Elastic curvature constants of lipid monolayers and bilayers

Growth of Staphylococcus aureus in the presence of oleic acid shifts the glycolipid fatty acid profile and increases resistance to antimicrobial peptides

Staphylococcus aureus readily adapts to various environments and quickly develops antibiotic resistance, which has led to an increase in multidrug-resistant infections. Hence, S. aureus presents a significant global health issue and its adaptations to the host environment are crucial for understanding pathogenesis and antibiotic susceptibility. When S. aureus is grown conventionally, its membrane lipids contain a mix of branched-chain and straight-chain saturated fatty acids. However, when unsaturated fatty acids are present in the growth medium, they become a major part of the total fatty acid composition. This study explores the biophysical effects of incorporating straight-chain unsaturated fatty acids into S. aureus membrane lipids. Membrane preparations from cultures supplemented with oleic acid showed more complex differential scanning calorimetry scans than those grown in tryptic soy broth alone. When grown in the presence of oleic acid, the cultures exhibited a transition significantly above the growth temperature, attributed to the presence of glycolipids with long-chain fatty acids causing acyl chain packing frustration within the bilayer. Functional aspects of the membrane were assessed by studying the kinetics of dye release from unilamellar vesicles induced by the antimicrobial peptide mastoparan X. Dye release was slower from liposomes prepared from cells grown in oleic acid-supplemented cultures, suggesting that changes in membrane lipid composition and biophysics protect the cell membrane against peptide-induced lysis. These findings underscore the intricate relationship between the growth environment, membrane lipid composition, and the physical properties of the bacterial membrane, which should be considered when developing new strategies against S. aureus infections.

Exploration of lipid bilayer mechanical properties using molecular dynamics simulation

Important biological structures known for their exceptional mechanical qualities, lipid bilayers are essential to many cellular functions. Fluidity, elasticity, permeability, stiffness, tensile strength, compressibility, shear viscosity, line tension, and curvature elasticity are some of the fundamental characteristics affecting their behavior. The purpose of this review is to examine these characteristics in more detail by molecular dynamics simulation, elucidating their importance and the elements that lead to their appearance in lipid bilayers. Comprehending the mechanical characteristics of lipid bilayers is critical for creating medications, drug delivery systems, and biomaterials that interact with biological membranes because it allows one to understand how these materials respond to different stresses and deformations. The influence of mechanical characteristics on important lipid bilayer properties is examined in this review. The mechanical properties of lipid bilayers were clarified through the use of molecular dynamics simulation analysis techniques, including bilayer thickness, stress-strain analysis, lipid bilayer area compressibility, membrane bending rigidity, and time- or ensemble-averaged the area per lipid evaluation. We explain the significance of molecular dynamics simulation analysis methods, providing important new information about the stability and dynamic behavior of the bilayer. In the end, we hope to use molecular dynamics simulation to provide a comprehensive understanding of the mechanical properties and behavior of lipid bilayers, laying the groundwork for further studies and applications. Taken together, careful investigation of these mechanical aspects deepens our understanding of the adaptive capacities and functional roles of lipid bilayers in biological environments.

Dynamical modelling of lipid droplet formation suggests a key function of membrane phospholipids

Cells store triacylglycerol (TAG) within lipid droplets (LDs). A dynamic model describing complete LD formation at the endoplasmic reticulum (ER) membrane does not yet exist. A biochemical-biophysical model of LD synthesis is proposed. It describes the time-dependent accumulation of TAG in the ER membrane as the formation of a potential LD (pLD) bounded by spherical caps of the inner and outer monolayers of the membrane. The expansion rate of the pLD depends on the TAG supply, the elastic properties of the ER membrane, and the recruitment of phospholipids (PLs) to the cap-covering monolayers. Model simulations provided the following insights: (a) Marginal differences in the surface tension of the cap monolayers are sufficient to fully drive the expansion of the pLD towards the cytosol or lumen. (b) Selective reduction of PL supply to the luminal monolayer ensures stable formation of cytosolic LDs, irrespective of variations in the elasto-mechanical properties of the ER membrane. (c) The rate of TAG supply to the cytosolic monolayer has a major effect on the size and maturation time of LDs but has no significant effect on the TAG export per individual LD. The recruitment of additional PLs to the cap monolayers of pLDs critically controls the budding direction, size, and maturation time of LDs. The ability of cells to acquire additional LD initiation sites appears to be key to coping with acutely high levels of potentially toxic free fatty acids.

Growth of Staphylococcus aureus in the presence of oleic acid shifts the glycolipid fatty acid profile and increases resistance to antimicrobial peptides

Staphylococcus aureus readily adapts to various environments and quickly develops antibiotic resistance, which has led to an increase in multidrug-resistant infections. Hence, S. aureus presents a significant global health issue and its adaptations to the host environment are crucial for understanding pathogenesis and antibiotic susceptibility. When S. aureus is grown conventionally, its membrane lipids contain a mix of branched-chain and straight-chain saturated fatty acids. However, when unsaturated fatty acids are present in the growth medium, they become a major part of the total fatty acid composition. This study explores the biophysical effects of incorporating straight-chain unsaturated fatty acids into S. aureus membrane lipids. Membrane preparations from cultures supplemented with oleic acid showed more complex differential scanning calorimetry scans than those grown in tryptic soy broth alone. When grown in the presence of oleic acid, the cultures exhibited a transition significantly above the growth temperature, attributed to the presence of glycolipids with long-chain fatty acids causing acyl chain packing frustration within the bilayer. Functional aspects of the membrane were assessed by studying the kinetics of dye release from unilamellar vesicles induced by the antimicrobial peptide mastoparan X. Dye release was slower from liposomes prepared from cells grown in oleic acid-supplemented cultures, suggesting that changes in membrane lipid composition and biophysics protect the cell membrane against peptide-induced lysis. These findings underscore the intricate relationship between the growth environment, membrane lipid composition, and the physical properties of the bacterial membrane, which should be considered when developing new strategies against S. aureus infections.

