Interface Water Dynamics and Porating Electric Fields for Phospholipid Bilayers

Effects of Normal and Lateral Electric Fields on Membrane Mechanical Properties

As a core component of biological and synthetic membranes, lipid bilayers are key to compartmentalizing chemical processes. Bilayer morphology and mechanical properties are heavily influenced by electric fields, such as those caused by biological ion concentration gradients. We present atomistic simulations exploring the effects of electric fields applied normally and laterally to lipid bilayers. We find that normal fields decrease membrane tension, while lateral fields increase it. Free energy perturbation calculations indicate the importance of dipole-dipole interactions to these tension changes, especially for lateral fields. We additionally show that membrane area compressibilities can be related to their cohesive energies, allowing us to estimate changes in membrane bending rigidity under applied fields. We find that normal and lateral fields decrease and increase bending rigidity, respectively. These results point to the use of directed electric fields to locally control membrane stiffness, thereby modulating associated cellular processes.

Influence of cholesterol on hydrogen-bond dynamics of water molecules in lipid-bilayer systems at varying temperatures

Cholesterol (Chol) plays a crucial role in shaping the intricate physicochemical attributes of biomembranes, exerting a considerable influence on water molecules proximal to the membrane interface. In this study, we conducted molecular dynamics simulations on the bilayers of two lipid species, dipalmitoylphosphatidylcholine (DPPC) and palmitoyl sphingomyelin; they are distinct with respect to the structures of the hydrogen-bond (H-bond) acceptors. Our investigation focuses on the dynamic properties and H-bonds of water molecules in the lipid-membrane systems, with a particular emphasis on the influence of Chol at varying temperatures. Notably, in the gel phase at 303 K, the presence of Chol extends the lifetimes of H-bonds of the oxygen atoms acting as H-bond acceptors within DPPC with water molecules by a factor of 1.5-2.5. In the liquid-crystalline phase at 323 K, on the other hand, H-bonding dynamics with lipid membranes remain largely unaffected by Chol. This observed shift in H-bonding states serves as a crucial key to unraveling the subtle control mechanisms governing water dynamics in lipid-membrane systems.

Cell-inspired, massive electromodulation of friction via transmembrane fields across lipid bilayers

Transient electric fields across cell bilayer membranes can lead to electroporation and cell fusion, effects crucial to cell viability whose biological implications have been extensively studied. However, little is known about these behaviours in a materials context. Here we find that transmembrane electric fields can lead to a massive, reversible modulation of the sliding friction between surfaces coated with lipid-bilayer membranes-a 200-fold variation, up to two orders of magnitude greater than that achieved to date. Atomistic simulations reveal that the transverse fields, resembling those at cell membranes, lead to fully reversible electroporation of the confined bilayers and the formation of inter-bilayer bridges analogous to the stalks preceding intermembrane fusion. These increase the interfacial dissipation through reduced hydration at the slip plane, forcing it to revert in part from the low-dissipation, hydrated lipid-headgroup plane to the intra-bilayer, high-dissipation acyl tail interface. Our results demonstrate that lipid bilayers under transmembrane electric fields can have striking materials modification properties.

Molecular Simulations Reveal the Free Energy Landscape and Transition State of Membrane Electroporation

The formation of pores over lipid membranes by the application of electric fields, termed membrane electroporation, is widely used in biotechnology and medicine to deliver drugs, vaccines, or genes into living cells. Continuum models for describing the free energy landscape of membrane electroporation were proposed decades ago, but they have never been tested against spatially detailed atomistic models. Using molecular dynamics (MD) simulations with a recently proposed reaction coordinate, we computed potentials of mean force of pore nucleation and pore expansion in lipid membranes at various transmembrane potentials. Whereas the free energies of pore expansion are compatible with previous continuum models, the experimentally important free energy barrier of pore nucleation is at variance with established models. The discrepancy originates from different geometries of the transition state; previous continuum models assumed the presence of a membrane-spanning defect throughout the process, whereas, according to the MD simulations, the transition state of pore nucleation is typically passed before a transmembrane defect has formed. A modified continuum model is presented that qualitatively agrees with the MD simulations. Using kinetics of pore opening together with transition state theory, our free energies of pore nucleation are in excellent agreement with previous experimental data.

Studying the roles of salt ions in the pore initiation and closure stages in the biomembrane electroporation

Electroporation shows great potential in biology and biomedical applications. However, there is still a lack of reliable protocol for cell electroporation to achieve a high perforation efficiency due to the unclear influence mechanism of various factors, especially the salt ions in buffer solution. The tiny membrane structure of a cell and the electroporation scale make it difficult to monitor the electroporation process. In this study, we used both molecular dynamics (MD) simulation and experimental methods to explore the influence of salt ions on the electroporation process. Giant unilamellar vesicles (GUVs) were constructed as the model, and sodium chloride (NaCl) was selected as the representative salt ion in this study. The results show that the electroporation process follows lag-burst kinetics, where the lag period first appears after applying the electric field, followed by a rapid pore expansion. For the first time, we find that the salt ion plays opposite roles in different stages of the electroporation process. The accumulation of salt ions near the membrane surface provides an extra potential to promote the pore initiation, while the charge screening effect of the ions within the pore increases the line tension of the pore to induce the instability of the pore and lead to the closure. The GUV electroporation experiments obtain qualitatively consistent results with MD simulations. This work can provide guidance for the selection of parameters for cell electroporation process.

