Electric-field-dependent thermal fluctuations of giant vesicles

Benefits and challenges of reconstituting the actin cortex

The cell's ability to change shape is a central feature in many cellular processes, including cytokinesis, motility, migration, and tissue formation. The cell constructs a network of contractile proteins underneath the cell membrane to form the cortex, and the reorganization of these components directly contributes to cellular shape changes. The desire to mimic these cell shape changes to aid in the creation of a synthetic cell has been increasing. Therefore, membrane-based reconstitution experiments have flourished, furthering our understanding of the minimal components the cell uses throughout these processes. Although biochemical approaches increased our understanding of actin, myosin II, and actin-associated proteins, using membrane-based reconstituted systems has further expanded our understanding of actin structures and functions because membrane-cortex interactions can be analyzed. In this review, we highlight the recent developments in membrane-based reconstitution techniques. We examine the current findings on the minimal components needed to recapitulate distinct actin structures and functions and how they relate to the cortex's impact on cellular mechanical properties. We also explore how co-processing of computational models with wet-lab experiments enhances our understanding of these properties. Finally, we emphasize the benefits and challenges inherent to membrane-based, reconstitution assays, ranging from the advantage of precise control over the system to the difficulty of integrating these findings into the complex cellular environment.

Fluctuating systems under cyclic perturbations: Relation between energy dissipation and intrinsic relaxation processes

This study focuses on fluctuating classical systems in contact with a thermal bath, and whose configurational energetics undergoes cyclic transformations due to interaction with external perturbing agents. Under the assumptions that the configurational dynamics is a stochastic Markov process in the overdamped regime and that the nonequilibrium configurational distribution remains close to the underlying equilibrium one, we derived an analytic approximation of the average dissipated energy per cycle in the asymptotic limit (i.e., after many cycles of perturbation). The energy dissipation is then readily translated into average entropy production, per cycle, in the environment. The accuracy of the approximation was tested by comparing the outcomes with the exact values obtained by stochastic simulations of a model case: a "particle on a ring" that fluctuates in a bistable potential perturbed in two different ways. As pointed out in previous studies on the stochastic resonance phenomenon, the dependence of the average dissipation on the perturbation period may unveil the inner spectrum of the system's fluctuation rates. In this respect, the analytical approximation presented here makes it possible to unveil the connection between average dissipation, intrinsic rates and modes of fluctuation of the system at the unperturbed equilibrium, and features of the perturbation itself (namely, the period of the cycle and the projections of the energy perturbation over the system's modes). The possibilities of employing the analytical results as a guide to devising and rationalizing a sort of "spectroscopic calorimetry" experiment, and of employing them in strategies aiming to optimize the system's features on the basis of a target average dissipation, are briefly discussed.

Membrane tubulation from giant lipid vesicles in alternating electric fields

We report on the formation of tubular membrane protrusions from giant unilamellar vesicles in alternating electric fields. The construction of the experimental chamber permitted the application of external AC fields with strength of dozens of V/mm and kHz frequency during relatively long time periods (several minutes). Besides the vesicle electrodeformation from quasispherical to prolate ellipsoidal shape, the formation of long tubular membrane protrusions with length of up to several vesicle diameters, arising from the vesicular surface in the field direction, was registered and analyzed. The threshold electric field at which the electro-induced protrusions appeared was lower than the field strengths inducing membrane electroporation.

Dynamics of three-dimensional vesicles in dc electric fields

A numerical and systematic parameter study of three-dimensional vesicle electrohydrodynamics is presented to investigate the effects of varying electric field strength and different fluid and membrane properties. The dynamics of vesicles in the presence of dc electric fields is considered, in both the presence and absence of linear shear flow. For suspended vesicles it is shown that the conductivity ratio and viscosity ratio between the interior and exterior fluids, as well as the vesicle membrane capacitance, substantially affect the minimum electric field strength required to induce a full prolate-oblate-prolate transition. In addition, there exists a critical electric field strength above which a vesicle will no longer tumble when exposed to linear shear flow.

