Bottom-up approach to explore alpha-amylase assisted membrane remodelling

Soluble alpha-amylases play an important role in the catabolism of polysaccharides. In this work, we show that the malt α -amylase can interact with the lipid membrane and further alter its mechanical properties. Vesicle fluctuation spectroscopy is used for quantitative measurement of the membrane bending rigidity of phosphatidylcholines lipid vesicles from the shape fluctuation based on the whole contour of Giant Unilamellar Vesicles (GUVs). The bending rigidity of the 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine lipid vesicles in water increases significantly with the presence of 0.14 micromolar alpha-amylase (AA) in the exterior solution. It appears that the enzyme present in the external solution interacts with the outer layer of the bilayer membrane, leading to an asymmetry of the solution on either side of the bilayer membrane and altering its elasticity. At AA concentration of 1.5 micromolars and above, changes in the morphology of the GUV membrane are observed. The interaction between AA in the external solution and the external leaflet causes the bilayer membrane to curve spontaneously, leading to the formation of outbuds, giving a positive spontaneous curvature of C0 ≤ 0.05 μm-1 at ≈ 1 mg / ml of the AA concentration. We validate and characterize its concentration-dependent role in stabilizing the membrane curvature. Our findings indicate that the involvement of the enzyme, depending on the concentration, can have a considerable effect on the mechanical characteristics of the membrane.

Softening in two-component lipid mixtures by spontaneous curvature variance

The bending modulus of a lipid bilayer quantifies its mechanical resistance to curvature. It is typically understood in terms of thickness, e.g., thicker bilayers are stiffer. Here, we describe an additional and powerful molecular determinant of stiffness - the variance in the distribution of curvature sensitivity of lipids and lipid conformations. Zwitterionic choline and ethanolamine head-groups of glycero-phospholipids dynamically explore inter- and intra-species interactions, leading to transient clustering. We demonstrate that these clusters couple strongly to negative curvature, exciting undulatory membrane modes and reducing the apparent bending modulus. Three forcefields (Martini 2, Martini 3, and all-atom CHARMM C36) each show the effect to a different extent, with the coarse-grained Martini models showing the most clustering and thus the most softening. The theory is a guide to understanding the stiffness of biological membranes with their complex composition, as well as how choices of forcefield parameterization are translated into mechanical stiffness.

Membrane buckling and the determination of Gaussian curvature modulus

Biological membranes can exhibit various morphology due to the fluidity of the lipid molecules within the monolayers. The shape transformation of membranes has been well described by the classical Helfrich theory, which consists only a few phenomenological parameters, including the mean and the Gaussian curvature modulus. Though various methods have been proposed to measure the mean curvature modulus, determining the Gaussian curvature modulus remains difficult both in experiments and in simulations. In this paper we study the buckling process of a rectangular membrane and a circular membrane subject to compressive stresses and under different boundary conditions. We find that the buckling of a rectangular membrane takes place continuously, while the buckling of a circular membrane can be discontinuous depending on the boundary conditions. Furthermore, our results show that the stress-strain relationship of a buckled circular membrane can be used to determine the Gaussian curvature modulus effectively.

Bio-membranes: Picosecond to second dynamics and plasticity as deciphered by solid state NMR

Since the first membrane models in the 1970s, the concept of biological membranes has evolved considerably. The membrane is now seen as a very complex mixture whose dynamic behavior is even more complex. Solid-state NMR is well suited for such studies as it can probe the movements of the membrane from picoseconds to seconds. Two NMR observables can be used: motionally averaged spectra and relaxation times. They bring information on order parameters, phase transitions, correlation times, activation energies and membrane elasticity. Spectra are used to determine the nature of the membrane phase. The order parameters can be measured directly from spectra that are dominated by quadrupolar, dipolar and chemical shielding magnetic interactions and allow describing the lipid membrane as being very rigid at the glycerol and chain level and very fluid at its center and surface. Correlation times and activation energies can be measured for intramolecular motions (pico to nanoseconds), molecular motions (nano to 100 ns) and collective modes of membrane deformation (microseconds). Sterols modulate membrane phases, order parameters, correlation times and membrane elasticity. In general terms, sterols tend to act to reduce the impact of environmental changes on molecular order and dynamics. They can be described as regulators of membrane dynamics by keeping them in a state of dynamics that changes very little when the temperature or other factors change. The presence of such large-scale membrane dynamics is proposed as a means of adapting to evolutionary constraints.

Determining the Bending Rigidity of Free-Standing Planar Phospholipid Bilayers

We describe a method to determine membrane bending rigidity from capacitance measurements on large area, free-standing, planar, biomembranes. The bending rigidity of lipid membranes is an important biological mechanical property that is commonly optically measured in vesicles, but difficult to quantify in a planar, unsupported system. To accomplish this, we simultaneously image and apply an electric potential to free-standing, millimeter area, planar lipid bilayers composed of DOPC and DOPG phospholipids to measure the membrane Young's (elasticity) modulus. The bilayer is then modeled as two adjacent thin elastic films to calculate bending rigidity from the electromechanical response of the membrane to the applied field. Using DOPC, we show that bending rigidities determined by this approach are in good agreement with the existing work using neutron spin echo on vesicles, atomic force spectroscopy on supported lipid bilayers, and micropipette aspiration of giant unilamellar vesicles. We study the effect of asymmetric calcium concentration on symmetric DOPC and DOPG membranes and quantify the resulting changes in bending rigidity. This platform offers the ability to create planar bilayers of controlled lipid composition and aqueous ionic environment, with the ability to asymmetrically alter both. We aim to leverage this high degree of compositional and environmental control, along with the capacity to measure physical properties, in the study of various biological processes in the future.