Equivalence of Charge Imbalance and External Electric Fields during Free Energy Calculations of Membrane Electroporation

Electric fields across lipid membranes play important roles in physiology, medicine, and biotechnology, rationalizing the wide interest in modeling transmembrane potentials in molecular dynamics simulations. Transmembrane potentials have been implemented with external electric fields or by imposing charge imbalance between the two water compartments of a stacked double-membrane system. We compare the two methods in the context of membrane electroporation, which involves a large change of membrane structure and capacitance. We show that, given that Ewald electrostatics are defined with tinfoil boundary conditions, the two methods lead to (i) identical potentials of mean force (PMFs) of pore formation and expansion at various potentials, demonstrating that the two methods impose equivalent driving forces for large-scale transitions at membranes, and (ii) to identical polarization of water within thin water wires or open pores, suggesting that the two methods furthermore impose equivalent local electric fields. Without tinfoil boundary conditions, effects from external fields on pore formation are spuriously suppressed or even removed. Together, our study shows that both methods, external fields and charge imbalance, are well suitable for studying large-scale transitions of lipid membranes that involve changes of membrane capacitance. However, using charge imbalance is technically more challenging for maintaining a constant transmembrane potential since it requires updating of the charge imbalance as the membrane capacitance changes.

Advances in pulsed electric stimuli as a physical method for treating liquid foods

There is a need for alternative technologies that can deliver safe and nutritious foods at lower costs as compared to conventional processes. Pulsed electric field (PEF) technology has been utilised for a plethora of different applications in the life and physical sciences, such as gene/drug delivery in medicine and extraction of bioactive compounds in food science and technology. PEF technology for treating liquid foods involves engineering principles to develop the equipment, and quantitative biochemistry and microbiology techniques to validate the process. There are numerous challenges to address for its application in liquid foods such as the 5-log pathogen reduction target in food safety, maintaining the food quality, and scale up of this physical approach for industrial integration. Here, we present the engineering principles associated with pulsed electric fields, related inactivation models of microorganisms, electroporation and electropermeabilization theory, to increase the quality and safety of liquid foods; including water, milk, beer, wine, fruit juices, cider, and liquid eggs. Ultimately, we discuss the outlook of the field and emphasise research gaps.

Interactions of Surfactants with the Bacterial Cell Wall and Inner Membrane: Revealing the Link between Aggregation and Antimicrobial Activity

Surfactants with their intrinsic ability to solubilize lipid membranes are widely used as antibacterial agents, and their interactions with the bacterial cell envelope are complicated by their differential aggregation tendencies. We present a combined experimental and molecular dynamics investigation to unravel the molecular basis for the superior antimicrobial activity and faster kill kinetics of shorter-chain fatty acid surfactant, laurate, when compared with the longer-chain surfactants studied in contact time assays with live Escherichia coli (E. coli). From all-atom molecular dynamics simulations, translocation events across peptidoglycan were the highest for laurate followed by sodium dodecyl sulfate, myristate, palmitate, oleate, and stearate. The translocation kinetics were positively correlated with the critical micellar concentration, which determined the free monomer surfactant concentration available for translocation across peptidoglycan. Interestingly, aggregates showed a lower propensity to translocate across the peptidoglycan layer and longer translocation times were observed for oleate, thereby revealing an intrinsic sieving property of the bacterial cell wall. Molecular dynamics simulations with surfactant-incorporated bacterial inner membranes revealed the greatest hydrophobic mismatch and membrane thinning in the presence of laurate when compared with the other surfactants. The enhanced antimicrobial efficacy of laurate over oleate was further verified by experiments with giant unilamellar vesicles, and electroporation molecular dynamics simulations revealed greater inner membrane poration tendency in the presence of laurate when compared with the longer-chain surfactants. Our study provides molecular insights into surfactant translocation across peptidoglycan and chain length-induced structural disruption of the inner membrane, which correlate with contact time kill efficacies observed as a function of chain length with E. coli. The insights gained from our study uncover unexplored barrier properties of the bacterial cell envelope to rationalize the development of antimicrobial formulations and therapeutics.

Modeling and simulation of current-clamp electroporation

Current-Clamp electroporation refers to the application of a constant current across a membrane which results in voltage fluctuations due to the creation of electropores. This method allows for the measurement of electroporation across a long timescale (minutes) and facilitates the comparison between experimental and theoretical studies. Of particular interest is the claim in the literature that current-clamp electroporation results in the creation of a single pore. We simulated current-clamp electroporation using the Smoluchowski and Langevin equations and identified two possible mechanisms to explain the observed voltage fluctuations. The voltage fluctuations may be due to a single pore or a few pores growing and shrinking via a negative feedback mechanism or the opening and closing of pores in a larger population of pores. Our results suggest that current-clamp conditions do not necessarily result in the creation of a single pore. Additionally, we showed that the Langevin model is more accurate than the Smoluchowski model under conditions where there are only a few pores.

All-atom molecular dynamics simulations of the combined effects of different phospholipids and cholesterol content on electroporation

The electroporation mechanism could be related to the composition of the plasma membrane, and the combined effect of different phospholipid molecules and cholesterol content on electroporation has rarely been studied nor conclusions drawn. In this paper, we applied all-atom molecular dynamics (MD) simulations to study the effects of phospholipids and cholesterol content on bilayer membrane electroporation. The palmitoyloleoylphosphatidylcholine (POPC) model, palmitoyloleoylphosphatidylethanolamine (POPE) model, and a 1 : 1 mixed model of POPC and POPE called PEPC, were the three basic models used. An electric field of 0.45 V nm-1 was applied to nine models, which were the three basic models, each with three different cholesterol content values of 0%, 24%, and 40%. The interfacial water molecules moved under the electric field and, once the first water bridge formed, the rest of the water molecules would dramatically flood into the membrane. The simulation showed that a rapid rise in the Z-component of the average dipole moment of the interfacial water molecules (Z-DM) indicated the occurrence of electroporation, and the same increment of Z-DM represented a similar change in the size of the water bridge. With the same cholesterol content, the formation of the first water bridge was the most rapid in the POPC model, regarding the average electroporation time (t ep), and the average t ep of the PEPC model was close to that of the POPE model. We speculate that the differences in membrane thickness and initial number of hydrogen bonds of the interfacial water molecules affect the average t ep for different membrane compositions. Our results reveal the influence of membrane composition on the electroporation mechanism at the molecular level.