Dynamic framework for large-scale modeling of membranes and peripheral proteins

In this chapter, we present a novel computational framework to study the dynamic behavior of extensive membrane systems, potentially in interaction with peripheral proteins, as an alternative to conventional simulation methods. The framework effectively describes the complex dynamics in protein-membrane systems in a mesoscopic particle-based setup. Furthermore, leveraging the hydrodynamic coupling between the membrane and its surrounding solvent, the coarse-grained model grounds its dynamics in macroscopic kinetic properties such as viscosity and diffusion coefficients, marrying the advantages of continuum- and particle-based approaches. We introduce the theoretical background and the parameter-space optimization method in a step-by-step fashion, present the hydrodynamic coupling method in detail, and demonstrate the application of the model at each stage through illuminating examples. We believe this modeling framework to hold great potential for simulating membrane and protein systems at biological spatiotemporal scales, and offer substantial flexibility for further development and parametrization.

The Chemical Reactivity of Membrane Lipids

It is well-known that aqueous dispersions of phospholipids spontaneously assemble into bilayer structures. These structures have numerous applications across chemistry and materials science and form the fundamental structural unit of the biological membrane. The particular environment of the lipid bilayer, with a water-poor low dielectric core surrounded by a more polar and better hydrated interfacial region, gives the membrane particular biophysical and physicochemical properties and presents a unique environment for chemical reactions to occur. Many different types of molecule spanning a range of sizes, from dissolved gases through small organics to proteins, are able to interact with membranes and promote chemical changes to lipids that subsequently affect the physicochemical properties of the bilayer. This Review describes the chemical reactivity exhibited by lipids in their membrane form, with an emphasis on conditions where the lipids are well hydrated in the form of bilayers. Key topics include the following: lytic reactions of glyceryl esters, including hydrolysis, aminolysis, and transesterification; oxidation reactions of alkenes in unsaturated fatty acids and sterols, including autoxidation and oxidation by singlet oxygen; reactivity of headgroups, particularly with reactive carbonyl species; and E/Z isomerization of alkenes. The consequences of reactivity for biological activity and biophysical properties are also discussed.

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.

Dynamic structure factor of undulating vesicles: finite-size and spherical geometry effects with application to neutron spin echo experiments

We consider the dynamic structure factor (DSF) of quasi-spherical vesicles and present a generalization of an expression that was originally formulated by Zilman and Granek (ZG) for scattering from isotropically oriented quasi-flat membrane plaquettes. The expression is obtained in the form of a multi-dimensional integral over the undulating membrane surface. The new expression reduces to the original stretched exponential form in the limit of sufficiently large vesicles, i.e., in the micron range or larger. For much smaller unilamellar vesicles, deviations from the asymptotic, stretched exponential equation are noticeable even if one assumes that the Seifert-Langer leaflet density mode is completely relaxed and membrane viscosity is neglected. To avoid the need for an exhaustive numerical integration while fitting to neutron spin echo (NSE) data, we provide a useful approximation for polydisperse systems that tests well against the numerical integration of the complete expression. To validate the new expression, we performed NSE experiments on variable-size vesicles made of a POPC/POPS lipid mixture and demonstrate an advantage over the original stretched exponential form or other manipulations of the original ZG expression that have been deployed over the years to fit the NSE data. In particular, values of the membrane bending rigidity extracted from the NSE data using the new approximations were insensitive to the vesicle radii and scattering wavenumber and compared very well with expected values of the effective bending modulus ([Formula: see text]) calculated from results in the literature. Moreover, the generalized scattering theory presented here for an undulating quasi-spherical shell can be easily extended to other models for the membrane undulation dynamics beyond the Helfrich Hamiltonian and thereby provides the foundation for the study of the nanoscale dynamics in more complex and biologically relevant model membrane systems.

Implicit model to capture electrostatic features of membrane environment

Membrane protein structure prediction and design are challenging due to the complexity of capturing the interactions in the lipid layer, such as those arising from electrostatics. Accurately capturing electrostatic energies in the low-dielectric membrane often requires expensive Poisson-Boltzmann calculations that are not scalable for membrane protein structure prediction and design. In this work, we have developed a fast-to-compute implicit energy function that considers the realistic characteristics of different lipid bilayers, making design calculations tractable. This method captures the impact of the lipid head group using a mean-field-based approach and uses a depth-dependent dielectric constant to characterize the membrane environment. This energy function Franklin2023 (F23) is built upon Franklin2019 (F19), which is based on experimentally derived hydrophobicity scales in the membrane bilayer. We evaluated the performance of F23 on five different tests probing (1) protein orientation in the bilayer, (2) stability, and (3) sequence recovery. Relative to F19, F23 has improved the calculation of the tilt angle of membrane proteins for 90% of WALP peptides, 15% of TM-peptides, and 25% of the adsorbed peptides. The performances for stability and design tests were equivalent for F19 and F23. The speed and calibration of the implicit model will help F23 access biophysical phenomena at long time and length scales and accelerate the membrane protein design pipeline.

Free Energy Surface and Molecular Mechanism of Slow Structural Transitions in Lipid Bilayers

Lipid membrane remodeling, crucial for many cellular processes, is governed by the coupling of membrane structure and shape fluctuations. Given the importance of the ∼ nm length scale, details of the transition intermediates for conformational change are not fully captured by a continuum-mechanical description. Slow dynamics and the lack of knowledge of reaction coordinates (RCs) for biasing methods pose a challenge for all-atom (AA) simulations. Here, we map system dynamics on Langevin dynamics in a normal mode space determined from an elastic network model representation for the lipid-water Hamiltonian. AA molecular dynamics (MD) simulations are used to determine model parameters, and Langevin dynamics predictions for bilayer structural, mechanical, and dynamic properties are validated against MD simulations and experiments. Transferability to describe the dynamics of a larger lipid bilayer and a heterogeneous membrane-protein system is assessed. A set of generic RCs for pore formation in two tensionless bilayers is obtained by coupling Langevin dynamics to the underlying energy landscape for membrane deformations. Structure evolution is carried out by AA MD, wherein the generic RCs are used in a path metadynamics or an umbrella sampling simulation to determine the thermodynamics of pore formation and its molecular determinants, such as the role of distinct bilayer motions, lipid solvation, and lipid packing.

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.