Lipid membranes in external electric fields: kinetics of large pore formation causing rupture

About 40 years ago, Helfrich introduced an elastic model to explain shapes and shape transitions of cells (Z Naturforsch C, 1973; 28:693). This seminal article stimulated numerous theoretical as well as experimental investigations and created new research fields. In particular, the predictive power of his approach was demonstrated in a large variety of lipid model system. Here in this review, we focus on the development with respect to planar lipid membranes in external electric fields. Stimulated by the early work of Helfrich on electric field forces acting on liposomes, we extended his early approach to understand the kinetics of lipid membrane rupture. First, we revisit the main forces determining the kinetics of membrane rupture followed by an overview on various experiments. Knowledge on the kinetics of defect formation may help to design stable membranes or serve for novel mechanism for controlled release.

Equilibrium electrodeformation of a spheroidal vesicle in an ac electric field

In this work, we develop a theoretical model to explain the equilibrium spheroidal deformation of a giant unilamellar vesicle (GUV) under an alternating (ac) electric field. Suspended in a leaky dielectric fluid, the vesicle membrane is modeled as a thin capacitive spheroidal shell. The equilibrium vesicle shape results from the balance between mechanical forces from the viscous fluid, the restoring elastic membrane forces, and the externally imposed electric forces. Our spheroidal model predicts a deformation-dependent transmembrane potential, and is able to capture large deformation of a vesicle under an electric field. A detailed comparison against both experiments and small-deformation (quasispherical) theory showed that the spheroidal model gives better agreement with experiments in terms of the dependence on fluid conductivity ratio, permittivity ratio, vesicle size, electric field strength, and frequency. The spheroidal model also allows for an asymptotic analysis on the crossover frequency where the equilibrium vesicle shape crosses over between prolate and oblate shapes. Comparisons show that the spheroidal model gives better agreement with experimental observations.

Registration and analysis of the shape fluctuations of nearly spherical lipid vesicles

The analysis of shape fluctuations of giant nearly spherical lipid vesicles observed via optical microscopy is one of the widely used methods for the determination of the bending elasticity of lipid membranes. Although the method has been used already for three decades, the values of this material constant, obtained by different groups for membranes of the same composition, in identical conditions, differ significantly. The aim of the present work is the development of the method, enabling us to avoid the influence of artifacts on the value of the measured bending modulus. This is achieved by rejection of some images of the vesicle or the whole vesicle when they do not satisfy the requirements (selection criteria) of the applied theory. The bending modulus of 1-stearoyl-2-oleoyl-sn-glycerol-3-phosphocholine lipid membranes is determined via the advanced method described here. The results are compared with the values in the literature and their difference is discussed.

Destabilizing giant vesicles with electric fields: an overview of current applications

This review presents an overview of the effects of electric fields on giant unilamellar vesicles. The application of electrical fields leads to three basic phenomena: shape changes, membrane breakdown, and uptake of molecules. We describe how some of these observations can be used to measure a variety of physical properties of lipid membranes or to advance our understanding of the phenomena of electropermeabilization. We also present results on how electropermeabilization and other liposome responses to applied fields are affected by lipid composition and by the presence of molecules of therapeutic interest in the surrounding solution.

Vesicle electrohydrodynamics

A small amplitude perturbation analysis is developed to describe the effect of a uniform electric field on the dynamics of a lipid bilayer vesicle in a simple shear flow. All media are treated as leaky dielectrics and fluid motion is described by the Stokes equations. The instantaneous vesicle shape is obtained by balancing electric, hydrodynamic, bending, and tension stresses exerted on the membrane. We find that in the absence of ambient shear flow, it is possible that an applied stepwise uniform dc electric field could cause the vesicle shape to evolve from oblate to prolate over time if the encapsulated fluid is less conducting than the suspending fluid. For a vesicle in ambient shear flow, the electric field damps the tumbling motion, leading to a stable tank-treading state.

