Kinetics of pore size during irreversible electrical breakdown of lipid bilayer membranes

Free energy of hydrophilic and hydrophobic pores in lipid bilayers by free energy perturbation of a restraint

The free energy of pore formation in lipid bilayers has been previously calculated using a variety of reaction coordinates. Here, we use free energy perturbation of a cylindrical lipid exclusion restraint to compute the free energy profile as a function of pore radius in dimyristoylphosphatidylcholine (DMPC) and dioleoylphosphatidylcholine (DOPC) bilayers. Additionally restraining the headgroups to lie on the membrane surface allows us to also calculate the free energy profile of hydrophobic pores, i.e., cylindrical pores lined by acyl chains. For certain pore radii, the free energy of wetting of hydrophobic pores is calculated using the density bias method. It is found that wetting of hydrophobic pores becomes thermodynamically favorable at 5.0 Å for DMPC and 6.5 Å for DOPC, although significant barriers prevent spontaneous wetting of the latter on a nanosecond time scale. The free energy of transformation of hydrophilic pores to hydrophobic ones is also calculated using free energy perturbation of headgroup restraints along the bilayer normal. This quantity, along with wetting and pore growth free energies, provides complete free energy profiles as a function of radius. Pore line tension values for the hydrophilic pores obtained from the slope of the free energy profiles are 37.6 pN for DMPC and 53.7 pN for DOPC. The free energy profiles for the hydrophobic pores are analyzed in terms of elementary interfacial tensions. It is found that a positive three-phase line tension is required to explain the results. The estimated value for this three-phase line tension (51.2 pN) lies within the expected range.

Electroporation of a hybrid bilayer membrane by scanning electrochemical microscope

A novel method, suitable for targeted electroporation of hybrid bilayer membranes (hBLMs) by scanning electrochemical microscope (SECM) is introduced by this work. A redox-probe-free system was applied for (i) SECM-based electroporation of a hBLM and for (ii) SECM-based visualization of pores formed by SECM-based electroporation in the hBLM. The hBLM was formed on a glass substrate modified by fluorine-doped tin oxide, and the structure (glass/FTO/hBLM) was used for further investigations. A specific 'constant-current region' at 1-30 µm distances between the UME and the hBLM surface was observed in the approach curves, which were registered while a Pt-based ultramicroelectrode (UME) was approaching the glass/FTO/hBLM surface. This 'constant-current region' was used as the characteristic feature for characterisation of the hBLM, and by assessment of the approach curves it was possible to distinguish whether an area of the hBLM was electroporated. SECM-based electroporation of the hBLM was performed by using increased potential difference between the reference electrode and the UME. Depending on the duration of the applied potential-pulse and on the distance between the UME and the hBLM surface, irreversible or reversible electroporation of the hBLM was achieved. The data shows that SECM can be successfully applied for both electroporation and characterisation of the hBLM.

Cyclic Activity of an Osmotically Stressed Liposome in a Finite Hypotonic Environment

A lipid vesicle, or simply called a liposome, represents a synthetic compartment for the examination of transmembrane transport and signaling phenomena. Yet, a liposome is always subjected to size and shape fluctuations due to local and global imbalance of internal and external osmotic pressures. Here, we show that an osmotically stressed liposome placed within a hypotonic spherical bath undergoes cyclic dynamics described by a periodic sequence of swelling and relaxation phases. These two phases are interfaced by the appearance of a transient transmembrane pore through which chemical delivery occurs. An analytical model was formulated for the recurrent differential equations that convey the time-dependent swelling phase of a pulsatory liposome during individual cycles. We demonstrate that the time-dependent swelling phases of the last several cycles of a pulsatory liposome are strongly dependent on the size of the external bath. Furthermore, decreasing the size of the hypotonic medium reduces the number of cycles of a pulsatory liposome. Comparisons and contrasts of an infinite hypotonic bath with finite external baths of varying radii are discussed.

A model of lipid rearrangements during pore formation in the DPPC lipid bilayer

CONTEXT

The molecular bases of pore formation in the lipid bilayer remain unclear, as do the exact characteristics of their sizes and distributions. To understand this process, numerous studies have been performed on model lipid membranes including cell-sized giant unilamellar vesicles (GUV). The effect of an electric field on DPPC GUV depends on the lipid membrane state: in the liquid crystalline phase the created pores have a cylinder-like shape, whereas in the gel phase a crack has been observed.

OBJECTIVE

The aim of the study was to investigate the geometry of pores created in a lipid bilayer in gel and liquid crystalline phases in reference to literature experimental data.

METHODS

A mathematical model of the pore in a DPPC lipid bilayer developed based on the law of conservation of mass and the assumption of constant volume of lipid molecules, independent of their conformation, allows for analysis of pore shape and accompanying molecular rearrangements.