Postsynthetic Photocontrol of Giant Liposomes via Fusion-Based Photolipid Doping

We report on photolipid doping of giant unilamellar vesicles (GUVs) via vesicle fusion with small unilamellar photolipid vesicles (pSUVs), which enables retroactive optical control of the membrane properties. We observe that vesicle fusion is light-dependent, if the phospholipids are neutral. Charge-mediated fusion involving anionic and cationic lipid molecules augments the overall fusion performance and doping efficiency, even in the absence of light exposure. Using phosphatidylcholine analogs with one or two azobenzene photoswitches (azo-PC and dazo-PC) affects domain formation, bending stiffness, and shape of the resulting vesicles in response to irradiation. Moreover, we show that optical membrane control can be extended to long wavelengths using red-absorbing photolipids (red-azo-PC). Combined, our findings present an attractive and practical method for the precise delivery of photolipids, which offers new prospects for the optical control of membrane function.

Scale-invariance in miniature coarse-grained red blood cells by fluctuation analysis

To accurately represent the morphological and elastic properties of a human red blood cell, Fu et al. [Fu et al., Lennard-Jones type pair-potential method for coarse-grained lipid bilayer membrane simulations in LAMMPS, 2017, 210, 193-203] recently developed a coarse-grained molecular dynamics model with particular detail in the membrane. However, such a model accrues an extremely high computational cost for whole-cell simulation when assuming an appropriate length scaling - that of the bilayer thickness. To date, the model has only simulated "miniature" cells in order to circumvent this, with the a priori assumption that these miniaturised cells correctly represent their full-sized counterparts. The present work assesses the validity of this approach, by testing the scale invariance of the model through simulating cells of various diameters; first qualitatively in their shape evolution, then quantitatively by measuring their bending rigidity through fluctuation analysis. Cells of diameter of at least 0.5 μm were able to form the characteristic biconcave shape of human red blood cells, though smaller cells instead equilibrated to bowl-shaped stomatocytes. Thermal fluctuation analysis showed the bending rigidity to be constant over all cell sizes tested, and consistent between measurements on the whole-cell and on a planar section of bilayer. This is as expected from the theory on both counts. Therefore, we confirm that the evaluated model is a good representation of a full-size RBC when the model diameter is ≥0.5 μm, in terms of the morphological and mechanical properties investigated.

Optical Membrane Control with Red Light Enabled by Red-Shifted Photolipids

Photoswitchable phospholipids, or "photolipids", that harbor an azobenzene group in their lipid tails are versatile tools to manipulate and control lipid bilayer properties with light. So far, the limited ultraviolet-A/blue spectral range in which the photoisomerization of regular azobenzene operates has been a major obstacle for biophysical or photopharmaceutical applications. Here, we report on the synthesis of nano- and micrometer-sized liposomes from tetra-ortho-chloro azobenzene-substituted phosphatidylcholine (termed red-azo-PC) that undergoes photoisomerization on irradiation with tissue-penetrating red light (≥630 nm). Photoswitching strongly affects the fluidity and mechanical properties of lipid membranes, although small-angle X-ray scattering and dynamic light scattering measurements reveal only a minor influence on the overall bilayer thickness and area expansion. By controlling the photostationary state and the photoswitching efficiency of red-azo-PC for specific wavelengths, we demonstrate that shape transitions such as budding or pearling and the division of cell-sized vesicles can be achieved. These results emphasize the applicability of red-azo-PC as a nanophotonic tool in synthetic biology and for biomedical applications.

Surface Properties of Synaptosomes in the Presence of L-Glutamic and Kainic Acids: In Vitro Alteration of the ATPase and Acetylcholinesterase Activities

Morphologically and functionally identical to brain synapses, the nerve ending particles synaptosomes are biochemically derived membrane structures responsible for the transmission of neural information. Their surface and mechanical properties, measured in vitro, provide useful information about the functional activity of synapses in the brain in vivo. Glutamate and kainic acid are of particular interest because of their role in brain pathology (including causing seizure, migraine, ischemic stroke, aneurysmal subarachnoid hemorrhage, intracerebral hematoma, traumatic brain injury and stroke). The effects of the excitatory neurotransmitter L-glutamic acid and its agonist kainic acid are tested on Na⁺, K⁺-ATPase and Mg²⁺-ATPase activities in synaptic membranes prepared from the cerebral cortex of rat brain tissue. The surface parameters of synaptosome preparations from the cerebral cortex in the presence of L-glutamic and kainic acids are studied by microelectrophoresis for the first time. The studied neurotransmitters promote a significant increase in the electrophoretic mobility and surface electrical charge of synaptosomes at 1–4 h after isolation. The measured decrease in the bending modulus of model bimolecular membranes composed of monounsaturated lipid 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine provides evidence for softer membranes in the presence of L-glutamate. Kainic acid does not affect membrane mechanical stability even at ten-fold higher concentrations. Both the L-glutamic and kainic acids reduce acetylcholinesterase activity and deviation from the normal functions of neurotransmission in synapses is presumed. The presented results regarding the modulation of the enzyme activity of synaptic membranes and surface properties of synaptosomes are expected by biochemical and biophysical studies to contribute to the elucidation of the molecular mechanisms of neurotransmitters/agonists’ action on membranes.