Ultralong recovery time in nanosecond electroporation systems enabled by orientational-disordering processes

The growing importance of applications based on molecular medicine and genetic engineering is driving the need to develop high-performance electroporation technologies. The electroporation phenomenon involves disruption of the cell for increasing membrane permeability. Although there is a multitude of research focused on exploring new electroporation techniques, the engineering of programming schemes suitable for these electroporation methods remains a challenge. Nanosecond stimulations could be promising candidates for these techniques owing to their ability to generate a wide range of biological responses. Here we control the membrane permeabilization of cancer cells using different numbers of electric-field pulses through orientational disordering effects. We then report our exploration of a few-volt nanosecond alternating-current (AC) stimulation method with an increased number of pulses for developing electroporation systems. A recovery time of ∼720 min was achieved, which is above the average of ∼76 min for existing electroporation methods using medium cell populations, as well as a previously unreported increased conductance with an increase in the number of pulses using weak bias amplitudes. All-atom molecular dynamics (MD) simulations reveal the orientation-disordering-facilitated increase in the degree of permeabilization. These findings highlight the potential of few-volt nanosecond AC-stimulation with an increased number of pulse strategies for the development of next-generation low-power electroporation systems.

Identification of electroporation sites in the complex lipid organization of the plasma membrane

The plasma membrane of a biological cell is a complex assembly of lipids and membrane proteins, which tightly regulate transmembrane transport. When a cell is exposed to strong electric field, the membrane integrity becomes transiently disrupted by formation of transmembrane pores. This phenomenon termed electroporation is already utilized in many rapidly developing applications in medicine including gene therapy, cancer treatment, and treatment of cardiac arrhythmias. However, the molecular mechanisms of electroporation are not yet sufficiently well understood; in particular, it is unclear where exactly pores form in the complex organization of the plasma membrane. In this study, we combine coarse-grained molecular dynamics simulations, machine learning methods, and Bayesian survival analysis to identify how formation of pores depends on the local lipid organization. We show that pores do not form homogeneously across the membrane, but colocalize with domains that have specific features, the most important being high density of polyunsaturated lipids. We further show that knowing the lipid organization is sufficient to reliably predict poration sites with machine learning. Additionally, by analysing poration kinetics with Bayesian survival analysis we show that poration does not depend solely on local lipid arrangement, but also on membrane mechanical properties and the polarity of the electric field. Finally, we discuss how the combination of atomistic and coarse-grained molecular dynamics simulations, machine learning methods, and Bayesian survival analysis can guide the design of future experiments and help us to develop an accurate description of plasma membrane electroporation on the whole-cell level. Achieving this will allow us to shift the optimization of electroporation applications from blind trial-and-error approaches to mechanistic-driven design.

Electric-driven membrane poration: A rationale for water role in the kinetics of pore formation

Electroporation is a well-established technique used to stimulate cells, enhancing membrane permeability by inducing reversible membrane pores. In the absence of experimental observation of the dynamics of pore creation, molecular dynamics studies provide the molecular-level evidence that the electric field promotes pore formation. Although single steps in the pore formation process are well assessed, a kinetic model representing the mathematical description of the electroporation process, is lacking. In the present work we studied the basis of the pore formation process, providing a rationale for the definition of a first-order kinetic scheme. Here, authors propose a three-state kinetic model for the process based on the assessed mechanism of water defects intruding at the water/lipid interface, when applying electric field intensities at the edge of the linear regime. The methodology proposed is based on the use of two robust biophysical quantities analyzed for the water molecules intruding at the water/lipid interface: (i) number of hydrogen bonds; (ii) number of contacts. The final model, sustained by a robust statistical sampling, provides kinetic constants for the transitions from the intact bilayer state to the hydrophobic pore state.

Genetic, cellular, and structural characterization of the membrane potential-dependent cell-penetrating peptide translocation pore

Cell-penetrating peptides (CPPs) allow intracellular delivery of bioactive cargo molecules. The mechanisms allowing CPPs to enter cells are ill-defined. Using a CRISPR/Cas9-based screening, we discovered that KCNQ5, KCNN4, and KCNK5 potassium channels positively modulate cationic CPP direct translocation into cells by decreasing the transmembrane potential (V_m). These findings provide the first unbiased genetic validation of the role of V_m in CPP translocation in cells. In silico modeling and live cell experiments indicate that CPPs, by bringing positive charges on the outer surface of the plasma membrane, decrease the V_m to very low values (–150 mV or less), a situation we have coined megapolarization that then triggers formation of water pores used by CPPs to enter cells. Megapolarization lowers the free energy barrier associated with CPP membrane translocation. Using dyes of varying dimensions in CPP co-entry experiments, the diameter of the water pores in living cells was estimated to be 2 (–5) nm, in accordance with the structural characteristics of the pores predicted by in silico modeling. Pharmacological manipulation to lower transmembrane potential boosted CPP cellular internalization in zebrafish and mouse models. Besides identifying the first proteins that regulate CPP translocation, this work characterized key mechanistic steps used by CPPs to cross cellular membranes. This opens the ground for strategies aimed at improving the ability of cells to capture CPP-linked cargos in vitro and in vivo.