RESULTS

The membrane area occupied by the pore of a cylinder-like shape is greater than the membrane area occupied by lipid molecules creating the pore structure (before pore appearance). Creation of such pores requires more space, which can be achieved by conformational changes of lipid chains toward a more compact state. This process is impossible for a membrane in the most compact, gel phase.

DISCUSSION AND CONCLUSIONS

We show that the geometry of the pores formed in the lipid bilayer in the gel phase must be different from the cylinder shape formed in the lipid bilayer in a liquid crystalline state, confirming experimental studies. Furthermore, we characterize the occurrence of the 'buffer' zone surrounding pores in the liquid crystalline phase as a mechanism of separation of neighbouring pores.

Imaging the dynamics of individual electropores

Electroporation is a widely used technique to permeabilize cell membranes. Despite its prevalence, our understanding of the mechanism of voltage-mediated pore formation is incomplete; methods capable of visualizing the time-dependent behavior of individual electropores would help improve our understanding of this process. Here, using optical single-channel recording, we track multiple isolated electropores in real time in planar droplet interface bilayers. We observe individual, mobile defects that fluctuate in size, exhibiting a range of dynamic behaviors. We observe fast (25 s(-1)) and slow (2 s(-1)) components in the gating of small electropores, with no apparent dependence on the applied potential. Furthermore, we find that electropores form preferentially in the liquid disordered phase. Our observations are in general supportive of the hydrophilic toroidal pore model of electroporation, but also reveal additional complexity in the interactions, dynamics, and energetics of electropores.

Transdermal delivery of vancomycin hydrochloride using combination of nano-ethosomes and iontophoresis: in vitro and in vivo study

This study aimed to evaluate transdermal delivery of vancomycin hydrochloride using the combination of ethosomes as an encapsulating vesicle and iontophoresis. Ethosomes were prepared and evaluated in terms of electrochemical stability. Cathodal iontophoresis of negatively charged ethosomes and anodal iontophoresis of free drug solution and positively charged vesicles were conducted. The effect of current mode, density, concentration of drug and ionic strength was studied. In vivo study was performed by inducing mediastinitis in Sprague-Dawley rats using methicillin-resistant Staphylococcus aureus as infected pathogen, the mean bacterial count was compared between groups of rats, one of the treated groups received drug intramuscularly while the other group received vancomycin using iontophoretic delivery of optimized ethosomal formula. Ethosomes showed efficient electrochemical stability, cathodal iontophoresis of negatively charged vesicle (F2) showed maximum transdermal flux (550 µg/cm(2)/h) compared to free drug solution and other ethosomal formulae, transdermal flux was reduced by altering current mode from continuous to ON/OFF mode, reducing current density and by using normal saline as drug solvent; on the other hand, flux was potentiated by increasing drug concentration from 25 to 75 mg/ml. In vivo study revealed that there was a significant difference in terms of bacterial count between untreated and treated groups, while there was no statistically significant difference between the I.M. vancomycin treatment and treatment conducted by iontophoretic delivery of vancomycin encapsulated in ethosomal formula. Combination between ethosomes and iontophoresis had succeeded in delivering vancomycin transdermally.

Anthrax toxin-induced rupture of artificial lipid bilayer membranes

We demonstrate experimentally that anthrax toxin complexes rupture artificial lipid bilayer membranes when isolated from the blood of infected animals. When the solution pH is temporally acidified to mimic that process in endosomes, recombinant anthrax toxin forms an irreversibly bound complex, which also destabilizes membranes. The results suggest an alternative mechanism for the translocation of anthrax toxin into the cytoplasm.

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.

Pore formation in lipid bilayer membranes made of phosphatidylcholine and cholesterol followed by means of constant current

This paper describes the application of chronopotentiometry to lipid bilayer research. The experiments were performed on bilayer lipid membranes composed of phosphatidylcholine and cholesterol and formed using the painting technique. Chronopotentiometric (U = f(t)) measurements were used to determine the membrane capacitance, resistance, and breakdown voltage as well as pore conductance and diameter.

The effects of diffusion on an exonuclease/nanopore-based DNA sequencing engine

Over 15 years ago, the ability to electrically detect and characterize individual polynucleotides as they are driven through a single protein ion channel was suggested as a potential method for rapidly sequencing DNA, base-by-base, in a ticker tape-like fashion. More recently, a variation of this method was proposed in which a nanopore would instead detect single nucleotides cleaved sequentially by an exonuclease enzyme in close proximity to one pore entrance. We analyze the exonuclease/nanopore-based DNA sequencing engine using analytical theory and computer simulations that describe nucleotide transport. The available data and analytical results suggest that the proposed method will be limited to reading <80 bases, imposed, in part, by the short lifetime each nucleotide spends in the vicinity of the detection element within the pore and the ability to accurately discriminate between the four mononucleotides.

