Vesicle shapes from molecular dynamics simulations

Lipid bilayer membranes are known to form various structures such as large sheets or vesicles. When the two leaflets of the bilayer have an equal composition, the membrane preferentially forms a flat sheet or a spherical vesicle. However, a difference in the composition of the two leaflets may result in a curved bilayer or in a wide variety of vesicle shapes. Vesicles with different shapes have already been shown in experiments and diverse vesicle shapes have been predicted theoretically from energy minimization of continuous curves. Here we present a molecular dynamics study of the effect of small changes in the phospholipid headgroups on the spontaneous curvature of the bilayer and on the resulting vesicle shape transformations. Small asymmetries in the bilayers already result in high spontaneous curvature and large vesicle deformations. Vesicle shapes that are formed include ellipsoids, discoids, pear-shaped vesicles, cup-shaped vesicles, as well as budded vesicles. Comparison of these vesicles with theoretically derived vesicle shapes shows both resemblances and differences.     

Coarse-grained transmembrane proteins: hydrophobic matching, aggregation, and their effect on fusion

Molecular transport between organelles is predominantly governed by vesicle fission and fusion. Unlike experimental vesicles, the fused vesicles in molecular dynamics simulations do not become spherical readily, because the lipid and water distribution is inappropriate for the fused state and spontaneous amendment is slow. Here, we study the hypothesis that enhanced transport across the membrane of water, lipids, or both is required to produce spherical vesicles. This is done by adding several kinds of model proteins to fusing vesicles. The results show that equilibration of both water and lipid content is a requirement for spherical vesicles. In addition, the effect of these transmembrane proteins is studied in bilayers and vesicles, including investigations into hydrophobic matching and aggregation. Our simulations show that the level of aggregation does not only depend on hydrophobic mismatch, but also on protein shape. Additionally, one of the proteins promotes fusion by inducing pore formation. Incorporation of these proteins allows even flat membranes to fuse spontaneously. Moreover, we encountered a novel spontaneous vesicle enlargement mechanism we call the engulfing lobe, which may explain how lipids added to a vesicle solution are quickly incorporated into the inner monolayer.     

Shear-driven release of a bud from a multicomponent vesicle

The authors study the response of a multicomponent budded vesicle to an imposed shear flow using dissipative particle dynamics. Under certain circumstances, phase separation in the vesicle membrane leads to the formation of a minority domain which deforms into a nearly spherical bud in order to reduce its interfacial energy. The authors show that an imposed shear force has a varying effect on the vesicle, tending either to separate the bud from the vesicle or to stretch the bud open, depending on the vesicle orientation. The authors examine the interplay of membrane bending rigidity, line tension, and shear in determining the behavior of the vesicle. With the appropriate design, vesicles can be made to release buds in a controlled manner in response to shear. The authors outline a regime in which bud release is favorable.     

Dynamics of vesicle self-assembly and dissolution

The dynamics of membranes is studied on the basis of a particle-based meshless surface model, which was introduced earlier [Phys. Rev. E 73, 021903 (2006)]. The model describes fluid membranes with bending energy and-in the case of membranes with boundaries-line tension. The effects of hydrodynamic interactions are investigated by comparing Brownian dynamics with a particle-based mesoscale solvent simulation (multiparticle collision dynamics). Particles self-assemble into vesicles via disk-shaped membrane patches. The time evolution of assembly is found to consist of three steps: particle assembly into discoidal clusters, aggregation of clusters into larger membrane patches, and finally vesicle formation. The time dependence of the cluster distribution and the mean cluster size is evaluated and compared with the predictions of Smoluchowski rate equations. On the other hand, when the line tension is suddenly decreased (or the temperature is increased), vesicles dissolve via pore formation in the membrane. Hydrodynamic interactions are found to speed up the dynamics in both cases. Furthermore, hydrodynamics makes vesicle more spherical in the membrane-closure process.     

Shrink-wrap vesicles

We describe a simple approach to the controlled removal of molecules from the membrane of large unilamellar vesicles made of fatty acids. Such vesicles shrink dramatically upon mixing with micelles composed of a mixture of fatty acid and a phospholipid (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC)), as fatty acid molecules leave the vesicle membrane and accumulate within the mixed micelles. Vesicle shrinkage was confirmed by dynamic light scattering, fluorescence recovery after photobleaching of labeled vesicles, and fluorescence resonance energy transfer between lipid dyes incorporated into the vesicle membrane. Most of the encapsulated impermeable solute is retained during shrinkage, becoming concentrated by a factor of at least 50-fold in the final small vesicles. This unprecedented combination of vesicle shrinkage with retention of contents allows for the preparation of small vesicles containing high solute concentrations, and may find applications in liposomal drug delivery.     

