Free energy of a trans-membrane pore calculated from atomistic molecular dynamics simulations

Processes and mechanisms underlying burst of giant unilamellar vesicles induced by antimicrobial peptides and compounds

To clarify the damage of lipid bilayer region in bacterial cell membrane caused by antimicrobial peptides (AMPs) and antimicrobial compounds (AMCs), their interactions with giant unilamellar vesicles (GUVs) of various lipid compositions have been examined. The findings revealed two main causes for the leakage: nanopore formation in the membrane and burst of GUVs. Although GUV burst has been explained previously based on the carpet model, the supporting evidence is limited. In this review, to better clarify the mechanism of GUV burst by AMPs, AMCs, and other membrane-active peptides, we described current knowledge of the conditions, characteristics, and detailed processes of GUV burst and the changes in the shape of the GUVs during burst. We identified several physical factors that affect GUV burst, such as membrane tension, electrostatic interaction, structural changes of GUV membrane such as membrane folding, and oil in the membrane. We also clarified one of the physical mechanisms underlying the instability of lipid bilayers that are associated with leakage in the carpet model. Based on these results, we propose a mechanism underlying some types of GUV burst induced by these substances: the growth of a nanopore to a micropore, resulting in GUV burst.

Effect of Phosphatidylethanolamine on Pore Formation Induced by the Antimicrobial Peptide PGLa

Most antimicrobial peptides (AMPs) induce pore formation and a burst of lipid bilayers and plasma membranes. This causes severe leakage of the internal contents and cell death. The AMP PGLa forms nanopores in giant unilamellar vesicles (GUVs) comprising dioleoylphosphatidylcholine (DOPC) and dioleoylphosphatidylglycerol (DOPG). We here elucidated the effect of the line tension of a prepore rim on PGLa-induced nanopore formation by investigating the interaction of PGLa with single GUVs comprising dioleoylphosphatidylethanolamine (DOPE)/DOPG (6:4) in buffer using the single GUV method. We found that PGLa forms nanopores in the GUV membrane, which evolved into a local burst and burst of GUVs. The rate of pore formation in DOPE/DOPG-GUVs was smaller than that in DOPC/DOPG-GUVs. PGLa is located only in the outer leaflet of a GUV bilayer just before a fluorescent probe AF647 leakage from the inside, indicating that this asymmetric distribution induces nanopore formation. PGLa-induced local burst and burst of GUVs were observed at 10 ms-time resolution. After nanopore formation started, dense particles and small vesicles appeared in the GUVs, followed by a decrease in the GUV diameter. The GUV was finally converted into smaller GUV or lipid membrane aggregates. We discuss the mechanisms of PGLa-induced nanopore formation and its direct evolution to a GUV burst.

Effect of membrane tension on antimicrobial peptide PGLa-induced pore formation in lipid bilayers

The osmotic pressure (Π) method has recently been developed to quantitatively examine the effect of membrane tension (σ) on pore formation in giant unilamellar vesicles (GUVs) induced by antimicrobial peptides (AMPs). Here, we used the Π method to reveal the effect of σ on the interaction of an AMP, PGLa, with lipid bilayers comprising dioleoylphosphatidylglycerol (DOPG) and dioleoylphosphatidylcholine (DOPC) (4/6). PGLa induced leakage of fluorescent probes from single GUVs under Π, indicating nanopore formation. Membrane tension did not transform a PGLa-induced nanopore into a micropore nor cause GUV burst up to 3.4 mN/m, which is in contrast with the effect of σ on another AMP, magainin 2-induced pore formation, where lower σ resulted in GUV burst. The fraction of leaking GUVs at a specific time increased with increasing σ, indicating that the rate of PGLa-induced pore formation increases with increasing σ. The rate of transfer of fluorescent probe-labeled PGLa across the lipid bilayer without pore formation also increased with increasing σ. PGLa-induced pore formation requires a symmetric distribution of peptides in both leaflets of the GUV bilayer, and thus we infer that the increase in the rate of PGLa transfer from the outer leaflet to the inner leaflet underlies the increase in the rate of pore formation with increasing σ. On the basis of these results, we discuss the difference between the effect of σ on nanopore formation in GUV membranes induced by PGLa and that by magainin 2.

Membrane Binding Strength vs Pore Formation Cost─What Drives the Membrane Permeation of Nanoparticles Coated with Cell-Penetrating Peptides?

Cell-penetrating peptides (CPPs) enable the transport of nanoparticles through cell membranes. Using molecular simulations, we conduct an in-depth investigation into the thermodynamic forces governing the passive translocation of CPP-coated nanoparticles across lipid bilayers, contrasting their behavior with that of bare particles to dissect the contribution of the peptides. Our analysis unveils a distinctive two-stage translocation mechanism, where the adsorption energy of the particles overcomes the cost of forming a hydrophilic transmembrane pore. Proper evaluation of the translocation mechanisms is only possible when using two reaction coordinates, in particular, one that explicitly includes the density of the lipids on the binding site of the particle. An analysis of adsorption and activation free energies in terms of a simple kinetic model provides a clearer understanding of the CPP effect. Experimental validation using nonendocytic cells confirms the superior membrane permeation of CPP-coated particles. Our findings have implications for the rational design of more efficient cell-permeating particles.

