Compound giant unilamellar vesicles as a bio-mimetic model for electrohydrodynamics of a nucleate cell.

The understanding obtained by studies on the electrohydrodynamics (EHD) of single giant unilamellar vesicles (sGUVs) has contributed significantly towards a better comprehension of the response of biological cells to electric fields. This has subsequently helped in developing technologies such as cell dielectrophoresis and cell electroporation. For nucleate eukaryotic cells though, a vesicle-in-vesicle compound giant unilamellar vesicle (cGUV) is a more appropriate bio-mimic than a sGUV. In this work, we present an improvised method for the formation of cGUVs, wherein the electrical conductivities of the inner, annular and outer regions of the cGUVs can be modified. A comprehensive experimental study is presented on the EHD of these cGUVs under weak AC fields over a wide range of frequencies, and an encouraging agreement is observed between the experiments and earlier published theoretical studies on concentric cGUVs. The spherical, prolate or oblate spheroidal deformations of a cGUV under AC electric fields depend upon the membrane electromechanical properties as well as the magnitude and direction of the electric traction at the membrane produced by the Maxwell stress that varies with the relative timescales associated with the frequency of the applied AC electric field and that of the membrane charging time and the Maxwell-Wagner relaxation time. This work establishes cGUVs as appropriate bio-mimics for conducting EHD studies relevant to eukaryotic cells.

Forecasting the Problem of Excessive Oil Entrainment in a Desalter Using Spinning Drop Method.

Frequent desalter upsets in the refineries processing opportunity crude oils are often triggered by a rapid and uncontrollable buildup of the rag layer, a thick water-in-oil emulsion, at the oil-brine interface. This is caused by spontaneous emulsification of brine in oil. This study investigates a unique observation from a spinning drop (SD) tensiometer, revealing the low apparent interfacial tension and rigidity of SD caused by spontaneous emulsification. Fine droplets of brine generated through spontaneous emulsification decorate the SD surface and form a stable, low-energy bilayer. Simulated rag layers using the brines from upset incidences exhibit similar behavior, indicating that spontaneous emulsification is driven by chemical species in brine, which promote osmotic water transport. The rate of rag layer buildup correlates with the rate of spontaneous emulsification, with the temperature coefficient of interfacial tension reduction serving as a sensitive indicator. An imminent upset in the operation can be forecasted by measuring this temperature coefficient, enabling preventive measures.

Study of the interfacial viscoelasticity of human serum albumin microcapsules using a viscoelasto-electrohydrodynamic technique.

Crosslinked proteins are widely used as the encapsulating membranes in microcapsules for many biomedical and food industries. The interfacial rheological properties of these capsules are due to the complex microstructure of cross-linked globular proteins owing to structural changes at quaternary, tertiary and secondary levels. These changes in structure can be induced by high protein concentration, hydrophobic-hydrophillic interfaces, and pH. In this work, the interfacial viscoelastic rheological properties of human serum albumin (HSA) microcapsules are estimated using a novel electrodeformation technique exhibiting creep and oscillatory responses. Insights into the microstructure-rheology relationship are obtained using FTIR and SEM studies. The results show a complex dependence of the interfacial properties on the size, concentration and pH of the capsules. An interplay of inter-molecular interactions, adsorption and multilayer formation, accessibility to reactive functional groups, and dependence on the relative content of alpha helix, beta sheet and beta turn is observed. The interfacial rheological properties are estimated using the Burger model and creep is found to sensitively affect the rheological properties due to irreversible changes in microstructure. Furthermore, the electrodeformation technique allows analysis of interfacial rheology at high frequencies, 10 Hz to 1 kHz, which is otherwise not easily possible with conventional rheometers.

Effect of the Waveform of the Pulsed Electric Field on the Cylindrical Deformation of Uncharged Giant Unilamellar Vesicles.