RE, Mocskos EE, Facelli JC, Pickholz M, Ferraro MB. Molecular dynamics study of the mechanical properties of drug loaded model systems: A comparison of a polymersome with a bilayer

In this work we implement a new methodology to study structural and mechanical properties of systems having spherical and planar symmetries throughout Molecular Dynamics simulations. This methodology is applied here to a drug delivery system based in polymersomes, as an example. The chosen model drug was the local anesthetic prilocaine due to previous parameterization within the used coarse grain scheme. In our approach, mass density profiles (MDPs) are used to obtain key structural parameters of the systems, and pressure profiles are used to estimate the curvature elastic parameters. The calculation of pressure profiles and radial MPDs required the development of specific methods, which were implemented in an in-house built version of the GROMACS 2018 code. The methodology presented in this work is applied to characterize poly(ethylene oxide)-poly(butadiene) polymersomes and bilayers loaded with the model drug prilocaine. Our results show that structural properties of the polymersome membrane could be obtained from bilayer simulations, with significantly lower computational cost compared to whole polymersome simulations, but the bilayer simulations are insufficient to get insights on their mechanical aspects, since the elastic parameters are canceled out for the complete bilayer (as consequence of the symmetry). The simulations of entire polymersomes, although more complex, offer a complementary approach to get insights on the mechanical behavior of the systems.

Clustering of lipids driven by integrin

Integrin is an important transmembrane receptor protein which remodels the actin network and anchors the cell membrane towards the extracellular matrix via mechanochemical pathways. The clustering of specific lipids and lipid-anchored proteins, which is essential for a certain type of endocytosis process, is facilitated at integrin-mediated active regions. To study this, we propose a minimal exactly solvable model which includes the interplay of stochastic shuttling between integrin on and off states with the intrinsic dynamics of the membrane. We propose a two-step mechanism in which the integrin induces an aster-like arrangement in the actin network, followed by clustering of lipids in that region. We obtain an analytic expression for the deformation and local membrane velocity, and thereby the evolution of clustering mediated by a single integrin. The deformation evolves nonmonotonically and its dependence on the stochastic shuttling timescales and membrane properties is elucidated. Our estimates of the area of the deformed region and the number of lipids in it indicate strong clustering.

Effect of naproxen on the model lipid membrane formed on the water-chitosan subphase

Non steroidal anti-inflammatory drugs (NSAIDs) are those of the most common over the counter (OTC) medications widely used by millions of people every day. Unfortunately, despite their popularity those drugs can cause serious side effects in the digestive system (ulcers, bleeding, and pain). These inconveniences are caused by the changes in the structures of the outer phospholipid layers of gastric mucus and mucosa. As a result the H⁺ ions from the stomach acid can pass easily through these natural protective barriers and damage the epithelial cells which causes ulcers and bleeding. Chitosan as a polysaccharide known for its unique biocompatibility, drug delivery possibilities and wound healing effect has been chosen to examine if it can induce the reduction of undesirable effects of naproxen. This paper focuses on the interactions of the naproxen with a model biological membrane with and without the presence of chitosan. Applying the Langmuir technique coupled with the surface potential measurements and the Brewster angle microscope imaging allowed to characterize successfully examined systems in terms of the monolayer compressibility, thickness, stability, electric properties and morphology. The results proved that the presence of naproxen alters the mechanical and electrical properties of the model membrane depending on its surface pressure. Moreover, the addition of chitosan to the lipid-drug system causes significant changes in the properties of the layer, i.e. a reduction of its compressibility, thickness and morphology modification. Nevertheless, chitosan suppresses some changes induced by naproxen such as alteration of the apparent dipole moment and film stability.

Effect of monolayer spontaneous curvature on constant tension-induced pore formation in lipid bilayers

The methodology of constant tension-induced rupture of giant unilamellar vesicles (GUVs) has provided information on tension-induced pore formation. This method was used to investigate the effect of spontaneous curvature (H₀) for a lipid monolayer on the rate constant (k_r) for constant tension (σ)-induced rupture, which originates from pore formation in lipid bilayers. Lipids were incorporated with different H₀ values into GUV membranes to change the overall H₀ value for the GUV monolayer. The dioleoylphosphatidylglycerol (DOPG)/dioleoylphosphatidylethanolamine (DOPE) (4/6, molar ratio, here and elsewhere) monolayer has a negative H₀, whereas the DOPG/dioleoylphosphatidylcholine (DOPC) (4/6) monolayer has an essentially zero H₀. A higher tension was required to induce the rupture of DOPG/DOPE (4/6)-GUVs compared with DOPG/DOPC (4/6)-GUVs. The line tension (Γ) for a pre-pore in DOPG/DOPE (4/6)-GUVs, determined by the analysis of the tension dependence of k_r, was 1.5 times larger than that in DOPG/DOPC (4/6)-GUVs. The k_r values for GUVs comprising DOPG/DOPC/18:1 lysophosphatidylcholine (LPC) (40/55/10), which has a positive H₀, were larger than those for DOPG/DOPC (4/6)-GUVs under the same tension. The Γ value for DOPG/DOPC/LPC (40/55/10)-GUVs was almost half that for DOPG/DOPC (4/6)-GUVs. These results indicate that Γ decreases with increasing H₀, which results in an increase in k_r. Based on these results, the effect of H₀ on k_r and Γ is discussed.

Effects of various thermal treatments on interfacial composition and physical properties of bovine milk fat globules

This study aimed to investigate changes of milk fat globules (MFG) and their membranes after thermal treatments, and further analyzed the relationship between the stability of MFG and interfacial compositions of milk fat globule membrane (MFGM). We characterized the influence of three kinds of thermal treatments on fat globule interfacial components (including interfacial phospholipids and interfacial protein) and physical properties using phospholipidomics and several microscopy techniques. The results showed that size of MFG increased from 2.96 μm to 3.59 μm and ζ-potential decreased from -9.71 mV to -13.23 mV after thermal treatment, suggesting that MFGM was damaged and MFG occurred coalescence. Thermal treatment increased the Young's modulus of MFGM and made membranes more fragile. The abundance of MFGM proteins decreased while casein and β-lactoglobulin increased after thermal treatment. Results of phospholipidomics showed that 27 phospholipid species could be used to distinguish the samples. Pasteurization reduced mainly SM and PC located in the outer bilayer of MFGM, while ultra-pasteurization reduced not only SM and PC but also PI and PE located in the inner leaflet. Based on correlation analysis, the increase in Young's modulus of MFGM during thermal treatment might be related to changes in chemical components on the membrane, suggesting a potential link between the change of MFGM components and fat globule coalescence behavior.