Engineering nanostructures with enhanced thermoplasmonic properties for biosensing and selective targeting applications

This paper connects the study of thermoplasmonic properties in nanoscale particles with areas of biophysics involving a cell membrane with or without conductive pores. Using a quasistatic finite element modeling of the heat transfer equation in three dimensions we simulate the stationary heat generation and temperature field around several types of gold-based nanostructures. Models were constructed that emphasized the importance of obtaining precise temperature fields that might subsequently be used for biosensing and selective targeting applications. By analyzing the observed temperature increase, effective complex permittivity, and electric field enhancement that result from plasmonic resonance, this theoretical framework provides insight into the role of the nanoparticle shape in heat generation. To illustrate the usefulness of this approach for biosensing applications, we consider how the positioning of the nanoantenna affects heating efficiency. Linear response calculations of the temperature increase reveal that symmetric gold nanosphere dimers are not only suitable for sensing applications, but can also play the role of heat sources which are more efficient than the case of a single nanosphere. We also predict that this specific type of nanoantenna allows us to detect the presence and size of a hole in the cell membrane. These results provide insight into the physics of the cell membrane and provide guidance for more detailed studies of the nanoscale control of temperature in biological materials.

Aqueous viscosity is the primary source of friction in lipidic pore dynamics

A new theory, to our knowledge, is developed that describes the dynamics of a lipidic pore in a liposome. The equations of the theory capture the experimentally observed three-stage functional form of pore radius over time--stage 1, rapid pore enlargement; stage 2, slow pore shrinkage; and stage 3, rapid pore closure. They also show that lipid flow is kinetically limited by the values of both membrane and aqueous viscosity; therefore, pore evolution is affected by both viscosities. The theory predicts that for a giant liposome, tens of microns in radius, water viscosity dominates over the effects of membrane viscosity. The edge tension of a lipidic pore is calculated by using the theory to quantitatively account for pore kinetics in stage 3, rapid pore closing. This value of edge tension agrees with the value as standardly calculated from the stage of slow pore closure, stage 2. For small, submicron liposomes, membrane viscosity affects pore kinetics, but only if the viscosity of the aqueous solution is comparable to that of distilled water. A first-principle fluid-mechanics calculation of the friction due to aqueous viscosity is in excellent agreement with the friction obtained by applying the new theory to data of previously published experimental results.

Theoretical and experimental analysis of electroporated membrane conductance in cell suspension

An intense electric field can be applied to increase the membrane conductance G(m) and consequently, the conductivity of cell suspension. This phenomenon is called electroporation. This mechanism is used in a wide range of medical applications, genetic engineering, and therapies. Conductivity measurements of cell suspensions were carried out during application of electric fields from 40 to 165 kV/m. Experimental results were analyzed with two electroporation models: the asymptotic electroporation model was used to estimate G(m) at the beginning and at the end of electric field pulse, and the extended Kinosita electroporation model to increase G(m) linearly in time. The maximum G(m) was 1-7 × 10(4) S/m(2), and the critical angle (when the G(m) is insignificant) was 50°-65°. In addition, the sensitivity of electroporated membrane conductance to extracellular and cytoplasmatic conductivity and cell radius has been studied. This study showed that external conductivity and cell radius are important parameters affecting the pore-opening phenomenon. However, if the cell radius is larger than 7 μm in low conductivity medium, the cell dimensions are not so important.

Analysis of cell membrane permeabilization mechanics and pore shape due to ultrashort electrical pulsing

Cell membrane permeabilization mechanics and the resulting shape of nanopores in response to electrical pulsing are probed based on a continuum approach. This has implications for electropermeabilization and cell membrane transport. It is argued that small pores resulting from high-intensity (approximately 100 kV/cm), nanosecond pulsing would have an initial asymmetric shape. This would lead to asymmetric membrane current-voltage characteristics, at least at early times. The role of the cytoskeleton is ignored here, but can be expected to additionally contribute to such asymmetries. Furthermore, we show that the pore shape and membrane conduction would be dynamic, and evolve toward a symmetric characteristic over time. This duration has been shown to be in the micro-second range.