Polymer-Lipid Hybrid Materials

Hierarchic self-assembly underpins much of the form and function seen in synthetic or biological soft materials. Lipids are paramount examples, building themselves in nature or synthetically in a variety of meso/nanostructures. Synthetic block copolymers capture many of lipid's structural and functional properties. Lipids are typically biocompatible and high molecular weight polymers are mechanically robust and chemically versatile. The development of new materials for applications like controlled drug/gene/protein delivery, biosensors, and artificial cells often requires the combination of lipids and polymers. The emergent composite material, a "polymer-lipid hybrid membrane", displays synergistic properties not seen in pure components. Specific examples include the observation that hybrid membranes undergo lateral phase separation that can correlate in registry across multiple layers into a three-dimensional phase-separated system with enhanced permeability of encapsulated drugs. It is timely to underpin these emergent properties in several categories of hybrid systems ranging from colloidal suspensions to supported hybrid films. In this review, we discuss the form and function of a vast number of polymer-lipid hybrid systems published to date. We rationalize the results to raise new fundamental understanding of hybrid self-assembling soft materials as well as to enable the design of new supramolecular systems and applications.

The membrane transporter lactose permease increases lipid bilayer bending rigidity

Cellular life relies on membranes, which provide a resilient and adaptive cell boundary. Many essential processes depend upon the ease with which the membrane is able to deform and bend, features that can be characterized by the bending rigidity. Quantitative investigations of such mechanical properties of biological membranes have primarily been undertaken in solely lipid bilayers and frequently in the absence of buffers. In contrast, much less is known about the influence of integral membrane proteins on bending rigidity under physiological conditions. We focus on an exemplar member of the ubiquitous major facilitator superfamily of transporters and assess the influence of lactose permease on the bending rigidity of lipid bilayers. Fluctuation analysis of giant unilamellar vesicles (GUVs) is a useful means to measure bending rigidity. We find that using a hydrogel substrate produces GUVs that are well suited to fluctuation analysis. Moreover, the hydrogel method is amenable to both physiological salt concentrations and anionic lipids, which are important to mimic key aspects of the native lactose permease membrane. Varying the fraction of the anionic lipid in the lipid mixture DOPC/DOPE/DOPG allows us to assess the dependence of membrane bending rigidity on the topology and concentration of an integral membrane protein in the lipid bilayer of GUVs. The bending rigidity gradually increases with the incorporation of lactose permease, but there is no further increase with greater amounts of the protein in the membrane.

Electromechanical characterization of biomimetic membranes using electrodeformation of vesicles

We describe a facile method to simultaneously measure the bending rigidity and capacitance of biomimetic lipid bilayers. Our approach utilizes the ellipsoidal deformation of quasi-spherical giant unilamellar vesicles induced by a uniform AC electric field. Vesicle shape depends on the electric field frequency and amplitude. Membrane bending rigidity can be obtained from the variation of the vesicle elongation on either field amplitude at fixed frequency or frequency at fixed field amplitude. Membrane capacitance is determined from the frequency at which the vesicle shape changes from prolate to oblate ellipsoid as the frequency is increased at a given field amplitude.

Identifying systematic errors in a power spectral analysis of simulated lipid membranes

The elastic properties of lipid membranes can be measured by monitoring their thermal fluctuations. For instance, comparing the power spectra of membrane shape or lipid director fluctuations with predictions based on suitable continuum theories gives access to bending-, tilt-, and twist-moduli. However, to do so in a computer simulation, we must first define a continuum surface shape and lipid director field from the discrete configurations of lipid molecules in a typically fairly small box. Here, we show that the required mapping choices, as well as the details of the subsequent data analysis, can shift the measured values of these moduli by far more than their statistical uncertainties. We investigate the resulting systematic errors on the basis of atomistic simulation trajectories for 13 different lipids, previously published by Venable et al. [Chem. Phys. Lipids 192, 60-74 (2015)]. Specifically, we examine mapping choices for surface- and tilt-field definitions, normalizing and averaging lipid directors, accounting for wave vector dependent time autocorrelations, error propagation, and finding the right fitting range. We propose a set of criteria that may help to decide upon a particular combination of choices underlying the fluctuation analysis, and we make several recommendations based on these. While systematic shifts in observables that are extracted from large-wavelength limits vanish, in principle, for sufficiently large system size, no such exact limit exists for intrinsically local parameters, such as the twist modulus or the splay-tilt coupling, and so not all potential choices can be trivially verified.

Dynamic Nuclear Structure Emerges from Chromatin Cross-Links and Motors

The cell nucleus houses the chromosomes, which are linked to a soft shell of lamin protein filaments. Experiments indicate that correlated chromosome dynamics and nuclear shape fluctuations arise from motor activity. To identify the physical mechanisms, we develop a model of an active, cross-linked Rouse chain bound to a polymeric shell. System-sized correlated motions occur but require both motor activity and cross-links. Contractile motors, in particular, enhance chromosome dynamics by driving anomalous density fluctuations. Nuclear shape fluctuations depend on motor strength, cross-linking, and chromosome-lamina binding. Therefore, complex chromosome dynamics and nuclear shape emerge from a minimal, active chromosome-lamina system.

The use of giant unilamellar vesicles to study functional properties of pore-forming toxins

Pore-forming toxins (PFTs) act upon lipid membranes and appropriate model systems are of great importance in researching these proteins. Giant unilamellar vesicles (GUVs) are an excellent model membrane system to study interactions between lipids and proteins. Their main advantage is the size comparable to cells, which means that GUVs can be observed directly under the light microscope. Many PFTs properties can be studied by using GUVs, such as binding specificity, membrane reorganization upon protein binding and oligomerization, pore properties and mechanism of pore formation. GUVs also represent a good model for biotechnological approaches, e.g., in applications in synthetic biology and medicine. Each research area has its own demands for GUVs properties, so several different approaches for GUVs preparations have been developed and will be discussed in this chapter.