Determination of elastic parameters of lipid membranes from simulation under varied external pressure

Many cellular processes such as endocytosis, exocytosis, and vesicle trafficking involve membrane deformations, which can be analyzed in the framework of the elastic theories of lipid membranes. These models operate with phenomenological elastic parameters. A connection between these parameters and the internal structure of lipid membranes can be provided by three-dimensional (3D) elastic theories. Considering a membrane as a 3D layer, Campelo et al. [F. Campelo et al., Adv. Colloid Interface Sci. 208, 25 (2014)10.1016/j.cis.2014.01.018] developed a theoretical basis for the calculation of elastic parameters. In this work we generalize and improve this approach by considering a more general condition of global incompressibility instead of local incompressibility. Crucially, we find an important correction to the theory of Campelo et al., which if not taken into account leads to a significant miscalculation of elastic parameters. With the total volume conservation taken into account, we derive an expression for the local Poisson's ratio, which determines how the local volume changes upon stretching and permits a more precise determination of elastic parameters. Also, we substantially simplify the procedure by calculating the derivatives of the moments of the local tension with respect to stretching instead of calculating the local stretching modulus. We obtain a relation between the Gaussian curvature modulus as a function of stretching and the bending modulus, showing that these two elastic parameters are not independent, as was previously assumed. The proposed algorithm is applied to membranes composed of pure dipalmitoylphosphatidylcholine (DPPC), dioleoylphosphatidylcholine (DOPC), and their mixture. The following elastic parameters of these systems are obtained: the monolayer bending and stretching moduli, spontaneous curvature, neutral surface position, and local Poisson's ratio. It is shown that the bending modulus of the DPPC/DOPC mixture follows a more complex trend than predicted by the classical Reuss averaging, which is often employed in theoretical frameworks.

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.

Tilt Modulus of Bilayer Membranes Self-Assembled from Rod-Coil Diblock Copolymers

Quantitatively understanding membrane fission and fusion requires a mathematical model taking their underlying elastic degrees of freedom, such as the molecule's tilt, into account. Hamm-Kozlov's model is such a framework that includes a tilt modulus along with the bending modulus and Gaussian modulus. This paper investigates the tilt modulus of liquid-crystalline bilayer membranes by applying self-consistent field theory. Unlike the widely used method in molecular dynamics simulation which extracts the tilt modulus by simulating bilayer buckles with various single modes, we introduce a tilt constrain term in the free energy to stabilize bilayers with various tilt angles. Fitting the energy curve as a function of the tilt angle to Hamm-Kozlov's elastic energy allows us to extract the tilt modulus directly. Based on this novel scheme and focused on the bilayers self-assembled from rod-coil diblock copolymers, we carry out a systematic study of the dependence of the tensionless A-phase bilayer's tilt modulus on the microscopic parameters.

High-Efficiency Capture of Cells by Softening Cell Membrane

The capture of circulating tumor cells (CTCs) by nanostructured substrate surface is a useful method for early diagnosis of cancer. At present, most methods used to improve the cell capture efficiency are based on changing substrate surface properties. However, there are still some gaps between these methods and practical applications. Here, a method is presented for improving cell capture efficiency from a different perspective, that is, changing the properties of the cells. Concretely, the mechanical properties of the cell membrane are changed by adding Cytochalasin D to soften the cell membrane. Furthermore, a corresponding theoretical model is proposed to explain the experimental results. It is found that cell softening can reduce the resistance of cell adhesion, which makes the adhesion ability stronger. The high-efficiency capture of cells by softening the cell membrane provides a potential method to improve the detection performance of CTCs.

Effects of cholesterol on the size distribution and bending modulus of lipid vesicles

The influence of cholesterol fraction in the membranes of giant unilamellar vesicles (GUVs) on their size distributions and bending moduli has been investigated. The membranes of GUVs were synthesized by a mixture of two elements: electrically neutral lipid 1, 2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) and cholesterol and also a mixture of three elements: electrically charged lipid 1,2-dioleoyl-sn-glycero-3-phospho-(1′-rac-glycerol) (DOPG), DOPC and cholesterol. The size distributions of GUVs have been presented by a set of histograms. The classical lognormal distribution is well fitted to the histograms, from where the average size of vesicle is obtained. The increase of cholesterol content in the membranes of GUVs increases the average size of vesicles in the population. Using the framework of Helmholtz free energy of the system, the theory developed by us is extended to explain the experimental results. The theory determines the influence of cholesterol on the bending modulus of membranes from the fitting of the proper histograms. The increase of cholesterol in GUVs increases both the average size of vesicles in population and the bending modulus of membranes.

Simple Does Not Mean Trivial: Behavior of Phosphatidic Acid in Lipid Mono- and Bilayers

Phosphatidic acid (PA) is one of the simplest membrane phospholipids, yet it plays a crucial role in various biologically relevant processes that take place in cells. Since PA generation may be triggered by a variety of factors, very often of antagonistic character, the specific nature of physiological responses driven by PA is not clear. In order to shed more light on these issues, we carried out a systematic characterization of membranes containing one of the three biologically significant PA molecular species. The effect of these molecules on the properties of membranes composed of phosphatidylcholine and/or cholesterol was assessed in a multidisciplinary approach, including molecular dynamic simulations, flicker noise spectroscopy, and Langmuir monolayer isotherms. The first enables the determination of various macroscopic and microscopic parameters such as lateral diffusion, membrane thickness, and defect analysis. The obtained data revealed a strong interaction between unsaturated PA species and phosphatidylcholine. On the other hand, the behavior of saturated PA was greatly influenced by cholesterol. Additionally, a strong effect on mechanical properties was observed in the case of three-component systems, which could not be explained by the simple extrapolation of parameters of the corresponding two-component systems. Our data show that various PA species are not equivalent in terms of their influence on lipid mono- and bilayers and that membrane composition/properties, particularly those related to the presence of cholesterol, may strongly modulate PA behavior.

Stiffness of Fluid and Gel Phase Lipid Nanovesicles: Weighting the Contributions of Membrane Bending Modulus and Luminal Pressurization

The mechanical properties of biogenic membranous compartments are thought to be relevant in numerous biological processes; however, their quantitative measurement remains challenging for most of the already available force spectroscopy (FS)-based techniques. In particular, the debate on the mechanics of lipid nanovesicles and on the interpretation of their mechanical response to an applied force is still open. This is mostly due to the current lack of a unified model being able to describe the mechanical response of both gel and fluid phase lipid vesicles and to disentangle the contributions of membrane rigidity and luminal pressure. In this framework, we herein propose a simple model in which the interplay of membrane rigidity and luminal pressure to the overall vesicle stiffness is described as a series of springs; this approach allows estimating these two contributions for both gel and fluid phase liposomes. Atomic force microscopy-based FS, performed on both vesicles and supported lipid bilayers, is exploited for obtaining all the parameters involved in the model. Moreover, the use of coarse-grained full-scale molecular dynamics simulations allowed for better understanding of the differences in the mechanical responses of gel and fluid phase bilayers and supported the experimental findings. The results suggest that the pressure contribution is similar among all the probed vesicle types; however, it plays a dominant role in the mechanical response of lipid nanovesicles presenting a fluid phase membrane, while its contribution becomes comparable to the one of membrane rigidity in nanovesicles with a gel phase lipid membrane. The results presented herein offer a simple way to quantify two of the most important parameters in vesicle nanomechanics (membrane rigidity and internal pressurization), and as such represent a first step toward a currently unavailable, unified model for the mechanical response of gel and fluid phase lipid nanovesicles.

Hydrodynamic coupling for particle-based solvent-free membrane models

The great challenge with biological membrane systems is the wide range of scales involved, from nanometers and picoseconds for individual lipids to the micrometers and beyond millisecond for cellular signaling processes. While solvent-free coarse-grained membrane models are convenient for large-scale simulations and promising to provide insight into slow processes involving membranes, these models usually have unrealistic kinetics. One major obstacle is the lack of an equally convenient way of introducing hydrodynamic coupling without significantly increasing the computational cost of the model. To address this, we introduce a framework based on anisotropic Langevin dynamics, for which major in-plane and out-of-plane hydrodynamic effects are modeled via friction and diffusion tensors from analytical or semi-analytical solutions to Stokes hydrodynamic equations. Using this framework, in conjunction with our recently developed membrane model, we obtain accurate dispersion relations for planar membrane patches, both free-standing and in the vicinity of a wall. We briefly discuss how non-equilibrium dynamics is affected by hydrodynamic interactions. We also measure the surface viscosity of the model membrane and discuss the affecting dissipative mechanisms.

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.

Recent developments in membrane curvature sensing and induction by proteins

BACKGROUND

Membrane-bound intracellular organelles have characteristic shapes attributed to different local membrane curvatures, and these attributes are conserved across species. Over the past decade, it has been confirmed that specific proteins control the large curvatures of the membrane, whereas many others due to their specific structural features can sense the curvatures and bind to the specific geometrical cues. Elucidating the interplay between sensing and induction is indispensable to understand the mechanisms behind various biological processes such as vesicular trafficking and budding.

SCOPE OF REVIEW

We provide an overview of major classes of membrane proteins and the mechanisms of curvature sensing and induction. We then discuss the importance of membrane elastic characteristics to induce the membrane shapes similar to intracellular organelles. Finally, we survey recently available assays developed for studying the curvature sensing and induction by many proteins.

MAJOR CONCLUSIONS

Recent theoretical/computational modeling along with experimental studies have uncovered fascinating connections between lipid membrane and protein interactions. However, the phenomena of protein localization and synchronization to generate spatiotemporal dynamics in membrane morphology are yet to be fully understood.

GENERAL SIGNIFICANCE

The understanding of protein-membrane interactions is essential to shed light on various biological processes. This further enables the technological applications of many natural proteins/peptides in therapeutic treatments. The studies of membrane dynamic shapes help to understand the fundamental functions of membranes, while the medicinal roles of various macromolecules (such as proteins, peptides, etc.) are being increasingly investigated.

Manufacture of Multilayered Artificial Cell Membranes through Sequential Bilayer Deposition on Emulsion Templates

Efforts to manufacture artificial cells that replicate the architectures, processes and behaviours of biological cells are rapidly increasing. Perhaps the most commonly reconstructed cellular structure is the membrane, through the use of unilamellar vesicles as models. However, many cellular membranes, including bacterial double membranes, nuclear envelopes, and organelle membranes, are multilamellar. Due to a lack of technologies available for their controlled construction, multilayered membranes are not part of the repertoire of cell-mimetic motifs used in bottom-up synthetic biology. To address this, we developed emulsion-based technologies that allow cell-sized multilayered vesicles to be produced layer-by-layer, with compositional control over each layer, thus enabling studies that would otherwise remain inaccessible. We discovered that bending rigidities scale with the number of layers and demonstrate inter-bilayer registration between coexisting liquid-liquid domains. These technologies will contribute to the exploitation of multilayered membrane structures, paving the way for incorporating protein complexes that span multiple bilayers.

The neuronal calcium sensor Synaptotagmin-1 and SNARE proteins cooperate to dilate fusion pores

All membrane fusion reactions proceed through an initial fusion pore, including calcium-triggered release of neurotransmitters and hormones. Expansion of this small pore to release cargo is energetically costly and regulated by cells, but the mechanisms are poorly understood. Here, we show that the neuronal/exocytic calcium sensor Synaptotagmin-1 (Syt1) promotes expansion of fusion pores induced by SNARE proteins. Pore dilation relied on calcium-induced insertion of the tandem C2 domain hydrophobic loops of Syt1 into the membrane, previously shown to reorient the C2 domain. Mathematical modelling suggests that C2B reorientation rotates a bound SNARE complex so that it exerts force on the membranes in a mechanical lever action that increases the height of the fusion pore, provoking pore dilation to offset the bending energy penalty. We conclude that Syt1 exerts novel non-local calcium-dependent mechanical forces on fusion pores that dilate pores and assist neurotransmitter and hormone release.

A plasmon-based nanoruler to probe the mechanical properties of synthetic and biogenic nanosized lipid vesicles

Nanosized lipid vesicles are ubiquitous in living systems (e.g. cellular compartments or extracellular vesicles, EVs) and in formulations for nanomedicine (e.g. liposomes for RNA vaccine formulations). The mechanical properties of such vesicles are crucial in several physicochemical and biological processes, ranging from cellular uptake to stability in aerosols. However, their accurate determination remains challenging and requires sophisticated instruments and data analysis. Here we report the first evidence that the surface plasmon resonance (SPR) of citrated gold nanoparticles (AuNPs) adsorbed on synthetic vesicles is finely sensitive to the vesicles' mechanical properties. We then leverage this finding to show that the SPR tracking provides quantitative access to the stiffness of vesicles of synthetic and natural origin, such as EVs. The demonstration of this plasmon-based "stiffness nanoruler" paves the way for developing a facile, cost-effective and high-throughput method to assay the mechanical properties of dispersions of vesicles of nanometric size and unknown composition at a collective level.