The current-voltage relation for electropores with conductivity gradients

In electroporation, an electric field transiently permeabilizes the cell membrane to gain access to the cytoplasm, and to deliver active agents such as DNA, proteins, and drug molecules. Past work suggests that the permeabilization is caused by the formation of aqueous, conducting pores on the lipid membrane, which are also known as electropores. The current-voltage relation across the membrane-bound pores is critical for understanding and predicting electroporation. In this work, we solve the Nernst-Planck equations in a geometry encompassing an isolated electropore to investigate this relation. In particular, we study cases where the intra- and extracellular electrical conductivities differ. We first derive an analytical solution, which is subsequently validated with a direct numerical simulation using a finite volume method. The main result of the current work is a formula for the effective pore resistance as a function of the pore radius, the membrane thickness, and the intra- and extracellular conductivities. This formula can be incorporated into whole-cell or planar-membrane electroporation models for system-level prediction and understanding.

Synthetic protocells to mimic and test cell function

Synthetic protocells provide a new means to probe, mimic and deconstruct cell behavior; they are a powerful tool to quantify cell behavior and a useful platform to explore nanomedicine. Protocells are not simple particles; they mimic cell design and typically consist of a stabilized lipid bilayer with membrane proteins. With a finite number of well characterized components, protocells can be designed to maximize useful outputs. Energy conversion in cells is an intriguing output; many natural cells convert transmembrane ion gradients into electricity by membrane-protein regulated ion transport. Here, a synthetic cell system comprising two droplets separated by a lipid bilayer is described that functions as a biological battery. The factors that affect its electrogenic performance are explained and predicted by coupling equations of the electrodes, transport proteins and membrane behavior. We show that the output of such biological batteries can reach an energy density of 6.9 x 10(6) J m(-3), which is approximately 5% of the volumetric energy density of a lead-acid battery. The configuration with maximum power density has an energy conversion efficiency of 10%.

A system for the determination of planar lipid bilayer breakdown voltage and its applications

In this paper, we focus on measurement principles used in electroporation studies on planar lipid bilayers. In particular, we point out the voltage-clamp measurement principle that has great importance when the breakdown voltage of a planar lipid bilayer is under consideration; however, it is also appropriate for the determination of other planar lipid bilayer electrical properties such as resistance and capacitance. A new experimental system that is based on the voltage-clamp measurement principle is described. With the use of a generator that can generate arbitrary-type signals, many specific shapes of a voltage signal could be generated, and therefore, the experimental system is appropriate for a broad spectrum of measurements.

Stability and rupture of archaebacterial cell membrane: a model study

It is known that the thermoacidophilic archaebacterium Sulfolobus acidocaldarius can grow in hot springs at 65-80 degrees C and live in acidic environments (pH 2-3); however, the origin of its unusual thermal stability remains unclear. In this work, using a vesicle as a model, we study the thermal stability and rupture of archaebacterial cell membrane. We perform a simulation investigation of the structure-property relationship of monolayer membrane formed by bolaform lipids and compare it with that of bilayer membrane formed by monopolar lipids. The origin of the unusually thermal stability of archaebacterial cell and the mechanism for its rupture are presented in molecular details.

Curvature-driven pore growth in charged membranes during charge-pulse and voltage-clamp experiments

We find that curvature-driven growth of pores in electrically charged membranes correctly reproduces charge-pulse experiments. Our model, consisting of a Langevin equation for the time dependence of the pore radius coupled to an ordinary differential equation for the number of pores, captures the statistics of the pore population and its effect on the membrane conductance. The calculated pore radius is a linear, and not an exponential, function of time, as observed experimentally. Two other important features of charge-pulse experiments are recovered: pores reseal for low and high voltages but grow irreversibly for intermediate values of the voltage. Our set of coupled ordinary differential equations is equivalent to the partial differential equation used previously to study pore dynamics, but permits the study of longer timescales necessary for the simulations of voltage-clamp experiments. An effective phase diagram for such experiments is obtained.

Membrane perturbation by an external electric field: a mechanism to permit molecular uptake

Electropermeabilisation is a well established physical method, based on the application of electric pulses, which induces the transient permeabilisation of the cell membrane. External molecules, otherwise nonpermeant, can enter the cell. Electropermeabilisation is now in use for the delivery of a large variety of molecules, as drugs and nucleic acids. Therefore, the method has great potential in the fields of cancer treatment and gene therapy. However many open questions about the underlying physical mechanisms involved remain to be answered or fully elucidated. In particular, the induced changes by the effects of the applied field on the membrane structure are still far from being fully understood. The present review focuses on questions related to the current theories, i.e. the basic physical processes responsible for the electropermeabilisation of lipid membranes. It also addresses recent findings using molecular dynamics simulations as well as experimental studies of the effect of the field on membrane components.