Photolipid Bilayer Permeability is Controlled by Transient Pore Formation

Controlling the release or uptake of (bio-) molecules and drugs from liposomes is critically important for a range of applications in bioengineering, synthetic biology, and drug delivery. In this paper, we report how the reversible photoswitching of synthetic lipid bilayer membranes made from azobenzene-containing phosphatidylcholine (azo-PC) molecules (photolipids) leads to increased membrane permeability. We show that cell-sized, giant unilamellar vesicles (GUVs) prepared from photolipids display leakage of fluorescent dyes after irradiation with UV-A and visible light. Langmuir-Blodgett and patch-clamp measurements show that the permeability is the result of transient pore formation. By comparing the trans-to-cis and cis-to-trans isomerization process, we find that this pore formation is the result of area fluctuations and a change of the area cross-section between both photolipid isomers.

Wrapping of Microparticles by Floppy Lipid Vesicles

Lipid membranes, the barrier defining living cells and many of their subcompartments, bind to a wide variety of nano- and micrometer sized objects. In the presence of strong adhesive forces, membranes can strongly deform and wrap the particles, an essential step in crossing the membrane for a variety of healthy and disease-related processes. A large body of theoretical and numerical work has focused on identifying the physical properties that underly wrapping. Using a model system of micron-sized colloidal particles and giant unilamellar lipid vesicles with tunable adhesive forces, we measure a wrapping phase diagram and make quantitative comparisons to theoretical models. Our data are consistent with a model of membrane-particle interactions accounting for the adhesive energy per unit area, membrane bending rigidity, particle size, and vesicle radius.

Fluctuation spectroscopy of giant unilamellar vesicles using confocal and phase contrast microscopy

A widely used method to measure the bending rigidity of bilayer membranes is fluctuation spectroscopy, which analyses the thermally-driven membrane undulations of giant unilamellar vesicles recorded with either phase-contrast or confocal microscopy. Here, we analyze the fluctuations of the same vesicle using both techniques and obtain consistent values for the bending modulus. We discuss the factors that may lead to discrepancies.

Cellular Membranes, a Versatile Adaptive Composite Material

Cellular membranes belong to the most vital yet least understood biomaterials of live matter. For instance, its biomechanical requirements substantially vary across species and subcellular sites, raising the question how membranes manage to adjust to such dramatic changes. Central to its adaptability at the cell surface is the interplay between the plasma membrane and the adjacent cell cortex, forming an adaptive composite material that dynamically adjusts its mechanical properties. Using a hypothetical composite material, we identify core challenges, and discuss how cellular membranes solved these tasks. We further muse how pathological changes in material properties affect membrane mechanics and cell function, before closing with open questions and future challenges arising when studying cellular membranes.

The unprecedented membrane deformation of the human nuclear envelope, in a magnetic field, indicates formation of nuclear membrane invaginations

Human nuclear membrane (hNM) invaginations are thought to be crucial in fusion, fission and remodeling of cells and present in many human diseases. There is however little knowledge, if any, about their lipid composition and dynamics. We therefore isolated nuclear envelope lipids from human kidney cells, analyzed their composition and determined the membrane dynamics after resuspension in buffer. The hNM lipid extract was composed of a complex mixture of phospholipids, with high amounts of phosphatidylcholines, phosphatidylinositols (PI) and cholesterol. hNM dynamics was determined by solid-state NMR and revealed that the lamellar gel-to-fluid phase transition occurs below 0 °C, reflecting the presence of elevated amounts of unsaturated fatty acid chains. Fluidity was higher than the plasma membrane, illustrating the dual action of Cholesterol (ordering) and PI lipids (disordering). The most striking result was the large magnetic field-induced membrane deformation allowing to determine the membrane bending elasticity, a property related to hydrodynamics of cells and organelles. Human Nuclear Lipid Membranes were at least two orders of magnitude more elastic than the classical plasma membrane suggesting a physical explanation for the formation of nuclear membrane invaginations.

A consistent quadratic curvature-tilt theory for fluid lipid membranes

The tilt of a lipid molecule describes the deviation of its orientation away from the local normal of its embedding membrane. Tilt is the subleading degree of freedom after a membrane's geometry, and it becomes relevant at scales comparable to lipid bilayer thickness. Building on earlier work by Hamm and Kozlov [Eur. Phys. J. E 3, 323 (2000)], who envisioned lipid membranes as thin prestressed fluid elastic films, and Terzi and Deserno [J. Chem. Phys. 147, 084702 (2017)], who discovered a new coupling term between splay and tilt divergence, we construct a theory of membrane elasticity that is quadratic in geometry and tilt and complete at order 1/length². We show that a general and consistent treatment of both lateral and transverse depth-dependent shear stresses creates several contributions to the elastic energy density, of which only a subset had previously been identified. Apart from the well-known penalty of lipid twist (the curl of tilt), these terms generate no qualitatively new phenomenology, but they quantitatively revise the connections between the moduli of a tilt-curvature theory and its underlying microscopic foundation. In particular, we argue that the monolayer Gaussian curvature modulus κ¯_m, widely believed to be equal to the second moment of the transmonolayer stress profile, acquires a second contribution from lipid twist, which is always negative. This could resolve the long-standing conundrum that many measured values of κ¯_m appeared to have a sign that violates basic stability considerations. We also show that the previously discovered novel coupling between splay and tilt divergence is not simply proportional to κ¯_m but acquires its own splay-tilt coupling modulus, κ_st,m. We explore the predictions of our theory for various elastic moduli and their mutual interrelations and use an extensive set of existing atomistic molecular dynamics simulations for 12 different lipid types to collectively reason about such predictions. We find that bending rigidities are captured fairly well by existing theories, while reliable predictions for local moduli, especially the splay-tilt coupling modulus, remain challenging.

Membrane stretching elasticity and thermal shape fluctuations of nearly spherical lipid vesicles

One of the most widely used methods for determination of the bending elasticity modulus of model lipid membranes is the analysis of the shape fluctuations of nearly spherical lipid vesicles. The theoretical basis of this analysis is given by Milner and Safran [Phys. Rev. A 36, 4371 (1987)0556-279110.1103/PhysRevA.36.4371]. In their theory the stretching effects are not considered. In the present study we generalized their approach including the stretching effects deduced after application of the statistical mechanics to vesicles.

