Membrane Bending Rigidity Research Articles

A review on the measurement of the bending rigidity of lipid membranes.

This review provides an overview of the latest developments in both experimental and simulation techniques used to assess the bending rigidity of lipid membranes. It places special emphasis on experimental methods that utilize model vesicles to manipulate lipid compositions and other experimental parameters to determine the bending rigidity of the membrane. It also describes two commonly used simulation methods for estimating bending rigidity. The impact of various factors on membrane bending rigidity is summarized, including cholesterol, lipids, salt concentration, surface charge, membrane phase state, peptides, proteins, and polyethylene glycol. These factors are shown to influence the bending rigidity, contributing to a better understanding of the biophysical properties of membranes and their role in biological processes. Furthermore, the review discusses future directions and potential advancements in this research field, highlighting areas where further investigation is required.

Simulation study of membrane bending by protein crowding: a case study with the epsin N-terminal homology domain.

The mechanisms by which peripheral membrane proteins generate curvature is currently an active area of research. One of the proposed mechanisms is amphipathic insertion or the 'wedge' mechanism in which the protein shallowly inserts an amphipathic helix inside the membrane to drive the curvature. However, recent experimental studies have challenged the efficiency of the 'wedge' mechanism as it requires unusual protein densities. These studies proposed an alternative mechanism, namely 'protein-crowding', in which the lateral pressure generated by the random collisions among the membrane bound proteins drives the bending. In this study, we employ atomistic and coarse-grained molecular dynamics simulations to investigate the effects of amphipathic insertion and protein crowding on the membrane surface. Considering epsin N-terminal homology (ENTH) domain as a model protein, we show that amphipathic insertion is not essential for membrane bending. Our results suggest that ENTH domains can aggregate on the membrane surface by employing another structured region (H3 helix). And this protein crowding decreases the cohesive energy of the lipid tails which causes a significant decrease in the membrane bending rigidity. The ENTH domain can generate a similar degree of membrane curvature irrespective of the activity of its H0 helix. Our results are consistent with the recent experimental results.

Investigating the cut-off effect of n-alcohols on lipid movement: a biophysical study.

Cellular membranes are responsible for absorbing the effects of external perturbants for the cell's survival. Such perturbants include small ubiquitous molecules like n-alcohols which were observed to exhibit anesthetic capabilities, with this effect tapering off at a cut-off alcohol chain length. To explain this cut-off effect and complement prior biochemical studies, we investigated a series of n-alcohols (with carbon lengths 2-18) and their impact on several bilayer properties, including lipid flip-flop, intervesicular exchange, diffusion, membrane bending rigidity and more. To this end, we employed an array of biophysical techniques such as time-resolved small angle neutron scattering (TR-SANS), small angle X-ray scattering (SAXS), all atomistic and coarse-grained molecular dynamics (MD) simulations, and calcein leakage assays. At an alcohol concentration of 30 mol% of the overall lipid content, TR-SANS showed 1-hexanol (C6OH) increased transverse lipid diffusion, i.e. flip-flop. As alcohol chain length increased from C6 to C10 and longer, lipid flip-flop slowed by factors of 5.6 to 32.2. Intervesicular lipid exchange contrasted these results with only a slight cut-off at alcohol concentrations of 30 mol% but not 10 mol%. SAXS, MD simulations, and leakage assays revealed changes to key bilayer properties, such as bilayer thickness and fluidity, that correlate well with the effects on lipid flip-flop rates. Finally, we tie our results to a defect-mediated pathway for alcohol-induced lipid flip-flop.

Unraveling How Cholesterol Affects Multivalency-Induced Membrane Deformation of Sub-100 nm Lipid Vesicles.