Self-consistent analyses for potential conduction block in nerves by an ultrashort high-intensity electric pulse

Simulation studies are presented that probe the possibility of using high-field (> 100 kV/cm) , short-duration ( approximately 50 ns) electrical pulses for nonthermal and reversible cessation of biological electrical signaling pathways. This would have obvious applications in neurophysiology, clinical research, neuromuscular stimulation therapies, and even nonlethal bioweapons development. The concept is based on the creation of a sufficiently high density of pores on the nerve membrane by an electric pulse. This modulates membrane conductance and presents an effective "electrical short" to an incident voltage wave traveling across a nerve. Net blocking of action potential propagation can then result. A continuum approach based on the Smoluchowski equation is used to treat electroporation. This is self-consistently coupled with a distributed circuit representation of the nerve dynamics. Our results indicate that poration at a single neural segment would be sufficient to produce an observable, yet reversible, effect.

Generation of focused electric field patterns at dielectric surfaces

We here report on a concept for creating well-defined electric field gradients between the boundaries of capillary electrode (a capillary of a nonconducting material equipped with an interior metal electrode) outlets, and dielectric surfaces. By keeping a capillary electrode opening close to a boundary between a conducting solution and a nonconducting medium, a high electric field can be created close to the interface by field focusing effects. By varying the inner and outer diameters of the capillary, the span of electric field strengths and the field gradient obtained can be controlled, and by varying the slit height between the capillary rim and the surface, or the applied current, the average field strength and gradient can be varied. Field focusing effects and generation of electric field patterns were analyzed using finite element method simulations. We experimentally verified the method by electroporation of a fluorescent dye (fluorescein diphosphate) into adherent, monolayered cells (PC-12 and WSS-1) and obtained a pattern of fluorescent cells corresponding to the focused electric field.

Nonlinear current–voltage relationship of the plasma membrane of single CHO cells

The application of electric field pulses to Chinese Hamster Ovary (CHO) cells causes membrane electroporation (MEP). If a voltage or current ramp is applied to the cellular membrane of a single CHO cell, the membrane conductance increases nonlinearly with field strength reaching saturation. In particular, the kinetics of the induced conductance changes represents the data basis for the interpretation in terms of underlying structural changes. The current/voltage characteristic is found to be continuous, but displays occasionally a sharp increase in the conductance. The step-like increases are interpreted to reflect the formation of one (or more) larger pore(s). The analysis of current clamp data yields pores of radius (r(p)) in the range of 2.5< or =r(p)/nm< or =20; the pores of the voltage clamp data are in the range of 2.5< or =r(p)/nm< or =55. The larger pores occur predominantly during hyperpolarising and less frequently during depolarising conditions, respectively. The different kinetics of pore formation in the hyperpolarising condition, where the inward field increases, and the depolarising condition, where the inward field first decreases and then increases in the opposite direction, suggests structural asymmetry with respect to the direction of the electric membrane field. At the required higher voltage, the effect of the resting potential is negligibly small.

Effect of pore size on the calculated pressure at biological cells pore wall

A transient nonlinear finite-element program has been used to calculate the electric field distribution as a function of time for a spherical cell with a pore in a conducting medium during application of a subnanosecond rise time "step" wave, including the effects of dipolar saturation in the water-based cytoplasm and cell medium. The time-dependent pressure on the pore wall has been computed as a function of time as the system polarizes from the change of the energy in the electric field to the left (inside the pore) and to the right (inside the membrane) of the pore wall. The computations suggest that dipolar saturation, while significant, has little effect on the time-dependent electric field distribution but a substantial effect on the field-induced pore wall pressure. Also, the effect of pore size on both the computed electric field and field-induced pressure was studied. As the pore size increases, a collapse in both the electric field and field-induced pressure has been noticed. This suggests that as the pore size increases, the driving force for further opening the pore is not electrical.

Secretion without membrane fusion: porocytosis

We have recently proposed a mechanism to describe secretion, a fundamental process in all cells. That hypothesis, called porocytosis, embodies all available data and encompasses both forms of secretion, i.e., vesicular and constitutive. The current accepted view of exocytotic secretion involves the physical fusion of vesicle and plasma membranes; however, that hypothesized mechanism does not fit all available physiological data. Energetics of apposed lipid bilayers do not favor unfacilitated fusion. We consider that calcium ions (e.g., 10(-4) to 10(-3) M calcium in microdomains when elevated for 1 ms or less), whose mobility is restricted in space and time, establish salt bridges among adjacent lipid molecules. This establishes transient pores that span both the vesicle and plasma membrane lipid bilayers; the diameter of this transient pore would be approximately 1 nm (the diameter of a single lipid molecule). The lifetime of the transient pore is completely dependent on the duration of sufficient calcium ion levels. This places the porocytosis hypothesis for secretion squarely in the realm of the physical and physical chemical interactions of calcium and phospholipids and places mass action as the driving force for release of secretory material. The porocytosis hypothesis that we propose satisfies all of the observations and provides a framework to integrate our combined knowledge of vesicular and constitutive secretion.

Pore formation in fluctuating membranes

We study the nucleation of a single pore in a fluctuating lipid membrane, specifically taking into account the membrane fluctuations, as well as the shape fluctuations of the pore. For large enough pores, the nucleation free energy is well-described by shifts in the effective membrane surface tension and the pore line tension. Using our framework, we derive the stability criteria for the various pore formation regimes. In addition to the well-known large-tension regime from the classical nucleation theory of pores, we also find a low-tension regime in which the effective line and surface tensions can change sign from their bare values. The latter scenario takes place at sufficiently high temperatures, where the opening of a stable pore of finite size is entropically favorable.

Soft perforation of planar bilayer lipid membranes of dipalmitoylphosphatidylcholine at the temperature of the phase transition from the liquid crystalline to the gel state

In contrast to the widely used method of electroporation, the method of soft perforation of lipid bilayers is proposed. It is based on the structural rearrangement of the lipid bilayer formed from disaturated phospholipids at the temperature of the phase transition from the liquid crystalline state to the gel state. This allows us to obtain a lipid pore population without the use of a strong electric field. It is shown that the planar lipid bilayer membrane (pBLM) formed from dipalmitoylphosphatidylcholine in 1 M LiCl aqueous solution exhibits the appearance of up to 50 lipid pores per 1 mm(2) of membrane surface, with an average single pore conductivity of 31 +/- 13 nS. The estimation of a single pore radius carried out with water-soluble poly(ethylene glycol)s (PEGs) showed that the average pore radius ranged between 1.0-1.7 nm. It was found experimentally that PEG-1450, PEG-2000, and PEG-3350 should be in a position to block the single pore conductivity completely, while PEG-6000 fully restored the ionic conductivity. The similarity of these PEG effects to ionic conductivity in protein pores makes it possible to suggest that the partition of the PEG molecules between the pore and the bulk solution does not depend on the nature of the chemical groups located in the pore wall.

Energy-landscape-model analysis for irreversibility and its pulse-width dependence in cells subjected to a high-intensity ultrashort electric pulse

We provide a simple, but physical analysis for cell irreversibility and apoptosis in response to an ultrashort (nanosecond), high-intensity electric pulse. Our approach is based on an energy landscape model for determining the temporal evolution of the configurational probability function p(q). The primary focus is on obtaining qualitative predictions of a pulse width dependence to apoptotic cell irreversibility that has been observed experimentally. The analysis couples a distributed electrical model for current flow with the Smoluchowski equation to provide self-consistent, time-dependent transmembrane voltages. The model captures the essence of the experimentally observed pulse-width dependence, and provides a possible physical picture that depends only on the electrical trigger. A number of interesting features are predicted.

Fields and forces acting on a planar membrane with a conducting channel

Modeling electric fields and forces around a channel in a planar membrane is still an open problem. Until now, most of the existing theories have oversimplified the electric field distribution by placing the electrode directly at the entry of the channel. However, in any relevant experimental setup the electrodes are placed far away in the electrolyte solution. We demonstrate that long-range deformation of the electric field distribution appears around the membrane, spanning on distances of the order of the distance between the membrane and the electrode. The forces acting due to this distribution are in most of the cases negligible. They can be important for channels with radii of the order of the thickness of the layer of structured water at the oil-water interface.

Fast Electrical Lysis of Cells for Capillary Electrophoresis

In the past decade, capillary electrophoresis has demonstrated increasing utility for the quantitative analysis of single cells. New applications for the analysis of dynamic cellular properties demand sampling methods with sufficient temporal resolution to accurately measure these processes. In particular, intracellular signaling pathways involving many enzymes can be modulated on subsecond time scales. We have developed a technique to rapidly lyse an adherent mammalian cell using a single electrical pulse followed by efficient loading of the cellular contents into a capillary. Microfabricated electrodes were designed to create a maximum voltage drop across the flattened cell's plasma membrane at a minimum interelectrode voltage. The influence of the interelectrode distance, pulse duration, and pulse strength on the rate of cell lysis was determined. The ability to rapidly lyse a cell and collect and separate the cellular contents was demonstrated by loading cells with Oregon Green and two isomers of carboxyfluorescein. All three fluorophores were detected with a separation efficiency comparable to that of standards. Parallel comparison of electrical lysis to that produced by a laser-based lysis system revealed that the sampling efficiencies of the two techniques were comparable. Rapid cell lysis by an electrical pulse may increase the application of capillary electrophoresis to the study of cellular dynamics requiring fast sampling times.

