayer vesicles. The method derives the bending rigidity of vesicle bilayers from vesicle size dependence on softener concentration. To exemplify the method, we studied mixtures of soybean phosphatidylcholine with anionic sodium deoxycholate, non-ionic polyoxyethylene (20) sorbitan oleyl ester (polysorbate 80), or non-ionic polyoxyethylene (20) oleyl ether (C18:1EO20, Brij® 98). With each of the tested bilayer softeners, the bending rigidity of the resulting mixed-amphipat vesicle bilayers decreased quasi-exponentially as the concentration of the bilayer softener increased, as one would expect on theoretical ground. The bilayer bending rigidity reached low values, near the thermal stability limit, i.e. kBT, before vesicle transformation into non-vesicular aggregates began. For a soybean phosphatidylcholine concentration of 5.0mmolkg−1, the bilayer bending rigidity reached 1.5kBT at the total deoxycholate concentration of 4.1mmolkg−1 and 3.4kBT at the total polysorbate 80 concentration of 2.0mmolkg−1. In the case of C18:1EO20, the bilayer bending rigidity reached 1.5kBT at the bilayer surface occupancy α=0.1. The dependence of vesicle size on bilayer softener concentration thus reveals vesicle transformation into different aggregate structures (such as mixed micelles with poor skin penetrability) and practically valuable information on vesicle deformability. Our results compare favorably with results of literature measurements. We provide practical guidance on using the new analytical method to optimize deformable vesicle formulations.

Spontaneous bending of pre-stretched bilayers

We discuss spontaneously bent configurations of pre-stretched bilayer sheets that can be obtained by tuning the pre-stretches in the two layers. The two-dimensional nonlinear plate model we use for this purpose is an adaptation of the one recently obtained for thin sheets of nematic elastomers, by means of a rigorous dimensional reduction argument based on the theory of Gamma-convergence (Agostiniani and DeSimone in Meccanica. doi:10.1007/s11012-017-0630-4, 2017, Math Mech Solids. doi:10.1177/1081286517699991, arXiv:1509.07003, 2017). We argue that pre-stretched bilayer sheets provide us with an interesting model system to study shape programming and morphing of surfaces in other, more complex systems, where spontaneous deformations are induced by swelling due to the absorption of a liquid, phase transformations, thermal or electro-magnetic stimuli. These include bio-mimetic structures inspired by biological systems from both the plant and the animal kingdoms.

Molecular-Scale Biophysical Modulation of an Endothelial Membrane by Oxidized Phospholipids

The influence of two bioactive oxidized phospholipids on model bilayer properties, membrane packing, and endothelial cell biomechanics was investigated computationally and experimentally. The truncated tail phospholipids, 1-palmitoyl-2-(5-oxovaleroyl)-sn-glycero-3-phosphocholine (POVPC) and 1-palmitoyl-2-glutaroyl-sn-glycero-3-phosphocholine (PGPC), are two major oxidation products of the unsaturated phospholipid 1-palmitoyl-2-arachidonoyl-sn-glycero-phosphocholine. A combination of coarse-grained molecular dynamics simulations, Laurdan multiphoton imaging, and atomic force microscopy microindentation experiments was used to determine the impact of POVPC and PGPC on the structure of a multicomponent phospholipid bilayer and to assess the consequences of their incorporation on membrane packing and endothelial cell stiffness. Molecular simulations predicted differential bilayer perturbation effects of the two oxidized phospholipids based on the chemical identities of their truncated tails, including decreased bilayer packing, decreased bilayer bending modulus, and increased water penetration. Disruption of lipid order was consistent with Laurdan imaging results indicating that POVPC and PGPC decrease the lipid packing of both ordered and disordered membrane domains. Computational predictions of a larger membrane perturbation effect by PGPC correspond to greater stiffness of PGPC-treated endothelial cells observed by measuring cellular elastic moduli using atomic force microscopy. Our results suggest that disruptions in membrane structure by oxidized phospholipids play a role in the regulation of overall endothelial cell stiffness.