Elastic property of membranes self-assembled from diblock and triblock copolymers

The elastic property of membranes self-assembled from AB diblock and ABA triblock copolymers, as coarse-grained model of lipids and the bolalipids, are studied using the self-consistent field theory (SCFT). Specifically, solutions of the SCFT equations, corresponding to membranes in different geometries (planar, cylindrical, spherical, and pore) have been obtained for a model system composed of amphiphilic AB diblock copolymers and ABA triblock copolymers dissolved in A homopolymers. The free energy of the membranes with different geometries is then used to extract the bending modulus, Gaussian modulus, and line tension of the membranes. The results reveal that the bending modulus of the triblock membrane is greater than that of the diblock membrane. Furthermore, the Gaussian modulus and line tension of the triblock membrane indicate that the triblock membranes have higher pore formation energy than that of the diblock membranes. The equilibrium bridging and looping fractions of the triblock copolymers are also obtained. Implications of the theoretical results on the elastic properties of biologically equivalent lipid bilayers and the bolalipid membranes are discussed.

Rapid confocal imaging of vesicle-to-sponge phase droplet transition in dilute dispersions of the C10E3 surfactant

The lamellar-to-sponge phase transition of fluorescently labelled large unilamellar vesicles (LUVs) of the non-ionic surfactant triethylene glycol mono n-decyl ether (C₁₀E₃) was investigated in situ by confocal laser scanning microscopy (CLSM). Stable dispersions of micrometer-sized C₁₀E₃ LUVs were prepared at 20 °C and quickly heated at different temperatures close to the lamellar-to-sponge phase transition temperature. Phase transition of the strongly fluctuating individual vesicles into micrometre-sized sponge phase droplets was observed to occur via manyfold multilamellar morphologies with increasing membrane confinement through inter- and intra- lamellar fusion. The very low bending rigidity and lateral tension of the C₁₀E₃ bilayer were supported by quantitative image analysis of a stable fluctuating membrane using both flicker noise spectroscopy and spatial autocorrelation function.

A gradient-based, GPU-accelerated, high-precision contour-segmentation algorithm with application to cell membrane fluctuation spectroscopy

We present a novel intensity-gradient based algorithm specifically designed for nanometer-segmentation of cell membrane contours obtained with high-resolution optical microscopy combined with high-velocity digital imaging. The algorithm relies on the image oversampling performance and computational power of graphical processing units (GPUs). Both, synthetic and experimental data are used to quantify the sub-pixel precision of the algorithm, whose analytic performance results comparatively higher than in previous methods. Results from the synthetic data indicate that the spatial precision of the presented algorithm is only limited by the signal-to-noise ratio (SNR) of the contour image. We emphasize on the application of the new algorithm to membrane fluctuations (flickering) in eukaryotic cells, bacteria and giant vesicle models. The method shows promising applicability in several fields of cellular biology and medical imaging for nanometer-precise boundary-determination and mechanical fingerprinting of cellular membranes in optical microscopy images. Our implementation of this high-precision flicker spectroscopy contour tracking algorithm (HiPFSTA) is provided as open-source at www.github.com/michaelmell/hipfsta.

Novel tilt-curvature coupling in lipid membranes

On mesoscopic scales, lipid membranes are well described by continuum theories whose main ingredients are the curvature of a membrane's reference surface and the tilt of its lipid constituents. In particular, Hamm and Kozlov [Eur. Phys. J. E 3, 323 (2000)] have shown how to systematically derive such a tilt-curvature Hamiltonian based on the elementary assumption of a thin fluid elastic sheet experiencing internal lateral pre-stress. Performing a dimensional reduction, they not only derive the basic form of the effective surface Hamiltonian but also express its emergent elastic couplings as trans-membrane moments of lower-level material parameters. In the present paper, we argue, though, that their derivation unfortunately missed a coupling term between curvature and tilt. This term arises because, as one moves along the membrane, the curvature-induced change of transverse distances contributes to the area strain-an effect that was believed to be small but nevertheless ends up contributing at the same (quadratic) order as all other terms in their Hamiltonian. We illustrate the consequences of this amendment by deriving the monolayer and bilayer Euler-Lagrange equations for the tilt, as well as the power spectra of shape, tilt, and director fluctuations. A particularly curious aspect of our new term is that its associated coupling constant is the second moment of the lipid monolayer's lateral stress profile-which within this framework is equal to the monolayer Gaussian curvature modulus, κ¯_m. On the one hand, this implies that many theoretical predictions now contain a parameter that is poorly known (because the Gauss-Bonnet theorem limits access to the integrated Gaussian curvature); on the other hand, the appearance of κ¯_m outside of its Gaussian curvature provenance opens opportunities for measuring it by more conventional means, for instance by monitoring a membrane's undulation spectrum at short scales.

Statistical Analysis of Bending Rigidity Coefficient Determined Using Fluorescence-Based Flicker-Noise Spectroscopy

Bending rigidity coefficient describes propensity of a lipid bilayer to deform. In order to measure the parameter experimentally using flickering noise spectroscopy, the microscopic imaging is required, which necessitates the application of giant unilamellar vesicles (GUV) lipid bilayer model. The major difficulty associated with the application of the model is the statistical character of GUV population with respect to their size and the homogeneity of lipid bilayer composition, if a mixture of lipids is used. In the paper, the bending rigidity coefficient was measured using the fluorescence-enhanced flicker-noise spectroscopy. In the paper, the bending rigidity coefficient was determined for large populations of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine and 1,2-dioleoyl-sn-glycero-3-phosphocholine vesicles. The quantity of obtained experimental data allows to perform statistical analysis aiming at the identification of the distribution, which is the most appropriate for the calculation of the value of the membrane bending rigidity coefficient. It has been demonstrated that the bending rigidity coefficient is characterized by an asymmetrical distribution, which is well approximated with the gamma distribution. Since there are no biophysical reasons for that we propose to use the difference between normal and gamma fits as a measure of the homogeneity of vesicle population. In addition, the effect of a fluorescent label and types of instrumental setups on determined values has been tested. Obtained results show that the value of the bending rigidity coefficient does not depend on the type of a fluorescent label nor on the type of microscope used.

