Electroporation of biological cell membranes is a phenomena that occurs almost universally at a transmembrane potential of approximately 1000 mV. Theories of pore formation have been proposed based on electrocompression (Crowley 1972, Malderelli and Steebe 1992), local membrane defects (Abidor and Chizdhmazdev 1979, Weaver and Mintzer 1981, Sugar 1981), and Statistical models were proposed by (Sowers and Lieber 1986). However, these theories do not in general derive the form of the electric field within the pore. In this paper, we present a view that is useful in describing the biological membrane. We also derive an approximate functional form for the electric field in the region of a pore formed in the membrane.
The electropermeabilization of biological cell membranes by the application of an external field occurs whenever an applied field exceeds a threshold value. For fields above this threshold value but less than another critical value, the pores formed in the membrane are transient or reversible. Several mechanisms have been proposed for the formation of these transient pores. Here we examine the local electric fields generated for the configuration of cells embedded in a polycarbonate filter, both in the region in and around the pore. We consider the shear forces created in the membrane due to t…
This paper presents a model and numerical analysis (simulations) of transmembrane potential induced in biological cell membrane under the influence of externally applied electric field (i.e., electroporation). This model differs from the established models of electroporation in two distinct ways. Firstly, it incorporates the presence of cholesterol (~20% mole-fraction) in biological membrane. Secondly, it considers the distribution of pores as a function of the variation of transmembrane potential from one region of the cell to another. Formulation is based on the role of membrane tension and …
We present an experimental study of the pore formation processes of small amphipathic peptides in model phosphocholine lipid membranes. We used atomic force microscopy to characterize the spatial organization and structure of alamethicin- and melittin- induced defects in lipid bilayer membranes and the influence of the peptide on local membrane properties. Alamethicin induced holes in gel DPPC membranes were directly visualized at different peptide concentrations. We found that the thermodynamic state of lipids in gel membranes can be influenced by the presence of alamethicin such that nanosco…
We investigated the X-ray scattering signal of highly aligned multilayers of the zwitterionic lipid 1,2-dilauroyl-sn-glycero-3-phosphatidylcholine containing pores formed by the antimicrobial peptide gramicidin as a function of the peptide/lipid ratio. We are able to obtain information on the structure factor of the pore fluid, which then yields the interaction potential between pores in the plane of the bilayers. Aside from a hard core with a radius close to the geometric radius of the pore, we find a repulsive exponential lipid-mediated interaction with a decay length of 2.5 Å and an amplitu…
The function of many membrane-enclosed intracellular structures relies on release of diffusing particles that exit through narrow pores or channels in the membrane. The rate of release varies with pore size, density, and length of the channel. We propose a simple approximate model, validated with stochastic simulations, for estimating the effective release rate from cylinders, and other simple-shaped domains, as a function of channel parameters. The results demonstrate that, for very small pores, a low density of channels scattered over the boundary is sufficient to achieve substantial rates o…
We study the indentation of a free-standing lipid membrane suspended over a nanopore on a hydrophobic substrate by means of molecular dynamics simulations. We find that in the course of indentation, the membrane bends at the point of contact, and the fringes of the membrane glide downward intermittently along the pore edges and stop gliding when the fringes reach the edge bottoms. The bending continues afterwards, and the large strain eventually induces a phase transition in the membrane, transformed from a bilayered structure to an interdigitated structure. The membrane is finally ruptured wh…
Standard model of electropration (EP) has long emphasized a single pore lifetime to explain post-pulse transport across cell membranes. However, pore lifetimes estimated from molecular dynamics (MD) models and and those measured from experimental data differ by several orders of magnitude. We hypothesize that a broad distribution of lifetimes may describe the post-pulse behavior. Here, we show that pore distribution, number and size of pores, show interesting behavior in different ranges of pore lifetimes. Interestingly, for large electric fields (greater than 1 kV/cm) and short pore lifetimes…