Frequency-dependent electrodeformation of giant phospholipid vesicles in AC electric field

A model of vesicle electrodeformation is described which obtains a parametrized vesicle shape by minimizing the sum of the membrane bending energy and the energy due to the electric field. Both the vesicle membrane and the aqueous media inside and outside the vesicle are treated as leaky dielectrics, and the vesicle itself is modeled as a nearly spherical shape enclosed within a thin membrane. It is demonstrated (a) that the model achieves a good quantitative agreement with the experimentally determined prolate-to-oblate transition frequencies in the kilohertz range and (b) that the model can explain a phase diagram of shapes of giant phospholipid vesicles with respect to two parameters: the frequency of the applied alternating current electric field and the ratio of the electrical conductivities of the aqueous media inside and outside the vesicle, explored in a recent paper (S. Aranda et al., Biophys J 95:L19-L21, 2008). A possible use of the frequency-dependent shape transitions of phospholipid vesicles in conductometry of microliter samples is discussed.

Electrohydrodynamic model of vesicle deformation in alternating electric fields

We develop an analytical theory to explain the experimentally observed morphological transitions of quasispherical giant vesicles induced by alternating electric fields. The model treats the inner and suspending media as lossy dielectrics, and the membrane as an impermeable flexible incompressible-fluid sheet. The vesicle shape is obtained by balancing electric, hydrodynamic, bending, and tension stresses exerted on the membrane. Our approach, which is based on force balance, also allows us to describe the time evolution of the vesicle deformation, in contrast to earlier works based on energy minimization, which are able to predict only stationary shapes. Our theoretical predictions for vesicle deformation are consistent with experiment. If the inner fluid is more conducting than the suspending medium, the vesicle always adopts a prolate shape. In the opposite case, the vesicle undergoes a transition from a prolate to oblate ellipsoid at a critical frequency, which the theory identifies with the inverse membrane charging time. At frequencies higher than the inverse Maxwell-Wagner polarization time, the electrohydrodynamic stresses become too small to alter the vesicle's quasispherical rest shape. The model can be used to rationalize the transient and steady deformation of biological cells in electric fields.

Morphological transitions of vesicles induced by alternating electric fields

When subjected to alternating electric fields in the frequency range 10(2)-10(8) Hz, giant lipid vesicles attain oblate, prolate, and spherical shapes and undergo morphological transitions between these shapes as one varies the field frequency and/or the conductivities lambda(in) and lambda(ex) of the aqueous solution inside and outside the vesicles. Four different transitions are observed with characteristic frequencies that depend primarily on the conductivity ratio lambda(in)/lambda(ex). The theoretical models that have been described in the literature are not able to describe all of these morphological transitions.

Giant vesicles in electric fields

This review is dedicated to electric field effects on giant unilamellar vesicles, a cell-size membrane system. We summarize various types of behavior observed when vesicles are subjected either to weak AC fields at various frequency, or to strong DC pulses. Different processes such as electro-deformation, -poration and -fusion of giant vesicles are considered. We describe some recent developments, which allowed us to detect the dynamics of the vesicle response with a resolution below milliseconds for all of these processes. Novel aspects on electric field effects on vesicles in the gel phase are introduced.

Electric pulses induce cylindrical deformations on giant vesicles in salt solutions

In this article, we report for the first time unusual shape changes of vesicles subjected to strong electric pulses in salt solutions of low concentration. The electric field is created by two parallel electrodes between which the vesicle solution is located. Surprisingly, the vesicles assume cylindrical shapes during the pulse. These deformations are short-lived (their lifetime is approximately 1 ms) and occur only in the presence of salt outside the vesicles, irrespective of their content. When the solution conductivities inside and outside are the same, vesicles with square cross section are observed. Using a fast digital camera, we were able to record these deformations and study the vesicle shape dynamics. The aims of this article are to report the new vesicle morphologies and their dynamics and to provoke theoretical work in this direction.

A practical guide to giant vesicles. Probing the membrane nanoregime via optical microscopy

Research on giant vesicles is becoming increasingly popular. Giant vesicles provide model biomembrane systems for systematic measurements of mechanical and rheological properties of bilayers as a function of membrane composition and temperature, as well as hydrodynamic interactions. Membrane response to external factors (for example electric fields, ions and amphiphilic molecules) can be directly visualized under the microscope. In this paper we review our current understanding of lipid bilayers as obtained from studies on giant unilamellar vesicles. Because research on giant vesicles increasingly attracts the interest of scientists from various backgrounds, we also try to provide a concise introduction for newcomers in the field. Finally, we summarize some recent developments on curvature effects induced by polymers, domain formation in membranes and shape transitions induced by electric fields.