Effects of membrane potentials on the electroporation of giant unilamellar vesicles

Living organisms maintain a resting membrane potential, which plays an important role in various biophysical and biological processes. In the context of medical applications, irreversible electroporation (IRE) is a non-thermal and minimally invasive technique that utilizes precisely controlled electric field pulses of micro- to millisecond durations to effectively ablate cancer and tumor cells. Previous studies on IRE-induced rupture of cell-mimetic giant unilamellar vesicles (GUVs) have primarily been conducted in the absence of membrane potentials. In this study, we investigated the electroporation of GUVs, including parameters such as the rate constant of rupture and the probability of rupture, in the presence of various negative membrane potentials. The membranes of GUVs were prepared using lipids and channel forming proteins. As the membrane potential increased from 0 to -90 mV, the rate constant of rupture showed a significant increase from (7.5 ± 1.6)×10-3 to (35.6 ± 5.5)×10-3 s-1. The corresponding probability of rupture also exhibited a notable increase from 0.40 ± 0.05 to 0.68 ± 0.05. To estimate the pore edge tension, the electric tension-dependent logarithm of the rate constant was fitted with the Arrhenius equation for different membrane potentials. The presence of membrane potential did not lead to any significant changes in the pore edge tension. The increase in electroporation is reasonably explained by the decrease in the prepore free energy barrier. The choice of buffer used in GUVs can significantly influence the kinetics of electroporation. This study provides valuable insights that can contribute to the application of electroporation techniques in the biomedical field.

Interaction of Macromolecular Chain with Phospholipid Membranes in Solutions: A Dissipative Particle Dynamics Simulation Study

The interaction between macromolecular chains and phospholipid membranes in aqueous solution was investigated using dissipative particle dynamics simulations. Two cases were considered, one in which the macromolecular chains were pulled along parallel to the membrane surfaces and another in which they were pulled vertical to the membrane surfaces. Several parameters, including the radius of gyration, shape factor, particle number, and order parameter, were used to investigate the interaction mechanisms during the dynamics processes by adjusting the pulling force strength of the chains. In both cases, the results showed that the macromolecular chains undergo conformational transitions from a coiled to a rod-like structure. Furthermore, the simulations revealed that the membranes can be damaged and repaired during the dynamic processes. The role of the pulling forces and the adsorption interactions between the chains and membranes differed in the parallel and perpendicular pulling cases. These findings contribute to our understanding of the interaction mechanisms between macromolecules and membranes, and they may have potential applications in biology and medicine.

Antimicrobial peptide magainin 2-induced rupture of single giant unilamellar vesicles comprising E. coli polar lipids

Most antimicrobial peptides (AMPs) damage the cell membrane of bacterial cells and induce rapid leakage of the internal cell contents, which is a main cause of their bactericidal activity. One of the AMPs, magainin 2 (Mag), forms nanopores in giant unilamellar vesicles (GUVs) comprising phosphatidylcholine (PC) and phosphatidylglycerol (PG), inducing leakage of fluorescent probes. In this study, to elucidate the Mag-induced pore formation in lipid bilayer region in E. coli cell membrane, we examined the interaction of Mag with single GUVs comprising E. coli polar lipids (E. coli-lipid-GUVs). First, we investigated the Mag-induced leakage of a fluorescent probe AF488 from single E. coli-lipid-GUVs, and found that Mag caused rupture of GUVs, inducing rapid AF488 leakage. The rate constant of Mag-induced GUV rupture increased with the Mag concentration. Using fluorescence microscopy with a time resolution of 5 ms, we revealed the GUV rupture process: first, a small micropore was observed in the GUV membrane, then the pore radius increased within 50 ms without changing the GUV diameter, the thickness of the membrane at the pore rim concomitantly increased, and eventually membrane aggregates were formed. Mag bound to only the outer monolayer of the GUV before GUV rupture, which increased the area of the GUV bilayer. We also examined the physical properties of E. coli-lipid-GUVs themselves. We found that the rate constant of the constant tension-induced rupture of E. coli-lipid-GUVs was higher than that of PG/PC-GUVs. Based on these results, we discussed the Mag-induced rupture of E. coli-lipid-GUVs and its mechanism.

Effect of monolayer spontaneous curvature on constant tension-induced pore formation in lipid bilayers

The methodology of constant tension-induced rupture of giant unilamellar vesicles (GUVs) has provided information on tension-induced pore formation. This method was used to investigate the effect of spontaneous curvature (H₀) for a lipid monolayer on the rate constant (k_r) for constant tension (σ)-induced rupture, which originates from pore formation in lipid bilayers. Lipids were incorporated with different H₀ values into GUV membranes to change the overall H₀ value for the GUV monolayer. The dioleoylphosphatidylglycerol (DOPG)/dioleoylphosphatidylethanolamine (DOPE) (4/6, molar ratio, here and elsewhere) monolayer has a negative H₀, whereas the DOPG/dioleoylphosphatidylcholine (DOPC) (4/6) monolayer has an essentially zero H₀. A higher tension was required to induce the rupture of DOPG/DOPE (4/6)-GUVs compared with DOPG/DOPC (4/6)-GUVs. The line tension (Γ) for a pre-pore in DOPG/DOPE (4/6)-GUVs, determined by the analysis of the tension dependence of k_r, was 1.5 times larger than that in DOPG/DOPC (4/6)-GUVs. The k_r values for GUVs comprising DOPG/DOPC/18:1 lysophosphatidylcholine (LPC) (40/55/10), which has a positive H₀, were larger than those for DOPG/DOPC (4/6)-GUVs under the same tension. The Γ value for DOPG/DOPC/LPC (40/55/10)-GUVs was almost half that for DOPG/DOPC (4/6)-GUVs. These results indicate that Γ decreases with increasing H₀, which results in an increase in k_r. Based on these results, the effect of H₀ on k_r and Γ is discussed.

Effect of Cobalt Ferrite Nanoparticles in a Hydrophilic Shell on the Conductance of Bilayer Lipid Membrane

We measured the conductance of bilayer lipid membranes of diphytanoylphosphatidylcholine induced by interaction with cubic magnetic nanoparticles (MNPs) of cobalt ferrite 12 and 27 nm in size and coated with a hydrophilic shell. The MNP coating is human serum albumin (HSA) or polyethylene glycol (PEG). The interaction of nanoparticles added to the bulk solution with the lipid bilayer causes the formation of metastable conductive pores, which, in turn, increases the integral conductance of the membranes. The increase in conductance with increasing MNP concentration was practically independent of the particle size. The dependence of the bilayer conductance on the concentration of PEG-coated MNPs was much weaker than that on the concentration with a shell of HSA. Analyzing the current traces, we believe that the conductive pores formed as a result of the interaction of nanoparticles with the membrane can change their size, remaining metastable. The form of multilevel current traces allows us to assume that there are several metastable pore states close in energy. The average radius of the putative cylindrical pores is in the range of 0.4-1.3 nm.

Self-Assembly of Lipid Mixtures in Solutions: Structures, Dynamics Processes and Mechanical Properties

The self-assembly of lipid mixtures in aqueous solution was investigated by dissipative particle dynamics simulation. Two types of lipid molecules were modelled, where three mixed structures, i.e., the membrane, perforated membrane and vesicle, were determined in the self-assembly processes. Phase behaviour was investigated by using the phase diagrams based on the tail chain lengths for the two types of lipids. Several parameters, such as chain number and average radius of gyration, were employed to explore the structural formations of the membrane and perforated membrane in the dynamic processes. Interface tension was used to demonstrate the mechanical properties of the membrane and perforated membrane in the equilibrium state and dynamics processes. Results help us to understand the self-assembly mechanism of the biomolecule mixtures, which has a potential application for designing the lipid molecule-based bio-membranes in solutions.

Effects of sugar concentration on the electroporation, size distribution and average size of charged giant unilamellar vesicles

We investigated the effects of sugar concentration on the electroporation, size distribution and average size of giant unilamellar vesicles (GUVs). GUVs were prepared from 40 mol% of 1,2-dioleoyl-sn-glycero-3-phospho-(1'-rac-glycerol) (DOPG) and 60 mol% of 1, 2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) lipids. Pulsed electric field was applied to the 40%DOPG/60%DOPC-GUVs and it induced lateral electric tension (σ_c) in the membranes of vesicles. The σ_c-induced probability of rupture (P_pore) and the rate constant of rupture (k_p) of GUVs under the sugar concentration, c = 40, 100 and 300 mM, were determined. Both the P_pore and k_p increased with the increase of σ_c, but higher tension was required to generate the same values of P_pore and k_p with increasing c. We also investigated average sizes of GUVs from the size distribution of vesicles under various sugar concentrations. With the increase of c, the peak of the size distribution histograms shifted to the region of smaller vesicles. The average size decreased 1.6-fold when c increased from 10 to 300 mM. These investigations help to understand various biomedical, biophysical, and biochemical processes in vesicles and cells. Electroporation, size distribution and average size of charged GUVs were investigated under various sugar concentrations. The sugar concentration influences the electroporation of vesicles and the average size of GUVs.

Effect of Osmotic Pressure on Pore Formation in Lipid bilayers by the Antimicrobial Peptide Magainin 2

Osmotic pressure (Π) induces membrane tension in cells and lipid vesicles, which may affect the activity of antimicrobial peptides (AMPs) by an unknown mechanism. We recently quantitated the membrane tension...

Electroporation-Based Therapy for Brain Tumors: A Review

Electroporation-based therapy (EBT), as a high-voltage-pulse technology has been prevalent with favorable clinical outcomes in the treatment of various solid tumors. This review paper aims to promote the clinical translation of EBT for brain tumors. First, we briefly introduced the mechanism of pore formation in a cell membrane activated by external electric fields using a single cell model. Then, we summarized and discussed the current in vitro and in vivo preclinical studies, in terms of (1) the safety and effectiveness of EBT for brain tumors in animal models, and (2) the blood-brain barrier (BBB) disruption induced by EBT. Two therapeutic effects could be achieved in EBT for brain tumors simultaneously, i.e., the tumor ablation induced by irreversible electroporation (IRE) and transient BBB disruption induced by reversible electroporation (RE). The BBB disruption could potentially improve the uptake of antitumor drugs thereby enhancing brain tumor treatment. The challenges that hinder the application of EBT in the treatment of human brain tumors are discussed in the review paper as well.

Recent developments in the kinetics of ruptures of giant vesicles under constant tension

External tension in membranes plays a vital role in numerous physiological and physicochemical phenomena. In this review, recent developments in the constant electric- and mechanical-tension-induced rupture of giant unilamellar vesicles (GUVs) are considered. We summarize the results relating to the kinetics of GUV rupture as a function of membrane surface charge, ions in the bathing solution, lipid composition, cholesterol content in the membrane, and osmotic pressure. The mechanical stability and line tension of the membrane under these conditions are discussed. The membrane tension due to osmotic pressure and the critical tension of rupture for various membrane compositions are also discussed. The results and their analysis provide a biophysical description of the kinetics of rupture, along with insight into biological processes. Future directions and possible developments in this research area are included.

Role of cholesterol in substrate recognition by [Formula: see text]-secretase

[Formula: see text]-Secretase is an enzyme known to cleave multiple substrates within their transmembrane domains, with the amyloid precursor protein of Alzheimer's Disease among the most prominent examples. The activity of [Formula: see text]-secretase strictly depends on the membrane cholesterol content, yet the mechanistic role of cholesterol in the substrate binding and cleavage remains unclear. In this work, we used all-atom molecular dynamics simulations to examine the role of cholesterol in the initial binding of a direct precursor of [Formula: see text]-amyloid polypeptides by [Formula: see text]-secretase. We showed that in cholesterol-rich membranes, both the substrate and the enzyme region proximal to the active site induce a local membrane thinning. With the free energy methods we found that in the presence of cholesterol the substrate binds favorably to the identified exosite, while cholesterol depletion completely abolishes the binding. To explain these findings, we directly examined the role of hydrophobic mismatch in the substrate binding to [Formula: see text]-secretase, showing that increased membrane thickness results in higher propensity of the enzyme to bind substrates. Therefore, we propose that cholesterol promotes substrate binding to [Formula: see text]-secretase by increasing the membrane thickness, which leads to the negative hydrophobic mismatch between the membrane and binding partners.

Effects of osmotic pressure on the irreversible electroporation in giant lipid vesicles

Irreversible electroporation (IRE) is a nonthermal tumor/cell ablation technique in which a series of high-voltage short pulses are used. As a new approach, we aimed to investigate the rupture of giant unilamellar vesicles (GUVs) using the IRE technique under different osmotic pressures (Π), and estimated the membrane tension due to Π. Two categories of GUVs were used in this study. One was prepared with a mixture of dioleoylphosphatidylglycerol (DOPG), dioleoylphosphatidylcholine (DOPC) and cholesterol (chol) for obtaining more biological relevance while other with a mixture of DOPG and DOPC, with specific molar ratios. We determined the rate constant (kp) of rupture of DOPG/DOPC/chol (46/39/15)-GUVs and DOPG/DOPC (40/60)-GUVs induced by constant electric tension (σc) under different Π. The σc dependent kp values were fitted with a theoretical equation, and the corresponding membrane tension (σoseq) at swelling equilibrium under Π was estimated. The estimated membrane tension agreed well with the theoretical calculation within the experimental error. Interestingly, the values of σoseq were almost same for both types of synthesized GUVs under same osmotic pressure. We also examined the sucrose leakage, due to large osmotic pressure-induced pore formation, from the inside of DOPG/DOPC/chol(46/39/15)-GUVs. The estimated membrane tension due to large Π at which sucrose leaked out was very similar to the electric tension at which GUVs were ruptured without Π. We explained the σc and Π induced pore formation in the lipid membranes of GUVs.

Joint Reaction Coordinate for Computing the Free-Energy Landscape of Pore Nucleation and Pore Expansion in Lipid Membranes

Topological transitions of membranes, such as pore formation or membrane fusion, play key roles in biology, biotechnology, and in medical applications. Calculating the related free-energy landscapes has been complicated by the fact that such processes involve a sequence of transitions along highly distinct directions in conformational space, making it difficult to define good reaction coordinates (RCs) for the overall process. In this study, a new RC capable of driving both pore nucleation and pore expansion in lipid membranes is presented. The potential of mean force (PMF) along the RC computed with molecular dynamics simulations provides a comprehensive view on the free-energy landscape of pore formation, including a barrier for pore nucleation; the size, free energy, and metastability of the open pore; and the energetic cost for further pore expansion against the line tension of the pore rim. The RC is illustrated by quantifying the effects of (i) simulation system size and (ii) the addition of dimethyl sulfoxide on the free-energy landscape of pore formation. PMF calculations along the RC provide mechanistic and energetic understanding of pore formation, hence they will be useful to rationalize the effects of membrane-active peptides, electric fields, and membrane composition on transmembrane pores.

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.

Interaction between Bottlebrush Polymers and Phospholipid Membranes in Solutions

In this work, the interactions between bottlebrush polymers and phospholipid membranes were investigated using dissipative particle dynamics simulations. The weak and strong adsorption phenomena between the polymers and membranes were examined by calculating the system parameters. A spring model was introduced to explain the variances in the shape factors and the radius of gyration of the bottlebrush polymers, as well as the order parameters of the phospholipid membrane in the pulling processes. This work provides further understanding for the application of bottlebrush polymers in biological processes.

Sequential Water and Headgroup Merger: Membrane Poration Paths and Energetics from MD Simulations

Membrane topology changes such as poration, stalk formation, and hemifusion rupture are essential to cellular function, but their molecular details, energetics, and kinetics are still not fully understood. Here, we present a unified energetic and mechanistic picture of metastable pore defects in tensionless lipid membranes. We used an exhaustive committor analysis to test and select optimal reaction coordinates and also to determine the nucleation mechanism. These reaction coordinates were used to calculate free-energy landscapes that capture the full process and end states. The identified barriers agree with the committor analysis. To enable sufficient sampling of the complete transition path for our molecular dynamics simulations, we developed a “gizmo” potential biasing scheme. The simulations suggest that the essential step in the nucleation is the initial merger of lipid headgroups at the nascent pore center. To facilitate this event, an indentation pathway is energetically preferred to a hydrophobic defect. Continuous water columns that span the indentation were determined to be on-path transients that precede the nucleation barrier. This study gives a quantitative description of the nucleation mechanism and energetics of small metastable pores and illustrates a systematic approach to uncover the mechanisms of diverse cellular membrane remodeling processes.

Actin networks regulate the cell membrane permeability during electroporation

Transient physical disruption of cell membranes by electric pulses (or electroporation) has significance in biomedical and biological applications requiring the delivery of exogenous (bio)molecules to living cells. We demonstrate that actin networks regulate the cell membrane permeability during electroporation. Disruption of actin networks increases the uptake of membrane-impermeable molecules such as propidium iodide during electroporation. Our experiments at different temperatures ranging from 11 °C to 37 °C show that molecular uptake during electroporation increases with temperature. Furthermore, by examining the temperature-dependent kinetics of propidium iodide uptake, we infer that the activation energy barrier of electroporation is lowered when the actin networks are disrupted. Our numerical calculations of transmembrane voltage show that the reduced activation energy barrier for the cells with disrupted actin is not a consequence of the changes in transmembrane voltage associated with changes in the cell shape due to the disruption of actin, indicating that this could be due to changes in membrane mechanical properties. Our results suggest that the current theoretical models of electroporation should be advanced further by including the contributions of the cytoskeletal networks on the cell membrane permeability during the delivery of exogenous materials.

Density Field Thermodynamic Integration (DFTI): A "Soft" Approach to Calculate the Free Energy of Surfactant Self-Assemblies

Thermodynamic integration is one of the most established methods to quantify excess free energies between different metastable states. Excess intermolecular interactions in surfactant assemblies are on the scale of the energy of thermal fluctuations. Therefore, these materials can be deformed and topologically altered via relatively small mechanical stresses. It is thus intuitive to design reaction paths and associated order parameters that exploit the "soft" nature of these materials to mechanically rather than alchemically morph surfactant assemblies from state to state. Here, we propose a novel method coined "density field thermodynamic integration" (DFTI) that adopts the universality and transferability of alchemical methods while simultaneously exploiting the soft excess interactions between surfactant molecules. DFTI was designed for a rapid quantification of the free energy differences between different metastable structures in soft fluid materials. The DFTI method uses an external field coupled to the local density to mechanically morph the system between metastable states of interest. Here, we explored the capability of the DFTI method to swiftly and accurately calculate free energy differences between states. To this aim, we studied two different coarse-grained lipidic surfactant systems: (i) a fusion stalk and (ii) a worm-like micelle. Our results illustrate that DFTI can provide an efficient, versatile, and rather reliable method to calculate the free energy differences between surfactant assemblies.

Electrostatic effects on the electrical tension-induced irreversible pore formation in giant unilamellar vesicles

Irreversible electroporation (IRE) is a new technique in which a series of short pulses with high frequency electrical energy is applied on the targeted regions of cells or vesicles for their destruction or rupture formation. IRE induces lateral tension in the membranes of vesicles. We have investigated the electrostatic interaction effects on the constant electrical tension-induced rate constant of irreversible pore formation in the membranes of giant unilamellar vesicles (GUVs). The electrostatic interaction has been varied by changing the salt concentration in buffer and the surface charge density of membranes. The membranes of GUVs are synthesized by a mixture of negatively charged lipid dioleoylphosphatidylglycerol (DOPG) and neutral lipid dioleoylphosphatidylcholine (DOPC) using the natural swelling method. The rate constant of pore formation increases with the decrease of salt concentration in buffer along with the increase of surface charge density of membranes. The tension dependent probability of pore formation and the rate constant of pore formation are fitted to the theoretical equation, and obtained the line tension of membranes. The decrease in energy barrier of a prepore due to electrostatic interaction is the key factor causing an increase of rate constant of pore formation.

Influence of cholesterol on electroporation in lipid membranes of giant vesicles

Irreversible electroporation (IRE) is primarily a nonthermal ablative technology that uses a series of high-voltage and ultra-short pulses with high-frequency electrical energy to induce cell death. This paper presents the influence of cholesterol on the IRE-induced probability of pore formation and the rate constant of pore formation in giant unilamellar vesicles (GUVs). The GUVs are prepared by a mixture of dioleoylphosphatidylglycerol (DOPG), dioleoylphosphatidylcholine (DOPC) and cholesterol using the natural swelling method. An IRE signal of frequency 1.1 kHz is applied to the membranes of GUVs. The probability of pore formation and the rate constant of pore formation events are obtained using statistical analysis from several single GUVs. The time-dependent fraction of intact GUVs among all those examined is fitted to a single exponential decay function from where the rate constant of pore formation is calculated. The probability of pore formation and the rate constant of pore formation decreases with an increase in cholesterol content in the membranes of GUVs. Theoretical equations are fitted to the tension-dependent rate constant of pore formation and to the probability of pore formation, which allows us to obtain the line tension of membranes. The obtained line tension increases with an increase in cholesterol in the membranes. The increase in the energy barrier of the prepore state, due to the increase of cholesterol in membranes, is the main factor explaining the decrease in the rate constant of pore formation.

Kinetics of irreversible pore formation under constant electrical tension in giant unilamellar vesicles

Stretching in the plasma membranes of cells and lipid membranes of vesicles plays important roles in various physiological and physicochemical phenomena. Irreversible electroporation (IRE) is a minimally invasive non-thermal tumor ablation technique where a series of short electrical energy pulses with high frequency is applied to destabilize the cell membranes. IRE also induces lateral tension due to stretching in the membranes of giant unilamellar vesicles (GUVs). Here, the kinetics of irreversible pore formation under constant electrical tension in GUVs has been investigated. The GUVs are prepared by a mixture of dioleoylphosphatidylglycerol and dioleoylphosphatidylcholine using the natural swelling method. An IRE signal of frequency 1.1 kHz is applied to the GUVs through a gold-coated electrode system. Stochastic pore formation is observed for several 'single GUVs' at a particular constant tension. The time course of the fraction of intact GUVs among all the examined GUVs is fitted with a single-exponential decay function from which the rate constant of pore formation in the vesicle, k_p, is calculated. The value of k_p increases with an increase of membrane tension. An increase in the proportion of negatively charged lipids in a membrane gives a higher k_p. Theoretical equations are fitted to the tension-dependent k_p and to the probability of pore formation, which allows us to obtain the line tension of the membranes. The decrease in the energy barrier for formation of the nano-size nascent or prepore state, due to the increase in electrical tension, is the main factor explaining the increase of k_p.

Role of Membrane Potential on Entry of Cell-Penetrating Peptide Transportan 10 into Single Vesicles

Cell-penetrating peptides (CPPs) can translocate across plasma membranes to enter the cytosol of eukaryotic cells without decreasing cell viability. We revealed the mechanism underlying this translocation by examining the effect of membrane potential, φ_m, on the entry of a CPP, transportan 10 (TP10), into the lumen of single giant unilamellar vesicles (GUVs). For this purpose, we used the single GUV method to detect the entry of carboxyfluorescein (CF)-labeled TP10 (CF-TP10) into the lumen of single GUVs. First, we used various K⁺ concentration differences to apply different negative membrane potentials on single GUVs containing gramicidin A in their membrane and confirmed these potentials using the φ_m-sensitive fluorescent probe 3,3'-dihexyloxacarbocyanine iodine. The fluorescence intensity of the GUV membranes (i.e., the rim intensity) due to 3,3'-dihexyloxacarbocyanine iodine increased with |φ_m| up to 118 mV, and its dependence on |φ_m| less than 28 mV agreed with a theoretical estimation (i.e., the dye concentration in the inner leaflet of a GUV is larger than that in the outer leaflet according to the Boltzmann distribution). We then examined the effect of φ_m on the entry of CF-TP10 into GUVs using single GUVs containing small GUVs or large unilamellar vesicles inside the mother GUV lumen. We found that CF-TP10 entered the GUV lumen without pore formation and the rate of entry of CF-TP10 into the GUV lumen, V_entry, increased with an increase in |φ_m|. The rim intensity due to CF-TP10 increased with an increase in |φ_m|, indicating that the CF-TP10 concentration in the inner leaflet of the GUV increased with |φ_m|. These results indicate that the φ_m-induced elevation in V_entry can be explained by the increase in CF-TP10 concentration in the inner leaflet with |φ_m|. We discuss the mechanism underlying this effect of membrane potential based on the pre-pore model of the translocation of CF-TP10 across a GUV membrane.

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.

Adsorption and insertion of polyarginine peptides into membrane pores: The trade-off between electrostatics, acid-base chemistry and pore formation energy

The mechanism that arginine-rich cell penetrating peptides (ARCPPs) use to translocate lipid membranes is not entirely understood. In the present work, we develop a molecular theory that allows to investigate the adsorption and insertion of ARCPPs on membranes bearing hydrophilic pores. This method accounts for size, shape, conformation, protonation state and charge distribution of the peptides; it also describes the state of protonation of acidic membrane lipids. We present a systematic investigation of the effect of pore size, peptide concentration and sequence length on the extent of peptide adsorption and insertion into the pores. We show that adsorption on the intact (non-porated) lipid membrane plays a key role on peptide translocation. For peptides shorter than nona-arginine, adsorption on the intact membrane increases significantly with chain length, but it saturates for longer peptides. However, this adsorption behavior only occurs at relatively low peptide concentrations; increasing peptide concentration favors adsorption of the shorter molecules. Adsorption of longer peptides increases the intact membrane negative charge as a result of further deprotonation of acidic lipids. Peptide insertion into the pores depends non-monotonically on pore radius, which reflects the short range nature of the effective membrane-peptide interactions. The size of the pore that promotes maximum adsorption depends on the peptide chain length. Peptide translocation is a thermally activated process, so we complement our thermodynamic approach with a simple kinetic model that allows to rationalize the ARCPPs translocation rate in terms of the free energy gain of adsorption, and the energy cost of creating a transmembrane pore with peptides in it. Our results indicate that strategies to improve translocation efficiency should focus on enhancing peptide adsorption.