Determination of bending rigidity and tilt modulus of lipid membranes from real-space fluctuation analysis of molecular dynamics simulations

We have recently developed a novel computational methodology (termed RSF for Real-Space Fluctuations) to quantify the bending rigidity and tilt modulus of lipid membranes from real-space analysis of fluctuations in the tilt and splay degrees of freedom as sampled in molecular dynamics (MD) simulations. In this article, we present a comprehensive study that combines results from the application of the RSF method to a wide range of lipid bilayer systems that encompass membranes of different fluidities and sizes, including lipids with saturated and unsaturated lipid tails, single and multi-component lipid systems, as well as non-standard lipids such as the four-tailed cardiolipin. By comparing the material properties calculated with the RSF method to those obtained from experimental data and from other computational methodologies, we rigorously demonstrate the validity of our approach and show its robustness. This should allow for future applications of even more complex lipidic assemblies, whose material properties are not tractable by other computational techniques. In addition, we discuss the relationship between different definitions of the tilt modulus appearing in current literature to address some important unresolved discrepancies in the 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.

Permeability modes in fluctuating lipid membranes with DNA-translocating pores

Membrane pores can significantly alter not only the permeation dynamics of biological membranes but also their elasticity. Large membrane pores able to transport macromolecular contents represent an interesting model to test theoretical predictions that assign active-like (non-equilibrium) behavior to the permeability contributions to the enhanced membrane fluctuations existing in permeable membranes [Maneville et al. Phys. Rev. Lett. 82, 4356 (1999)]. Such high-amplitude active contributions arise from the forced transport of solvent and solutes through the open pores, which becomes even dominant at large permeability. In this paper, we present a detailed experimental analysis of the active shape fluctuations that appear in highly permeable lipid vesicles with large macromolecular pores inserted in the lipid membrane, which are a consequence of transport permeability events occurred in an osmotic gradient. The experimental results are found in quantitative agreement with theory, showing a remarkable dependence with the density of membrane pores and giving account of mechanical compliances and permeability rates that are compatible with the large size of the membrane pore considered. The presence of individual permeation events has been detected in the fluctuation time-series, from which a stochastic distribution of the permeation events compatible with a shot-noise has been deduced. The non-equilibrium character of the membrane fluctuations in a permeation field, even if the membrane pores are mere passive transporters, is clearly demonstrated. Finally, a bio-nano-technology outlook of the proposed synthetic concept is given on the context of prospective uses as active membrane DNA-pores exploitable in gen-delivery applications based on lipid vesicles.

Determining the Gaussian Modulus and Edge Properties of 2D Materials: From Graphene to Lipid Bilayers

The dominant deformation behavior of two-dimensional materials (bending) is primarily governed by just two parameters: bending rigidity and the Gaussian modulus. These properties also set the energy scale for various important physical and biological processes such as pore formation, cell fission and generally, any event accompanied by a topological change. Unlike the bending rigidity, the Gaussian modulus is, however, notoriously difficult to evaluate via either experiments or atomistic simulations. In this Letter, recognizing that the Gaussian modulus and edge tension play a nontrivial role in the fluctuations of a 2D material edge, we derive closed-form expressions for edge fluctuations. Combined with atomistic simulations, we use the developed approach to extract the Gaussian modulus and edge tension at finite temperatures for both graphene and various types of lipid bilayers. Our results possibly provide the first reliable estimate of this elusive property at finite temperatures and appear to suggest that earlier estimates must be revised. In particular, we show that, if previously estimated properties are employed, the graphene-free edge will exhibit unstable behavior at room temperature. Remarkably, in the case of graphene, we show that the Gaussian modulus and edge tension even change sign at finite temperatures.

Clathrin polymerization exhibits high mechano-geometric sensitivity

How tension modulates cellular transport has become a topic of interest in the recent past. However, the effect of tension on clathrin assembly and vesicle growth remains less understood. Here, we use the classical Helfrich theory to predict the energetic cost that clathrin is required to pay to remodel the membrane at different stages of vesicle formation. Our study reveals that this energetic cost is highly sensitive to not only the tension in the membrane but also to the instantaneous geometry of the membrane during shape evolution. Our study predicts a sharp reduction in clathrin coat size in the intermediate tension regime (0.01-0.1 mN m-1). Remarkably, the natural propensity of the membrane to undergo bending beyond the Ω shape causes a significant decrease in the energy needed from clathrin to drive vesicle growth. Our studies in mammalian cells confirm a reduction in clathrin coat size in an increased tension environment. In addition, our findings suggest that the two apparently distinct clathrin assembly modes, namely coated pits and coated plaques, observed in experimental investigations might be a consequence of varied tensions in the plasma membrane. Overall, the mechano-geometric sensitivity revealed in this study might also be at play during the polymerization of other membrane remodeling proteins.