Analytical Calculation of the Elastic Moduli of Self-Assembled Liquid-Crystalline Bilayer Membranes

Liquid-crystalline orders are ubiquitous in membranes and could significantly affect the elastic properties of the self-assembled bilayers. Calculating the free energy of bilayer membranes with different geometries and fitting them to their theoretical expressions allow us to extract the elastic moduli, such as the bending modulus and Gaussian modulus. However, this procedure is time-consuming for liquid-crystalline bilayers. In paper reports a novel method to calculate the elastic moduli of the self-assembled liquid-crystalline bilayers within the self-consistent field theory framework. Based on the asymptotic expansion method, we derive the analytical expression of the elastic moduli, which reduces the computational cost significantly. Numerical simulations illustrate the validity and efficiency of the proposed method.

Curvature Energetics Determined by Alchemical Simulation on Four Topologically Distinct Lipid Phases

The relative curvature energetics of two lipids are tested using thermodynamic integration (TI) on four topologically distinct lipid phases. Simulations use TI to switch between choline headgroup lipids (POPC; that prefers to be flat) and ethanolamine headgroup lipids (POPE; that prefer, for example, the inner monolayer of vesicles). The thermodynamical moving of the lipids between planar, inverse hexagonal (HII), cubic (QII; Pn3m space group), and vesicle topologies reveals differences in material parameters that were previously challenging to access. The methodology allows for predictions of two important lipid material properties: the difference in POPC/POPE monolayer intrinsic curvature (ΔJ0) and the difference in POPC/POPE monolayer Gaussian curvature modulus (Δκ̅m), both of which are connected to the energetics of topological variation. Analysis of the TI data indicates that, consistent with previous experiment and simulation, the J0 of POPE is more negative than POPC (ΔJ0 = -0.018 ± 0.001 Å-1). The theoretical framework extracts significant differences in κ̅m of which POPE is less negative than POPC by 2.0 to 4.0 kcal/mol. The range of these values is determined by considering subsets of the simulations, and disagreement between these subsets suggests separate mechanical parameters at very high curvature. Finally, the fit of the TI data to the model indicates that the position of the pivotal plane of curvature is not constant across topologies at high curvature. Overall, the results offer insights into lipid material properties, the limits of a single HC model, and how to test them using simulation.

Penetration mechanism of cells by vertical nanostructures

Cell penetration by high aspect-ratio vertical nanostructures such as nanowires and nanopillars provides a powerful method for accessing the cell interior for delivery and sensing. However, there is a lack of studies on the understanding of the mechanism of cell membrane penetration and how design nanostructures to optimize the efficiency of penetration remains unclear. Here, we propose an analytical model to elucidate the mechanism of cells penetration by analyzing the free-energy change of cells adhered to the nanostructures surface. Furthermore, we provide a simple method to evaluate the crossover radius or density for cell membrane penetration. By introducing a dimensionless parameter, i.e., adhesion area factor, we investigated the effects of the radius and distribution densities of nanostructures on cell membrane penetration which is determined by the competition between adhesion energy and deformation energy. Besides, a diagram of the distribution of cell penetration and no penetration is obtained. From the cell penetration diagram, one can determine easily and intuitively the relations of cell penetration state with the radius and distribution densities of nanostructures. Our theoretical results seem to show broad agreement with experimental observations, which implies that these studies would provide useful guidance to the design of nanopatterned surfaces for biomedical applications.

Additional contributions to elastic energy of lipid membranes: Tilt-curvature coupling and curvature gradient

Lipid bilayer membranes under biologically relevant conditions are flexible thin laterally fluid films consisting of two unimolecular layers (monolayers) each about 2 nm thick. On spatial scales much larger than the bilayer thickness, the membrane elasticity is well determined by its shape. The classical Helfrich theory considers the membrane as an elastic two-dimensional (2D) film, which has no particular internal structure. However, various local membrane heterogeneities can result in a lipids tilt relative to the membrane surface normal. On the basis of the classical elasticity theory of 3D bodies, Hamm and Kozlov [Eur. Phys. J. E 3, 323 (2000)10.1007/s101890070003] derived the most general energy functional, taking into account the tilt and lipid monolayer curvature. Recently, Terzi and Deserno [J. Chem. Phys. 147, 084702 (2017)10.1063/1.4990404] showed that Hamm and Kozlov's derivation was incomplete because the tilt-curvature coupling term had been missed. However, the energy functional derived by Terzi and Deserno appeared to be unstable, thereby being invalid for applications that require minimizations of the overall energy of deformations. Here, we derive a stable elastic energy functional, showing that the squared gradient of the curvature was missed in both of these works. This change in the energy functional arises from a more accurate consideration of the transverse shear deformation terms and their influence on the membrane stability. We also consider the influence of the prestress terms on the stability of the energy functional, and we show that it should be considered small and the effective Gaussian curvature should be neglected because of the stability requirements. We further generalize the theory, including the stretching-compressing deformation modes, and we provide the geometrical interpretation of the terms that were previously missed by Hamm and Kozlov. The physical consequences of the new terms are analyzed in the case of a membrane-mediated interaction of two amphipathic peptides located in the same monolayer. We also provide the expression for director fluctuations, comparing it with that obtained by Terzi and Deserno.

Effect of the Hydrocarbon Chain Disorder in Phosphatidylcholine Bilayers on Gigahertz Sound Velocity

Suspensions of multilamellar vesicles of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and hydrated and dehydrated aligned multilamellar samples of DMPC were studied by Brillouin spectroscopy in the temperature range from 90 to 333 K. The sound velocity of the longitudinal acoustic wave was evaluated from the Brillouin spectra. It was found that phase transition, hydration state, and planar or vesicular form of bilayers affect the gigahertz sound velocity. Usually, the temperature dependence of the sound velocity is weak in solid substances. Amazingly, the sound velocity of hydrated DMPC samples showed significant temperature-induced changes of up to 1.8 times, even within the solid-like gel phase. We explained this effect by temperature-induced excitations of the disordered conformational states of the hydrocarbon chains as well as anharmonic effects. In addition, the relevance of the gigahertz sound velocity to the description of subterahertz Raman features was demonstrated.

