Simulations of Pore Formation in Lipid Membranes: Reaction Coordinates, Convergence, Hysteresis, and Finite-Size Effects

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.

Interface Water Assists in Dimethyl Sulfoxide Crossing and Poration in Model Bilayer

Understanding the mechanism of transport and pore formation by a commonly used cryoprotectant, dimethyl sulfoxide (DMSO), across cell membranes is fundamentally crucial for drug delivery and cryopreservation. To shed light on the mechanism and thermodynamics of pore formation and crossing behavior of DMSO, extensive all-atom molecular dynamics simulations of 1,2-dimyristoyl-rac-glycero-3-phosphocholine (DMPC) bilayers are performed at various concentrations of DMSO at a temperature above the physiological temperature. Our results unveil that DMSO partially depletes water from the interface and positions itself between lipid heads without full dehydration. This induces a larger area per headgroup, increased disorder, and enhanced fluidity without any disintegration even at the highest DMSO concentration studied. The enhanced disorder fosters local fluctuations at the interface that nucleate dynamic and transient pores. The potential of mean force (PMF) of DMSO crossing is derived from two types of biased simulations: a single DMSO pulling using the umbrella sampling technique and a cylindrical pore formation using the recently developed chain reaction coordinate method. In both cases, DMSO crossing encounters a barrier attributed to unfavorable polar nonpolar interactions between DMSO and lipid tails. As the DMSO concentration increases, the barrier height reduces along with the faster lateral and perpendicular diffusion of DMSO suggesting favorable permeation. Our findings suggest that the energy required for pore formation decreases when water assists in the formation of DMSO pores. Although DMSO displaces water from the interface toward the far interface region without complete dehydration, the presence of interface water diminishes pore formation free energy. The existence of interface water leads to the formation of a two-dimensional percolated water-DMSO structure at the interface, which is absent otherwise. Overall, these insights into the mechanism of DMSO crossing and pore formation in the bilayer will contribute to understanding cryoprotectant behavior under supercooled conditions in the future.

Designing Reaction Coordinate for Ion-Induced Pore-Assisted Mechanism of Halide Ions Permeation through Lipid Bilayer by Umbrella Sampling

Ion permeation mechanism through lipid membranes helps to understand cellular processes. We propose new reaction coordinates that allow ions to permeate according to their water affinity and interaction with the hydrophilic layer. Simulations were done for three different halides (F-, Cl-, and I-) in two different lipid bilayers, 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and 1,2-dinervonoyl-sn-glycero-3-phosphocholine (DNPC). It is found that the involvement of the water molecules decreases the free energy barrier. The ions were found to follow different pathways for permeation. Formation of proper pores required a collaboration effort of the hydration shell water molecules and the hydrophilic lipid layer, which was favored in the case of Cl- ions. The optimum charge density and good water affinity of Cl- with respect to F- and I- ions helped to form the pore. The effect was prominently seen in the case of DNPC membrane because of its higher hydrophobic thickness. The umbrella sampling results were compared with other methods such as the Markov state model (MSM) and well-tempered metadynamics (WT-metaD).

Free Energy Surface and Molecular Mechanism of Slow Structural Transitions in Lipid Bilayers

Lipid membrane remodeling, crucial for many cellular processes, is governed by the coupling of membrane structure and shape fluctuations. Given the importance of the ∼ nm length scale, details of the transition intermediates for conformational change are not fully captured by a continuum-mechanical description. Slow dynamics and the lack of knowledge of reaction coordinates (RCs) for biasing methods pose a challenge for all-atom (AA) simulations. Here, we map system dynamics on Langevin dynamics in a normal mode space determined from an elastic network model representation for the lipid-water Hamiltonian. AA molecular dynamics (MD) simulations are used to determine model parameters, and Langevin dynamics predictions for bilayer structural, mechanical, and dynamic properties are validated against MD simulations and experiments. Transferability to describe the dynamics of a larger lipid bilayer and a heterogeneous membrane-protein system is assessed. A set of generic RCs for pore formation in two tensionless bilayers is obtained by coupling Langevin dynamics to the underlying energy landscape for membrane deformations. Structure evolution is carried out by AA MD, wherein the generic RCs are used in a path metadynamics or an umbrella sampling simulation to determine the thermodynamics of pore formation and its molecular determinants, such as the role of distinct bilayer motions, lipid solvation, and lipid packing.

Nanoparticle-induced biomembrane fusion: unraveling the effect of core size on stalk formation

Membrane fusion in vitro is a strategy to load model or cell-derived vesicles with proteins, drugs, and genetic materials for theranostic applications. It is thus crucial to develop strategies to control the fusion process, also through synthetic fusogenic agents. Ligand-protected, membrane-penetrating gold nanoparticles (Au NPs) can facilitate membrane fusion, but the molecular mechanisms remain unresolved. Here, we tackle NP-induced stalk formation using a coarse-grained molecular dynamics approach and enhanced sampling techniques. We show that smaller (2 nm in diameter) NPs lead to a lower free energy barrier and higher stalk stability than larger NPs (4 nm). We demonstrate that this difference is due to a different ligand conformational freedom, which in turn depends on the Au core curvature. Our study provides precious insights into the mechanisms underlying NP-mediated membrane fusion, while our computational approach is general and applicable to studying stalk formation caused by other fusogenic agents.

Converging PMF Calculations of Antibiotic Permeation across an Outer Membrane Porin with Subkilocalorie per Mole Accuracy

The emergence of multidrug-resistant pathogens led to a critical need for new antibiotics. A key property of effective antibiotics against Gram-negative bacteria is their ability to permeate through the bacterial outer membrane via transmembrane porin proteins. Molecular dynamics (MD) simulations are, in principle, capable of modeling antibiotic permeation across outer membrane porins (OMPs). However, owing to sampling problems, it has remained challenging to obtain converged potentials of mean force (PMFs) for antibiotic permeation across OMPs. Here, we investigated the convergence of PMFs along a single collective variable aimed at quantifying the permeation of the antibiotic fosmidomycin across the OprO porin. We compared standard umbrella sampling (US) with three advanced flavors of the US technique: (i) Hamiltonian replica exchange with solute tempering in combination with US, (ii) simulated tempering-enhanced US, and (iii) replica-exchange US. To quantify the PMF convergence and to reveal hysteresis problems, we computed several independent sets of US simulations starting from pulling simulations in the outward and inward permeation directions. We find that replica-exchange US in combination with well-chosen restraints is highly successful for obtaining converged PMFs of fosmidomycin permeation through OprO, reaching PMFs converged to subkilocalorie per mole accuracy.

Intrinsic Disorder in α-Synuclein Regulates the Exocytotic Fusion Pore Transition

Today, it is widely accepted that intrinsic disorder is strongly related to the cell cycle, during mitosis, differentiation, and apoptosis. Of particular interest are hybrid proteins possessing both structured and unstructured domains that are critical in human health and disease, such as α-synuclein. In this work, we describe how α-synuclein interacts with the nascent fusion pore as it evolves toward expansion. We unveil the key role played by its intrinsically disordered region as a thermodynamic regulator of the nucleation-expansion energy barrier. By analyzing a truncated variant of α-synuclein that lacks the disordered region, we find that the landscape of protein interactions with PIP₂ and POPS lipids is highly altered, ultimately increasing the energy cost for the fusion pore to transit from nucleation to expansion. We conclude that the intrinsically disordered region in full-length α-synuclein recognizes and allocates pivotal protein:lipid interactions during membrane remodeling in the first stages of the fusion pore.

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.

Passive transport of Ca2+ ions through lipid bilayers imaged by widefield second harmonic microscopy

In biology, release of Ca2+ ions in the cytosol is essential to trigger or control many cell functions. Calcium signaling acutely depends on lipid membrane permeability to Ca2+. For proper understanding of membrane permeability to Ca2+, both membrane hydration and the structure of the hydrophobic core must be taken into account. Here, we vary the hydrophobic core of bilayer membranes and observe different types of behavior in high-throughput wide-field second harmonic imaging. Ca2+ translocation is observed through mono-unsaturated (DOPC:DOPA) membranes, reduced upon the addition of cholesterol, and completely inhibited for branched (DPhPC:DPhPA) and poly-unsaturated (SLPC:SLPA) lipid membranes. We propose, using molecular dynamics simulations, that ion transport occurs through ion-induced transient pores, which requires nonequilibrium membrane restructuring. This results in different rates at different locations and suggests that the hydrophobic structure of lipids plays a much more sophisticated regulating role than previously thought.

Molecular dynamics simulations reveal the importance of amyloid-beta oligomer β-sheet edge conformations in membrane permeabilization

Oligomeric aggregates of the amyloid-beta peptide(1-42) (Aβ42) are regarded as a primary cause of cytotoxicity related to membrane damage in Alzheimer's disease. However, a dynamical and structural characterization of pore-forming Aβ42 oligomers at atomic detail has not been feasible. Here, we used Aβ42 oligomer structures previously determined in a membrane-mimicking environment as putative model systems to study the pore formation process in phospholipid bilayers with all-atom molecular dynamics simulations. Multiple Aβ42 oligomer sizes, conformations, and N-terminally truncated isoforms were investigated on the multi-μs time scale. We found that pore formation and ion permeation occur via edge conductivity and exclusively for β-sandwich structures that feature exposed side-by-side β-strand pairs formed by residues 9 to 21 of Aβ42. The extent of pore formation and ion permeation depends on the insertion depth of hydrophilic residues 13 to 16 (HHQK domain) and thus on subtle differences in the overall stability, orientation, and conformation of the aggregates in the membrane. Additionally, we determined that backbone carbonyl and polar side-chain atoms from the edge strands directly contribute to the coordination sphere of the permeating ions. Furthermore, point mutations that alter the number of favorable side-chain contacts correlate with the ability of the Aβ42 oligomer models to facilitate ion permeation in the bilayer center. Our findings suggest that membrane-inserted, layered β-sheet edges are a key structural motif in pore-forming Aβ42 oligomers independent of their size and play a pivotal role in aggregate-induced membrane permeabilization.

Determination of Elastic Parameters of Lipid Membranes with Molecular Dynamics: A Review of Approaches and Theoretical Aspects

Lipid membranes are abundant in living organisms, where they constitute a surrounding shell for cells and their organelles. There are many circumstances in which the deformations of lipid membranes are involved in living cells: fusion and fission, membrane-mediated interaction between membrane inclusions, lipid-protein interaction, formation of pores, etc. In all of these cases, elastic parameters of lipid membranes are important for the description of membrane deformations, as these parameters determine energy barriers and characteristic times of membrane-involved phenomena. Since the development of molecular dynamics (MD), a variety of in silico methods have been proposed for the determination of elastic parameters of simulated lipid membranes. These MD methods allow for the consideration of details unattainable in experimental techniques and represent a distinct scientific field, which is rapidly developing. This work provides a review of these MD approaches with a focus on theoretical aspects. Two main challenges are identified: (i) the ambiguity in the transition from the continuum description of elastic theories to the discrete representation of MD simulations, and (ii) the determination of intrinsic elastic parameters of lipid mixtures, which is complicated due to the composition-curvature coupling effect.

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.

Enhanced Expansion and Reduced Kiss-and-Run Events in Fusion Pores Steered by Synaptotagmin-1 C2B Domains

The fusion pore controls the release of exocytotic vesicle contents through a precise orchestration of lipids from the fusing membranes and proteins. There is a major lipid reorganization during the different stages in life of the fusion pore (membrane fusion, nucleation, and expansion) that can be scrutinized thermodynamically. In this work, using umbrella sampling simulations we describe the expansion of the fusion pore. We have calculated free energy profiles to drive a nascent, just nucleated, fusion pore to its expanded configuration. We have quantified the effects on the free energy of one and two Synaptotagmin-1 C2B domains in the cytosolic space. We show that C2B domains cumulatively reduce the cost for expansion, favoring the system to evolve toward full fusion. Finally, by conducting thousands of unbiased molecular dynamics simulations, we show that C2B domains significantly decrease the probability of kiss-and-run events.

Synaptotagmin-1 C2B domains cooperatively stabilize the fusion stalk via a master-servant mechanism

Synaptotagmin-1 is a low-affinity Ca2+ sensor that triggers synchronous vesicle fusion. It contains two similar C2 domains (C2A and C2B) that cooperate in membrane binding, being the C2B domain the...

Free energies of membrane stalk formation from a lipidomics perspective

Many biological membranes are asymmetric and exhibit complex lipid composition, comprising hundreds of distinct chemical species. Identifying the biological function and advantage of this complexity is a central goal of membrane biology. Here, we study how membrane complexity controls the energetics of the first steps of membrane fusions, that is, the formation of a stalk. We first present a computationally efficient method for simulating thermodynamically reversible pathways of stalk formation at coarse-grained resolution. The method reveals that the inner leaflet of a typical plasma membrane is far more fusogenic than the outer leaflet, which is likely an adaptation to evolutionary pressure. To rationalize these findings by the distinct lipid compositions, we computed ~200 free energies of stalk formation in membranes with different lipid head groups, tail lengths, tail unsaturations, and sterol content. In summary, the simulations reveal a drastic influence of the lipid composition on stalk formation and a comprehensive fusogenicity map of many biologically relevant lipid classes.

Fusion of cellular membranes begins with the formation of a stalk. Here, the authors develop a computationally efficient method for coarse-grained simulations of stalk formation and apply this approach to comprehensively analyse how stalk formation is influenced by the membrane lipid composition.

Spontaneous transmembrane pore formation by short-chain synthetic peptide

Amphiphilic β-peptides, which are synthetically designed short-chain helical foldamers of β-amino acids, are established potent biomimetic alternatives of natural antimicrobial peptides. An intriguing question is how the distinct molecular architecture of these short-chain and rigid synthetic peptides translates to its potent membrane-disruption ability. Here, we address this question via a combination of all-atom and coarse-grained molecular dynamics simulations of the interaction of mixed phospholipid bilayer with an antimicrobial 10-residue globally amphiphilic helical β-peptide at a wide range of concentrations. The simulation demonstrates that multiple copies of this synthetic peptide, initially placed in aqueous solution, readily self-assemble and adsorb at membrane interface. Subsequently, beyond a threshold peptide/lipid ratio, the surface-adsorbed oligomeric aggregate moves inside the membrane and spontaneously forms stable water-filled transmembrane pores via a cooperative mechanism. The defects induced by these pores lead to the dislocation of interfacial lipid headgroups, membrane thinning, and substantial water leakage inside the hydrophobic core of the membrane. A molecular analysis reveals that despite having a short architecture, these synthetic peptides, once inside the membrane, would stretch themselves toward the distal leaflet in favor of potential contact with polar headgroups and interfacial water layer. The pore formed in coarse-grained simulation was found to be resilient upon structural refinement. Interestingly, the pore-inducing ability was found to be elusive in a non-globally amphiphilic sequence isomer of the same β-peptide, indicating strong sequence dependence. Taken together, this work puts forward key perspectives of membrane activity of minimally designed synthetic biomimetic oligomers relative to the natural antimicrobial peptides.

How arginine derivatives alter the stability of lipid membranes: dissecting the roles of side chains, backbone and termini

Arginine (R)-rich peptides constitute the most relevant class of cell-penetrating peptides and other membrane-active peptides that can translocate across the cell membrane or generate defects in lipid bilayers such as water-filled pores. The mode of action of R-rich peptides remains a topic of controversy, mainly because a quantitative and energetic understanding of arginine effects on membrane stability is lacking. Here, we explore the ability of several oligo-arginines R[Formula: see text] and of an arginine side chain mimic R[Formula: see text] to induce pore formation in lipid bilayers employing MD simulations, free-energy calculations, breakthrough force spectroscopy and leakage assays. Our experiments reveal that R[Formula: see text] but not R[Formula: see text] reduces the line tension of a membrane with anionic lipids. While R[Formula: see text] peptides form a layer on top of a partly negatively charged lipid bilayer, R[Formula: see text] leads to its disintegration. Complementary, our simulations show R[Formula: see text] causes membrane thinning and area per lipid increase beside lowering the pore nucleation free energy. Model polyarginine R[Formula: see text] similarly promoted pore formation in simulations, but without overall bilayer destabilization. We conclude that while the guanidine moiety is intrinsically membrane-disruptive, poly-arginines favor pore formation in negatively charged membranes via a different mechanism. Pore formation by R-rich peptides seems to be counteracted by lipids with PC headgroups. We found that long R[Formula: see text] and R[Formula: see text] but not short R[Formula: see text] reduce the free energy of nucleating a pore. In short R[Formula: see text], the substantial effect of the charged termini prevent their membrane activity, rationalizing why only longer [Formula: see text] are membrane-active.

Selecting Collective Variables and Free-Energy Methods for Peptide Translocation across Membranes

The selective permeability of cellular membranes is a crucial property for controlled transport into and out of cells. Molecules that can bypass the cellular machinery and spontaneously translocate across membranes could be used as therapeutics or drug carriers. Peptides are a prominent class of such molecules, which include natural and man-developed antimicrobial and cell-penetrating peptides. However, the necessary peptide properties for translocation remain elusive. Computer simulations could uncover these properties once we have a good collective variable (CV) that accurately describes the translocation process. Here, we developed a new CV, which includes a description of peptide insertion, local membrane deformation, and peptide internal degrees of freedom related to its charged groups. By comparison of CVs, we demonstrated that all these components are necessary for an accurate description of peptide translocation. Moreover, the advantages and disadvantages of three common methods for free-energy calculations with our CV were evaluated using the MARTINI coarse-grained model: umbrella sampling, umbrella sampling with replica exchange, and metadynamics. The developed CV leads to the reliable and effective calculation of the free energy of peptide translocation, and thus, it could be useful in the design of spontaneously translocating peptides.

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.

How Alcoholic Disinfectants Affect Coronavirus Model Membranes: Membrane Fluidity, Permeability, and Disintegration

Atomistic molecular dynamics simulations have been carried out with a view to investigating the stability of the SARS-CoV-2 exterior membrane with respect to two common disinfectants, namely, aqueous solutions of ethanol and n-propanol. We used dipalmitoylphosphatidylcholine (DPPC) as a model membrane material and did simulations on both gel and liquid crystalline phases of membrane surrounded by aqueous solutions of varying alcohol concentrations (up to 17.5 mol %). While a moderate effect of alcohol on the gel phase of membrane is observed, its liquid crystalline phase is shown to be influenced dramatically by either alcohol. Our results show that aqueous solutions of only 5 and 10 mol % alcohol already have significant weakening effects on the membrane. The effects of n-propanol are always stronger than those of ethanol. The membrane changes its structure, when exposed to disinfectant solutions; uptake of alcohol causes it to swell laterally but to shrink vertically. At the same time, the orientational order of lipid tails decreases significantly. Metadynamics and grand-canonical ensemble simulations were done to calculate the free-energy profiles for permeation of alcohol and alcohol/water solubility in the DPPC. We found that the free-energy barrier to permeation of the DPPC liquid crystalline phase by all permeants is significantly lowered by alcohol uptake. At a disinfectant concentration of 10 mol %, it becomes insignificant enough to allow almost free passage of the disinfectant to the inside of the virus to cause damage there. It should be noted that the disinfectant also causes the barrier for water permeation to drop. Furthermore, the shrinking of the membrane thickness shortens the gap needed to be crossed by penetrants from outside the virus into its core. The lateral swelling also increases the average distance between head groups, which is a secondary barrier to membrane penetration, and hence further increases the penetration by disinfectants. At alcohol concentrations in the disinfectant solution above 15 mol %, we reliably observe disintegration of the DPPC membrane in its liquid crystalline phase.

Shifting Polar Residues Across Primary Sequence Frames of Transmembrane Domains Calibrates Membrane Permeation Thermodynamics

Permeation of the mitochondrial outer membrane (MOM) using the transmembrane domains (TMDs) is the key step of the Bcl-2 family of proteins to control apoptosis. The primary sequences of the TMDs of the family members like Bcl-xL, Bcl-2, Bak, etc. indicate the presence of charged residues at the C-terminal tip to be essential for drilling the membrane. However, Bax, a variant of the same family, is an exception, as the charged residues are shifted away from the tip by two positional frames in the primary sequence, but does it matter really? The free energy landscapes of membrane permeation, computed from a total of ∼13.3 μs of conformational sampling, show how such shifting of the amino acid frames in the primary sequence is correlated with the energy landscape that ensures the balance between membrane permeation and cytosolic population. Shifting the charged residues back to the terminal, in suitable mutants of Bax, proves the necessity of terminal charged residues by improving the insertion free energy but adds a high energy barrier unless some other polar residues are adjusted further. The difference in the TMDs of Bcl-xL and Bax is also reflected in their mechanism to drill the MOM-like anionic membrane; only Bax-TMD requires surface crowding to favorably shape the permeation landscape by weakening the bilayer integrity. So, this investigation suggests that such proteins can calibrate the free energy landscape of membrane permeation by adjusting the positions of the charged or polar residues in the primary sequence frames, a strategy analogous to the game of the "sliding tile puzzle" but played with primary sequence frames.

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.

Cooperative Effects of an Antifungal Moiety and DMSO on Pore Formation over Lipid Membranes Revealed by Free Energy Calculations

Itraconazole is a triazole drug widely used in the treatment of fungal infections, and it is in clinical trials for treatment of several cancers. However, the drug suffers from poor solubility, while experiments have shown that itraconazole delivery in liposome nanocarriers improves both circulation half-life and tissue distribution. The drug release mechanism from the nanocarrier is still unknown, and it depends on several factors including membrane stability against defect formation. In this work, we used molecular dynamics simulations and potential of mean force (PMF) calculations to quantify the influence of itraconazole on pore formation over lipid membranes, and we compared the effect by itraconazole with a pore-stabilizing effect by the organic solvent dimethyl sulfoxide (DMSO). According to the PMFs, both itraconazole and DMSO greatly reduce the free energy of pore formation, by up to ∼20 kJ mol^-1. However, whereas large concentrations of itraconazole of 8 mol % (relative to lipid) were required, only small concentrations of a few mole % DMSO (relative to water) were sufficient to stabilize pores. In addition, itraconazole and DMSO facilitate pore formation by different mechanisms. Whereas itraconazole predominantly aids the formation of a partial defect with a locally thinned membrane, DMSO mainly stabilizes a transmembrane water needle by shielding it from the hydrophobic core. Notably, the two distinct mechanisms act cooperatively upon adding both itraconazole and DMSO to the membrane, as revealed by an additional reduction of the pore free energy. Overall, our simulations reveal molecular mechanisms and free energies of membrane pore formation by small molecules. We suggest that the stabilization of a locally thinned membrane as well as the shielding of a transmembrane water needle from the hydrophobic membrane core may be a general mechanism by which amphiphilic molecules facilitate pore formation over lipid membranes at sufficient concentrations.

Order–disorder skewness in alpha-synuclein: a key mechanism to recognize membrane curvature

Currently, membrane curvature is understood as an active mechanism to control cells spatial organization and activity.

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.

All-Factor Analysis and Correlations on the Transmembrane Process for Arginine-Rich Cell-Penetrating Peptides

Currently, arginine-rich cell-penetrating peptides (CPPs), due to their little cytotoxicity and high transmembrane efficiency, are considered as one of the important intracellular carriers. Although the mechanism of the transmembrane process for arginine-rich CPPs was proposed, the quantitative correlations and the key factors involved in this process still deserve further investigation. In this study, all-atom molecular dynamics and the umbrella sampling technique were employed to study the arginine-rich CPPs transmembrane process. In the adsorption process of CPPs from solution to the surface of the lipid bilayer, the adsorption free energy (ΔG_A) is found to be linearly related to the interaction energy change (ΔE_A): ΔG_A = 0.0426ΔE_A + 36.7, R² = 0.92. In the CPPs transmembrane process, the transmembrane free energy barrier (ΔG_B) is roughly correlated with the corresponding interaction energy change (ΔE_B): ΔG_B = 0.108ΔE_B +135, R² = 0.73. The multiple salt bridges of guanidinium-PO₄ account for 65% of the overall interaction energy, so the increased negative charges of the lipid bilayer or more salt bridges would facilitate CPPs adsorption and transmembrane processes. Also, the increased negative charges of the lipid bilayer would reduce the amount of water to be carried into the pore and further reduce the ΔG_B. The peptide backbone would not have a direct impact on transmembrane efficiency. The ΔG_B is also found to be related to the length of the pore (L): ΔG_B = 46.2L - 31.3, R² = 0.92, which makes the transmembrane efficiency estimable. This work is expected to deliver an in-depth understanding and help the optimization of CPPs.

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.

Membrane-mediated interaction of amphipathic peptides can be described by a one-dimensional approach

Amphipathic alpha-helical peptides, among other peripheral components of plasma membranes, are promising antimicrobial agents. Partial incorporation of a peptide into a lipid monolayer causes elastic deformations. Deformations induced by two peptides distant from each other are independent; when peptides get closer, interference between the deformations causes effective lateral interaction. We quantified the energy of membrane deformations for arbitrary configuration of two amphipathic peptides on the membrane surface. The global minimum of the deformation energy proved to be achieved when two parallel peptides are in registry at the distance of about 6 nm between the axes of peptides. The energy calculated in the unidimensional approach provides a good approximation for the dependence of the energy of peptides being in the registered configuration upon the distance between them, valid for a broad range of peptide lengths. The effective interactional length of peptides for the unidimensional approach is close to their actual length. If two parallel peptides are shifted along their axes with respect to each other, the interaction energy is also well approximated by the unidimensional potential, within the projection of one peptide onto the other. In the case when the axes of alpha helices cross at a substantial angle, the main contribution to peptide interactions comes from their edges: the effective length of peptides for the unidimensional approach is almost equal to the characteristic length of decay of deformations. Based on the results we obtained it can be concluded that interaction of membrane inclusions is quite adequately described by the potential calculated in the unidimensional approach.

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.

Sugar-based bactericides targeting phosphatidylethanolamine-enriched membranes

Anthrax is an infectious disease caused by Bacillus anthracis, a bioterrorism agent that develops resistance to clinically used antibiotics. Therefore, alternative mechanisms of action remain a challenge. Herein, we disclose deoxy glycosides responsible for specific carbohydrate-phospholipid interactions, causing phosphatidylethanolamine lamellar-to-inverted hexagonal phase transition and acting over B. anthracis and Bacillus cereus as potent and selective bactericides. Biological studies of the synthesized compound series differing in the anomeric atom, glycone configuration and deoxygenation pattern show that the latter is indeed a key modulator of efficacy and selectivity. Biomolecular simulations show no tendency to pore formation, whereas differential metabolomics and genomics rule out proteins as targets. Complete bacteria cell death in 10 min and cellular envelope disruption corroborate an effect over lipid polymorphism. Biophysical approaches show monolayer and bilayer reorganization with fast and high permeabilizing activity toward phosphatidylethanolamine membranes. Absence of bacterial resistance further supports this mechanism, triggering innovation on membrane-targeting antimicrobials.

Bacillus anthracis causes the infectious disease anthrax. Here, the authors synthesized deoxy glycosides that are effective against B. anthracis and related bacteria and found that these amphiphilic compounds kill bacteria via an unusual mechanism of action.

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'.

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.

Probing a Continuous Polar Defect: A Reaction Coordinate for Pore Formation in Lipid Membranes

Various biophysical processes involve the formation of aqueous pores over lipid membranes, including processes of membrane fusion, antimicrobial peptide activity, lipid flip-flop, and membrane permeation. Reliable and efficient free-energy calculations of pore formation using molecular dynamics simulations remained challenging due to the lack of good reaction coordinates (RCs) for pore formation. We present a new RC for pore formation that probes the formation and rupture of a continuous polar defect over the membrane. Potential of mean force (PMF) calculations along the new RC rapidly converge and exhibit no hysteresis between pore-opening and pore-closing pathways, in contrast to calculations based on previous RCs. We show that restraints along the new RC may restrain the system tightly to the transition state of pore formation, rationalizing the absence of hysteresis. We observe that the PMF of pore formation in a tension-free membrane of dimyristoylphosphatidylcholine (DMPC) reveals a free-energy barrier for pore nucleation, confirming a long-hypothesized metastable prepore state. We test the influence of the lipid force field, the cutoff distance used for Lennard-Jones interactions, and the lateral membrane size on the free energies of pore formation. In contrast to PMF calculations based on previous RCs, we find that such parameters have a relatively small influence on the free energies of pore nucleation. However, the metastability of the open pore in DMPC may depend on such parameters. The RC has been implemented into an extension of the GROMACS simulation software. The new RC allows for reliable and computationally efficient free-energy calculations of pore formation in lipid membranes.

SNARE-mediated membrane fusion trajectories derived from force-clamp experiments

Fusion of lipid bilayers is usually prevented by large energy barriers arising from removal of the hydration shell, formation of highly curved structures, and, eventually, fusion pore widening. Here, we measured the force-dependent lifetime of fusion intermediates using membrane-coated silica spheres attached to cantilevers of an atomic-force microscope. Analysis of time traces obtained from force-clamp experiments allowed us to unequivocally assign steps in deflection of the cantilever to membrane states during the SNARE-mediated fusion with solid-supported lipid bilayers. Force-dependent lifetime distributions of the various intermediate fusion states allowed us to propose the likelihood of different fusion pathways and to assess the main free energy barrier, which was found to be related to passing of the hydration barrier and splaying of lipids to eventually enter either the fully fused state or a long-lived hemifusion intermediate. The results were compared with SNARE mutants that arrest adjacent bilayers in the docked state and membranes in the absence of SNAREs but presence of PEG or calcium. Only with the WT SNARE construct was appreciable merging of both bilayers observed.

The Effect of Tethers on Artificial Cell Membranes: A Coarse-Grained Molecular Dynamics Study

Tethered bilayer lipid membranes (tBLMs) provide a stable platform for modeling the dynamics and order of biological membranes where the tethers mimic the cytoskeletal supports present in biological cell membranes. In this paper coarse-grained molecular dynamics (CGMD) is applied to study the effects of tethers on lipid membrane properties. Using results from the CGMD model and the overdamped Fokker-Planck equation, we show that the diffusion tensor and particle density of water in the tBLM is spatially dependent. Further, it is shown that the membrane thickness, lipid diffusion, defect density, free energy of lipid flip-flop, and membrane dielectric permittivity are all dependent on the tether density. The numerically computed results from the CGMD model are in agreement with the experimentally measured results from tBLMs containing different tether densities and lipids derived from Archaebacteria. Additionally, using experimental measurements from Escherichia coli bacteria and Saccharomyces Cerevisiae yeast tethered membranes, we illustrate how previous molecular dynamics results can be combined with the proposed model to estimate the dielectric permittivity and defect density of these membranes as a function of tether density.