An effect of membrane surface charge on mechanical properties of the phospholipid bilayer membrane and pores formation is considered. It is shown that the outer and inner surfaces of the phospholipid membrane is always subject to tension, regardless of magnitude and sign of the charges on its surface. This is due to the fact that the Debye length of the extracellular and intracellular electrolyte is always much smaller than the thickness of the membrane, and accordingly the electric field on the outer surface of the membrane is always much larger than the field inside the membrane. This result…
We establish a biophysical model for the dynamics of lipid vesicles exposed to surfactants. The solubilization of the lipid membrane due to the insertion of surfactant molecules induces a reduction of membrane surface area at almost constant vesicle volume. This results in a rate-dependent increase of membrane tension and leads to the opening of a micron-sized pore. We show that solubilization kinetics due to surfactants can determine the regimes of pore dynamics: either the pores open and reseal within a second (short-lived pore), or the pore stays open up to a few minutes (long-lived pore). …
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), the thickness of the hydrophobic part of the bilayer, the hydrophobicity and a parameter 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 conserv…
We describe a concept that has the potential to change how we think about the underlying mechanisms of cell membrane electroporation (EP). Prior experimental, theoretical and modeling have emphasized a single pore lifetime as adequate for particular conditions. Here we introduce a much more complex response: The rapid creation of many types of pore structures, of which some are traditional transient lipidic pores (TPs), but the great majority are complex pores (CPs) based on both lipids and other molecules or molecular segments. At the inner leaflet of the cell plasma membrane (PM) non-lipidic…
Pore-forming toxins (PFT) are cytolytic proteins belonging to the molecular warfare apparatus of living organisms. The assembly of the functional transmembrane pore requires several intermediate steps ranging from a water-soluble monomeric species to the multimeric ensemble inserted in the cell membrane. The non-lytic oligomeric intermediate known as prepore plays an essential role in the mechanism of insertion of the class of $β$-PFT. However, in the class of $α$-PFT like the actinoporins produced by sea anemones, evidence of membrane-bound prepores is still lacking. We have employed single-p…
The finely tuned structures of membrane channels allow selective passage of ions through the available aqueous pores. In order to understand channel function, it is crucial to locate the pore and study its physical and chemical properties. Recently obtained X-ray crystal structures of bacterial chloride channel homologues reveal a complicated topology with curvilinear pores. The commonly used HOLE program encounters difficulties in studying such pores. Here we propose a new pore-searching algorithm (TransPath) which uses the Configurational Bias Monte Carlo (CBMC) method to generate transmembr…
Under externally applied electric fields, lipid membranes tend to permeate and change their electrical resistance by the combined processes of pore creation and pore evolution (expansion or contraction). This study is focused on the pore creation process, represented by an empirical expression currently used in the electroporation (EP) models, for which an alternative theoretically based expression was provided. The choice of this expression was motivated by the role the DLVO's (disjoining) pressures may play in the process of EP. The electrostatic energy effects on each sides of a lipid membr…
The translocation of a short DNA fragment through a nanopore is addressed when the perforated membrane contains an embedded electrode. Accurate numerical solutions of the coupled Poisson, Nernst-Planck, and Stokes equations for a realistic, fully three-dimensional setup as well as analytical approximations for a simplified model are worked out. By applying a suitable voltage to the membrane electrode, the DNA can be forced to preferably traverse the pore either along the pore axis or at a small but finite distance from the pore wall.