Cholesterol plays a critical role in modulating the lipid membrane properties of biological and biomimetic systems and recent attention has focused on its role in the functions of sub-100 nm lipid vesicles and lipid nanoparticles. These functions often rely on multivalent ligand-receptor interactions involving membrane attachment and dynamic shape transformations while the extent to which cholesterol can influence such interaction processes is largely unknown. To address this question, herein, we investigated the attachment of sub-100 nm lipid vesicles containing varying cholesterol fractions (0-45 mol %) to membrane-mimicking supported lipid bilayer (SLB) platforms. Biotinylated lipids and streptavidin proteins were used as model ligands and receptors, respectively, while the localized surface plasmon resonance sensing technique was employed to track vesicle attachment kinetics in combination with analytical modeling of vesicle shape changes. Across various conditions mimicking low and high multivalency, our findings revealed that cholesterol-containing vesicles could bind to receptor-functionalized membranes but underwent appreciably less multivalency-induced shape deformation than vesicles without cholesterol, which can be explained by a cholesterol-mediated increase in membrane bending rigidity. Interestingly, the extent of vesicle deformation that occurred in response to increasingly strong multivalent interactions was less pronounced for vesicles with greater cholesterol fraction. The latter trend was rationalized by taking into account the strong dependence of the membrane bending energy on the area of the vesicle-SLB contact region and such insights can aid the engineering of membrane-enveloped nanoparticles with tailored biophysical properties.

Indentation of pore-spanning lipid membranes: Spring-stiffening or -softening responses and apparent stiffness prediction

Atomic force microscopy (AFM)-based nanoindentation has emerged as a key nanomechanical mapping method to probe mechanical properties of two-dimensional engineering and biological materials. In comparison with extensive analytical studies on the indentation of freestanding solid thin films, surprisingly little attention has been drawn on analytical predictions of mechanical responses of freestanding lipid membranes to indentation in the framework of Helfrich membrane theory. Here we perform systematic theoretical studies with formulated analysis on indentation of nanopore-spanning lipid membranes. Two types of lipid membranes are considered. One is the membrane subject to uniform area stretching and the membrane is found to exhibit a spring-stiffening behavior during indentation, while the other is the membrane of constant tension and a spring-softening behavior at intermediate indentation is exhibited. The smaller the membrane tension is, the clearer the spring-softening feature is. For both types of membranes, analytical solutions of load–depth relationship at small indentation and apparent membrane stiffnesses are obtained at small and large tension. For the stretched lipid membranes, a cubic nonlinearity arising from membrane stretching is specified. Roles of membrane bending rigidity, (pre-)tension, or area compression modulus, and indenter size in membrane indentation are elucidated. Moreover, pressure of contact between the membrane and indenter and a line load of contact acting along the contact edge are obtained based on the shell theory. Our results provide fundamental insights on nonlinear mechanical behaviors of the lipid membrane indentation.

Cholesterol Stiffening of Lipid Membranes.

Biomembrane order, dynamics, and other essential physicochemical parameters are controlled by cholesterol, a major component of mammalian cell membranes. Although cholesterol is well known to exhibit a condensing effect on fluid lipid membranes, the extent of stiffening that occurs with different degrees of lipid acyl chain unsaturation remains an enigma. In this review, we show that cholesterol locally increases the bending rigidity of both unsaturated and saturated lipid membranes, suggesting there may be a length-scale dependence of the bending modulus. We review our published data that address the origin of the mechanical effects of cholesterol on unsaturated and polyunsaturated lipid membranes and their role in biomembrane functions. Through a combination of solid-state deuterium NMR spectroscopy and neutron spin-echo spectroscopy, we show that changes in molecular packing cause the universal effects of cholesterol on the membrane bending rigidity. Our findings have broad implications for the role of cholesterol in lipid–protein interactions as well as raft-like mixtures, drug delivery applications, and the effects of antimicrobial peptides on lipid membranes.Graphical

The bending rigidity of the red blood cell cytoplasmic membrane.