Increased Binding of Calcium Ions at Positively Curved Phospholipid Membranes

Calcium ion is the ubiquitous messenger in cells and plays a key role in neuronal signaling and fusion of synaptic vesicles. These vesicles are typically ∼20-50 nm in diameter, and thus their interaction with calcium ions cannot be modeled faithfully with a conventional flat membrane bilayer setup. Within our newly developed molecular dynamics simulations setup, we characterize here interactions of the calcium ion with curved membrane interfaces with atomistic detail. The present molecular dynamics simulations together with time-dependent fluorescence shift experiments suggest that the mode and strength of interaction of calcium ion with a phospholipid bilayer depends on its curvature. Potential of mean force calculations demonstrate that the binding of calcium ion to the positively curved side of the bilayer is significantly stronger compared with that to a flat membrane.

Relaxation dynamics of a compressible bilayer vesicle containing highly viscous fluid

We study the relaxation dynamics of a compressible bilayer vesicle with an asymmetry in the viscosity of the inner and outer fluid medium. First we explore the stability of the vesicle free energy which includes a coupling between the membrane curvature and the local density difference between the two monolayers. Two types of instabilities are identified: a small wavelength instability and a larger wavelength instability. Considering the bulk fluid viscosity and the inter-monolayer friction as the dissipation sources, we next employ Onsager's variational principle to derive the coupled equations both for the membrane and the bulk fluid. The three relaxation modes are coupled to each other due to the bilayer and the spherical structure of the vesicle. Most importantly, a higher fluid viscosity inside the vesicle shifts the crossover mode between the bending and the slipping to a larger value. As the vesicle parameters approach the unstable regions, the relaxation dynamics is dramatically slowed down, and the corresponding mode structure changes significantly. In some limiting cases, our general result reduces to the previously obtained relaxation rates.

Cell-sized liposome doublets reveal active tension build-up driven by acto-myosin dynamics

Cells modulate their shape to fulfill specific functions, mediated by the cell cortex, a thin actin shell bound to the plasma membrane. Myosin motor activity, together with actin dynamics, contributes to cortical tension. Here, we examine the individual contributions of actin polymerization and myosin activity to tension increase with a non-invasive method. Cell-sized liposome doublets are covered with either a stabilized actin cortex of preformed actin filaments, or a dynamic branched actin network polymerizing at the membrane. The addition of myosin II minifilaments in both cases triggers a change in doublet shape that is unambiguously related to a tension increase. Preformed actin filaments allow us to evaluate the effect of myosin alone while, with dynamic actin cortices, we examine the synergy of actin polymerization and myosin motors in driving shape changes. Our assay paves the way for a quantification of tension changes triggered by various actin-associated proteins in a cell-sized system.

Membrane remodeling and mechanics: Experiments and simulations of α-Synuclein

We review experimental and simulation approaches that have been used to determine curvature generation and remodeling of lipid bilayers by membrane-bending proteins. Particular emphasis is placed on the complementary approaches used to study α-Synuclein (αSyn), a major protein involved in Parkinson's disease (PD). Recent cellular and biophysical experiments have shown that the protein 1) deforms the native structure of mitochondrial and model membranes; and 2) inhibits vesicular fusion. Today's advanced experimental and computational technology has made it possible to quantify these protein-induced changes in membrane shape and material properties. Collectively, experiments, theory and multi-scale simulation techniques have established the key physical determinants of membrane remodeling and rigidity: protein binding energy, protein partition depth, protein density, and membrane tension. Despite the exciting and significant progress made in recent years in these areas, challenges remain in connecting biophysical insights to the cellular processes that lead to disease. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Nanometric thermal fluctuations of weakly confined biomembranes measured with microsecond time-resolution

We probe the bending fluctuations of bio-membranes using highly deflated giant unilamellar vesicles (GUVs) bound to a substrate by a weak potential arising from generic interactions. The substrate is either homogeneous, with GUVs bound only by the weak potential, or is chemically functionalized with a micro-pattern of very strong specific binders. In both cases, the weakly adhered membrane is seen to be confined at a well-defined distance above the surface while it continues to fluctuate strongly. We quantify the fluctuations of the weakly confined membrane at the substrate proximal surface as well as of the free membrane at the distal surface of the same GUV. This strategy enables us to probe in detail the damping of fluctuations in the presence of the substrate, and to independently measure the membrane tension and the strength of the generic interaction potential. Measurements were done using two complementary techniques - dynamic optical displacement spectroscopy (DODS, resolution: 20 nm, 10 μs), and dual wavelength reflection interference contrast microscopy (DW-RICM, resolution: 4 nm, 50 ms). After accounting for the spatio-temporal resolution of the techniques, an excellent agreement between the two measurements was obtained. For both weakly confined systems we explore in detail the link between fluctuations on the one hand and membrane tension and the interaction potential on the other hand.

Experimental observation of the asymmetric instability of intermediate-reduced-volume vesicles in extensional flow

Vesicles provide an attractive model system to understand the deformation of living cells in response to mechanical forces. These simple, enclosed lipid bilayer membranes are suitable for complementary theoretical, numerical, and experimental analysis. A recent study [Narsimhan, Spann, Shaqfeh, J. Fluid Mech., 2014, 750, 144] predicted that intermediate-aspect-ratio vesicles extend asymmetrically in extensional flow. Upon infinitesimal perturbation to the vesicle shape, the vesicle stretches into an asymmetric dumbbell with a cylindrical thread separating the two ends. While the symmetric stretching of high-aspect-ratio vesicles in extensional flow has been observed and characterized [Kantsler, Segre, Steinberg, Phys. Rev. Lett., 2008, 101, 048101] as well as recapitulated in numerical simulations by Narsimhan et al., experimental observation of the asymmetric stretching has not been reported. In this work, we present results from microfluidic cross-slot experiments observing this instability, along with careful characterization of the flow field, vesicle shape, and vesicle bending modulus. The onset of this shape transition depends on two non-dimensional parameters: reduced volume (a measure of vesicle asphericity) and capillary number (ratio of viscous to bending forces). We observed that every intermediate-reduced-volume vesicle that extends forms a dumbbell shape that is indeed asymmetric. For the subset of the intermediate-reduced-volume regime we could capture experimentally, we present an experimental phase diagram for asymmetric vesicle stretching that is consistent with the predictions of Narsimhan et al.