嵌段序列对聚合物囊泡形成过程影响的Monte Carlo模拟

采用Monte Carlo模拟方法研究了具有相同链长和组分比的不同嵌段序列的AB两嵌段共聚物与ABA三嵌段共聚物在选择性溶剂中形成囊泡的动力学过程. 模拟结果表明, AB两嵌段共聚物囊泡的形成与ABA三嵌段共聚物囊泡的形成的动力学过程不同. 在慢速退火条件下, ABA三嵌段共聚物囊泡是通过亲水链段向胶束的表面和中心扩散而形成的, 而AB两嵌段共聚物囊泡则由片层弯曲闭合而形成. 相对而言, 退火速度对AB两嵌段共聚物囊泡形成的动力学过程没有显著影响, 其改变仅影响亲水链段与疏水链段发生相分离的难易程度. 当退火速度较快时, 亲水链段和疏水链段发生相分离的速度较快且相分离发生在囊泡形成之前; 而当退火速度较慢时亲水链段和疏水链段之间的相分离在囊泡形成之后仍在进行.     

Mechanical stability of micropipet-aspirated giant vesicles with fluid phase coexistence

Micropipet aspiration of phase-separated lipid bilayer vesicles can elucidate physicochemical aspects of membrane fluid phase coexistence. Recently, we investigated the composition dependence of line tension at the boundary between liquid-ordered and liquid-disordered phases of giant unilamellar vesicles obtained from ternary lipid mixtures using this approach. Here we examine mechanical equilibria and stability of dumbbell-shaped vesicles deformed by line tension. We present a relationship between the pipet aspiration pressure and the aspiration length in vesicles with two coexisting phases. Using a strikingly simple mechanical model for the free energy of the vesicle, we predict a relation that is in almost quantitative agreement with experiment. The model considers the vesicle free energy to be proportional to line tension and assumes that the vesicle volume, domain area fraction, and total area are conserved during aspiration. We also examine a mechanical instability encountered when releasing a vesicle from the pipet. We find that this releasing instability is observed within the framework of our model that predicts a change of the compressibility of a pipet-aspirated membrane cylinder from positive (i.e., stable) to negative (unstable) values, at the experimental instability. The model furthermore includes an aspiration instability that has also previously been experimentally described. Our method of studying micropipet-induced shape transitions in giant vesicles with fluid domains could be useful for investigating vesicle shape transitions modulated by bending stiffness and line tension.     

Some solutions of a cell model for a suspension of spherical vesicles in osmophoresis

The problem of the osmophoretic motion of a homogeneous suspension of identical spherical vesicles is analyzed in the limit of negligible Reynolds and Peclet numbers. The effects of interaction among individual vesicles are taken into explicit account by employing a unit cell model which is known to provide good predictions for the sedimentation of monodisperse suspensions of spherical particles. The appropriate equations of conservation of mass and momentum are solved for each cell, in which a spherical vesicle is envisaged to be surrounded by a concentric shell of suspending fluid, and the osmophoretic velocity of the vesicle is calculated for various cases. Analytical expressions of this mean vesicle velocity are obtained in closed form as functions of the volume fraction of the vesicles. Comparisons between the approximate ensemble-averaged osmophoretic velocity of a test vesicle in a dilute suspension and our cell-model results are made.     

Vesicle Tubulation with Self‐Assembling DNA Nanosprings

A major goal of nanotechnology and bioengineering is to build artificial nanomachines capable of generating specific membrane curvatures on demand. Inspired by natural membrane‐deforming proteins, we designed DNA‐origami curls that polymerize into nanosprings and show their efficacy in vesicle deformation. DNA‐coated membrane tubules emerge from spherical vesicles when DNA‐origami polymerization or high membrane‐surface coverage occurs. Unlike many previous methods, the DNA self‐assembly‐mediated membrane tubulation eliminates the need for detergents or top‐down manipulation. The DNA‐origami design and deformation conditions have substantial influence on the tubulation efficiency and tube morphology, underscoring the intricate interplay between lipid bilayers and vesicle‐deforming DNA structures.     