Simulation of pore formation in lipid bilayers by mechanical stress and electric fields

We describe computer simulations of pore formation and membrane rupture of phospholipid bilayers under mechanical and electrical stress. On the nanosecond simulation time scale, pores are induced by a lateral pressure exceeding -200 bar or by an applied electric field of 0.5 V/nm.

Lattice model for the kinetics of rupture of fluid bilayer membranes

We have constructed a model for the kinetics of rupture of membranes under tension, applying physical principles relevant to lipid bilayers held together by hydrophobic interactions. The membrane is characterized by the bulk compressibility (for expansion) K, the thickness 2h(t) of the hydrophobic part of the bilayer, the hydrophobicity sigma, and a parameter gamma characterizing the tail rigidity of the lipids. The model is a lattice model which incorporates strain relaxation, and considers the nucleation of pores at constant area, constant temperature, and constant particle number. The particle number is conserved by allowing multiple occupancy of the sites. An equilibrium "phase diagram" is constructed as a function of temperature and strain with the total pore surface and distribution as the order parameters. A first-order rupture line is found with increasing tension, and a continuous increase in protopore concentration with rising temperature till instability. The model explains current results on saturated and unsaturated phosphatidylcholine lipid bilayers and thicker artificial bilayers made of diblock copolymers. Pore size distributions are presented for various values of area expansion and temperature, and the fractal dimension of the pore edge is evaluated.

Programmable chronopotentiometry as a tool for the study of electroporation and resealing of pores in bilayer lipid membranes

This paper presents the application of chronopotentiometry in the study of membrane electroporation. Chronopotentiometry with a programmable current intensity was used. The experiments were performed on planar bilayer phosphatidylcholine and cholesterol membranes formed by the Mueller-Rudin method. It was demonstrated that a constant-intensity current flow through the bilayer membranes generated voltage fluctuations during electroporation. These fluctuations (following an increase and decrease in membrane conductance) were interpreted as a result of the opening and closing of pores in membrane structures. The decrease in membrane potential to zero did not cause the pore to close immediately. The pore was maintained for about 200 s. The closing of the pore and recovery of the continuous structure of the membrane proceeded not only when the membrane potential equalled zero, but also at membrane potentials up to several tens of millivolts. The fluctuations of the pore were possible at values of membrane potential in the order of at least 100 mV. The size of the pore changed slightly and it closed after some time below this potential value.

Voltage-induced nonconductive pre-pores and metastable single pores in unmodified planar lipid bilayer

Electric fields promote pore formation in both biological and model membranes. We clamped unmodified planar bilayers at 150-550 mV to monitor transient single pores for a long period of time. We observed fast transitions between different conductance levels reflecting opening and closing of metastable lipid pores. Although mean lifetime of the pores was 3 +/- 0.8 ms (250 mV), some pores remained open for up to approximately 1 s. The mean amplitude of conductance fluctuations (approximately 500 pS) was independent of voltage and close for bilayers of different area (40,000 and 10 microm(2)), indicating the local nature of the conductive defects. The distribution of pore conductance was rather broad (dispersion of approximately 250 pS). Based on the conductance value and its dependence of the ion size, the radius of the average pore was estimated as approximately 1 nm. Short bursts of conductance spikes (opening and closing of pores) were often separated by periods of background conductance. Within the same burst the conductance between spikes was indistinguishable from the background. The mean time interval between spikes in the burst was much smaller than that between adjacent bursts. These data indicate that opening and closing of lipidic pores proceed through some electrically invisible (silent) pre-pores. Similar pre-pore defects and metastable conductive pores might be involved in remodeling of cell membranes in different biologically relevant processes.

Characterization of single-cell electroporation by using patch-clamp and fluorescence microscopy

Electroporation of single NG108-15 cells with carbon-fiber microelectrodes was characterized by patch-clamp recordings and fluorescence microscopy. To minimize adverse capacitive charging effects, the patch-clamp pipette was sealed on the cell at a 90(o) angle with respect to the microelectrodes where the applied potential reaches a minimum. From transmembrane current responses, we determined the electric field strengths necessary for ion-permeable pore formation and investigated the kinetics of pore opening and closing as well as pore open times. From both patch-clamp and fluorescence microscopy experiments, the threshold transmembrane potentials for dielectric breakdown of NG108-15 cells, using 1-ms rectangular waveform pulses, was approximately 250 mV. The electroporation pulse preceded pore formation, and analyte entry into the cells was dictated by concentration, and membrane resting potential driving forces. By stepwise moving a cell out of the focused field while measuring the transmembrane current response during a supramaximal pulse, we show that cells at a distance of approximately 30 microm from the focused field were not permeabilized.