Elastic properties of self-assembled bilayer membranes: Analytic expressions via asymptotic expansion

Bilayer membranes self-assembled from amphiphilic molecules are ubiquitous in biological and soft matter systems. The elastic properties of bilayer membranes are essential in determining the shape and structure of bilayers. A novel method to calculate the elastic moduli of the self-assembled bilayers within the framework of the self-consistent field theory is developed based on an asymptotic expansion of the order parameters in terms of the bilayer curvature. In particular, the asymptotic expansion method is used to derive analytic expressions of the elastic moduli, which allows us to design more efficient numerical schemes. The efficiency of the proposed method is illustrated by a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents.

Saddle-curvature instability of lipid bilayer induced by amphipathic peptides: a molecular model

Amphipathic peptides that partition into lipid bilayers affect the curvature elastic properties of their host. Some of these peptides are able to shift the Gaussian modulus to positive values, thus triggering an instability with respect to the formation of saddle curvatures. To characterize the generic aspects of the underlying mechanism, we employ a molecular lipid model that accounts for the interfacial tension between the polar and apolar regions of the membrane, for interactions between the lipid headgroups, and for the energy to stretch or compress the hydrocarbon chains. Peptides are modeled as cylinders that partition into the host membrane in a parallel orientation where they diminish the space available to the lipid headgroups and chains. The penetration depth into the membrane is determined by the angular size of the peptide's hydrophilic region. We demonstrate that only peptides with a small angular size of their hydrophilic region have an intrinsic tendency to render the Gaussian modulus more positive, and we identify conditions at which the Gaussian modulus adopts a positive sign upon increasing the peptide concentration. Our model allows us to also incorporate electrostatic interactions between cationic peptides and anionic lipids on the level of the linear Debye-Hückel model. We show that electrostatic interactions tend to shift the Gaussian modulus toward more positive values. Steric and electrostatic lipid-peptide interactions jointly decrease the effective interaction strength in the headgroup region of the host membrane thus suggesting a generic mechanisms of how certain amphipathic peptides are able to induce the formation of saddle curvatures.

Continuum Models of Membrane Fusion: Evolution of the Theory

Starting from fertilization, through tissue growth, hormone secretion, synaptic transmission, and sometimes morbid events of carcinogenesis and viral infections, membrane fusion regulates the whole life of high organisms. Despite that, a lot of fusion processes still lack well-established models and even a list of main actors. A merger of membranes requires their topological rearrangements controlled by elastic properties of a lipid bilayer. That is why continuum models based on theories of membrane elasticity are actively applied for the construction of physical models of membrane fusion. Started from the view on the membrane as a structureless film with postulated geometry of fusion intermediates, they developed along with experimental and computational techniques to a powerful tool for prediction of the whole process with molecular accuracy. In the present review, focusing on fusion processes occurring in eukaryotic cells, we scrutinize the history of these models, their evolution and complication, as well as open questions and remaining theoretical problems. We show that modern approaches in this field allow continuum models of membrane fusion to stand shoulder to shoulder with molecular dynamics simulations, and provide the deepest understanding of this process in multiple biological systems.

Vesicle formation mechanisms: an overview

Vesicle structures primarily embody spherical capsules composed of a single or multiple bilayers, entrapping a pool of aqueous solution in their interior. The bilayers can be synthesised by phospholipids or other amphiphiles (surfactants, block copolymers, etc.). Vesicles with broad-spectrum applications in numerous scientific disciplines, including biochemistry, biophysics, biology, and various pharmaceutical industries, have attracted widespread attention. Consequently, a multitude of protocols have been devised and proposed for their fabrication. In this review, with a motivation to derive the basic conditions for the formation of vesicles, the associated thermodynamic and kinetic aspects are comprehensively appraised. Contextually, an all-purpose overview of the underlying thermodynamics of bilayer/membrane generation and deformation, including the chemical potential of aggregates, geometric packing and the concept of elastic properties, is presented. Additionally, the current review highlights the probable, inherent mechanisms of vesicle formation under distinct modes of manufacturing. We lay focus on vesicle formation from pre-existing bilayers, as well as from bilayers, which form when lipids from an organic solvent are transferred into an aqueous medium. Furthermore, we outline the kinetic effects on vesicle formation from the lamellar phase, with and without the presence of shearing force. Wherever required, the experimental and/or theoretical outcomes, the driving forces for vesicle size selection, and various scaling laws are also reviewed, all of which facilitate an overall improved understanding of the vesicle formation mechanisms.

Transverse lipid organization dictates bending fluctuations in model plasma membranes

Membrane undulations play a vital role in many biological processes, including the regulation of membrane protein activity. The asymmetric lipid composition of most biological membranes complicates theoretical description of these bending fluctuations, yet experimental data that would inform any such a theory is scarce. Here, we used neutron spin-echo (NSE) spectroscopy to measure the bending fluctuations of large unilamellar vesicles (LUV) having an asymmetric transbilayer distribution of high- and low-melting lipids. The asymmetric vesicles were prepared using cyclodextrin-mediated lipid exchange, and were composed of an outer leaflet enriched in egg sphingomyelin (ESM) and an inner leaflet enriched in 1-palmitoyl-2-oleoyl-phosphoethanolamine (POPE), which have main transition temperatures of 37 °C and 25 °C, respectively. The overall membrane bending rigidity was measured at three temperatures: 15 °C, where both lipids are in a gel state; 45 °C, where both lipids are in a fluid state; and 30 °C, where there is gel-fluid co-existence. Remarkably, the dynamics for the fluid asymmetric LUVs (aLUVs) at 30 °C and 45 °C do not follow trends predicted by their symmetric counterparts. At 30 °C, compositional asymmetry suppressed the bending fluctuations, with the asymmetric bilayer exhibiting a larger bending modulus than that of symmetric bilayers corresponding to either the outer or inner leaflet. We conclude that the compositional asymmetry and leaflet coupling influence the internal dissipation within the bilayer and result in membrane properties that cannot be directly predicted from corresponding symmetric bilayers.