GM1 Softens POPC Membranes and Induces the Formation of Micron-Sized Domains

The influence of the glycolipid GM1 on the physical properties of POPC membranes was studied systematically by using different methods applied to giant and large unilamellar vesicles. The charge per GM1 molecule in the membrane was estimated from electrophoretic mobility measurements. Optical microscopy and differential scanning calorimetry were employed to construct a partial phase diagram of the GM1/POPC system. At room temperature, phase separation in the membrane was detected for GM1 fractions at and above ∼5 mol %, whereby GM1-rich gel-like domains were observed by fluorescent microscopy. Fluctuation analysis, vesicle electrodeformation, and micropipette aspiration were used to assess the bending rigidity of the membrane as a function of GM1 content. In the fluid phase, GM1 was shown to strongly soften the bilayer. In the region of coexistence of fluid and gel-like domains, the micropipette aspiration technique allowed measurements of the bending rigidity of the fluid phase only, whereas electrodeformation and fluctuation analysis were affected by the presence of the gel-phase domains. The observation that GM1 decreased the bilayer bending rigidity is important for understanding the role of this ganglioside in the flexibility of neuronal membranes.

Effect of Lung Surfactant Protein SP-C and SP-C-Promoted Membrane Fragmentation on Cholesterol Dynamics

To allow breathing and prevent alveolar collapse, lung surfactant (LS) develops a complex membranous system at the respiratory surface. LS is defined by a specific protein and lipid composition, including saturated and unsaturated phospholipid species and cholesterol. Surfactant protein C (SP-C) has been suggested to be an essential element for sustaining the presence of cholesterol in surfactant without functional impairment. In this work, we used a fluorescent sterol-partitioning assay to assess the effect of the surfactant proteins SP-B and SP-C on cholesterol distribution in membranes. Our results suggest that in the LS context, the combined action of SP-B and SP-C appears to facilitate cholesterol dynamics, whereas SP-C does not seem to establish a direct interaction with cholesterol that could increase the partition of free cholesterol into membranes. Interestingly, SP-C exhibits a membrane-fragmentation behavior, leading to the conversion of large unilamellar vesicles into highly curved vesicles ∼25 nm in diameter. Sterol partition was observed to be sensitive to the bending of bilayers, indicating that the effect of SP-C to mobilize cholesterol could be indirectly associated with SP-C-mediated membrane remodeling. Our results suggest a potential role for SP-C in generating small surfactant structures that may participate in cholesterol mobilization and pulmonary surfactant homeostasis at the alveolar interfaces.

Analytical and numerical analysis of swelling-induced large bending of thermally-activated hydrogel bilayers

Temperature-sensitive hydrogels have recently been implemented vastly for biomedical and microfluidic sensors and actuators. The accurate and efficient design of the bilayer sensors and actuators made of temperature sensitive hydrogels are of crucial importance. In this work, we develop an analytical method to solve the swelling induced bending of temperature responsive hydrogel bilayer under plane strain condition. The bilayer consists of a neutral incompressible elastomer layer attached to a temperature sensitive hydrogel layer. An analytical approach is developed to predict the thermomechanical response of these bilayers. At the other hand, the finite bending of the bilayer is simulated applying the finite element method. Several cases are solved to demonstrate the validity and performance of the proposed analytical method. The deformation and the stresses inside the layers are presented for various material parameters employing both the developed analytical formulation as well as the finite element method. A good correspondence between the presented method and the finite element method is observed. Finally, the effect of material and geometrical parameters on curvature are also investigated.

Ionoprinted Multi-Responsive Hydrogel Actuators.

We report multi-responsive and double-folding bilayer hydrogel sheet actuators, whose directional bending response is tuned by modulating the solvent quality and temperature and where locally crosslinked regions, induced by ionoprinting, enable the actuators to invert their bending axis. The sheets are made multi-responsive by combining two stimuli responsive gels that incur opposing and complementary swelling and shrinking responses to the same stimulus. The lower critical solution temperature (LCST) can be tuned to specific temperatures depending on the EtOH concentration, enabling the actuators to change direction isothermally. Higher EtOH concentrations cause upper critical solution temperature (UCST) behavior in the poly(N-isopropylacrylamide) (pNIPAAm) gel networks, which can induce an amplifying effect during bilayer bending. External ionoprints reliably and repeatedly invert the gel bilayer bending axis between water and EtOH. Placing the ionoprint at the gel/gel interface can lead to opposite shape conformations, but with no clear trend in the bending behavior. We hypothesize that this is due to the ionoprint passing through the neutral axis of the bilayer during shrinking in hot water. Finally, we demonstrate the ability of the actuators to achieve shapes unique to the specific external conditions towards developing more responsive and adaptive soft actuator devices.

Cantilever bending based on humidity-actuated mesoporous silica/silicon bilayers.