Electroporation dynamics in biological cells subjected to ultrafast electrical pulses: a numerical simulation study

A model analysis of electroporation dynamics in biological cells has been carried out based on the Smoluchowski equation. Results of the cellular response to short, electric pulses are presented, taking account of the growth and resealing dynamics of transient aqueous pores. It is shown that the application of large voltages alone may not be sufficient to cause irreversible breakdown, if the time duration is too short. Failure to cause irreversible damage at small pulse widths could be attributed to the time inadequacy for pores to grow and expand beyond a critical threshold radius. In agreement with earlier studies, it is shown that irreversible breakdown would lead to the formation of a few large pores, while a large number of smaller pores would appear in the case of reversible breakdown. Finally, a pulse width dependence of the applied voltage for irreversible breakdown has been obtained. It is shown that in the absence of dissipation, the associated energy input necessary reduces with decreasing pulse width to a limiting value. However, with circuit effects taken into account, a local minima in the pulse dependent energy function is predicted, in keeping with previously published experimental reports.

Detection of complement activity by using a polysaccharide-protected membrane

The complement system of mammalian blood is a nonspecific part of the immune system involved in a number of disease conditions. We report the observation of pore creation caused by its activation in blood applied to the front gel layer of a bilayer membrane formed from dioleoylphosphatidyl choline and protected by a polysaccharide gel. The pores were detected by measuring the DC conductivity between nonblocking Ag/AgCl electrodes. The thickness of the protective gel was approximately 100 µm, and the complement response was seen within 3 min after application of activator. The lifetime of such membranes is limited only by hydrolysis of the phospholipid constituting the membrane. This easily prepared system is suitable for examining the kinetics of complement component interactions with inhibitors.

Transdermal iontophoretic delivery of enoxacin from various liposome-encapsulated formulations

The major purpose of this work was to study the effect of various liposome formulations on the iontophoretic transport of enoxacin through excised rat skin. The electrochemical stability of these liposomes was also evaluated. The encapsulation percentage of enoxacin was significantly enhanced after 6 h incubation in an electric field; whereas the fusion of liposomes was inhibited by application of electric current. The results of iontophoretic drug transport showed that the permeability of enoxacin released from liposomes was higher compared with that of free drug. The iontophoretic permeability of enoxacin released from liposomes increased with a decrease in the fatty acid chain length of the phospholipid, which may be due to the different phase transition temperatures of the phospholipids. Incorporation of charged phospholipid resulted in an alteration of the transdermal behavior of enoxacin: the iontophoretic permeation as well as the amount of enoxacin partitioned in skin was greatly reduced after incorporation of stearylamine in liposomes, which can be attributed to the competitive ion effect. The enoxacin released from stratum corneum-based liposomes showed the highest amount of enoxacin partitioned into skin depot. The results of employing cathodal iontophoresis on negative charged liposomes suggested that the liposomal vesicles or phospholipids may carry enoxacin into deeper skin strata via the follicular route.

Chemical transformations in individual ultrasmall biomimetic containers

Individual phospholipid vesicles, 1 to 5 micrometers in diameter, containing a single reagent or a complete reaction system, were immobilized with an infrared laser optical trap or by adhesion to modified borosilicate glass surfaces. Chemical transformations were initiated either by electroporation or by electrofusion, in each case through application of a short (10-microsecond), intense (20 to 50 kilovolts per centimeter) electric pulse delivered across ultramicroelectrodes. Product formation was monitored by far-field laser fluorescence microscopy. The ultrasmall characteristic of this reaction volume led to rapid diffusional mixing that permits the study of fast chemical kinetics. This technique is also well suited for the study of reaction dynamics of biological molecules within lipid-enclosed nanoenvironments that mimic cell membranes.

Chinese hamster ovary cells sensitivity to localized electrical stresses

Application of an external electric field on a cell suspension induces an alteration in the membrane structure giving free access to the cell cytoplasm. Under mild pulsation conditions, permeabilization is a reversible process which weakly affects cell viability while drastic electrical conditions lead to cell death. The field pulse must be considered as a complex stress applied on the cell assembly. This study is a systematic investigation of the stress effects of field strength, pulse duration and number of pulses, at given joule energy. The loss in cell viability is not related to the energy delivered to the system. At a given joule energy, a strong field during a short cumulated pulse duration affects more viability than using a weak field associated with a long cumulated pulsation. At a given field strength and for a given cumulated pulse duration an accumulation of short pulses is also observed to be very damaging for cells. A control by the delay between the pulses suggests a memory effect. The field effect appears also to be vectorial in line with the known asymmetry of the membrane organization. These results suggest that processes at a cellular level are involved, either an activation of cell death or damage in cellular functions.