Aging membranes: Unexplored functions for lipids in the lifespan of the central nervous system

Lipids constitute a significant group of biological metabolites and the building blocks of all cell membranes. The abundance and stoichiometries of different lipid species are known to vary across the lifespan and metabolic state, yet the functional effects of these changes have been challenging to understand. Here we review the potentially powerful intersection of lipid metabolism, which determines membrane composition, and aging. We first introduce several key lipid classes that are associated with aging and aging-related disease, where they are found in organisms, and how they act on membrane structure and function. Instead of neutral lipids, which have primary roles in energy storage and homeostasis, we review known functions for polar lipids that control the physicochemical properties of cell membranes. We then focus on aging processes in the central nervous system (CNS), which is enriched in lipids and is highly dependent on membrane structure for function. Recent studies show how lipids act not just as biomarkers of aging and associated changes in the CNS, but as direct mediators of these processes. As a model system, we explore how fatty acid composition in the retina impact aging and aging-related disease. We propose that the biophysical effects of membrane structure on fundamental eukaryotic processes - mitochondrial respiration and autophagy - provide avenues by which lipid dysregulation can accelerate aging processes. Finally, we lay out ways in which an increased understanding of lipid membrane biology can be applied to studies of aging and lifespan.

Elastic properties of liquid-crystalline bilayers self-assembled from semiflexible-flexible diblock copolymers

The mechanical response and shape of self-assembled bilayer membranes depend crucially on their elastic properties. Most of the studies focused on the elastic properties of fluid membranes, despite the ubiquitous presence of membranes with liquid-crystalline order. Here the elastic properties of liquid-crystalline bilayers self-assembled from diblock copolymers composed of a semiflexible block are studied theoretically. Specifically, the self-consistent field theory (SCFT) is applied to a model system composed of semiflexible-flexible diblock copolymers dissolved in flexible homopolymers that act as solvents. The free energy of self-assembled tensionless bilayer membranes in three different geometries, i.e. planar, cylindrical and spherical, is obtained by solving the SCFT equations using a hybrid method, in which the orientation-dependent functions are treated using the spherical harmonics, whereas the position-dependent operators are treated using the compact difference schemes. The bending modulus κ_M and Gaussian modulus κ_G of the bilayer are extracted from the free energies. The effects of the molecular parameters of the system, such as the chain rigidity and the orientational interaction, are systematically examined.

RNA Homopolymers Form Higher-Curvature Virus-like Particles Than Do Normal-Composition RNAs

Unlike double-stranded DNA, single-stranded RNA can be spontaneously packaged into spherical capsids by viral capsid protein (CP) because it is a more compact and flexible polymer. Many systematic investigations of this self-assembly process have been carried out using CP from cowpea chlorotic mottle virus, with a wide range of sequences and lengths of single-stranded RNA. Among these studies are measurements of the relative packaging efficiencies of these RNAs into spherical capsids. In this work, we address a fundamental issue that has received very little attention, namely the question of the preferred curvature of the capsid formed around different RNA molecules. We show in particular that homopolymers of RNA-polyribouridylic acid and polyriboadenylic acid-form exclusively T = 2-sized (∼22-nm diameter) virus-like particles (VLPs) when mixed with cowpea chlorotic mottle virus CP, independent of their length, ranging from 500 to more than 4000 nucleotides. This is in contrast to "normal-composition" RNAs (i.e., molecules with comparable numbers of each of the four nucleotides and hence capable of developing a large amount of secondary structure because of intramolecular complementarity/basepairing); a curvature corresponding to T = 3-size (∼28 nm in diameter) is preferred for the VLPs formed with such RNAs. Our work is consistent with the preferred curvature of VLPs being a consequence of interaction of CP with RNA-in particular, the presence or absence of short RNA duplexes-and suggests that the equilibrium size of the capsid results from a trade-off between this optimum size and the cost of confinement.

Accelerating Membrane Simulations with Hydrogen Mass Repartitioning

The time step of atomistic molecular dynamics (MD) simulations is determined by the fastest motions in the system and is typically limited to 2 fs. An increasingly popular approach is to increase the mass of the hydrogen atoms to ∼3 amu and decrease the mass of the parent atom by an equivalent amount. This approach, known as hydrogen-mass repartitioning (HMR), permits time steps up to 4 fs with reasonable simulation stability. While HMR has been applied in many published studies to date, it has not been extensively tested for membrane-containing systems. Here, we compare the results of simulations of a variety of membranes and membrane-protein systems run using a 2 fs time step and a 4 fs time step with HMR. For pure membrane systems, we find almost no difference in structural properties, such as area-per-lipid, electron density profiles, and order parameters, although there are differences in kinetic properties such as the diffusion constant. Conductance through a porin in an applied field, partitioning of a small peptide, hydrogen-bond dynamics, and membrane mixing show very little dependence on HMR and the time step. We also tested a 9 Å cutoff as compared to the standard CHARMM cutoff of 12 Å, finding significant deviations in many properties tested. We conclude that HMR is a valid approach for membrane systems, but a 9 Å cutoff is not.

Coherent Timescales and Mechanical Structure of Multicellular Aggregates

Multicellular aggregates are an excellent model system to explore the role of tissue biomechanics in specifying multicellular reorganization during embryonic developments and malignant invasion. Tissue-like spheroids, when subjected to a compressive force, are known to exhibit liquid-like behaviors at long timescales (hours), largely because of cell rearrangements that serve to effectively dissipate the applied stress. At short timescales (seconds to minutes), before cell rearrangement, the mechanical behavior is strikingly different. The current work uses shape relaxation to investigate the structural characteristics of aggregates and discovers two coherent timescales: one on the order of seconds, the other tens of seconds. These timescales are universal, conserved across a variety of tested species, and persist despite great differences in other properties such as tissue surface tension and adhesion. A precise mathematical theory is used to correlate the timescales with mechanical properties and reveals that aggregates have a relatively strong envelope and an unusually "soft" interior (weak bulk elastic modulus). This characteristic is peculiar, considering that both layers consist of identical units (cells), but is consistent with the fact that this structure can engender both structural integrity and the flexibility required for remodeling. In addition, tissue surface tension, elastic modulus, and viscosity are proportional to each other. Considering that these tissue-level properties intrinsically derive from cellular-level properties, the proportionalities imply precise coregulation of the latter and in particular of the tension on the cell-medium and cell-cell interfaces.