We use a soft templating approach in combination with evaporation induced self-assembly to prepare mesoporous films containing cylindrical pores with elliptical cross-section on an ordered pore lattice. The film is deposited on silicon-based commercial atomic force microscope (AFM) cantilevers using dip coating. This bilayer cantilever is mounted in a humidity controlled AFM, and its deflection is measured as a function of relative humidity. We also investigate a similar film on bulk silicon substrate using grazing-incidence small-angle X-ray scattering (GISAXS), in order to determine nanostructural parameters of the film as well as the water-sorption-induced deformation of the ordered mesopore lattice. The strain of the mesoporous layer is related to the cantilever deflection using simple bilayer bending theory. We also develop a simple quantitative model for cantilever deflection which only requires cantilever geometry and nanostructural parameters of the porous layer as input parameters.

Bilayer-thickness-mediated interactions between integral membrane proteins.

Hydrophobic thickness mismatch between integral membrane proteins and the surrounding lipid bilayer can produce lipid bilayer thickness deformations. Experiment and theory have shown that protein-induced lipid bilayer thickness deformations can yield energetically favorable bilayer-mediated interactions between integral membrane proteins, and large-scale organization of integral membrane proteins into protein clusters in cell membranes. Within the continuum elasticity theory of membranes, the energy cost of protein-induced bilayer thickness deformations can be captured by considering compression and expansion of the bilayer hydrophobic core, membrane tension, and bilayer bending, resulting in biharmonic equilibrium equations describing the shape of lipid bilayers for a given set of bilayer-protein boundary conditions. Here we develop a combined analytic and numerical methodology for the solution of the equilibrium elastic equations associated with protein-induced lipid bilayer deformations. Our methodology allows accurate prediction of thickness-mediated protein interactions for arbitrary protein symmetries at arbitrary protein separations and relative orientations. We provide exact analytic solutions for cylindrical integral membrane proteins with constant and varying hydrophobic thickness, and develop perturbative analytic solutions for noncylindrical protein shapes. We complement these analytic solutions, and assess their accuracy, by developing both finite element and finite difference numerical solution schemes. We provide error estimates of our numerical solution schemes and systematically assess their convergence properties. Taken together, the work presented here puts into place an analytic and numerical framework which allows calculation of bilayer-mediated elastic interactions between integral membrane proteins for the complicated protein shapes suggested by structural biology and at the small protein separations most relevant for the crowded membrane environments provided by living cells.

On the influence of interfacial properties to the bending rigidity of layered structures

Layered structures are ubiquitous, from one-atom thick layers in two-dimensional materials, to nanoscale lipid bi-layers, and to micro and millimeter thick layers in composites. The mechanical behavior of layered structures heavily depends on the interfacial properties and is of great interest in engineering practice. In this work, we give an analytical solution of the bending rigidity of bilayered structures as a function of the interfacial shear strength. Our results show that while the critical bending stiffness when the interface starts to slide plastically is proportional to the interfacial shear strength, there is a strong nonlinearity between the rigidity and the applied bending after interfacial plastic shearing. We further give semi-analytical solutions to the bending of bilayers when both interfacial shearing and pre-existing crack are present in the interface of rectangular and circular bilayers. The analytical solutions are validated by using finite element simulations. Our analysis suggests that interfacial shearing resistance, interfacial stiffness and preexisting cracks dramatically influence the bending rigidity of bilayers. The results can be utilized to understand the significant stiffness difference in typical biostructures and novel materials, and may also be used for non-destructive detection of interfacial crack in composites when stiffness can be probed through vibration techniques.

Sugar does not affect the bending and tilt moduli of simple lipid bilayers

The diffuse X-ray scattering method has been applied to samples composed of SOPC, DOPC, DMPC, and POPC with added sugar, either sucrose, glucose, fructose, maltose, or trehalose. Several sugar concentrations in the range 200–500mM were investigated for each of the lipid/sugar samples. We observed no systematic change in the bending modulus KC or in the tilt modulus Kθ with increasing sugar concentration. The average values of both these moduli were the same as those of the respective pure lipid controls within statistical uncertainty of 2%. These results are inconsistent with previous reports of sugar concentration dependent values of KC.

α-Synuclein Bound to Mitochondrial Membranes—Changes in Lipid Bilayer Structure and Mechanics

The association between α-Synuclein and mitochondrial membranes is believed to be an important event in the neuronal degeneration that leads to Parkinson Disease (PD). In particular,α-Synuclein binding to mitochondrial membranes has recently been seen to cause organelle fragmentation and suppression of mitochondrial fusion. The partitioning of monomeric α-Synuclein in the lipid bilayer and subsequent bilayer remodeling has been previously described for simple, model lipid bilayers that lack the complexity of mitochondrial membranes. Here, we ran a series of coarse-grain molecular dynamics MARTINI simulations of α-Synuclein absorbed in either pure cardiolipin bilayers or in mixed lipid bilayers that reflect the lipid composition of inner mitochondrial membrane of rat brain mitochondria. We investigated changes in bilayer structure and variations in lipid solvation near α-synuclein. A thinning of the bilayer is observed in simulations having higher levels of added protein. Other aspects studied include α-Synuclein partition depth (investigated by potential of mean force calculations), bilayer bending rigidities and curvature as a function of protein and/or cardiolipin density.

The modified fluorescence based vesicle fluctuation spectroscopy technique for determination of lipid bilayer bending properties

Lipid bilayer is the main constitutive element of biological membrane, which confines intracellular space. The mechanical properties of biological membranes may be characterized by various parameters including membrane stiffness or membrane bending rigidity, which can be measured using flicker noise spectroscopy. The flicker noise spectroscopy exploits the spontaneous thermal undulations of the membrane. The method is based on the quantitative analysis of a series of microscopic images captured during thermal membrane fluctuations. Thus, measured bending rigidity coefficient depends on the image quality as well as the selection of computational tools for image processing and mathematical model used. In this work scanning and spinning disc confocal microscopies were used to visualize fluctuating membranes of giant unilamellar vesicles. The bending rigidity coefficient was calculated for different acquisition modes, using different fluorescent probes and different image processing methods. It was shown that both imaging approaches gave similar bending coefficient values regardless of acquisition time. Using the developed methodology the effect of fluorescent probe type and aqueous phase composition on the value of the membrane bending rigidity coefficient was measured. Specifically it was found that the bending rigidity coefficient of DOPC bilayer in water is smaller than that determined for POPC membrane. It has been found that the POPC and DOPC bending rigidities coefficient in sucrose solution was lower than that in water. Fluorescence imaging makes possible the quantitative analysis of membrane mechanical properties of inhomogeneous membrane.

The effect of carbon nanofillers on the performance of electromechanical polyaniline-based composite actuators

Different types of crystalline carbon nanomaterials were used to reinforce polyaniline for use in electromechanical bilayer bending actuators. The objective is to analyze how the different graphitic structures of the nanocarbons affect and improve the in situ polymerized polyaniline composites and their subsequent actuator behavior. The nanocarbons investigated were multiwalled carbon nanotubes, nitrogen-doped carbon nanotubes, helical-ribbon carbon nanofibers and graphene oxide, each one presenting different shape and structural characteristics. Films of nanocarbon-PAni composite were tested in a liquid electrolyte cell system. Experimental design was used to select the type of nanocarbon filler and composite loadings, and yielded a good balance of electromechanical properties. Raman spectroscopy suggests good interaction between PAni and the nanocarbon fillers. Electron microscopy showed that graphene oxide dispersed the best, followed by multiwall carbon nanotubes, while nitrogen-doped nanotube composites showed dispersion problems and thus poor performance. Multiwall carbon nanotube composite actuators showed the best performance based on the combination of bending angle, bending velocity and maximum working cycles, while graphene oxide attained similarly good performance due to its best dispersion. This parallel testing of a broad set of nanocarbon fillers on PAni-composite actuators is unprecedented to the best of our knowledge and shows that the type and properties of the carbon nanomaterial are critical to the performance of electromechanical devices with other conditions remaining equal.

Nanostructured MWCNT/Polypyrrole Actuators with Anisotropic Strain Response

Conducting polymers (CP) as an active material in electrochemical actuators are often likened to “artificial muscles”. To transfer the isotropic change of volume in the CP component into an anisotropic actuation as in a natural muscle, different design approaches, mostly bilayer or triple layer bending devices, have been studied. Herein, we report a novel actuator design with an almost linear strain response, consisting of nanostructured aligned multi‐walled carbon nanotube arrays in which each MWCNT is individually coated with a thin layer of polypyrrole.

Fluctuations of red blood cell membranes: The role of the cytoskeleton.

We theoretically investigate the membrane fluctuations of red blood cells with focus laid on the role of the cytoskeleton, viewing the system as a membrane coupled to a sparse spring network. This model is exactly solvable and enables us to examine the coupling strength dependence of the membrane undulation. We find that the coupling modifies the fluctuation spectrum at wavelengths longer than the mesh size of the network, while leaving the fluid-like behavior of the membrane intact at shorter wavelengths. The fluctuation spectra can be markedly different, depending on not only the relative amplitude of the bilayer bending energy with respect to the cytoskeleton deformation energy but also the bilayer-cytoskelton coupling strength.