An important mechanical property of cells is the membrane bending modulus, κ. In the case of red blood cells (RBCs) there is a composite membrane consisting of a cytoplasmic membrane and an underlying spectrin network. Literature values of κ are puzzling, as they are reported over a wide range, from 5 kBT to 230 kBT. To disentangle the contribution of the cytoplasmic membrane from the spectrin network, we investigated the bending of red blood cell cytoplasmic membranes (RBCcm) in the absence of spectrin and adenosine triphosphate (ATP). We used a combination of X-ray diffuse scattering (XDS), neutron spin-echo (NSE) spectrometry and Molecular Dynamics (MD) simulations. Our results indicate values of κ of order 4 kBT to 6 kBT, relatively small compared to literature values for most single component lipid bilayers. We suggest two ways this relative softness might confer biological advantage.

Peptide-Based Coacervate-Core Vesicles with Semipermeable Membranes.

Coacervates droplets have long been considered as potential protocells to mimic living cells. However, these droplets lack a membrane and are prone to coalescence, limiting their ability to survive, interact, and organize into higher-order assemblies. This work shows that tyrosine-rich peptide conjugates can undergo liquid-liquid phase separation in a well-defined pH window and transform into stable membrane-enclosed protocells by enzymatic oxidation and cross-linking at the liquid-liquid interface. The oxidation of the tyrosine-rich peptides into dityrosine creates a semipermeable, flexible membrane around the coacervates with tunable thickness, which displays strong intrinsic fluorescence, and stabilizes the coacervate protocells against coalescence. The membranes have an effective molecular weight cut-off of 2.5kDa, as determined from the partitioning of small dyes and labeled peptides, RNA, and polymers into the membrane-enclosed coacervate protocells. Flicker spectroscopy reveals a membrane bending rigidity of only 0.1kB T, which is substantially lower than phospholipid bilayers despite a larger membrane thickness. Finally, it is shown that enzymes can be stably encapsulated inside the protocells and be supplied with substrates from outside, which opens the way for these membrane-bound compartments to be used as molecularly crowded artificial cells capable of communication or as a vehicle for drug delivery.

Translocation kinetics of vesicles through narrow pores

We use extensive Molecular Dynamics (MD) simulations to study the osmotically induced translocation of partially filled vesicles through narrow pores. The dependence of the average translocation time, , on vesicle size M, pore radius R p , and strength of the driving force, , is examined for vesicles in a broad interval of sizes M. The time is found to grow with decreasing pore size by an universal scaling law, , where denotes the critical pore radius when the vesicle gets stuck in the pore. With regard to applied pressure, P, we find a power law relationship, , where with P cr being the least pressure that can still drive the vesicle through a pore of size R p . The exponent ω varies with R p and tends to unity as the pore size narrows, . In addition, is found to attain a minimum for an optimal value of the membrane bending rigidity. The variation of vesicle shape, surface area, volume and translocated fraction of the vesicle with time elapsed since the onset of the process is shown to change qualitatively with varying pore size.

Formation of Oxidation- and Acid-Sensitive Assemblies from Sterols and a Quaternary Ammonium Ferrocene Derivative: Quatsome- and Onion-like Vesicles and Extended Nanoribbons.

Quatsomes are a class of nonphospholipid vesicles in which bilayers are formed from mixtures of quaternary ammonium (QA) amphiphiles and sterols. We describe the formation of oxidation and acid-sensitive quatsome-like vesicles and other bilayer assemblies from mixtures of a ferrocenylated QA amphiphile (FTDMA) and several cholesterol derivatives. The influence of the sterol and the preparation method (extrusion or probe sonication) on the stability and morphology of the resulting vesicles is explored; a variety of structures can be obtained from small (ca. 30 nm) spherical unilamellar and oligolamellar quatsome-like vesicles to large (ca. 200 nm) multilamellar onion-like vesicles to extended nanoribbons many micrometers long. FTDMA-sterol vesicles undergo drastic shifts in vesicle and membrane structure when treated with a chemical oxidant (Frémy's salt), a feature previously observed in liposomes containing FTDMA and now confirmed in nonphospholipid vesicles. Size distributions of spherical quatsome-like vesicles obtained from cryo-TEM are examined to estimate the membrane bending rigidity, and a hypothesis is presented to explain the underlying mechanism of the profound membrane alterations observed as a consequence of ferrocene oxidation.

Probing lipid membrane bending mechanics using gold nanorod tracking.