Before a drug can have its desired effect, it must reach its target tissue or organ, and enter its cells. This is not easy because cells are surrounded by the plasma membrane, a fat-based barrier that separates the cell from its external environment. The plasma membrane contains proteins that act as channels, shuttling specific molecules in and out of the cell, and it also holds charge, with its inside surface being more negatively charged than its outside surface.

Cell-penetrating peptides are short sequences of amino acids (the building blocks that form proteins) that carry positive charges. These positive charges allow them to cross the membrane easily, but it is not well understood how.

To find out how cell-penetrating peptides cross the membrane, Trofimenko et al. attached them to dyes of different sizes. This revealed that the cell-penetrating peptides enter the cell through temporary holes called water pores, which measure about two nanometres across. The water pores form when the membrane becomes ‘megapolarized’, this is, when the difference in charge between the inside and the outside of the membrane becomes greater than normal. This can happen when the negative charge on the inside surface or the positive charge on the outer surface of the membrane increase. Megapolarization depends on potassium channels, which transport positive potassium ions outside the cell, making the outside of the membrane positive. When cell-penetrating peptides arrive at the outer surface of the cell near potassium channels, they make it even more positive. This increases the charge difference between the inside and the outside of the cell, allowing water pores to form. Once the peptides pass through the pores, the charge difference between the inside and the outside of the cell membrane dissipates, and the pores collapse.

Drug developers are experimenting with attaching cell-penetrating peptides to drugs to help them get inside their target cells. Currently there are several experimental medications of this kind in clinical trials. Understanding how these peptides gain entry, and what size of molecule they could carry with them, provides solid ground for further drug development.

Dye Transport through Bilayers Agrees with Lipid Electropore Molecular Dynamics

Although transport of molecules into cells via electroporation is a common biomedical procedure, its protocols are often based on trial and error. Despite a long history of theoretical effort, the underlying mechanisms of cell membrane electroporation are not sufficiently elucidated, in part, because of the number of independent fitting parameters needed to link theory to experiment. Here, we ask if the electroporation behavior of a reduced cell membrane is consistent with time-resolved, atomistic, molecular dynamics (MD) simulations of phospholipid bilayers responding to electric fields. To avoid solvent and tension effects, giant unilamellar vesicles (GUVs) were used, and transport kinetics were measured by the entry of the impermeant fluorescent dye calcein. Because the timescale of electrical pulses needed to restructure bilayers into pores is much shorter than the time resolution of current techniques for membrane transport kinetics measurements, the lifetimes of lipid bilayer electropores were measured using systematic variation of the initial MD simulation conditions, whereas GUV transport kinetics were detected in response to a nanosecond timescale variation in the applied electric pulse lifetimes and interpulse intervals. Molecular transport after GUV permeabilization induced by multiple pulses is additive for interpulse intervals as short as 50 ns but not 5-ns intervals, consistent with the 10-50-ns lifetimes of electropores in MD simulations. Although the results were mostly consistent between GUV and MD simulations, the kinetics of ultrashort, electric-field-induced permeabilization of GUVs were significantly different from published results in cells exposed to ultrashort (6 and 2 ns) electric fields, suggesting that cellular electroporation involves additional structures and processes.

Cationic Antiseptics Facilitate Pore Formation in Model Bacterial Membranes

Antiseptics are an essential line of defense against bacterial and viral infections in modern medical practice. Many of them are supposed to act on microbial membranes. However, the detailed mechanisms of their action are still elusive. Here, we utilized coarse-grained molecular dynamics simulations to investigate interactions of different types of cationic antiseptics (CAs) with a model bacterial membrane. The simulations revealed qualitatively distinct patterns of dynamic and structural alterations of membrane induced by different types of antiseptics although none of them caused disintegration or solubilization of the bilayer even at the highest explored concentration. At the same time, the adsorption of antiseptics rendered membranes more vulnerable to poration under exposure to the external electric field. We further discuss the possible relation of the enhanced pore formation induced by CAs to their cytotoxic action.

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.

Spontaneous and Stress-Induced Pore Formation in Membranes: Theory, Experiments and Simulations

The large plasticity, dynamics and adaptability of biological membranes allow different modes of intrinsic and inducible permeability. These phenomena are of physiological importance for a number of natural functions related to cell death and can also be manipulated artificially for practical purposes like gene transfer, drug delivery, prevention of infections or anticancer therapy. For these advances to develop in a controllable and specific way, we need a sufficient understanding of the membrane permeability phenomena. Since the formulation of early concepts of pore formation, there has been an enormous effort to describe membrane permeability by using theory, simulations and experiments. A major breakthrough has come recently through theoretical developments that allow building continuous trajectories of pore formation both in the absence and presence of stress conditions. The new model provides a coherent quantitative view of membrane permeabilization, useful to test the impact of known lipid properties, make predictions and postulate specific pore intermediates that can be studied by simulations. For example, this theory predicts unprecedented dependencies of the line tension on the pore radius and on applied lateral tension which explain previous puzzling results. In parallel, important concepts have also come from molecular dynamics simulations, of which the role of water for membrane permeabilization is of special interest. These advances open new challenges and perspectives for future progress in the study of membrane permeability, as experiments and simulations will need to test the theoretical predictions, while theory achieves new refinements that provide a physical ground for observations.