Energy transfer of ionic dyes in mixed surfactant vesicle

Stable vesicles composed of cationic and anionic single-tailed-surfactant were prepared, and their image obtained by electron microscopy with negative staining technique. Significant fluorescence enhancement for acridine orange in vesicle with regards to water has been observed. In heterogeneous vesicle solution composed of mixed cationic and anionic surfactants for the energy transfer between acridine orange (D) and pyronine (A), the Förster dipole-dipole model was valid, and it is interesting to note that the energy transfer rate constant (k_ET) was smaller than that in homogeneous aqueous solution. On the inside and outside of the stable vesicle, immiscible water solution of acridine orange and pyronine could be obtained, and the distance calculated from the energy transfer between D and A separated by the bilayer membrane implied that the location of ionic dye molecules was in the Gouy-Chapman layers of the vesicles. Furthermore, due to the electrostatic absorption of the dye molecules to charged headgroups of surfactants, acridine orange and pyronine accumulated and aggregated to the vesicle bilayer membrane.     

Interaction and aggregation of lipid vesicles (DLVO theory versus modified DLVO theory)

Interaction and aggregation of acidic phospholipid (phosphatidylserine) vesicles were studied with variation of cation species and their concentrations in vesicle suspensions, and of vesicle sizes. Aggregation was determined by measuring turbidity of vesicle suspension. The experimental results of aggregation of vesicles induced by monovalent cations (Na⁺, K⁺, Cs⁺ and TMA⁺) were explained well in terms of the interaction energy of two interacting vesicles using the ordinary Derjaguin–Landau–Verwey–Overbeek (DLVO) theory for both small and large lipid vesicles. However, the experimental results of aggregation of vesicles induced by divalent cations (Ca²⁺, Mg²⁺ and Ba²⁺) were not explained by the ordinary DLVO theory. In order to explain the experimental results of these vesicle aggregation phenomena, it was necessary to modify the theory by including hydration interaction energies which are due to hydrated water at membrane surfaces, and their magnitude and sign depend upon the nature (hydrophobicity) of the membrane surface.     

Shape transformation of giant phospholipid vesicles at high concentrations of C12E8

Giant unilamellar phospholipid vesicles were prepared by the method of electroformation from 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (POPC). We studied the influence of different concentrations of the surfactant octaethyleneglycol dodecylether (C(12)E(8)) on the spontaneous shape transformations of POPC vesicles at room temperature. In accordance with previous results, we observed that low concentration of C(12)E(8) increased the speed of the characteristic vesicle shape transformation, starting from the initial shape with thin tubular protrusion, through beaded protrusion where the number of beads gradually decreased, to final spherical shapes with invagination, whereby the average mean curvature of the vesicle membrane monotonously decreased. In contrast, higher concentration of C(12)E(8) initially induced the shape transformation in the "opposite direction": in the protrusion, the number of beads gradually increased and eventually a tube was formed whereby the average mean curvature of the vesicle membrane gradually increased. However, at a certain point, an abrupt shape change took place to yield the vesicle with invagination. In this transition, the average mean curvature of the vesicle membrane discontinuously decreased. After this transition, the vesicle began to shrink and finally disappeared. We discuss possible mechanisms involved in the observed transformations.     

Vesicle growth and deformation in a surfactant solution below the Krafft temperature

We have studied vesicle growth and deformation in aqueous solutions of nonionic surfactant C(16)E(7) below the Krafft temperature by means of an optical microscope. It has been found that vesicles become larger by fusing together, and that the growth rate is slower than that of the unilamellar vesicle or emulsion systems due to the multilamellar structures of shells in a vesicle. The deformation of the vesicles depends on the temperature quench depth, and we found the transformation from spherical vesicles to string-like domains at a certain quench-temperature. From the small angle X-ray scattering and confocal microscope experiments, it can be deduced that the deformation of vesicles would be induced by osmotic pressure due to the micellar concentration difference between inside and outside of vesicles.     