Direct Cytoskeleton Forces Cause Membrane Softening in Red Blood Cells

Erythrocytes are flexible cells specialized in the systemic transport of oxygen in vertebrates. This physiological function is connected to their outstanding ability to deform in passing through narrow capillaries. In recent years, there has been an influx of experimental evidence of enhanced cell-shape fluctuations related to metabolically driven activity of the erythroid membrane skeleton. However, no direct observation of the active cytoskeleton forces has yet been reported to our knowledge. Here, we show experimental evidence of the presence of temporally correlated forces superposed over the thermal fluctuations of the erythrocyte membrane. These forces are ATP-dependent and drive enhanced flickering motions in human erythrocytes. Theoretical analyses provide support for a direct force exerted on the membrane by the cytoskeleton nodes as pulses of well-defined average duration. In addition, such metabolically regulated active forces cause global membrane softening, a mechanical attribute related to the functional erythroid deformability.

The Combined Effect of Hydrophobic Mismatch and Bilayer Local Bending on the Regulation of Mechanosensitive Ion Channels

The hydrophobic mismatch between the lipid bilayer and integral membrane proteins has well-defined effect on mechanosensitive (MS) ion channels. Also, membrane local bending is suggested to modulate MS channel activity. Although a number of studies have already shown the significance of each individual factor, the combined effect of these physical factors on MS channel activity have not been investigated. Here using finite element simulation, we study the combined effect of hydrophobic mismatch and local bending on the archetypal mechanosensitive channel MscL. First we show how the local curvature direction impacts on MS channel modulation. In the case of MscL, we show inward (cytoplasmic) bending can more effectively gate the channel compared to outward bending. Then we indicate that in response to a specific local curvature, MscL inserted in a bilayer with the same hydrophobic length is more expanded in the constriction pore region compared to when there is a protein-lipid hydrophobic mismatch. Interestingly in the presence of a negative mismatch (thicker lipids), MscL constriction pore is more expanded than in the presence of positive mismatch (thinner lipids) in response to an identical membrane curvature. These results were confirmed by a parametric energetic calculation provided for MscL gating. These findings have several biophysical consequences for understanding the function of MS channels in response to two major physical stimuli in mechanobiology, namely hydrophobic mismatch and local membrane curvature.

Thermal fluctuations of vesicles and nonlinear curvature elasticity--implications for size-dependent renormalized bending rigidity and vesicle size distribution

Both closed and open biological membranes noticeably undulate at physiological temperatures. These thermal fluctuations influence a broad range of biophysical phenomena, ranging from self-assembly to adhesion. In particular, the experimentally measured thermal fluctuation spectra also provide a facile route to the assessment of mechanical and certain other physical properties of biological membranes. The theoretical assessment of thermal fluctuations, be it for closed vesicles or the simpler case of flat open lipid bilayers, is predicated upon assuming that the elastic curvature energy is a quadratic functional of the curvature tensor. However, a qualitatively correct description of several phenomena such as binding-unbinding transition, vesicle-to-bicelle transition, appearance of hats and saddles among others, appears to require consideration of constitutively nonlinear elasticity that includes fourth order curvature contributions rather than just quadratic. In particular, such nonlinear considerations are relevant in the context of large-curvature or small-sized vesicles. In this work we discuss the statistical mechanics of closed membranes (vesicles) incorporating both constitutive and geometrical nonlinearities. We derive results for the renormalized bending rigidity of small vesicles and show that significant stiffening may occur for sub-20 nm vesicle sizes. Our closed-form results may also be used to determine nonlinear curvature elasticity properties from either experimentally measured fluctuation spectra or microscopic calculations such as molecular dynamics. Finally, in the context of our results on thermal fluctuations of vesicles and nonlinear curvature elasticity, we reexamine the problem of determining the size distribution of vesicles and obtain results that reconcile well with experimental observations. However, our results are somewhat paradoxical. Specifically, the molecular dynamics predictions for the thermo-mechanical behavior of small vesicles of prior studies appear to be inconsistent with the nonlinear elastic properties that we estimate by fitting to the experimentally determined vesicle size-distribution trends and data.

Phospholipase A2-Induced Remodeling Processes on Liquid-Ordered/Liquid-Disordered Membranes Containing Docosahexaenoic or Oleic Acid: A Comparison Study

Vesicle cycling, which is an important biological event, involves the interplay between membrane lipids and proteins, among which the enzyme phospholipase A2 (PLA2) plays a critical role. The capacity of PLA2 to trigger the budding and fission of liquid-ordered (L(o)) domains has been examined in palmitoyl-docosahexaenoylphosphatidylcholine (PDPC) and palmitoyl-oleoylphosphatidylcholine (POPC)/sphingomyelin/cholesterol membranes. They both exhibited a L(o)/liquid-disordered (L(d)) phase separation. We demonstrated that PLA2 was able to trigger budding in PDPC-containing vesicles but not POPC ones. The enzymatic activity, line tension, and elasticity of the membrane surrounding the L(o) domains are critical for budding. The higher line tension of Lo domains in PDPC mixtures was assigned to the greater difference in order parameters of the coexisting phases. The higher amount of lysophosphatidylcholine generated by PLA2 in the PDPC-containing mixtures led to a less-rigid membrane, compared to POPC. The more elastic L(d) membranes in PDPC mixtures exert a lower counteracting force against the L(o) domain bending.

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 200-500 mM 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.