The role of membrane tension in the action of antimicrobial peptides and cell-penetrating peptides in biomembranes

For antimicrobial peptides (AMPs) with antimicrobial and bactericidal activities and cell-penetrating peptides (CPPs) with activity to permeate through plasma membrane, their interactions with lipid bilayer region in plasma membrane play important roles in these functions. However, the elementary processes and mechanisms of their functions have not been clear. The single giant unilamellar vesicle (GUV) method has revealed the details of elementary processes of interaction of some AMPs and CPPs with lipid vesicles. In this review, we summarize the mode of action of AMPs such as magainin 2 (Mag) and CPPs such as transportan 10 (TP10), revealed by the single GUV methods, and especially we focus on the role of membrane tension in actions of Mag and TP10 and the mechanisms of their actions. First, we explain the characteristics of the single GUV method briefly. Next, we summarize the recent view on the effect of tension on physical properties of lipid bilayers and describe the role of tension in actions of Mag and TP10. Some experimental results indicate that Mag-induced pore is a stretch-activated pore. The effect of packing of transbilayer asymmetric lipid on Mag-induced pore formation is described. On the other hand, entry of fluorescent dye, carboxyfluorescein (CF)-labeled TP10 (i.e., CF-TP10), into single GUVs without pore formation is affected by tension and high concentration of cholesterol. Pre-pore model for translocation of CF-TP10 across lipid bilayer is described. The experimental methods and their analysis described here are useful for investigation of functions of the other types of AMPs, CPPs, and proteins.

Dissipative particle dynamics simulation of critical pore size in a lipid bilayer membrane

We investigate with computer simulations the critical radius of pores in a lipid bilayer membrane. Ilton et al. (Ilton et al. 2016 Phys. Rev. Lett. 117, 257801 (doi:10.1103/PhysRevLett.117.257801)) recently showed that nucleated pores in a homopolymer film can increase or decrease in size, depending on whether they are larger or smaller than a critical size which scales linearly with film thickness. Using dissipative particle dynamics, a particle-based simulation method, we investigate the same scenario for a lipid bilayer membrane whose structure is determined by lipid-water interactions. We simulate a perforated membrane in which holes larger than a critical radius grow, while holes smaller than the critical radius close, as in the experiment of Ilton et al. (Ilton et al. 2016 Phys. Rev. Lett. 117, 257801 (doi:10.1103/PhysRevLett.117.257801)). By altering key system parameters such as the number of particles per lipid and the periodicity, we also describe scenarios in which pores of any initial size can seal or even remain stable, showing a fundamental difference in the behaviour of lipid membranes from polymer films.

Simulation Best Practices for Lipid Membranes [Article v1.0]

We establish a reliable and robust standardization of settings for practical molecular dynamics (MD) simulations of pure and mixed (single- and multi-component) lipid bilayer membranes. In lipid membranes research, particle-based molecular simulations are a powerful tool alongside continuum theory, lipidomics, and model, in vitro, and in vivo experiments. Molecular simulations can provide precise and reproducible spatiotemporal (atomic- and femtosecond-level) information about membrane structure, mechanics, thermodynamics, kinetics, and dynamics. Yet the simulation of lipid membranes can be a daunting task, given the uniqueness of lipid membranes relative to conventional liquid-liquid and solid-liquid interfaces, the immense and complex thermodynamic and statistical mechanical theory, the diversity of multiscale lipid models, limitations of modern computing power, the difficulty and ambiguity of simulation controls, finite size effects, competitive continuum simulation alternatives, and the desired application, including vesicle experiments and biological membranes. These issues can complicate an essential understanding of the field of lipid membranes, and create major bottlenecks to simulation advancement. In this article, we clarify these issues and present a consistent, thorough, and user-friendly framework for the design of state-of-the-art lipid membrane MD simulations. We hope to allow early-career researchers to quickly overcome common obstacles in the field of lipid membranes and reach maximal impact in their simulations.

Transmembrane domain dimerization induces cholesterol rafts in curved lipid bilayers

Are the dimerization of transmembrane (TM) domains and the reorganization of the lipid bilayer two independent events?

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.

Nanoparticle-Engendered Rupture of Lipid Membranes

Tension-induced rupture of 1,2-dimyristoyl- sn-glycero-3-phosphocholine (DMPC) lipid membranes with encapsulated hydrophobic nanoparticles is elucidated using dissipative particle dynamics simulations. The dynamics of hole formation is studied, and a nanoparticle size-dependent relationship is established for the probability of membrane rupture within a given time as a function of the membrane tension. Two mechanisms of hole formation are explored: homogeneous nucleation and heterogeneous nucleation at the nanoparticle surface. While the kinetics of homogeneous nucleation in unloaded membranes complies with the predictions of the classical Deryagin-Gutop (DG) theory, the heterogeneous nucleation causes progressively lower lysis tensions as the particle size increases. The thermodynamics of heterogeneous nucleation is treated by introducing an effective contact angle at the three-phase, solvent-membrane-solid boundary into the DG theory. The proposed approach helps quantitatively interpret the simulation results and predict the membrane stability in real experiments with significantly larger (by many orders of magnitude) observation times and spatial scales.

Elucidating mysteries of phase-segregated membranes: mobile-lipid recruitment facilitates pores' passage to the fluid phase

Phase segregation of multicomponent lipid bilayers leads to, under phase-coexistence conditions, domain formation, featuring delimitation by essentially one-dimensional borders. (Micro-)phase segregation of bilayers is proposed to influence the physiological behaviour of cell membranes and provides the driving force for lipid-raft formation. Experiments show a maximum in the electrical-conductivity of membranes at the phase-transition point, which has been conjectured to arise from border-nucleated transmembrane-conducting defects or pores. However, recent electroporation experiments on phase-segregated bilayers demonstrate electro-pore detection in the liquid disordered phase (Ld), wherein they diffuse over macroscopic periods without absorption into the liquid ordered phase (Lo). Here, we scrutinise transmembrane-pore formation via molecular dynamics simulations on a multicomponent phase-segregated bilayer. We find that pores created in Lo domains always migrate spontaneously to the Ld phase, via 'recruitment' of unsaturated lipids to the pore's rim to transport the pore to the fluid phase under a large stress-field driving force. Once in Ld domains, pores migrate towards their centre, never returning or pinning to Lo. These findings are explained by thermodynamics. By comparing the free-energy cost for creating pores in the bulk of Ld and Lo membranes, and in the phase-segregated system, we show that it is always more energetically tractable to create pores in Ld domains, independent of the pore size.

Computational studies of peptide-induced membrane pore formation

A variety of peptides induce pores in biological membranes; the most common ones are naturally produced antimicrobial peptides (AMPs), which are small, usually cationic, and defend diverse organisms against biological threats. Because it is not possible to observe these pores directly on a molecular scale, the structure of AMP-induced pores and the exact sequence of steps leading to their formation remain uncertain. Hence, these questions have been investigated via molecular modelling. In this article, we review computational studies of AMP pore formation using all-atom, coarse-grained, and implicit solvent models; evaluate the results obtained and suggest future research directions to further elucidate the pore formation mechanism of AMPs.This article is part of the themed issue 'Membrane pores: from structure and assembly, to medicine and technology'.

Metastable Prepores in Tension-Free Lipid Bilayers

The formation and closure of aqueous pores in lipid bilayers is a key step in various biophysical processes. Large pores are well described by classical nucleation theory, but the free-energy landscape of small, biologically relevant pores has remained largely unexplored. The existence of small and metastable "prepores" was hypothesized decades ago from electroporation experiments, but resolving metastable prepores from theoretical models remained challenging. Using two complementary methods-atomistic simulations and self-consistent field theory of a minimal lipid model-we determine the parameters for which metastable prepores occur in lipid membranes. Both methods consistently suggest that pore metastability depends on the relative volume ratio between the lipid head group and lipid tails: lipids with a larger head-group volume fraction (or shorter saturated tails) form metastable prepores, whereas lipids with a smaller head-group volume fraction (or longer unsaturated tails) form unstable prepores.

Bending Lipid Bilayers: A Closed-Form Collective Variable for Effective Free-Energy Landscapes in Quantitative Biology

Curvature-related processes are of major importance during protein-membrane interactions. The illusive simplicity of membrane reshaping masks a complex molecular process crucial for a wide range of biological functions like fusion, endo- and exocytosis, cell division, cytokinesis, and autophagy. To date, no functional expression of a reaction coordinate capable of biasing molecular dynamics simulations to produce membrane curvature has been reported. This represents a major drawback given that the adequate identification of proper collective variables to enhance sampling is fundamental for restrained dynamics techniques. In this work, we present a closed-form equation of a collective variable that induces bending in lipid bilayers in a controlled manner, allowing for straightforward calculation of free energy landscapes of important curvature-related events, using standard methods such as umbrella sampling and metadynamics. As a direct application of the collective variable, we calculate the bending free energies of a ternary lipid bilayer in the presence and the absence of a Bin/Amphiphysin/Rvs domain with an N-terminal amphipathic helix (N-BAR), a well-known peripheral membrane protein that induces curvature.

Pore formation in lipid membrane II: Energy landscape under external stress

Lipid membranes are extremely stable envelopes allowing cells to survive in various environments and to maintain desired internal composition. Membrane permeation through formation of transversal pores requires substantial external stress. Practically, pores are usually formed by application of lateral tension or transmembrane voltage. Using the same approach as was used for obtaining continuous trajectory of pore formation in the stress-less membrane in the previous article, we now consider the process of pore formation under the external stress. The waiting time to pore formation proved a non-monotonous function of the lateral tension, dropping from infinity at zero tension to a minimum at the tension of several millinewtons per meter. Transmembrane voltage, on the contrary, caused the waiting time to decrease monotonously. Analysis of pore formation trajectories for several lipid species with different spontaneous curvatures and elastic moduli under various external conditions provided instrumental insights into the mechanisms underlying some experimentally observed phenomena.

Pore formation in lipid membrane I: Continuous reversible trajectory from intact bilayer through hydrophobic defect to transversal pore

Lipid membranes serve as effective barriers allowing cells to maintain internal composition differing from that of extracellular medium. Membrane permeation, both natural and artificial, can take place via appearance of transversal pores. The rearrangements of lipids leading to pore formation in the intact membrane are not yet understood in details. We applied continuum elasticity theory to obtain continuous trajectory of pore formation and closure, and analyzed molecular dynamics trajectories of pre-formed pore reseal. We hypothesized that a transversal pore is preceded by a hydrophobic defect: intermediate structure spanning through the membrane, the side walls of which are partially aligned by lipid tails. This prediction was confirmed by our molecular dynamics simulations. Conversion of the hydrophobic defect into the hydrophilic pore required surmounting some energy barrier. A metastable state was found for the hydrophilic pore at the radius of a few nanometers. The dependence of the energy on radius was approximately quadratic for hydrophobic defect and small hydrophilic pore, while for large radii it depended on the radius linearly. The pore energy related to its perimeter, line tension, thus depends of the pore radius. Calculated values of the line tension for large pores were in quantitative agreement with available experimental data.