It is known that lipid membranes become permeable in their melting regime. In microscopic conductance measurements on black lipid membranes one finds that conduction takes place via quantized events closely resembling those reported for protein ion channels. Here, we present data of ion currents through black lipid membranes in the presence and absence of the anesthetics octanol and ethanol, and compare them to a statistical thermodynamics model using parameters that are obtained from experimental calorimetric data. The conductance steps in pure lipid membrane suggest aqueous pores with the si…
In biological membranes, alpha-tocopherols (α-toc; vitamin E) protect polyunsaturated lipids from free radicals. Although the interactions of α-toc with non-oxidized lipid bilayers have been studied, their on oxidized bilayers remain unknown. In this study, atomistic molecular dynamics (MD) simulations of oxidized lipid bilayers were performed with varying concentrations of α-toc. Bilayers with 1-palmitoyl-2-lauroyl-sn-glycero-3-phosphocholine (PLPC) lipids and its aldehyde derivatives at 1:1 ratio were studied. Our simulations show that oxidized lipids self-assemble into aggregates with a wat…
Experiments on single ionic channels have contributed to a large extent to our current view on the function of cell membrane. In these experiments the main observables are the physical quantities: ionic concentration, membrane electrostatic potential and ionic fluxes, all of them presenting large fluctuations. The classical theory of Goldman--Hodking--Katz assumes that an open channel can be well described by a physical pore where ions follow statistical physics. Nevertheless real molecular channels are active pores with open and close dynamical states. By skipping the molecular complexity of …
Biomembranes, which are mainly composed of neutral and charged lipids, exhibit a large variety of functional structures and dynamics. Here, we report a coarse-grained molecular dynamics (MD) simulation of the phase separation and morphological dynamics in charged lipid bilayer vesicles. The screened long-range electrostatic repulsion among charged head groups delays or inhibits the lateral phase separation in charged vesicles compared with neutral vesicles, suggesting the transition of the phase-separation mechanism from spinodal decomposition to nucleation or homogeneous dispersion. Moreover,…
We combine quantum-chemical calculations and molecular dynamics simulations to consider aqueous ion flow across non-axisymmetric nanopores in monolayer graphene and MoS$_2$. When the pore-containing membrane is subject to uniaxial tensile strains applied in various directions, the corresponding permeability exhibits considerable directional dependence. This anisotropy is shown to arise from directed perturbations of the local electrostatics by the corresponding pore deformation, as enabled by the pore edge geometries and atomic compositions. By considering nanopores with ionic permeability tha…
The morphologies of genus-2 to -8 fluid vesicles are studied by using dynamically triangulated membrane simulations with area-difference elasticity. It is revealed that the alignments of the membrane pores alter the vesicle shapes and the types of shape transitions for the genus $g \ge 3$. At a high reduced volume, a stomatocyte with a circular alignment of $g+1$ pores continuously transforms into a discocyte with a line of $g$ pores with increasing intrinsic area difference. In contrast, at a low volume, a stomatocyte transforms into a ($g+1$)-hedral shape and subsequently exhibits a discrete…
Bilayer lipid membranes [BLMs] are an essential component of all biological systems, forming a functional barrier for cells and organelles from the surrounding environment. The lipid molecules that form membranes contain both permanent and induced dipoles, and an electric field can induce the formation of pores when the transverse field is sufficiently strong (electroporation). Here, a phenomenological free energy is constructed to model the response of a BLM to a transverse static electric field. The model contains a continuum description of the membrane dipoles and a coupling between the hea…
We have carried out extensive Monte Carlo simulations of the fusion of tense apposed bilayers formed by amphiphilic molecules within the framework of a coarse grained lattice model. The fusion pathway differs from the usual stalk mechanism. Stalks do form between the apposed bilayers, but rather than expand radially to form an axial-symmetric hemifusion diaphragm of the trans leaves of both bilayers, they promote in their vicinity the nucleation of small holes in the bilayers. Two subsequent paths are observed: (i) The stalk encircles a hole in one bilayer creating a diaphragm comprised of bot…
We have carried out Monte Carlo simulation of the fusion of bilayers of single chain amphiphiles which show phase behavior similar to that of biological lipids. The fusion mechanism we observe is very different from the ``stalk'' hypothesis. Stalks do form on the first stage of fusion, but they do not grow radially to form a hemifused state. Instead, stalk formation destabilizes the membranes and results in hole formation in the vicinity of the stalks. When holes in each bilayer nucleate spontaneously next to the same stalk, an incomplete fusion pore is formed. The fusion process is completed …