Adhesive interactions between vesicles in the strong adhesion limit

We consider the adhesive interaction energy between a pair of vesicles in the strong adhesion limit, in which bending forces play a negligible role in determining vesicle shape compared to forces due to membrane stretching. Although force?distance or energy?distance relationships characterizing adhesive interactions between fluid bilayers are routinely measured using the surface forces apparatus, the atomic force microscope, and the biomembrane force probe, the interacting bilayers in these methods are supported on surfaces (e.g., mica sheet) and cannot be deformed. However, it is known that, in a suspension, vesicles composed of the same bilayer can deform by stretching or bending, and can also undergo changes in volume. Adhesively interacting vesicles can thus form flat regions in the contact zone, which will result in an enhanced interaction energy as compared to rigid vesicles. The focus of this paper is to examine the magnitude of the interaction energy between adhesively interacting, deformed vesicles relative to free, undeformed vesicles as a function of the intervesicle separation. The modification of the intervesicle interaction energy due to vesicle deformability can be calculated knowing the undeformed radius of the vesicles, R0, the bending modulus, k(b), the area expansion modulus, k(a), and the adhesive minimum, W(P)(0), and separation, D(P)(0), in the energy of interaction between two flat bilayers, which can be obtained from the force?distance measurements made using the above supported-bilayer methods. For vesicles with constant volumes, we show that adhesive potentials between nondeforming bilayers such as |W(P)(0)| 5 × 10(?4) mJ/m2, which are ordinarily considered weak in the colloidal physics literature, can result in significantly deep (>10×) energy minima due to increase in vesicle area and flattening in the contact region. If the osmotic expulsion of water across the vesicles driven by the tense, stretched membrane in the presence of an osmotically active solute is also taken into account, the vesicles can undergo additional deformation (flattening), which further enhances the adhesive interaction between them. Finally, equilibration of ions and solutes due to the concentration differences created by the osmotic exchange of water can lead to further enhancement of the adhesion energy. Our result of the progressively increasing adhesive interaction energy between vesicles in the above regimes could explain why suspensions of very weakly attractive vesicles may undergo flocculation and eventual instability due to separation of vesicles from the suspending fluid by gravity. The possibility of such an instability is an extremely important issue for concentrated vesicle-based products and applications such as fabric softeners, hair therapeutics and drug delivery.     

Novel method for measuring the adhesion energy of vesicles

Adhering vesicles with osmotically stabilized volume are studied with Monte Carlo simulations and optical microscopy. The simulations are used to determine the dependence of the adhesion area on the vesicle volume, the surface area, the bending rigidity, the adhesion energy per membrane area, and the adhesion potential range. The simulation results lead to a simple functional expression that is supplemented by a correction term for gravity effects. The obtained equation provides a new tool to analyze optical microscopy data and, thus, to measure the adhesion energy per area by analyzing the geometry of the adhering vesicle. The method can be applied in the weak and ultra-weak adhesion regime, where the adhesion energy per area is below 10(-6) J/m(2). By comparing the shapes of adhering vesicles with different reduced volumes, the bending rigidity can be estimated as well. The new approach is applied to experimental data for lipid vesicles on (i) an untreated and (ii) a monolayer-coated glass surface, providing ultra-weak and weak adhesion strength, respectively.     

Membrane-bound protein in giant vesicles: induced contraction and growth

Cell-sized giant vesicles, produced by electroformation, were composed of phospholipids and zein (a hydrophobic protein that occupied a substantial percentage of the vesicle surface). Addition of sodium dodecyl sulfate removed the protein into the bulk phase, which led to a shrinkage of the vesicles. The vesicle bilayers were able to heal themselves from the damage caused by the departure of the zein, allowing the bilayers to maintain their spherical morphology. Giant vesicle growth was also observed when the following components were mixed (all four being necessary): (a) negatively charged giant vesicles, (b) membrane-incorporated zein, (c) positively charged submicroscopic vesicles (almost 103 times smaller than the giant vesicles), and (d) sodium dodecyl sulfate. The simplest mechanism consistent with literature data involves electrostatically promoted binding of the small vesicles (weakened by the surfactant) onto the giant vesicle surface, followed by the merging of membranes at protein-induced "fusion hot spots". The "feeding" of small vesicles by giant vesicles then leads to growth.     