Lipid bilayer membranes undergo rapid bending undulations with wavelengths from tens of nanometers to tens of microns due to thermal fluctuations. Here, we probe such undulations and the membranes’ mechanics by measuring the time-varying orientation of single gold nanorods (GNRs) adhered to the membrane, using high-speed dark field microscopy. In a lipid vesicle, such measurements allow the determination of the membrane’s viscosity, bending rigidity, and tension as well as the friction coefficient for sliding of the monolayers over one another. The in-plane rotation of the GNR is hindered by undulations in a tension dependent manner, consistent with simulations. The motion of single GNRs adhered to the plasma membrane of living cultured cells similarly reveals the membrane’s complex physics and coupling to the cell’s actomyosin cortex.

VV-hemorphin-5 association to lipid bilayers and alterations of membrane bending rigidity

<abstract> <p>The morphinomimetic properties of hemorphins are intensively studied with regard to new peptide drug developments. In this respect, the investigation of mechanical properties and stability of lipid membranes provides a useful background for advancement in pharmacological applications of liposomes. Here we probed the effect of the endogenous heptapeptide VV-hemorphin-5 (valorphin) on the bending elasticity of biomimetic lipid membranes of 1-palmitoyl-2-oleoyl-<italic>sn</italic>-glycero-3-phosphocholine (POPC) by analysis of thermal shape fluctuations of nearly spherical giant unilamellar vesicles. In a wide concentration range covering valorphin concentrations applied in nociceptive screening <italic>in vivo</italic>, we report alterations of the bilayer bending rigidity in a concentration-dependent non-monotonic manner. We performed quantitative characterization of VV-hemorphin-5 association to POPC membranes by isothermal titration calorimetry in order to shed light on the partitioning of the amphiphilic hemorphin between the aqueous solution and membranes. The calorimetric results correlate with flicker spectroscopy findings and support the hypothesis about the strength of valorphin-membrane interaction related to the peptide bulk concentration. A higher strength of valorphin interaction with the bilayer corresponds to a more pronounced effect of the peptide on the membrane's mechanical properties. The presented study features the comprehensive analysis of membrane bending elasticity as a biomarker for physicochemical effects of peptides on lipid bilayers. The reported data on thermodynamic parameters of valorphin interactions with phosphatidylcholine bilayers and alterations of their mechanical properties is expected to be useful for applications of lipid membrane systems in pharmacology and biomedicine.</p> </abstract>

Effect of encapsulated protein on the dynamics of lipid sponge phase: a neutron spin echo and molecular dynamics simulation study.

Lipid membranes are highly mobile systems with hierarchical, time and length scale dependent, collective motions including thickness fluctuations, undulations, and topological membrane changes, which play an important role in membrane interactions. In this work we have characterised the effect of encapsulating two industrially important enzymes, β-galactosidase and aspartic protease, in lipid sponge phase nanoparticles on the dynamics of the lipid membrane using neutron spin echo (NSE) spectroscopy and molecular dynamics (MD) simulations. From NSE, reduced membrane dynamics were observed upon enzyme encapsulation, which were dependent on the enzyme concentration and type. By fitting the intermediate scattering functions (ISFs) with a modified Zilman and Granek model including nanoparticle diffusion, an increase in membrane bending rigidity was observed, with a larger effect for β-galactosidase than aspartic protease at the same concentration. MD simulations for the system with and without aspartic protease showed that the lipids relax more slowly in the system with protein due to the replacement of the lipid carbonyl-water hydrogen bonds with lipid-protein hydrogen bonds. This indicates that the most likely cause of the increase in membrane rigidity observed in the NSE measurements was dehydration of the lipid head groups. The dynamics of the protein itself were also studied, which showed a stable secondary structure of protein over the simulation, indicating no unfolding events occurred.