High-speed imaging of giant unilamellar vesicles (GUVs) in recent years has shown significant shape deformation of these vesicles under electroporating direct current (DC) pulsed electric fields, possibly altering the surface distribution of transmembrane potential (TMP) and, thereby, the location and extent of electroporation on the bilayer membrane. The development of TMP, the corresponding shape deformation, and the extent of electroporation depend upon the waveform of the applied electric field. In this work, the deformation of vesicles was carried out under a high-intensity, single cycle of a sinusoidal pulsed electric field (SSPEF) and a square wave pulsed electric field (SWPEF). The cylindrical shape deformations of vesicles were observed for both SSPEF and SWPEF and were dependent upon the ratio of conductivity of the inner medium to the outer medium, α. For α = 1 and α > 1, the vesicles deformed into prolate cylinders as a result of Maxwell stress, whereas they were compressed into oblate cylinders for α < 1. Vesicles subjected to a SSPEF relaxed following either the pore closure dominated t2 or the efflux and lipid loss dominated, slow t3 mechanism depending upon the value of α. For α = 1 and α < 1, the relaxation of the vesicles was found to be predominantly dependent upon pore closure. On the other hand, a majority of vesicles gained excess area during poration when α > 1, which can be attributed to a higher TMP and faster charging of the membrane. The predictions of the approximate model for the deformation of vesicles agreed with the experiment, with deviations between the two as a result of the simplicity of the model. Moreover, the degree of deformation of vesicles [measured by the aspect ratio (AR)] and shape deformations of vesicles were found to be dependent upon the pulse width (TP) and amplitude (E0) of the SSPEF. The specific temporal variation of pore-forming tendencies of SSPEF and SWPEF, with their associated peculiarities, can be judiciously used for controlling electroporation in cells and vesicles.

Translation-deformation coupling effects on the Rayleigh instability of an electrodynamically levitated charged droplet.

The breakup pathway of the Rayleigh fission process observed in the past experiments carried out using high-speed imaging of a charged drop levitated in an AC quadrupole trap has shown to exhibit several cycles of shape and center-of-mass oscillations followed by asymmetric breakup by ejecting a jet in the upward direction (i.e., opposite to the direction of gravity). We recently attempted to explain this using boundary integral simulations in the Stokes flow limit, wherein the position of the droplet and the polarity of the end cap electrodes were assigned using physical arguments, and the center-of-mass motion was not estimated consistently invoking quasi-static conditions. In this work, we explain the experimental observation of upward breakup of charged droplets in a quadrupolar field, using numerical calculations based on the boundary element method considering inviscid droplets levitated electrodynamically using quadrupole electric fields. The center-of-mass motion and the end cap are consistently calculated in the numerical scheme. The simulations show that the gravity-induced downward shift in the equilibrium position of the drop in the trap causes significant, large-amplitude shape oscillations superimposed over the center-of-mass oscillations of the drop. An important observation here is that the shape oscillations due to the applied quadrupole fields result in sufficient deformations that act as triggers for the onset of the instability below the Rayleigh limit, thereby admitting a subcritical instability. The center-of-mass oscillations of the droplet within the trap, which follow the applied frequency, are out of phase with the applied AC signal. Thus the combined effect of shape deformations and dynamic position of the drop leads to an asymmetric breakup such that the Rayleigh fission occurs upward via the ejection of a jet at the north pole of the deformed drop.

Study of the Effect of Hydrolysis Time on the Mechanical Properties of Polysiloxane Microcapsules.

It is known that the microstructure and thereby the mechanical properties of membranes constituting microcapsules are sensitive to parameters such as precursor concentration and pH. In the case of polysiloxane microcapsules, the oligomers, which are already formed in the continuous oil phase, because of the inherent moisture content in the oil phase, deposit on the membrane surface, resulting in the formation of a microstructure with a hairy layer. An electrodeformation investigation shows that the deposition of these oligomers is predominant in the smaller microcapsules compared to the larger ones and results in strain hardening and plasticity in the microcapsule membrane at high deformation. However, if the hydrolysis time during the synthesis of microcapsules is controlled, a smooth morphology (with a diminished hairy layer) can be realized for smaller capsules, as well. This work, using the electrodeformation method, demonstrates significant viscoelasticity and plasticity in the response of the capsules to applied electric stress and establishes an equivalence between simple spring and dashpot element-based phenomenological models with respect to the membrane properties using a linearized viscoelastic elasto-electrohydrodynamic model. The model can capture plasticity and strain hardening that are otherwise missed in simplified elasticity-based models.

Subcritical asymmetric Rayleigh breakup of a charged drop induced by finite amplitude perturbations in a quadrupole trap.