Coarse‐grained molecular dynamics simulation study on spherical and tube‐like vesicles formed by amphiphilic copolymers

Molecular‐level understanding of the vesicular structure and formation process is beneficial for potential vesicle applications, especially in drug delivery. In this article, coarse‐grained molecular dynamics simulation was used to study the self‐assembly behavior of amphiphilic poly(acrylic acid)‐b‐polystyrene copolymers in water at different concentrations and PS/PAA block ratios. It was found that various spherical and tube‐like vesicles formed at PS/PAA 3:3 and 4:2. For spherical vesicles, analysis of vesicular structure indicated that the cavity size was influenced by copolymer concentration and wall thickness by the block ratio. Tube‐like vesicle was formed via the fusion of two spherical vesicles, and a key factor for this morphology is polymer movements between inner and outer layer. This simulation study identifies the key factors governing vesicle formation and structure, and provides a guidance to design and prepare various vesicles for wide applications in drug delivery. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1220–1226     

Effect of water content on the size and membrane thickness of polystyrene-block-poly(ethylene oxide) vesicles

The asymmetric amphiphilic block copolymer polystyrene962-block-poly(ethylene oxide)227(PS962-b-PEO227) canforms micelles with N, N-dimethylformamide(DMF) as co-solvent and water as selected solvent, and when the water content of the mixed solvent is higher than 4.5 wt%, the vesicle will be dominated. This work finds that once vesicles are formed in the DMF-water mixed solvent, the vesicle size and membrane thickness can be tuned by further increasing water content. As the water fraction elevated from 4.8 wt% to 13.0 wt%, the vesicle size dercreases from 246 nm to 150 nm, while the membrane thickness increases from 28 nm to 42 nm. In addition, the block copolymer packing and the free energy are analyzed as the vesicle size becomes small and the membrane becomes thick.     

The adhesion kinetics of sticky vesicles in tension: the distinction between spreading and receptor binding

We investigate the kinetics of spreading and adhesion between polymer vesicles decorated with avidin and biotin, held in micropipettes to maintain fixed tension and suppress membrane bending fluctuations. In this study, the density of avidin (actually Neutravidin) and biotin was varied, but was always sufficiently high so that lateral diffusion in the membrane was unimportant to the adhesive mechanism or rate. For a stunning result, we report a concentration-dependent distinction between adhesion and spreading: At low surface densities of avidin and biotin, irreversible vesicle adhesion is strong enough to break the membrane when vesicle separation is attempted, yet there is no spreading or "wetting". By this we mean that there is no development of an adhesion plaque beyond the initial radius of contact and there is no development of a meaningful contact angle. Conversely, at 30% functionalization and greater, membrane adhesion is manifest through a spreading process in which the vesicle held at lower tension partially engulfs the second vesicle, and the adhesion plaque grows, as does the contact angle. Generally, when spreading occurs, it starts abruptly, following a latent contact period whose duration decreases with increasing membrane functionality. A nucleation-type rate law describes the latency period, determined by competition between bending and sticking energy. The significance of this result is that, not only are membrane mechanics important to the development of adhesion in membranes of nanometer-scale thickness, mechanics can dominate and even mask adhesive features such as contact angle. This renders contact angle analyses inappropriate for some systems. The results also suggest that there exist large regions of parameter space where adhesive polymeric vesicles will behave qualitatively differently from their phospholipid counterparts. This motivates different strategies to design polymeric vesicles for applications such as targeted drug delivery and biomimetic scavengers.     

Preparation and properties of vesicles made of nonpolar/polar/nonpolar fullerene amphiphiles

Twenty potassium complexes of penta-[(4-substituted)phenyl][60]fullerene anions were synthesized and examined for their ability to form bilayer vesicles in water. The 4-substituents include alkyl groups ranging from methyl to icosanyl groups and perfluoromethyl, perfluorobutyl, and perfluorooctyl groups. The overall structure of the amphiphiles can be described as a nonpolar/polar/nonpolar (n-p-n') motif as opposed to the usual polar/nonpolar motif of lipid amphiphiles. Despite the hydrophobicity of the fullerene moiety (n-part) and alkyl/perfluoroalkyl chains (n'-part), all compounds except for the one with perfluoromethyl groups were soluble in water because of the centrally located fullerene cyclopentadienide (p-part) and spontaneously formed a vesicle of 25- to 60-nm diameter with a narrow unimodal size distribution. The vesicles are stable upon heating to 90 °C or standing over one year in air, as well as on a solid substrate in air or in vacuum, maintaining their spherical form. The vesicle membrane consists of an interdigitated bilayer of the amphiphile molecules, in which the fullerene n-part is inside and the n'-side is exposed to water. These vesicles, in particular the one bearing icosanyl chains, exhibit the smallest water permeability coefficient ever found for a self-assembled membrane in water.