Determining the ratio of the Gaussian curvature and bending elastic moduli of phospholipids from Q(II) phase unit cell dimensions

Lipid nanoparticle topology regulates endosomal escape and delivery of RNA to the cytoplasm

RNA therapeutics have the potential to resolve a myriad of genetic diseases. Lipid nanoparticles (LNPs) are among the most successful RNA delivery systems. Expanding their use for the treatment of more genetic diseases hinges on our ability to continuously evolve the design of LNPs with high potency, cellular-specific targeting, and low side effects. Overcoming the difficulty of releasing cargo from endocytosed LNPs remains a significant hurdle. Here, we investigate the fundamental properties of nonviral RNA nanoparticles pertaining to the activation of topological transformations of endosomal membranes and RNA translocation into the cytosol. We show that, beyond composition, LNP fusogenicity can be prescribed by designing LNP nanostructures that lower the energetic cost of fusion and fusion-pore formation with a target membrane. The inclusion of structurally active lipids leads to enhanced LNP endosomal fusion, fast evasion of endosomal entrapment, and efficacious RNA delivery. For example, conserving the lipid make-up, RNA-LNPs having cuboplex nanostructures are significantly more efficacious at endosomal escape than traditional lipoplex constructs.

Bicontinuous inverted cubic phase stabilization as an index of antimicrobial and membrane fusion peptide activity

Some antimicrobial peptides (AMPs) and membrane fusion-catalyzing peptides (FPs) stabilize bicontinuous inverted cubic (QII) phases. Previous authors proposed a topological rationale: since AMP-induced pores, fusion intermediates, and QII phases all have negative Gaussian curvature (NGC), peptides which produce NGC in one structure also do it in another. This assumes that peptides change the curvature energy of the lipid membranes. Here I test this with a Helfrich curvature energy model. First, experimentally, I show that lipid systems often used to study peptide NGC have NGC without peptides at higher temperatures. To determine the net effect of an AMP on NGC, the equilibrium phase behavior of the host lipids must be determined. Second, the model shows that AMPs must make large changes in the curvature energy to stabilize AMP-induced pores. Peptide-induced changes in elastic constants affect pores and QII phase differently. Changes in spontaneous curvature affect them in opposite ways. The observed correlation between QII phase stabilization and AMP activity doesn't show that AMPs act by lowering pore curvature energy. A different rationale is proposed. In theory, AMPs could simultaneously stabilize QII phase and pores by drastically changing two particular elastic constants. This could be tested by measuring AMP effects on the individual constants. I propose experiments to do that. Unlike AMPs, FPs must make only small changes in the curvature energy to catalyze fusion. It they act in this way, their fusion activity should correlate with their ability to stabilize QII phases.

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 (H_II), cubic (Q_II; 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 (Δκ̅_m), 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 κ̅_m 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.

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.

A consistent quadratic curvature-tilt theory for fluid lipid membranes

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

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

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

Exploiting Lipid Permutation Symmetry to Compute Membrane Remodeling Free Energies

A complete physical description of membrane remodeling processes, such as fusion or fission, requires knowledge of the underlying free energy landscapes, particularly in barrier regions involving collective shape changes, topological transitions, and high curvature, where Canham-Helfrich (CH) continuum descriptions may fail. To calculate these free energies using atomistic simulations, one must address not only the sampling problem due to high free energy barriers, but also an orthogonal sampling problem of combinatorial complexity stemming from the permutation symmetry of identical lipids. Here, we solve the combinatorial problem with a permutation reduction scheme to map a structural ensemble into a compact, nondegenerate subregion of configuration space, thereby permitting straightforward free energy calculations via umbrella sampling. We applied this approach, using a coarse-grained lipid model, to test the CH description of bending and found sharp increases in the bending modulus for curvature radii below 10 nm. These deviations suggest that an anharmonic bending term may be required for CH models to give quantitative energetics of highly curved states.

Protein-induced membrane curvature alters local membrane tension

Adsorption of proteins onto membranes can alter the local membrane curvature. This phenomenon has been observed in biological processes such as endocytosis, tubulation, and vesiculation. However, it is not clear how the local surface properties of the membrane, such as membrane tension, change in response to protein adsorption. In this article, we show that the partial differential equations arising from classical elastic model of lipid membranes, which account for simultaneous changes in shape and membrane tension due to protein adsorption in a local region, cannot be solved for nonaxisymmetric geometries using straightforward numerical techniques; instead, a viscous-elastic formulation is necessary to fully describe the system. Therefore, we develop a viscous-elastic model for inhomogeneous membranes of the Helfrich type. Using the newly available viscous-elastic model, we find that the lipids flow to accommodate changes in membrane curvature during protein adsorption. We show that, at the end of protein adsorption process, the system sustains a residual local tension to balance the difference between the actual mean curvature and the imposed spontaneous curvature. We also show that this change in membrane tension can have a functional impact such as altered response to pulling forces in the presence of proteins.

Gaussian curvature elasticity determined from global shape transformations and local stress distributions: a comparative study using the MARTINI model

We calculate the Gaussian curvature modulus kappa of a systematically coarse-grained (CG) one-component lipid membrane by applying the method recently proposed by Hu et al. [Biophys. J., 2012, 102, 1403] to the MARTINI representation of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). We find the value kappa/kappa = -1.04 +/- 0.03 for the elastic ratio between the Gaussian and the mean curvature modulus and deduce kappa(m)/kappa(m) = -0.98 +/- 0.09 for the monolayer elastic ratio, where the latter is based on plausible assumptions for the distance z0 of the monolayer neutral surface from the bilayer midplane and the spontaneous lipid curvature K(0m). By also analyzing the lateral stress profile sigma0(z) of our system, two other lipid types and pertinent data from the literature, we show that determining K(0m) and kappa through the first and second moment of sigma0(z) gives rise to physically implausible values for these observables. This discrepancy, which we previously observed for a much simpler CG model, suggests that the moment conditions derived from simple continuum assumptions miss the effect of physically important correlations in the lipid bilayer.

Lipid sorting by ceramide and the consequences for membrane proteins

We mimicked the effect of sphingomyelinase activity on lipid mixtures of palmitoyl-oleoyl-phosphatidylcholine, sphingomyelin, ceramide, and 10 mol % cholesterol. Using x-ray diffraction experiments in combination with osmotic stress we found, in agreement with previous studies, that ceramide induces a coexistence of L(α) and L(β) domains. A detailed structural analysis of the coexisting domains demonstrated an increase of lipid packing density and membrane thickness in the L(α) domains upon increasing overall ceramide levels. This provides evidence for a ceramide-driven accumulation of cholesterol in the L(α) domains, in support of previous reports. We further determined the bending rigidities of the coexisting domains and found that the accumulation of cholesterol in the L(α) domains stabilizes their bending rigidity, which experiences a dramatic drop in the absence of cholesterol. Deriving experimental estimates for the spontaneous curvature and Gaussian modulus of curvature, we show, using a simple geometric model for ion channels, that in this way changes in the conformational equilibrium of membrane proteins can be kept small.

Determining the Gaussian curvature modulus of lipid membranes in simulations

The Gaussian curvature modulus κ¯ of lipid bilayers likely contributes more than 100 kcal/mol to every cellular fission or fusion event. This huge impact on membrane remodeling energetics might be a factor that codetermines the complex lipid composition of biomembranes through tuning of κ¯. Yet, its value has been measured only for a handful of simple lipids, and no simulation has so far determined it better than a factor of two, rendering a systematic investigation of such enticing speculations impossible. Here we propose a highly accurate method to determine κ¯ in computer simulations. It relies on the interplay between curvature stress and edge tension of partially curved axisymmetric membrane disks and requires determining their closing probability. For a simplified lipid model we obtain κ¯ and its relation to the normal bending modulus κ for membranes differing both in stiffness and spontaneous lipid curvature. The elastic ratio κ¯/κ can be determined with a few percent statistical accuracy. Its value agrees with the scarce experimental data, and its change with spontaneous lipid curvature is compatible with theoretical expectations, thereby granting additional information on monolayer properties. We also show that an alternative determination of these elastic parameters based on moments of the lateral stress profile gives markedly different and unphysical values.

Interaction of an antimicrobial peptide with membranes: experiments and simulations with NKCS

We used Monte Carlo simulations and biophysical measurements to study the interaction of NKCS, a derivative of the antimicrobial peptide NK-2, with a 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE) membrane. The simulations showed that NKCS adsorbed on the membrane surface and the dominant conformation featured two amphipathic helices connected by a hinge region. We designed two mutants in the hinge to investigate the interplay between helicity and membrane affinity. Simulations with a Leu-to-Pro substitution showed that the helicity and membrane affinity of the mutant (NKCS-[LP]) decreased. Two Ala residues were added to NKCS to produce a sequence that is compatible with a continuous amphipathic helix structure (NKCS-[AA]), and the simulations showed that the mutant adsorbed on the membrane surface with a particularly high affinity. The circular dichroism spectra of the three peptides also showed that NKCS-[LP] is the least helical and NKCS-[AA] is the most. However, the activity of the peptides, determined in terms of their antimicrobial potency and influence on the temperature of the transition of the lipid to hexagonal phase, displayed a complex behavior: NKCS-[LP] was the least potent and had the smallest influence on the transition temperature, and NKCS was the most potent and had the largest effect on the temperature.