Coupling of Membrane Nanodomain Formation and Enhanced Electroporation near Phase Transition

Biological cells are enveloped by a heterogeneous lipid bilayer that prevents the uncontrolled exchange of substances between the cell interior and its environment. In particular, membranes act as a continuous barrier for salt and macromolecules to ensure proper physiological functions within the cell. However, it has been shown that membrane permeability strongly depends on temperature and, for phospholipid bilayers, displays a maximum at the transition between the gel and fluid phase. Here, extensive molecular dynamics simulations of dipalmitoylphosphatidylcholine bilayers were employed to characterize the membrane structure and dynamics close to phase transition, as well as its stability with respect to an external electric field. Atomistic simulations revealed the dynamic appearance and disappearance of spatially related nanometer-sized thick ordered and thin interdigitating domains in a fluid-like bilayer close to the phase transition temperature (Tm). These structures likely represent metastable precursors of the ripple phase that vanished at increased temperatures. Similarly, a two-phase bilayer with coexisting gel and fluid domains featured a thickness minimum at the interface because of splaying and interdigitating lipids. For all systems, application of an external electric field revealed a reduced bilayer stability with respect to pore formation for temperatures close to Tm. Pore formation occurred exclusively in thin interdigitating membrane nanodomains. These findings provide a link between the increased membrane permeability and the structural heterogeneity close to phase transition.

Molecular Mechanism of Polycation-Induced Pore Formation in Biomembranes

Polycations are an attractive class of macromolecules with promising applications as drug/gene carriers and biocides. The chemical structure and concentration of a polycation determine its interaction with cellular membranes and, hence, are crucial parameters for designing efficient nontoxic polycations. However, the interaction of polycations with biomembranes at the molecular level and the corresponding free-energy landscape is not well understood. In this work, we investigate the molecular mechanism of interaction between a strong polycation substituted with alkyl moieties and zwitterionic membranes via long-time-scale all-atom molecular dynamics simulations and free-energy calculations combined with Langmuir monolayer, atomic force microscopy, and calcein-release experimental measurements. We found that the membrane activity of the polycation and its ability to induce pores in the membranes can be attributed to the polycation-induced changes in the bilayer organization, such as reduced membrane thickness, increased disorder of the acyl chains, reduced packing, and electrostatic field gradients between membrane leaflets. These changes facilitate the penetration of water into the membrane and the formation of aqueous defects/pores. The calculated free-energy profiles indicate that the polycation lowers the nucleation barrier for pore opening and the free energy for pore formation in a concentration-dependent manner. Above the critical coverage of the membrane, the polycation nucleates spontaneous pores in zwitterionic membranes. Our work demonstrates the potential of combining enhanced sampling methods in MD simulations with experiments for a quantitative description of various events in the polycation-membrane interaction cycle, such as strong adsorption on the membrane due to hydrophobic and electrostatic interactions, and pore formation.

Transprotein-Electropore Characterization: A Molecular Dynamics Investigation on Human AQP4

Electroporation characterization is a topic of intensive interest probed by extensive ongoing research efforts. Usually, these studies are carried out on lipid-bilayer electroporation. Surprisingly, the possibility of water-channel electropore formation across transmembrane proteins themselves, particularly in view of such a promising application, has not yet been elucidated. The present work examines the geometrical and kinetic aspects of electropores and their stability in such a protein milieux (as opposed through the phospholipid membranes) in depth, by means of scrutiny of such a process in human-AQP4 as a well-representative prototype. The residues forming the electropore's walls, organized in loops, reveal the formation mechanism by their dipole alignment and translational response in response to applied axial electric fields in nonequilibrium molecular dynamics simulation. The magnitude of sustaining electric fields (keeping a stable electropore open) were determined. This suggests that transmembrane proteins could play a central role in electroporation applications, e.g., in medicine and biotechnology.

Atomistic Simulations of Electroporation of Model Cell Membranes

Electroporation is a phenomenon that modifies the fundamental function of the cell since it perturbs transiently or permanently the integrity of its membrane. Today, this technique is applied in fields ranging from biology and biotechnology to medicine, e.g., for drug and gene delivery into cells, tumor therapy, etc., in which it made it to preclinical and clinical treatments. Experimentally, due to the complexity and heterogeneity of cell membranes, it is difficult to provide a description of the electroporation phenomenon in terms of atomically resolved structural and dynamical processes, a prerequisite to optimize its use. Atomistic modeling in general and molecular dynamics (MD) simulations in particular have proven to be an effective approach for providing such a level of detail. This chapter provides the reader with a comprehensive account of recent advances in using such a technique to complement conventional experimental approaches in characterizing several aspects of cell membranes electroporation.

Tumor cell death after electrotransfer of plasmid DNA is associated with cytosolic DNA sensor upregulation

Cytosolic DNA sensors are a subgroup of pattern recognition receptors (PRRs) and are activated by the abnormal presence of the DNA in the cytosol. Their activation leads to the upregulation of pro-inflammatory cytokines and chemokines and can also induce cell death. The presence of cytosolic DNA sensors and inflammatory cytokines in TS/A murine mammary adenocarcinoma and WEHI 164 fibrosarcoma cells was demonstrated using real time reverse transcription polymerase chain reaction (RT-PCR), western blotting and enzyme-linked immunosorbent assay (ELISA). After electrotransfer of plasmid DNA (pDNA) using two pulse protocols, the upregulation of DNA-depended activator of interferon regulatory factor or Z-DNA binding protein 1 (DAI/ZBP1), DEAD (Asp-Glu-Ala-Asp) box polypeptide 60 (DDX60) and interferon-inducible protein 204 (p204) mRNAs was observed in both tumor cell lines, but their expression was pulse protocol dependent. A decrease in cell survival was also observed; it was cell type, DNA concentration and pulse protocol dependent. Furthermore, the different protocols of electrotransfer led to different cell death outcomes, necrosis and apoptosis, as indicated by an annexin V and 7AAD assays. The obtained data provide new insights on the presence of cytosolic DNA sensors in tumor cells and the activation of different types of cells death after electrotransfer of pDNA. These observations have important implications on the planning of gene therapy or DNA vaccination protocols.