The breakup pathway of Rayleigh fission of a charged drop is unequivocally demonstrated by continuous, high-speed imaging of a drop levitated in an AC quadrupole trap. The experimental observations consistently exhibited asymmetric, subcritical Rayleigh breakup with an upward (i.e., opposite to the direction of gravity) ejection of a jet from the levitated drop. These experiments supported by numerical calculations show that the gravity induced downward shift of the equilibrium position of the drop in the trap causes significant, large amplitude shape oscillations superimposed over the center-of-mass oscillations. The shape oscillations result in sufficient deformations to act as triggers for the onset of instability below the Rayleigh limit (a subcritical instability). The concurrently occurring, center-of-mass oscillations, which are out of phase with the applied voltage, are shown to lead to an asymmetric breakup such that the Rayleigh fission occurs upwards via the ejection of a jet at the pole of the deformed drop. As an important application, it follows by inference that the nanodrop generation in electrospray devices will occur, more as a rule rather than as an exception, via asymmetric, subcritical Rayleigh fission events of microdrops due to inherent directionality provided by the external electric fields.

Development of transmembrane potential in concentric spherical, confocal spheroidal, and bispherical vesicles subjected to nanosecond-pulse electric field.

Electroporation of concentric compound spherical and confocal spheroidal as well as eccentric compound spherical vesicles, considered to be good models for corresponding nucleate cells, are investigated with an emphasis on their response to nanosecond pulse electric field (nsPEF). Analytical models are developed for the estimation of the transmembrane potential (TMP) across the bilayers of the inner and the outer vesicles and finite-element simulations are also carried out for the eccentric case. Our calculations show that with an increase in the aspect ratio, while the TMP decreases when nsPEF is used, it increases for confocal spheroids when the pulse width is greater than the membrane charging time, leading to fully charged vesicles. Bipolar pulses are shown to effectively control the TMP for a desired time period in the nsPEF regime, and a fast decay of the TMP to zero can be achieved by judicious use of pulse polarity. The external conductivity is found to significantly influence the TMP in nsPEF, unlike millisecond pulses where its effect is insignificant. Additionally the critical electric field required to induce a TMP of 1 V at the inner vesicle is presented for different pulse widths, rise time, as well as membrane capacitance, and the TMP of the outer vesicle is found to be within limits of reversible poration. It is found that the maximum TMP has a roughly linear dependence on the outer aspect ratio of the vesicle. We also introduce a new method to obtain the particular solution to the Laplace equation for bispherical system, and it is validated with finite-element simulations. Our study on nsPEF electroporation of bispherical vesicles shows that the north pole TMP is typically greater than the south pole, thereby suggesting the typical pathway a charged species might take inside an eccentric nucleate cell under electroporation.

Electrohydrodynamics of Vesicles and Capsules.

Giant unilamellar vesicles (GUVs) made up of phospholipid bilayer membranes (liposomes) and elastic capsules with a cross-linked, polymerized membrane, have emerged as biomimetic alternatives to investigating biological cells such as leukocytes and erythrocytes. This feature article looks at the similarities and differences in the electrohydrodynamics (EHD) of vesicles and capsules under electric fields that determines their electromechanical response. The physics of EHD is illustrated through several examples such as the electrodeformation of single and compound, spherical and cylindrical, and charged and uncharged vesicles in uniform and nonuniform electric fields, and the relevance and challenges are discussed. Both small and large deformation results are discussed. The use of EHD in understanding complex interfacial kinetics in capsules and the synthesis of nonspherical capsules using electric fields are also presented. Finally, the review looks at the large electrodeformation of water-in-water capsules and the relevance of constitutive laws in their response.

Coalescence, Partial Coalescence, and Noncoalescence of an Aqueous Drop at an Oil-Water Interface under an Electric Field.

Drop-interface interaction under an electric field is relevant in commercial desalters wherein water droplets suspended in oil coalesce under an electric field, move down under gravity, and eventually coalesce with the water pool at the bottom of the desalter. In this work, we report our observation that the transition from coalescence to partial coalescence can be described by a critical electrocapillary number and is independent of the Ohnesorge number. On the other hand, the partial coalescence to noncoalescence transition depends upon both the electrocapillary number and the Ohnesorge number. The bridge during partial coalescence exhibits an electrocapillary-number-independent growth and collapse dynamics, although the transition time for growth to collapse depends upon the electrocapillary number (CaE). Lastly, contrary to previous studies, our results indicate that the secondary droplet size varies as CaE3/2 unlike the CaE1/2 reported in the literature.

Starch aided synthesis of giant unilamellar vesicles.

Synthesis of giant unilamellar vesicles (GUVs) of charged and uncharged lipids at physiological salt concentration is presented using the starch hydrogel method as an example of the gel assisted synthesis method. The swelling of the gel is assisted by the presence of a high amount of amylopectin in starch and yields giant-sized vesicles, which are unilamellar in nature. This method holds promise since starch is a commonly available cheap bio-compatible material. This work indicates that native starch yields vesicles of better size range as compared to the acid-treated starch. It is demonstrated that contrary to the common belief, pre-hydration of bilayers is not critical to the success of this method. The synthesis of GUVs in physiological salt concentrations is possible since the salt does not produce any osmotic effect on its own. At low starch concentration, the size of the vesicles is found to correlate with the swelling factor. The conjugate effect of the starch concentration and ion leads to the change in the swelling factor of the gel and thereby influence the size and architecture of the vesicles. Also, interactions between starch and lipid play an important role in the formation of the giant vesicles.

Effect of noise on the stability of electrodynamically levitated one or many charged droplets.

The theory of the effect of external fluctuations on the stability and spatial distribution of mutually interacting and slowly evaporating charged drops, levitated in an electrodynamic balance, is presented using a classical pseudo-potential approach. The theory is supplemented with numerical simulations where the non-homogeneous modified Mathieu equation is solved for single-droplet as well as many-droplet systems. In this essentially non-equilibrium system a pseudo-potential is identified, and a Boltzmann-like pseudo-equilibrium distribution is suggested that describes the variance of the deterministic configuration of particles levitated in a quadrupolar trap. This formalism seems to explain the numerical results in a fairly close and convincing manner. A transition from a well-ordered Coulombic crystal to a randomly distributed liquid-like structure is observed above a threshold value of noise. A surprising finding of the present work is the observation that the strength of the threshold noise for the transition of a 2-particle system into a noise-dominated regime is identical to the critical noise required for a solid melting transition in a 100-particle system. The simulations could prove useful in analysing an ordered assembly of levitated micro- and nano-particles from the air streams using a contactless membrane.

Effect of the Quadrupolar Trap Potential on the Rayleigh Instability and Breakup of a Levitated Charged Droplet.

The experimental demonstration of Rayleigh instability that results in the breakup of a charged droplet, levitated in a quadrupole trap, has been investigated in the literature, but only scarcely. We report here the asymmetric breakup of a charged drop, levitated in a loose trap, wherein the droplet is stabilized at an off-center location in the trap. This aspect of levitation leads to an asymmetric breakup of the charged drop, predominantly in a direction opposite to that of gravity. In the present work, we report the evidence of successive events of the deformation and breakup of a charged drop and its subsequent relaxation after jet ejection using high-speed imaging at a couple of hundred thousand frames per second. Several relevant aspects of this phenomenon such as the effect of the electrodynamic (ED) trap parameters in terms of the applied potential as well as physical parameters such as the size of the drop, gravity, and conductivity on the characteristics of droplet breakup are explored. A clear effect of the trap strength on the deformation (both symmetric and asymmetric) is observed. Moreover, the cone angle at the pole undergoing asymmetric breakup is almost independent of the applied field investigated in the experiments. All of the experimental observations are compared with numerical simulations carried out using the boundary element method (BEM) in the Stokes flow limit. The BEM simulations are also extended to other experimentally achievable parameters. It is observed that the breakup in our study is mostly field-influenced and not field-induced. A plausible theory for the observations is reported, and a sensitive role of the sign of the charge on the droplet and the sign of the end-cap potential, as well as the off-center location of the droplet in the trap, is elucidated.

A theoretical study on the dynamics of a compound vesicle in shear flow.

The dynamics of nucleate cells in shear flow is of great relevance in cancer cells and circulatory tumor cells where they determine the flow properties of blood. Buoyed by the success of giant unilamellar vesicles in explaining the dynamics of anucleate cells such as red blood cells, compound vesicles have been suggested as a simple model for nucleate cells. A compound vesicle consists of two concentric unilamellar vesicles with the inner, annular and outer regions filled with aqueous Newtonian solvents. In this work, a theoretical model is presented to study the deformation and dynamics of a compound vesicle in linear shear flow using small deformation theory and spherical harmonics with higher order approximation to the membrane forces. A coupling of viscous and membrane stresses at the membrane interface of the two vesicles results in highly nonlinear shape evolution equations for the inner and the outer vesicles which are solved numerically. The results indicate that the size of the inner vesicle (χ) does not affect the tank-treading dynamics of the outer vesicle. The inner vesicle admits a greater inclination angle than the outer vesicle. However, the transition to trembling/swinging and tumbling is significantly affected. The inner and outer vesicles exhibit identical dynamics in the parameter space defined by the nondimensional rotational (Λan) and extensional (S) strength of the general shear flow. At moderate χ, a swinging mode is observed for the inner vesicle while the outer vesicle exhibits tumbling. The inner vesicle also exhibits modification of the TU mode to IUS (intermediate tumbling swinging) mode. Moreover, synchronization of the two vesicles at higher χ and a Capillary number sensitive motion at lower χ is observed in the tumbling regime. These results are in accordance with the few experimental observations reported by Levant and Steinberg. A reduction in the inclination angle is observed with an increase in χ when the inner vesicle is replaced by a solid inclusion. Additionally, a very elaborate phase diagram is presented in the Λan-S parameter space, which could be tested in future experiments or numerical simulations.

Establishing an Electrostatics Paradigm for Membrane Electroporation in the Framework of Dissipative Particle Dynamics.

With an exclusive aim to looking into a mechanism of membrane electroporation on mesoscopic length and time scales, we report the dissipative particle dynamics (DPD) simulation results for systems with and without electrolytes. A polarizable DPD model of water is employed for accurate modeling of long-range electrostatics near the water-lipid interfaces. A great deal of discussion on field induced change in dipole moments of water and lipids together with the special variation of electric field is made in order to understand the dielectrophoretic movement of water, initiating a pore formation via an intrusion through the bilayer core. The presence of salt alters the dipolar arrangement of lipids and water, and thereby it reduces the external field required to create a pore in the membrane. The species fluxes through the pore, distributions for bead density, electrostatic potential, stresses across the membrane, etc. are used to answer some of the key questions pertaining to mechanism of electroporation. The findings are compared with the molecular dynamics simulation results found in the literature, and the comparison successfully establishes an electrostatics paradigm for biomembrane studies using DPD simulations.

Shape deformation of a vesicle under an axisymmetric non-uniform alternating electric field.

We suggest that non-uniform electric fields that are commonly used to study vesicle dielectrophoresis can be employed in hitherto relatively unexplored areas of vesicle deformation (for electromechanical characterization) and electroporation. Conventionally, the tension generated in vesicles is commonly modeled to be entropic or enthalpic in origin. A comparison of the configuration of a vesicle in the enthalpic and entropic regimes as well as the cross over between the two regimes during vesicle deformation has eluded understanding. A lucid demonstration of this concept is provided by the study of vesicle deformation under axisymmetric quadrupole electric field and the shapes of the vesicles obtained using the entropic and the enthalpic approaches, show significant differences. A strong dependence of the final vesicle shapes on the ratio of electrical conductivities of the fluids inside and outside the vesicle as well as on the frequency of the applied quadrupole electric field is observed. A comparison with experimental data from the literature is also made. Moreover, an excess area dependent transition between the entropic and enthalpic regimes is observed. The method could be used to estimate electromechanical properties of the vesicle.

Electroporation Using Dissipative Particle Dynamics with a Novel Protocol for Applying Electric Field.

In molecular dynamics simulations of membrane electroporation, the bilayer is subjected to an electric field E either by direct addition of a force f = qE on the charge-bearing species or by imposing an ion imbalance in the salt solutions on the two sides of the bilayer. The former is believed to mimic electroporation with high fields over nanosecond pulse period, during which the membrane is almost uncharged, especially in the low salt limit. Conversely, the ion imbalance method elucidates a low electric field-induced poration over a longer period of micro- to milliseconds with a fully charged membrane. Both these methods of applying electric field have disadvantages while investigating electroporation using dissipative particle dynamics (DPD) simulations. The method involving direct addition of force fails to address the presence of a nonuniform dielectric background for ions embedded in nonpolarizable DPD water and those found in the core of the bilayer. The ion imbalance method in DPD simulations suffers from its unavoidable use of a wall potential to prevent the movement of ions across the periodic boundaries. To address the above issues, we propose a simple method for imposing a desired transmembrane potential (TMV) by placing oppositely but uniformly charged plates on either side of the bilayer. Our DPD simulations demonstrate that the profiles for bead density, mechanical stress, electrical potential, as well as the transient responses in the dipole moment and species fluxes obtained from the proposed method utilizing charged plates are quite similar to those obtained using the ion imbalance method. The proposed protocol is free from the aforementioned drawbacks of the direct force addition and ion imbalance methods.

Effect of ac electric field on the dynamics of a vesicle under shear flow in the small deformation regime.

Vesicles or biological cells under simultaneous shear and electric field can be encountered in dielectrophoretic devices or designs used for continuous flow electrofusion or electroporation. In this work, the dynamics of a vesicle subjected to simultaneous shear and uniform alternating current (ac) electric field is investigated in the small deformation limit. The coupled equations for vesicle orientation and shape evolution are derived theoretically, and the resulting nonlinear equations are handled numerically to generate relevant phase diagrams that demonstrate the effect of electrical parameters on the different dynamical regimes such as tank treading (TT), vacillating breathing (VB) [called trembling (TR) in this work], and tumbling (TU). It is found that while the electric Mason number (Mn), which represents the relative strength of the electrical forces to the shear forces, promotes the TT regime, the response itself is found to be sensitive to the applied frequency as well as the conductivity ratio. While higher outer conductivity promotes orientation along the flow axis, orientation along the electric field is favored when the inner conductivity is higher. Similarly a switch of orientation from the direction of the electric field to the direction of flow is possible by a mere change of frequency when the outer conductivity is higher. Interestingly, in some cases, a coupling between electric field-induced deformation and shear can result in the system admitting an intermediate TU regime while attaining the TT regime at high Mn. The results could enable designing better dielectrophoretic devices wherein the residence time as well as the dynamical states of the vesicular suspension can be controlled as per the application.

Large deformation electrohydrodynamics of a Skalak elastic capsule in AC electric field.

The axisymmetric electrohydrodynamic deformation of an elastic capsule with a capacitive membrane obeying the Skalak law under a uniform AC electric field is investigated using analytical and boundary integral theory. The low capillary number (the ratio of destabilizing shear or electric force to the stabilizing elastic force) regime shows that time-averaged prolate and oblate spheroid deformations, and the time-periodic prolate-sphere, oblate-sphere breathing modes are commensurate with the time averaged-deformation. A novel prolate-oblate breathing mode is observed due to an interplay of finite membrane charging time and the field reversal of the AC field. The study, when extended to high capillary numbers, shows new breathing modes of cylinder-prolate, cylinder-oblate, and biconcave-prolate deformation. These are the results of highly compressive normal Maxwell stress at the poles and are aided by a weak compressive equatorial stress, characteristic of a capacitive membrane. The findings of this work should form the basis for the understanding of more complex biological cells and synthetic capsules for industrial applications.

Electrohydrodynamics of a compound vesicle under an AC electric field.

Compound vesicles are relevant as simplified models for biological cells as well as in technological applications such as drug delivery. Characterization of these compound vesicles, especially the inner vesicle, remains a challenge. Similarly their response to electric field assumes importance in light of biomedical applications such as electroporation. Fields lower than that required for electroporation cause electrodeformation in vesicles and can be used to characterize their mechanical and electrical properties. A theoretical analysis of the electrohydrodynamics of a compound vesicle with outer vesicle of radius R o and an inner vesicle of radius [Formula: see text], is presented. A phase diagram for the compound vesicle is presented and elucidated using detailed plots of electric fields, free charges and electric stresses. The electrohydrodynamics of the outer vesicle in a compound vesicle shows a prolate-sphere and prolate-oblate-sphere shape transitions when the conductivity of the annular fluid is greater than the outer fluid, and vice-versa respectively, akin to single vesicle electrohydrodynamics reported in the literature. The inner vesicle in contrast shows sphere-prolate-sphere and sphere-prolate-oblate-sphere transitions when the inner fluid conductivity is greater and smaller than the annular fluid, respectively. Equations and methodology are provided to determine the bending modulus and capacitance of the outer as well as the inner membrane, thereby providing an easy way to characterize compound vesicles and possibly biological cells.