Nonlinear electrochemical relaxation around conductors

We analyze the simplest problem of electrochemical relaxation in more than one dimension-the response of an uncharged, ideally polarizable metallic sphere (or cylinder) in a symmetric, binary electrolyte to a uniform electric field. In order to go beyond the circuit approximation for thin double layers, our analysis is based on the Poisson-Nernst-Planck (PNP) equations of dilute solution theory. Unlike most previous studies, however, we focus on the nonlinear regime, where the applied voltage across the conductor is larger than the thermal voltage. In such strong electric fields, the classical model predicts that the double layer adsorbs enough ions to produce bulk concentration gradients and surface conduction. Our analysis begins with a general derivation of surface conservation laws in the thin double-layer limit, which provide effective boundary conditions on the quasineutral bulk. We solve the resulting nonlinear partial differential equations numerically for strong fields and also perform a time-dependent asymptotic analysis for weaker fields, where bulk diffusion and surface conduction arise as first-order corrections. We also derive various dimensionless parameters comparing surface to bulk transport processes, which generalize the Bikerman-Dukhin number. Our results have basic relevance for double-layer charging dynamics and nonlinear electrokinetics in the ubiquitous PNP approximation.

Direct Measurement of Ion Accumulation at the Electrode Electrolyte Interface under an Oscillatory Electric Field

The ionic charge accumulation at the metal-electrolyte interface is directly measured by using differential interferometry as a function of magnitude and frequency (2-50 kHz) of external electric field. The technique developed probes the ion dynamics confined to the electrical double layer. The amplitude of modulation of the ions is linearly proportional to the amplitude of applied potential. The linearity is observed up to high electrode potentials and salt concentrations. The frequency response of the ion dynamics at the interface is interpreted in terms of the classical RC model.

Diffuse-charge dynamics in electrochemical systems

The response of a model microelectrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem consists of a symmetric binary electrolyte between parallel-plate blocking electrodes, which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are first linearized and solved by Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The "weakly nonlinear" limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter epsilon= lambdaD/L, where lambdaD is the screening length and L the electrode separation. At leading order, the system initially behaves like an RC circuit with a response time of lambdaDL/D (not lambdaD2/D), where D is the ionic diffusivity, but nonlinearity violates this common picture and introduces multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, L2/D. In the "strongly nonlinear" regime (controlled by a dimensionless parameter resembling the Dukhin number), this effect produces bulk concentration gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multicomponent electrolytes, and Faradaic processes.

Shape transitions of giant liposomes induced by an anisotropic spontaneous curvature

We explore how a magnetic field breaks the symmetry of an initially spherical giant liposome filled with a magnetic colloid. The condition of rotational symmetry along the field axis leads either to a prolate or to an oblate ellipsoid. We demonstrate that an electrostatic interaction between the nanoparticles and the membrane triggers the shape transition.

Mechanical properties of model membranes studied from shape transformations of giant vesicles

Membrane deformations occur frequently in cell functioning. From the physical point of view, the understanding of such shape changes requires the introduction of mechanical parameters like bending elasticity. In this article it is shown how this physical property can be obtained from the analysis of small or large shape transformations from giant vesicles. Then it is demonstrated that the bending modulus is strongly dependent on the membrane composition and environmental conditions. This is the case for one-component bilayers (dilauroylphosphatidylcholine (DLPC), dimyristoylphosphatidylcholine (DMPC), dipalmitoylphosphatidylcholine and stearoyloleoyl-phosphatidylcholine (SOPC) and for two-component lipid mixtures (DMPC/cholesterol, DLPC/dilauroylphosphatidic acid). Further it is shown that the bending elasticity of natural lipid extracts (egg phosphatidylcholine, digalactosyl diglyceride and red blood cell lipid extracts) is generally smaller than that of comparable synthetic model membranes. The role of transmembrane proteins is examined by measuring the bending elasticity of SOPC/gramicidin mixtures. Finally, larger scale shape transformations of giant vesicles under an alternative electric field are discussed.