Characterization of Cell Membrane Permeability In Vitro Part II: Computational Model of Electroporation-Mediated Membrane Transport

Electroporation is the process by which applied electric fields generate nanoscale defects in biological membranes to more efficiently deliver drugs and other small molecules into the cells. Due to the complexity of the process, computational models of cellular electroporation are difficult to validate against quantitative molecular uptake data. In part I of this two-part report, we describe a novel method for quantitatively determining cell membrane permeability and molecular membrane transport using fluorescence microscopy. Here, in part II, we use the data from part I to develop a two-stage ordinary differential equation model of cellular electroporation. We fit our model using experimental data from cells immersed in three buffer solutions and exposed to electric field strengths of 170 to 400 kV/m and pulse durations of 1 to 1000 μs. We report that a low-conductivity 4-(2-hydroxyethyl)-1 piperazineethanesulfonic acid buffer enables molecular transport into the cell to increase more rapidly than with phosphate-buffered saline or culture medium-based buffer. For multipulse schemes, our model suggests that the interpulse delay between two opposite polarity electric field pulses does not play an appreciable role in the resultant molecular uptake for delays up to 100 μs. Our model also predicts the per-pulse permeability enhancement decreases as a function of the pulse number. This is the first report of an ordinary differential equation model of electroporation to be validated with quantitative molecular uptake data and consider both membrane permeability and charging.

Permeabilizing Phospholipid Bilayers with Non-normal Electric Fields

Since 2003, molecular dynamics simulations of lipid bilayers have provided valuable insights into the mechanisms underlying electropermeabilization (electroporation)-an electric field-induced increase in the permeability of biological membranes. The convention in these studies has been to apply the electric field normal to the plane of the membrane. In a typical electroporation application, however, where the electric field is reasonably uniform and unidirectional, the field is perpendicular to the membrane only at a few locations-for spherical cells only at the poles of the cells along the axis defined by the direction of the electric field. Everywhere else on the cell surface the field is applied at an angle that is oblique to the plane of the membrane. On a microscopic level, the invaginations and protrusions that characterize a living cell membrane also present many angles to the applied electric field. Here we report the results of molecular dynamics simulations of lipid electropore formation when the electric field is not normal to the membrane surface, which show that the tangential component of the field has a small but non-zero effect.

Lipid vesicles in pulsed electric fields: Fundamental principles of the membrane response and its biomedical applications

The present review focuses on the effects of pulsed electric fields on lipid vesicles ranging from giant unilamellar vesicles (GUVs) to small unilamellar vesicles (SUVs), from both fundamental and applicative perspectives. Lipid vesicles are the most popular model membrane systems for studying biophysical and biological processes in living cells. Furthermore, as vesicles are made from biocompatible and biodegradable materials, they provide a strategy to create safe and functionalized drug delivery systems in health-care applications. Exposure of lipid vesicles to pulsed electric fields is a common physical method to transiently increase the permeability of the lipid membrane. This method, termed electroporation, has shown many advantages for delivering exogenous molecules including drugs and genetic material into vesicles and living cells. In addition, electroporation can be applied to induce fusion between vesicles and/or cells. First, we discuss in detail how research on cell-size GUVs as model cell systems has provided novel insight into the basic mechanisms of cell electroporation and associated phenomena. Afterwards, we continue with a thorough overview how electroporation and electrofusion have been used as versatile methods to manipulate vesicles of all sizes in different biomedical applications. We conclude by summarizing the open questions in the field of electroporation and possible future directions for vesicles in the biomedical field.

Computing Spatiotemporal Heat Maps of Lipid Electropore Formation: A Statistical Approach

We extend the multiscale spatiotemporal heat map strategies originally developed for interpreting molecular dynamics simulations of well-structured proteins to liquids such as lipid bilayers and solvents. Our analysis informs the experimental and theoretical investigation of electroporation, that is, the externally imposed breaching of the cell membrane under the influence of an electric field of sufficient magnitude. To understand the nanoscale architecture of electroporation, we transform time domain data of the coarse-grained interaction networks of lipids and solvents into spatial heat maps of the most relevant constituent molecules. The application takes advantage of our earlier graph-based activity functions by accounting for the contact-forming and -breaking activity of the lipids in the bilayer. Our novel analysis of lipid interaction networks under periodic boundary conditions shows that the disruption of the bilayer, as measured by the breaking activity, is associated with the externally imposed pore formation. Moreover, the breaking activity can be used for statistically ranking the importance of individual lipids and solvent molecules through a bridging between fast and slow degrees of freedom. The heat map approach highlighted a small number of important lipids and solvent molecules, which allowed us to efficiently search the trajectories for any functionally relevant mechanisms. Our algorithms are freely disseminated with the open-source package TimeScapes.

A statistical analytical model for hydrophilic electropore characterization: a comparison study

A new procedure for lipid pore characterization, which extracts the pore geometry from a statistical analysis of the tridimensional surface of the pore, is compared with other methods in the literature.

Geometrical Characterization of an Electropore from Water Positional Fluctuations

We present here a new method for calculating the radius of a transmembrane pore in a phospholipid bilayer. To compare size-related properties of pores in bilayers of various compositions, generated and maintained under different physical and chemical conditions, reference metrics are needed. Operational metrics can be associated with some observed behavior. For example, pore size can be defined by the largest object that will pass through the length of the pore. The novelty of the present approach resides in the characterization of electropore geometry via a statistical approach, based on essential dynamics rules. We define the pore size geometrically with an algorithm for determining the pore radius. In particular, we extract the radius from the tri-dimensional surface of a defined pore region. The method is applied to a pore formed in a phospholipid bilayer by application of an external electric field. Although the details described here are specific for lipid pores in molecular dynamics simulations, the method can be generalized for any kind of pores for which appropriate structural information is available.