Fourth-order curvature energy model for the stability of bicontinuous inverted cubic phases in amphiphile-water systems

The bicontinuous inverted cubic (Q(II)) phases of amphiphiles in water have many practical applications. It is necessary to understand the stability of these phases as a function of composition and ambient conditions in order to make the best use of them. Moreover, many biomembrane lipids and some biomembrane lipid extracts form Q(II) phases. The stability of Q(II) phases in a given lipid composition is closely related to the susceptibility of that composition to membrane fusion: changes in composition that stabilize Q(II) phases usually increase the rate of membrane fusion. However, the factors determining Q(II) phase stability are not fully understood. Previously, an expression was derived for the curvature free energy of Q(II) phases with respect to that of the lamellar (L(alpha)) phase using a model for the curvature energy with terms up to fourth order in curvature as formulated by Mitov. Here this model is extended to account for the effects of water content on Q(II) phase stability. It is shown that the observed L(alpha)/Q(II) phase-transition temperature, transition enthalpy, and transition kinetics are all sensitive to water content. The same observables also become sensitive to small noncurvature energy contributions to the total free-energy difference between the Q(II) and L(alpha) phases, especially the unbinding energy in the L(alpha) phase. These predictions rationalize earlier observations of Q(II) phase formation in N-monomethylated dioleoylphosphatidylethanolamine that otherwise appear to be inconsistent. The model also provides a fundamental explanation of the hysteresis typically observed in transitions between the L(alpha) and Q(II) phases. It is an accurate model of Q(II) phase stability when the ratio of the volume fraction of the lipid in the Q(II) phase unit cell is < or = 0.5.

Free energies of stable and metastable pores in lipid membranes under tension

The free energy profile of pore formation in a lipid membrane, covering the entire range from a density fluctuation in an intact bilayer to a large tension-stabilized pore, has been calculated by molecular dynamics simulations with a coarse-grained lipid model. Several fixed elongations are used to obtain the Helmholtz free energy as a function of pore size for thermodynamically stable, metastable, and unstable pores, and the system-size dependence of these elongations is discussed. A link to the Gibbs free energy at constant tension, commonly known as the Litster model, is established by a Legendre transformation. The change of genus upon pore formation is exploited to estimate the saddle-splay modulus or Gaussian curvature modulus of the membrane leaflets. Details are provided of the simulation approach, which combines the potential of mean constraint force method with a reaction coordinate based on the local lipid density.

Minimum membrane bending energies of fusion pores

Membranes fuse by forming highly curved intermediates, culminating in structures described as fusion pores. These hourglass-like figures that join two fusing membranes have high bending energies, which can be estimated using continuum elasticity models. Fusion pore bending energies depend strongly on shape, and the present study developed a method for determining the shape that minimizes bending energy. This was first applied to a fusion pore modeled as a single surface and then extended to a more realistic model treating a bilayer as two monolayers. For the two-monolayer model, fusion pores were found to have metastable states with energy minima at particular values of the pore diameter and bilayer separation. Fusion pore energies were relatively insensitive to membrane thickness but highly sensitive to spontaneous curvature and membrane asymmetry. With symmetrical bilayers and monolayer spontaneous curvatures of -0.1 nm(-1) (a typical value) separated by 6 nm (closest distance determined by repulsive hydration forces), fusion pore formation required 43-65 kT. The pore radius of approximately 2.25 nm fell within the range estimated from conductance measurements. With bilayer separation >6 nm, fusion pore formation required less energy, suggesting that protein scaffolds can promote fusion by bending membranes toward one another. With nonzero spontaneous monolayer curvature, the shape that minimized the energy change during fusion pore formation differed from the shape that minimized its energy after it formed. Thus, a nascent fusion pore will relax spontaneously to a new shape, consistent with the experimentally observed expansion of nascent fusion pores during viral fusion.

Role of phospholipid asymmetry in the stability of inverted hexagonal mesoscopic phases

The role of phospholipid asymmetry in the transition from the lamellar (L(alpha)) to the inverted hexagonal (H(II)) phase upon the temperature increase was considered. The equilibrium configuration of the system was determined by the minimum of the free energy including the contribution of the isotropic and deviatoric bending and the interstitial energy of phospholipid monolayers. The shape and local interactions of a single lipid molecule were taken into account. The minimization with respect to the configuration of the lipid layers was performed by a numerical solution of the system of the Euler-Lagrange differential equations and by the Monte Carlo simulated annealing method. At high enough temperature, the lipid molecules attain a shape exhibiting higher intrinsic mean and deviatoric curvatures, which fits better into the H(II) phase than into the L(alpha) phase. Furthermore, the orientational ordering of lipid molecules in the curvature field expressed as the deviatoric bending provides a considerable negative contribution to the free energy, which stabilizes the nonlamellar H(II) phase. The nucleation configuration for the L(alpha)-H(II) phase transition is tuned by the isotropic and deviatoric bending energies and the interstitial energy.

The Gaussian curvature elastic energy of intermediates in membrane fusion

The Gaussian curvature elastic energy contribution to the energy of membrane fusion intermediates has usually been neglected because the Gaussian curvature elastic modulus, kappa, was unknown. It is now possible to measure kappa for phospholipids that form bicontinuous inverted cubic (Q(II)) phases. Here, it is shown that one can estimate kappa for lipids that do not form Q(II) phases by studying the phase behavior of lipid mixtures. The method is used to estimate kappa for several lipid compositions in excess water. The values of kappa are used to compute the curvature elastic energies of stalks and catenoidal fusion pores according to recent models. The Gaussian curvature elastic contribution is positive and similar in magnitude to the bending energy contribution: it increases the total curvature energy of all the fusion intermediates by 100 units of k(B)T or more. It is important to note that this contribution makes the predicted intermediate energies compatible with observed lipid phase behavior in excess water. An order-of-magnitude fusion rate equation is used to estimate whether the predicted stalk energies are consistent with the observed rates of stalk-mediated processes in pure lipid systems. The current theory predicts a stalk energy that is slightly too large, by approximately 30 k(B)T, to rationalize the observed rates of stalk-mediated processes in phosphatidylethanolamine or N-monomethylated dioleoylphosphatidylethanolamine systems. Despite this discrepancy, the results show that models of fusion intermediate energy are accurate enough to make semiquantitative predictions about how proteins mediate biomembrane fusion. The same rate model shows that for proteins to drive biomembrane fusion at observed rates, they have to perform mediating functions corresponding to a reduction in the energy of a purely lipidic stalk by several tens of k(B)T. By binding particular peptide sequences to the monolayer surface, proteins could lower fusion intermediate energies by altering the elastic constants of the patches of lipid monolayer that form the stalk. Here, it is shown that if peptide binding changes kappa or some other combinations of local elastic constants by only tens of percents, the stalk energy and the energy of catenoidal fusion pores would decrease by tens of k(B)T relative to the pure lipid value. This is comparable to the required mediating effect. The curvature energies of stalks and catenoidal fusion pores have almost the same dependence on monolayer elastic constants as the curvature energies of the rhombohedral and Q(II) phases; respectively. The effects of isolated fusion-relevant peptides on the energies of these intermediates can be determined by studying the effects of the peptides on the stability of rhombohedral and Q(II) phases.

The biophysical function of pulmonary surfactant

Pulmonary surfactant lowers surface tension in the lungs. Physiological studies indicate two key aspects of this function: that the surfactant film forms rapidly; and that when compressed by the shrinking alveolar area during exhalation, the film reduces surface tension to very low values. These observations suggest that surfactant vesicles adsorb quickly, and that during compression, the adsorbed film resists the tendency to collapse from the interface to form a 3D bulk phase. Available evidence suggests that adsorption occurs by way of a rate-limiting structure that bridges the gap between the vesicle and the interface, and that the adsorbed film avoids collapse by undergoing a process of solidification. Current models, although incomplete, suggest mechanisms that would partially explain both rapid adsorption and resistance to collapse as well as how different constituents of pulmonary surfactant might affect its behavior.

Influence of antimicrobial peptides on the formation of nonlamellar lipid mesophases

We have studied the influence of four antimicrobial peptides of different secondary and ternary structure--melittin (Mel), protegrin-1 (PG-1), peptidyl-glycylleucine-carboxyamide (PGLa), and gramicidin S (GS)--on the lamellar-to-nonlamellar transition of palmitoyloleoyl phosphatidylethanolamine (POPE) applying differential scanning calorimetry and small-angle X-ray diffraction. None of the peptides studied led to the formation of an inverted hexagonal phase observed for pure POPE at high temperatures. Instead either cubic or lamellar phases were stabilized to different degrees. GS was most effective in inducing a cubic phase, whereas Mel fully stabilized the lamellar phase. The behavior of POPE in the presence of PG-1 and PGLa was intermediate to GS and Mel. In addition to the known role of membrane elasticity we propose two mechanisms, which cause stabilization of the lamellar phase: electrostatic repulsion and lipid/peptide pore formation. Both mechanisms prevent transmembrane contact required to form either an inverted hexagonal phase or fusion pores, as precursors of the cubic phase.

Inhomogeneous NMR line shape as a probe of microscopic organization of bicontinuous cubic phases

NMR line shapes of the lipid and aqueous species in bicontinuous cubic phase (BCP) samples prepared by centrifugation are inhomogeneously broadened. The broadening of the lipid peaks is removed by magic-angle spinning (MAS). In this work, we studied the mechanism of this broadening using (1)H and (13)C NMR spectroscopy of a myverol/water BCP. It is demonstrated that the inhomogeneity possesses an intrinsic contribution that is independent of instrumental or setup factors and can be attributed to the microscopic organization of the BCP bilayer. A mechanism of the inhomogeneous broadening is proposed, which involves a spatially nonuniform diamagnetically induced magnetic field determined by the mesoscopic structure and the diamagnetic susceptibilities of the two BCP domains. The proposed mechanism does not require that molecular reorientation of the lipid be slow for the inhomogeneous broadening to survive. We discuss how this inhomogeneous broadening can be employed as a probe of compositional uniformity and microscopic organization of BCP samples.

Influence of the lamellar phase unbinding energy on the relative stability of lamellar and inverted cubic phases

Based on curvature energy considerations, nonbilayer phase-forming phospholipids in excess water should form stable bicontinuous inverted cubic (Q(II)) phases at temperatures between the lamellar (L(alpha)) and inverted hexagonal (H(II)) phase regions. However, the phosphatidylethanolamines (PEs), which are a common class of biomembrane phospholipids, typically display direct L(alpha)/H(II) phase transitions and may form intermediate Q(II) phases only after the temperature is cycled repeatedly across the L(alpha)/H(II) phase transition temperature, T(H), or when the H(II) phases are cooled from T > T(H). This raises the question of whether models of inverted phase stability, which are based on curvature energy alone, accurately predict the relative free energy of these phases. Here we demonstrate the important role of a noncurvature energy contribution, the unbinding energy of the L(alpha) phase bilayers, g(u), that serves to stabilize the L(alpha) phase relative to the nonlamellar phases. The planar L(alpha) phase bilayers must separate for a Q(II) phase to form and it turns out that the work of their unbinding can be larger than the curvature energy reduction on formation of Q(II) phase from L(alpha) at temperatures near the L(alpha)/Q(II) transition temperature (T(Q)). Using g(u) and elastic constant values typical of unsaturated PEs, we show that g(u) is sufficient to make T(Q) > T(H) for the latter lipids. Such systems would display direct L(alpha) --> H(II) transitions, and a Q(II) phase might only form as a metastable phase upon cooling of the H(II) phase. The g(u) values for methylated PEs and PE/phosphatidylcholine mixtures are significantly smaller than those for PEs and increase T(Q) by only a few degrees, consistent with observations of these systems. This influence of g(u) also rationalizes the effect of some aqueous solutes to increase the rate of Q(II) formation during temperature cycling of lipid dispersions. Finally, the results are relevant to protocols for determining the Gaussian curvature modulus, which substantially affects the energy of intermediates in membrane fusion and fission. Recently, two such methods were proposed based on measuring T(Q) and on measuring Q(II) phase unit cell dimensions, respectively. In view of the effect of g(u) on T(Q) that we describe here, the latter method, which does not depend on the value of g(u), is preferable.

Designing synthetic vesicles that engulf nanoscopic particles

We examine the interaction of a lipid bilayer membrane with a spherical particle in solution using dissipative particle dynamics, with the aim of controlling the passage of foreign objects into and out of vesicles. Parameters are chosen such that there is a favorable adhesive interaction between the membrane and the particle. Under these conditions, the membrane wraps the particle in a process resembling phagocytosis in biological cells. We find that, for a homogeneous membrane with a uniform attraction to the particle, the membrane is unable to fully wrap the particle when the adhesion strength is below a certain value. This is observed even in the limit of zero membrane tension. When the adhesion strength is increased above the threshold value, the membrane fully wraps the particle. However, the wrapped particle remains tethered to the larger membrane. We next consider an adhesive domain, or raft, in an otherwise nonadhesive membrane. We find that, when the particle is wrapped by the raft, the line tension at the raft interface promotes fission, allowing the wrapped particle to detach from the larger membrane. This mechanism could be used to allow particles to cross a vesicle membrane.