Curved membrane structures induced by native lipids in giant vesicles

Native lipids in cell-membrane support crucial functions like intercell communication via their ability to deform into curved membrane structures. Cell membrane mimicking Giant unilamellar vesicles (GUV) is imperative in understanding native lipid’s role in membrane transformation however remains challenging to assemble. We construct two giant vesicle models mimicking bacterial inner-membrane (IM) and outer-membrane (OM) under physiological conditions using single-step gel-assisted lipid swelling. IM vesicles composed of native bacterial lipids undergo small-scale membrane remodeling into bud and short-nanotube structures. In contrast, OM vesicles asymmetrically assembled from Lipopolysaccharide (LPS) and bacterial lipids underwent global membrane deformation under controlled osmotic stress. Remarkably, highly-curved structures mimicking cell-membrane architectures, including daughter vesicle networks interconnected by necks and nano-tubes ranging from micro to nanoscale, are generated in OM vesicles at osmotic stress comparable to that applied in IM vesicles. Further, we provide a quantitative description of the membrane structures by experimentally determining membrane elastic parameters, i.e., neck curvature and bending rigidity. We can conclude that a larger spontaneous curvature estimated from the neck curvature and softer membranes in OM vesicles is responsible for large-scale deformation compared to IM vesicles. Our findings will help comprehend the shape dynamics of complex native bacterial lipid membranes.

Blood bank storage of red blood cells increases RBC cytoplasmic membrane order and bending rigidity.

Blood banks around the world store blood components for several weeks ensuring its availability for transfusion medicine. Red blood cells (RBCs) are known to undergo compositional changes during storage, which may impact the cells’ function and eventually the recipients’ health. We extracted the RBC’s cytoplasmic membrane (RBCcm) to study the effect of storage on the membranes’ molecular structure and bending rigidity by a combination of X-ray diffraction (XRD), X-ray diffuse scattering (XDS) and coarse grained Molecular Dynamics (MD) simulations. Blood was stored in commercial blood bags for 2 and 5 weeks, respectively and compared to freshly drawn blood. Using mass spectrometry, we measured an increase of fatty acids together with a slight shift towards shorter tail lengths. We observe an increased fraction (6%) of liquid ordered (lo) domains in the RBCcms with storage time, and an increased lipid packing in these domains, leading to an increased membrane thickness and membrane order. The size of both, lo and liquid disordered (ld) lipid domains was found to decrease with increased storage time by up to 25%. XDS experiments reveal a storage dependent increase in the RBCcm’s bending modulus κ by a factor of 2.8, from 1.9 kBT to 5.3 kBT. MD simulations were conducted in the absence of proteins. The results show that the membrane composition has a small contribution to the increased bending rigidity and suggests additional protein-driven mechanisms.

Bulging-to-Budding Transition of Lipid Droplets Confined within Vesicle Membranes.

Lipid droplets (LDs) are intracellular organelles that act as reservoirs for energy homeostasis and phospholipid balance between supply and consumption. In comparison with extensive studies on LD biogenesis from a biological viewpoint, little is known about the mechanical interaction between LDs and vesicles. Here we perform a systematic theoretical study on the budding and morphological evolution of an artificial LD embedded within the lipid membrane of a pressurized vesicle. It is found that LD bulging and budding depend on the bending rigidity and spontaneous curvature of the vesicle membrane, LD-vesicle interfacial interaction energy strength and size ratio, and osmotic pressure of the vesicle. Beyond critical interfacial interaction strength, the embedded LD undergoes a discontinuous shape transition from a lens-shaped bulge to a spherical protrusion connecting to the nearly spherical vesicle lumen via an infinitesimally small monolayer neck. Moreover, a positive monolayer spontaneous curvature promotes budding transition. As the vesicle becomes smaller, higher cost of the monolayer stretching energy is required for an LD to achieve budding transition. Budding phase diagrams distinguishing the embedded and budding states of the LD-vesicle complex accounting for osmotic pressure and interfacial interaction strength are established with the budding transition boundary displaying a nonmonotonic feature. Our results reveal how embedded LDs overcome soft membrane confinement and protrude, and provide fundamental insights into the clustering of nanoparticles between vesicle monolayers.