Quantification of cell membrane permeability induced by monopolar and high-frequency bipolar bursts of electrical pulses

High-frequency bipolar electric pulses have been shown to mitigate undesirable muscle contraction during irreversible electroporation (IRE) therapy. Here, we evaluate the potential applicability of such pulses for introducing exogenous molecules into cells, such as in electrochemotherapy (ECT). For this purpose we develop a method for calculating the time course of the effective permeability of an electroporated cell membrane based on real-time imaging of propidium transport into single cells that allows a quantitative comparison between different pulsing schemes. We calculate the effective permeability for several pulsed electric field treatments including trains of 100μs monopolar pulses, conventionally used in IRE and ECT, and pulse trains containing bursts or evenly-spaced 1μs bipolar pulses. We show that shorter bipolar pulses induce lower effective membrane permeability than longer monopolar pulses with equivalent treatment times. This lower efficiency can be attributed to incomplete membrane charging. Nevertheless, bipolar pulses could be used for increasing the uptake of small molecules into cells more symmetrically, but at the expense of higher applied voltages. These data indicate that high-frequency bipolar bursts of electrical pulses may be designed to electroporate cells as effectively as and more homogeneously than conventional monopolar pulses.

Dependence of Electroporation Detection Threshold on Cell Radius: An Explanation to Observations Non Compatible with Schwan's Equation Model

It is widely accepted that electroporation occurs when the cell transmembrane voltage induced by an external applied electric field reaches a threshold. Under this assumption, in order to trigger electroporation in a spherical cell, Schwan's equation leads to an inversely proportional relationship between the cell radius and the minimum magnitude of the applied electric field. And, indeed, several publications report experimental evidences of an inverse relationship between the cell size and the field required to achieve electroporation. However, this dependence is not always observed or is not as steep as predicted by Schwan's equation. The present numerical study attempts to explain these observations that do not fit Schwan's equation on the basis of the interplay between cell membrane conductivity, permeability, and transmembrane voltage. For that, a single cell in suspension was modeled and the electric field necessary to achieve electroporation with a single pulse was determined according to two effectiveness criteria: a specific permeabilization level, understood as the relative area occupied by the pores during the pulse, and a final intracellular concentration of a molecule due to uptake by diffusion after the pulse, during membrane resealing. The results indicate that plausible model parameters can lead to divergent dependencies of the electric field threshold on the cell radius. These divergent dependencies were obtained through both criteria and using two different permeabilization models. This suggests that the interplay between cell membrane conductivity, permeability, and transmembrane voltage might be the cause of results which are noncompatible with the Schwan's equation model.

A molecular insight into the electro-transfer of small molecules through electropores driven by electric fields

The transport of chemical compounds across the plasma membrane into the cell is relevant for several biological and medical applications. One of the most efficient techniques to enhance this uptake is reversible electroporation. Nevertheless, the detailed molecular mechanism of transport of chemical species (dyes, drugs, genetic materials, …) following the application of electric pulses is not yet fully elucidated. In the past decade, molecular dynamics (MD) simulations have been conducted to model the effect of pulsed electric fields on membranes, describing several aspects of this phenomenon. Here, we first present a comprehensive review of the results obtained so far modeling the electroporation of lipid membranes, then we extend these findings to study the electrotransfer across lipid bilayers subject to microsecond pulsed electric fields of Tat11, a small hydrophilic charged peptide, and of siRNA. We use in particular a MD simulation protocol that allows to characterize the transport of charged species through stable pores. Unexpectedly, our results show that for an electroporated bilayer subject to transmembrane voltages in the order of 500mV, i.e. consistent with experimental conditions, both Tat11 and siRNA can translocate through nanoelectropores within tens of ns. We discuss these results in comparison to experiments in order to rationalize the mechanism of drug uptake by cells. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Phospholipid and Hydrocarbon Interactions with a Charged Electrode Interface

Using a combination of molecular dynamics simulations and experiments we examined the interactions of alkanes and phospholipids at charged interfaces in order to understand how interfacial charge densities affect the association of these two representative molecules with electrodes. Consistent with theory and experiment, these model systems reveal interfacial associations mediated through a combination of Coulombic and van der Waals forces. van der Waals forces, in particular, mediate rapid binding of decane to neutral electrodes. No decane binding was observed at high surface charge densities because of interfacial water polarization, which screens hydrophobic attractions. The positively charged choline moiety of the phospholipid palmitoyloleoylphosphatidylcholine (POPC) is primarily responsible for POPC attraction by a moderately negatively charged electrode. The hydrocarbon tails of POPC interact with the hydrophobic electrode interface similarly to decane. Previously reported electrochemical results confirm these findings by demonstrating bipolar displacement currents from PC vesicles adhering to moderately negatively charged interfaces, originating from the choline interactions observed in simulations. At more negatively charged interfaces, choline-to-surface binding was stronger. In both simulations and experiments the maximal interaction of anionic PS occurs with a positively charged interface, provided that the electrostatic forces outweigh local Lennard-Jones interactions. Direct comparisons between the binding affinities measured in experiments and those obtained in simulations reveal previously unobserved atomic interactions that facilitate lipid vesicle adhesion to charged interfaces. Moreover, the implementation of a charged interface in molecular dynamics simulations provides an alternative method for the generation of large electric fields across phospholipid bilayers, especially for systems with periodic boundary conditions, and may be useful for simulations of membrane electropermeabilization.

Specific electrical capacitance and voltage breakdown as a function of temperature for different planar lipid bilayers

The breakdown voltage and specific electrical capacitance of planar lipid bilayers formed from lipids isolated from the membrane of archaeon Aeropyrum pernix K1 as a function of temperature were studied and compared with data obtained previously in MD simulation studies. Temperature dependence of breakdown voltage and specific electrical capacitance was measured also for dipalmitoylphosphatidylcholine (DPPC) bilayers and bilayers formed from mixture of diphytanoylphosphocholine (DPhPC) and DPPC in ratio 80:20. The breakdown voltage of archaeal lipids planar lipid bilayers is more or less constant until 50°C, while at higher temperatures a considerable drop is observed, which is in line with the results from MD simulations. The breakdown voltage of DPPC planar lipid bilayer at melting temperature is considerably higher than in the gel phase. Specific electrical capacitance of planar lipid bilayers formed from archaeal lipids is approximately constant for temperatures up to 40°C and then gradually decreases. The difference with MD simulation predictions is discussed. Specific electrical capacitance of DPPC planar lipid bilayers in fluid phase is 1.75 times larger than that of the gel phase and it follows intermediated phases before phase transition. Increase in specific electrical capacitance while approaching melting point of DPPC is visible also for DPhPC:DPPC mixture.

Properties of lipid electropores I: Molecular dynamics simulations of stabilized pores by constant charge imbalance

Molecular dynamics (MD) simulations have become a powerful tool to study electroporation (EP) in atomic detail. In the last decade, numerous MD studies have been conducted to model the effect of pulsed electric fields on membranes, providing molecular models of the EP process of lipid bilayers. Here we extend these investigations by modeling for the first time conditions comparable to experiments using long (μs-ms) low intensity (~kV/cm) pulses, by studying the characteristics of pores formed in lipid bilayers maintained at a constant surface tension and subject to constant charge imbalance. This enables the evaluation of structural (size) and electrical (conductance) properties of the pores formed, providing information hardly accessible directly by experiments. Extensive simulations of EP of simple phosphatidylcholine bilayers in 1M NaCl show that hydrophilic pores with stable radii (1-2.5 nm) form under transmembrane voltages between 420 and 630 mV, allowing for ionic conductance in the range of 6.4-29.5 nS. We discuss in particular these findings and characterize both convergence and size effects in the MD simulations. We further extend these studies in a follow-up paper (Rems et al., Bioelectrochemistry, Submitted), by proposing an improved continuum model of pore conductance consistent with the results from the MD simulations.

Perspectives on external electric fields in molecular simulation: progress, prospects and challenges

In this review, the application of a wide variety of external electric fields in molecular simulation shall be discussed, including time-varying and electromagnetic, as well as the utility and potential impact and prospects for exploitation of such simulations for real-world and industrial end use. In particular, non-equilibrium molecular dynamics will be discussed, as well as challenges in addressing adequate thermostatting and scaling field amplitudes to more experimentally relevant levels. Attention shall be devoted to recent progress and advances in external fields in ab initio molecular simulation and dynamics, as well as elusive challenges thereof (and, to some extent, for molecular dynamics from empirical potentials), such as timescales required to observe low-frequency and intensity field effects. The challenge of deterministic molecular dynamics in external fields in sampling phase space shall be discussed, along with prospects for application of fields in enhanced-sampling simulations. Finally, the application of external electric fields to a wide variety of aqueous, nanoscale and biological systems will be discussed, often motivated by the possibility of exploitation in real-world applications, which serve to underpin our molecular-level understanding of field effects in terms of microscopic mechanisms, and possibly with a view to control thereof.

Membrane pore formation in atomistic and coarse-grained simulations

Biological cells and their organelles are protected by ultra thin membranes. These membranes accomplish a broad variety of important tasks like separating the cell content from the outer environment, they are the site for cell-cell interactions and many enzymatic reactions, and control the in- and efflux of metabolites. For certain physiological functions e.g. in the fusion of membranes and also in a number of biotechnological applications like gene transfection the membrane integrity needs to be compromised to allow for instance for the exchange of polar molecules across the membrane barrier. Mechanisms enabling the transport of molecules across the membrane involve membrane proteins that form specific pores or act as transporters, but also so-called lipid pores induced by external fields, stress, or peptides. Recent progress in the simulation field enabled to closely mimic pore formation as supposed to occur in vivo or in vitro. Here, we review different simulation-based approaches in the study of membrane pores with a focus on lipid pore properties such as their size and energetics, poration mechanisms based on the application of external fields, charge imbalances, or surface tension, and on pores that are induced by small molecules, peptides, and lipids. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

How Sensitive is the Amide I Vibration of the Polypeptide Backbone to Electric Fields?

Site-selective isotopic labeling of amide carbonyls offers a nonperturbative means to introduce a localized infrared probe into proteins. Although this strategy has been widely used to investigate various biological questions, the dependence of the underlying amide I vibrational frequency on electric fields (or Stark tuning rate) has not been fully determined, which prevents it from being used in a quantitative manner in certain applications. Herein, through the use of experiments and molecular dynamics simulations, the Stark tuning rate of the amide I vibration of an isotopically labeled backbone carbonyl in a transmembrane α-helix is determined to be approximately 1.4 cm(-1) /(MV/cm). This result provides a quantitative basis for using this vibrational model to assess local electric fields in proteins, among other applications. For instance, by using this value, we are able to show that the backbone region of a dipeptide has a surprisingly low dielectric constant.