The Effect of the Osmotically Active Compound Concentration Difference on the Passive Water and Proton Fluxes across a Lipid Bilayer.

The molecular details of the passive water flux across the hydrophobic membrane interior are still a matter of debate. One of the postulated mechanisms is the spontaneous, water-filled pore opening, which facilitates the hydrophilic connection between aqueous phases separated by the membrane. In the paper, we provide experimental evidence showing that the spontaneous lipid pore formation correlates with the membrane mechanics; hence, it depends on the composition of the lipid bilayer and the concentration of the osmotically active compound. Using liposomes as an experimental membrane model, osmotically induced water efflux was measured with the stopped-flow technique. Shapes of kinetic curves obtained at low osmotic pressure differences are interpreted in terms of two events: the lipid pore opening and water flow across the aqueous channel. The biological significance of the dependence of the lipid pore formation on the concentration difference of an osmotically active compound was illustrated by the demonstration that osmotically driven water flow can be accompanied by the dissipation of the pH gradient. The application of the Helfrich model to describe the probability of lipid pore opening was validated by demonstrating that the probability of pore opening correlates with the membrane bending rigidity. The correlation was determined by experimentally derived bending rigidity coefficients and probabilities of lipid pores opening.

Membrane-mediated interaction of intercellular cylindrical nanoparticles

Nanoparticles in intercellular gaps, junctions, or seals could have close contact with neighboring cells simultaneously. Understanding the interaction between intercellular nanoparticles and confining cell membranes is of fundamental importance, not only to the unravelling of endocytic mechanisms but also to implications such as controlled drug delivery in tumor tissues. Here we theoretically examine the mechanical behaviors of adhesive cylindrical nanoparticles confined between two lipid membrane patches of finite size. As the size of the particle-membrane contact region or wrapping degree increases, neighboring cylindrical nanoparticles become separated and the nanoparticle distance increases first and then decreases until the particles are fully trapped by adjacent membrane patches. Depending on the nanoparticle size, adhesion energy, membrane bending rigidity and tension, and intermembrane distance, three characteristic particle-membrane interaction phases are determined as no wrapping, partial trapping, and full trapping, and the corresponding interaction phase diagram is established. Further energy comparison indicates that multiple nanoparticles undergoing the two-membrane trapping process do not exhibit cooperative effects. Analytical estimations on the system energy and configurations at equilibrium are performed based on the force balance of the membranes at small deformation and match well with numerical solutions. The results shed light on the mechanical behaviors of multiple nanoparticles in cell junctions or gaps and may have implications for drug delivery in tumor tissues.

Lipid Hydroperoxide Compromises the Membrane Structure Organization and Softens Bending Rigidity.

Lipid hydroperoxides are key mediators of diseases and cell death. In this work, the structural and dynamic perturbations induced by the hydroperoxidized POPC lipid (POPC-OOH) in fluid POPC membranes, at both 23 and 37 °C, were addressed using advanced small-angle X-ray scattering (SAXS) and fluorescence methodologies. Notably, SAXS reveals that the hydroperoxide group decreases the lipid bilayer bending rigidity. This alteration disfavors the bilayer stacking and increases the swelling in-between stacked bilayers. We further investigated the changes in the apolar/polar interface of hydroperoxide-containing membranes through time-resolved fluorescence/anisotropy experiments of the probe TMA-DPH and time-dependent fluorescence shifts of Laurdan. A shorter mean fluorescence lifetime for TMA-DPH was obtained in enriched POPC-OOH membranes, revealing a higher degree of hydration near the membrane interface. Moreover, a higher microviscosity near TMA-DPH and lower order are predicted for these oxidized membranes, at variance with the usual trend of variation of these two parameters. Finally, the complex relaxation process of Laurdan in pure POPC-OOH membranes also indicates a higher membrane hydration and viscosity in the close vicinity of the -OOH moiety. Altogether, our combined approach reveals that the hydroperoxide group promotes alterations in the membrane structure organization, namely, at the level of membrane order, viscosity, and bending rigidity.

Erratum: Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions.

Erratum: Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions.