Mechanism of pore formation in stearoyl-oleoyl-phosphatidylcholine membranes subjected to lateral tension

Theoretical model of a through pore formation in lipid bilayer membrane under applied lateral tension was developed. In the framework of elastic theory of liquid crystals adapted to lipid membranes, we calculated a continuous trajectory from intact bilayer through a hydrophobic defect to a through pore. It was shown that the major energetic characteristic of membrane stability with respect to the pore formation, i. e., line tension, depends both on the pore radius and on the value of the applied lateral tension. This leads to a non-monotonous dependence of the average waiting time of the pore formation on the lateral tension: at low tensions the waiting time was large, then there was a local minimum, after which the average waiting time was increasing again. For membranes formed from stearoyl oleoyl phosphatidylcholine, the local minimum corresponded to the lateral tension of 7 mN/m; the calculated value of the edge line tension of a large pore was 16.5 pN. These results are consistent with available experimental data.     

Influence of lipids on the hydrophobic barrier within the pore of the TWIK-1 K2P channel

Several recent ion channel structures have revealed large side portals, or ‘fenestrations’ at the interface between their transmembrane helices that potentially expose the ion conduction pathway to the lipid core of the bilayer. In a recent study we demonstrated that functional activity of the TWIK-1 K2P channel is influenced by the presence of hydrophobic residues deep within the inner pore. These residues are located near the fenestrations in the TWIK-1 structure and promote dewetting of the pore by forming a hydrophobic barrier to ion conduction. During our previous MD simulations, lipid tails were observed to enter these fenestrations. In this addendum to that study, we investigate lipid contribution to the dewetting process. Our results demonstrate that lipid tails from both the upper and lower leaflets can occupy the fenestrations and partially penetrate into the pore. The lipid tails do not sterically occlude the pore, but there is an inverse correlation between the presence of water within the hydrophobic barrier and the number of lipids tails within the lining of the pore. However, dewetting still occurs in the absence of lipids tails, and pore hydration appears to be determined primarily by those side-chains lining the narrowest part of the pore cavity.     

Influence of lipids on the hydrophobic barrier within the pore of the TWIK-1 K2P channel

Several recent ion channel structures have revealed large side portals, or ‘fenestrations’ at the interface between their transmembrane helices that potentially expose the ion conduction pathway to the lipid core of the bilayer. In a recent study we demonstrated that functional activity of the TWIK-1 K2P channel is influenced by the presence of hydrophobic residues deep within the inner pore. These residues are located near the fenestrations in the TWIK-1 structure and promote dewetting of the pore by forming a hydrophobic barrier to ion conduction. During our previous MD simulations, lipid tails were observed to enter these fenestrations. In this addendum to that study, we investigate lipid contribution to the dewetting process. Our results demonstrate that lipid tails from both the upper and lower leaflets can occupy the fenestrations and partially penetrate into the pore. The lipid tails do not sterically occlude the pore, but there is an inverse correlation between the presence of water within the hydrophobic barrier and the number of lipids tails within the lining of the pore. However, dewetting still occurs in the absence of lipids tails, and pore hydration appears to be determined primarily by those side-chains lining the narrowest part of the pore cavity.     

Stabilization of bilayer structure of raft due to elastic deformations of membrane

Line tension of the boundary of specific domains (rafts) rich in sphingomyelin was calculated. The line tension was calculated based on macroscopic theory of elasticity under assumption that the bilayer in raft is thicker than in the surrounding membrane. The calculations took into account the possibility of lateral shift of the domain boundaries located in different monolayers of the membrane. The line tension was associated with the energy of elastic deformations appearing in the vicinity of the boundary in order to compensate for the difference in the thickness of the monolayers. Spatial distribution of deformations and the line tension was calculated by minimization of elastic free energy of the system. Dependence of the line tension on the distance between the domains boundaries located in different monolayers was obtained. It was shown that the line tension is minimal if the distance is about 4 nm. Thus, membrane deformations stabilize the bilayer structure of rafts observed experimentally. The calculated value of line tension is about 0.6 pN for the difference between the monolayer thickness of raft and surrounding membrane of about 0.5 nm, which is in agreement with the experimental data available.     

A BEST example of channel structure annotation by molecular simulation

An increasing number of ion channel structures are being determined. This generates a need for computational tools to enable functional annotation of channel structures. However, several studies of ion channel and model pores have indicated that the physical dimensions of a pore are not always a reliable indicator of its conductive status. This is due to the unusual behavior of water within nano-confined spaces, resulting in a phenomenon referred to as “hydrophobic gating”. We have recently demonstrated how simulating the behavior of water within an ion channel pore can be used to predict its conductive status. In this addendum to our study, we apply this method to compare the recently solved structure of a mutant of the bestrophin chloride channel BEST1 with that of the wild-type channel. Our results support the hypothesis of a hydrophobic gate within the narrow neck of BEST1. This provides further validation that this simulation approach provides the basis for an accurate and computationally efficient tool for the functional annotation of ion channel structures.     

The pore domain of the nicotinic acetylcholine receptor: molecular modeling, pore dimensions, and electrostatics.

The pore domain of the nicotinic acetylcholine receptor has been modeled as a bundle of five kinked M2 helices. Models were generated via molecular dynamics simulations incorporating restraints derived from 9-A resolution cryoelectron microscopy data (Unwin, 1993; 1995), and from mutagenesis data that identify channel-lining side chains. Thus, these models conform to current experimental data but will require revision as higher resolution data become available. Models of the open and closed states of a homopentameric alpha 7 pore are compared. The minimum radius of the closed-state model is less than 2 A; the minimum radius of the open-state models is approximately 6 A. It is suggested that the presence of "bound" water molecules within the pore may reduce the effective minimum radii below these values by up to approximately 3 A. Poisson-Boltzmann calculations are used to obtain a first approximation to the potential energy of a monovalent cation as it moves along the pore axis. The differences in electrostatic potential energy profiles between the open-state models of alpha 7 and of a mutant of alpha 7 are consistent with the experimentally observed change in ion selectivity from cationic to anionic. Models of the open state of the heteropentameric Torpedo nicotinic acetylcholine receptor pore domain are also described. Relatively small differences in pore radius and electrostatic potential energy profiles are seen when the Torpedo and alpha 7 models are compared.     

Model of membrane fusion: Continuous transition to fusion pore with regard of hydrophobic and hydration interactions

We consider the process of fusion of lipid membranes from the stage of stalk with minimal radius to the stage of fusion pore. We assume that stalk directly developed into the fusion pore, omitting the stage of hemifusion diaphragm. Energy of intermediate stages is calculated on the basis of the classical elasticity theory of liquid crystals adapted for lipid membranes. The trajectory of transition from stalk to pore is obtained with regard to hydrophobic and hydration interactions. Continuous change of orientation of lipids in distal monolayers occurs along the trajectory. The orientation changes from the direction along rotational axis of the system specific to stalk to the direction corresponding to the fusion pore. Dependence of energy of intermediate stages on the value of spontaneous curvature of distal monolayers of the fusing membranes is obtained. We demonstrate that the energy barrier of the stalk-to-pore transition decreases when distal monolayers have positive spontaneous curvature, which is in accordance with available experimental data.     

Line tension and interaction energies of membrane rafts calculated from lipid splay and tilt

Membrane domains known as rafts are rich in cholesterol and sphingolipids, and are thought to be thicker than the surrounding membrane. If so, monolayers should elastically deform so as to avoid exposure of hydrophobic surfaces to water at the raft boundary. We calculated the energy of splay and tilt deformations necessary to avoid such hydrophobic exposure. The derived value of energy per unit length, the line tension gamma, depends on the elastic moduli of the raft and the surrounding membrane; it increases quadratically with the initial difference in thickness between the raft and surround; and it is reduced by differences, either positive or negative, in spontaneous curvature between the two. For zero spontaneous curvature, gamma is approximately 1 pN for a monolayer height mismatch of approximately 0.3 nm, in agreement with experimental measurement. Our model reveals conditions that could prevent rafts from forming, and a mechanism that can cause rafts to remain small. Prevention of raft formation is based on our finding that the calculated line tension is negative if the difference in spontaneous curvature for a raft and the surround is sufficiently large: rafts cannot form if gamma < 0 unless molecular interactions (ignored in the model) are strong enough to make the total line tension positive. Control of size is based on our finding that the height profile from raft to surround does not decrease monotonically, but rather exhibits a damped, oscillatory behavior. As an important consequence, the calculated energy of interaction between rafts also oscillates as it decreases with distance of separation, creating energy barriers between closely apposed rafts. The height of the primary barrier is a complex function of the spontaneous curvatures of the raft and the surround. This barrier can kinetically stabilize the rafts against merger. Our physical theory thus quantifies conditions that allow rafts to form, and further, defines the parameters that control raft merger.     

A thermodynamic approach to alamethicin pore formation

The structure and energetics of alamethicin Rf30 monomer to nonamer in cylindrical pores of 5 to 11 Å radius are investigated using molecular dynamics simulations in an implicit membrane model that includes the free energy cost of acyl chain hydrophobic area exposure. Stable, low energy pores are obtained for certain combinations of radius and oligomeric number. The trimer and the tetramer formed 6 Å pores that appear closed while the larger oligomers formed open pores at their optimal radius. The hexamer in an 8 Å pore and the octamer in an 11 Å pore give the lowest effective energy per monomer. However, all oligomers beyond the pentamer have comparable energies, consistent with the observation of multiple conductance levels. The results are consistent with the widely accepted “barrel-stave” model. The N terminal portion of the molecule exhibits smaller tilt with respect to the membrane normal than the C terminal portion, resulting in a pore shape that is a hybrid between a funnel and an hourglass. Transmembrane voltage has little effect on the structure of the oligomers but enhances or decreases their stability depending on its orientation. Antiparallel bundles are lower in energy than the commonly accepted parallel ones and could be present under certain experimental conditions. Dry aggregates (without an aqueous pore) have lower average effective energy than the corresponding aggregates in a pore, suggesting that alamethicin pores may be excited states that are stabilized in part by voltage and in part by the ion flow itself.     

Cavity depth on the bacteriorhodopsin peptide surface near the proton carrier Asp96: Data of X-ray structure models

Three-dimensional X-ray models of the wild-type bacteriorhodopsin structure are investigated by means of the program PyMOL. Construction of the surfaces accessible to the solvent at the cytoplasmic side visualized a cavity near the proton carrier Asp96. The cavity shortens the way of the proton from the membrane surface to this carrier. The distance between the cavity surface and the centre of the carbonic atom of the Asp96 carboxylic group is ～6 Å. Besides, for model structures 1c3w, 1qhj, and 1BRR, a channel of radius 1.1 Å is revealed between the cytoplasmic surface and Asp96carboxyl. The channel diameter is narrower than the characteristic diameter of the water molecule and apparently does not create conductivity in the nonexcited pigment. It is possible however that along this channel a hydrated “gap” opens at the second phase of a bacteriorhodopsin photocycle related with reprotonation of Asp96.     

Analytical derivation of thermodynamic properties of bilayer membrane with interdigitation

We consider a model of bilayer lipid membrane with interdigitation, in which the lipid tails of the opposite monolayers interpenetrate. The interdigitation is modeled by linking tails of the hydrophobic chains in the opposite monolayers within bilayer as a first approximation. This model corresponds to the types of interdigitation that are not related with the areal “hydrophobic” dilation of the membrane. A number of essential thermodynamical characteristics are calculated analytically and compared with the ones of a regular bilayer membrane without interdigitation. Important difference between lateral pressure profiles at the layers interface for linked and regular bilayer models is found. In the linked case, the lateral pressure mid-plane peak disappears, while the entropy decreases and the free energy per chain increases. Within our model we found that in case of elongation of the chains inside a nucleus of, e.g., liquid-condensed phase, homogeneous interdigitation would be more costly for the membrane’s free energy than energy of the hydrophobic mismatch between the elongated chains and the liquid-expanded surrounding. Nonetheless, an inhomogeneous interdigitation along the nucleus boundary may occur inside a “belt” of a width that varies approximately with the hydrophobic mismatch amplitude.     

Hydrophobic core formation in protein complex of cathepsin

The “fuzzy oil drop” model assumes that the idealized hydrophobic core in a protein body can be described by a 3D Gauss function. The structure of the 1ICF protein (cathepsin), which participates in the proteolysis process and has cysteine-type peptidase activity, has been analyzed on the basis of the “fuzzy oil drop” model. The authors have determined the contribution of individual exon fragments to the creation of a common hydrophobic core and assessed the involvement of each chain in this process, depending on the number of complexed chains. Quantitative assessment of exons, chains, dimers, and the whole complex suggest that each of these units plays a different role in shaping the protein’s hydrophobic core.     

Wetting characterisation of silicon (1,0,0) surface

Water droplets on bare silicon surfaces are studied to examine the wetting behaviour as a function of the surface energy and to parameterise water–silicon interactions in order to recover the hydrophobic behaviour measured by experiments. Two different wetting regimes characterised by a critical interaction strength value are observed. At a threshold value of the water–silicon interaction parameter, water molecules start penetrating into the first layer of silicon surface under thermally vibrating walls, resulting in two distinct wetting behaviours. Fixed (cold) silicon walls do not exhibit the two different wetting characteristics. Size effects are studied for nano-scale droplets, and line tension influence is observed depending on the surface wettability. Decrease in the droplet size increases the contact angle values for the low wetting cases, while contact angles decrease for smaller droplets on the high wetting surfaces. Considering the line tension effects and droplet size, ?_Si–O for water–silicon interactions to recover the hydrophobic behaviour of silicon surfaces is estimated to be 12.5% of the value predicted using the Lorentz–Berthelot mixing rule.     

Investigating the size and dynamics of voltage-gated sodium channel fenestrations

Eukaryotic voltage-gated sodium channels (VGSCs) are essential for the initiation and propagation of action potentials in electrically excitable cells, and are important pharmaceutical targets for the treatment of neurological disorders such as epilepsy, cardiac arrhythmias, and chronic pain. Evidence suggests that small, hydrophobic, VGSC-blocking drugs can gain access to binding residues within the central cavity of these channels by passing through lateral, lipid-filled “fenestrations” which run between the exterior of the protein and its central pore. Here, we use molecular dynamics simulations to investigate how the size and shape of fenestrations change over time in several bacterial VGSC models and a homology model of Nav1.4. We show that over the course of the simulations, the size of the fenestrations is primarily influenced by rapid protein motions, such as amino acid side-chain rotation, and highlight that differences between fenestration bottleneck-contributing residues are the primary cause of variations in fenestration size between the 6 bacterial models. In the eukaryotic channel model, 2 fenestrations are wide, but 2 are narrow due to differences in the amino acid sequence in the 4 domains. Lipid molecules are found to influence the size of the fenestrations by protruding acyl chains into the fenestrations and displacing amino acid side-chains. Together, the results suggest that fenestrations provide viable pathways for small, flexible, hydrophobic drugs.     

The force exerted by the membrane potential during protein import into the mitochondrial matrix

The force exerted on a targeting sequence by the electrical potential across the inner mitochondrial membrane is calculated on the basis of continuum electrostatics. The force is found to vary from 3.0 pN to 2.2 pN (per unit elementary charge) as the radius of the inner membrane pore (assumed aqueous) is varied from 6.5 to 12 A, its measured range. In the present model, the decrease in force with increasing pore width arises from the shielding effect of water. Since the pore is not very much wider than the distance between water molecules, the full shielding effect of water may not be present; the extreme case of a purely membranous pore without water gives a force of 3.2 pN per unit charge, which should represent an upper limit. When applied to mitochondrial import experiments on the protein barnase, these results imply that forces between 11 +/- 2 pN and 13.5 +/- 2.5 pN catalyze the unfolding of barnase in those experiments. A comparison of these results with unfolding forces measured using atomic force microscopy is made.     

hERG Function in Light of Structure

The human ether-a-go-go-related gene1 (hERG) ion channel has been the subject of fascination since it was identified as a target of long QT syndrome more than 20 years ago. In this Biophysical Perspective, we look at what makes hERG intriguing and vexingly unique. By probing recent high-resolution structures in the context of functional and biochemical data, we attempt to summarize new insights into hERG-specific function and articulate important unanswered questions. X-ray crystallography and cryo-electron microscopy have revealed features not previously on the radar—the “nonswapped” transmembrane architecture, an “intrinsic ligand,” and hydrophobic pockets off a pore cavity that is surprisingly small. Advances in our understanding of drug block and inactivation mechanisms are noted, but a full picture will require more investigation.     

Lipid flow through fusion pores connecting membranes of different tensions.

When two membranes fuse, their components mix; this is usually described as a purely diffusional process. However, if the membranes are under different tensions, the material will spread predominantly by convection. We use standard fluid mechanics to rigorously calculate the steady-state convective flux of lipids. A fusion pore is modeled as a toroid shape, connecting two planar membranes. Each of the membrane monolayers is considered separately as incompressible viscous media with the same shear viscosity, etas. The two monolayers interact by sliding past each other, described by an intermonolayer viscosity, etar. Combining a continuity equation with an equation that balances the work provided by the tension difference, Deltasigma, against the energy dissipated by flow in the viscous membrane, yields expressions for lipid velocity, upsilon, and area of lipid flux, Phi. These expressions for upsilon and Phi depend on Deltasigma, etas, etar, and geometrical aspects of a toroidal pore, but the general features of the theory hold for any fusion pore that has a roughly hourglass shape. These expressions are readily applicable to data from any experiments that monitor movement of lipid dye between fused membranes under different tensions. Lipid velocity increases nonlinearly from a small value for small pore radii, rp, to a saturating value at large rp. As a result of velocity saturation, the flux increases linearly with pore radius for large pores. The calculated lipid flux is in agreement with available experimental data for both large and transient fusion pores.     

The influence of geometry, surface character, and flexibility on the permeation of ions and water through biological pores

A hydrophobic constriction site can act as an efficient barrier to ion and water permeation if its diameter is less than the diameter of an ion's first hydration shell. This hydrophobic gating mechanism is thought to operate in a number of ion channels, e.g. the nicotinic receptor, bacterial mechanosensitive channels (MscL and MscS) and perhaps in some potassium channels (e.g. KcsA, MthK and KvAP). Simplified pore models allow one to investigate the primary characteristics of a conduction pathway, namely its geometry (shape, pore length, and radius), the chemical character of the pore wall surface, and its local flexibility and surface roughness. Our extended (about 0.1 micros) molecular dynamic simulations show that a short hydrophobic pore is closed to water for radii smaller than 0.45 nm. By increasing the polarity of the pore wall (and thus reducing its hydrophobicity) the transition radius can be decreased until for hydrophilic pores liquid water is stable down to a radius comparable to a water molecule's radius. Ions behave similarly but the transition from conducting to non-conducting pores is even steeper and occurs at a radius of 0.65 nm for hydrophobic pores. The presence of water vapour in a constriction zone indicates a barrier for ion permeation. A thermodynamic model can explain the behaviour of water in nanopores in terms of the surface tensions, which leads to a simple measure of 'hydrophobicity' in this context. Furthermore, increased local flexibility decreases the permeability of polar species. An increase in temperature has the same effect, and we hypothesize that both effects can be explained by a decrease in the effective solvent-surface attraction which in turn leads to an increase in the solvent-wall surface free energy.     

Effects of pulmonary surfactant proteins SP-B and SP-C and calcium ions on the surface properties of hydrophobic fractions of lung surfactant

This study focused on two hydrophobic fractions (HF-A and HF-B) isolated from porcine lung surfactant (LS) that had similar phospholipid composition, but HF-A consisted of the hydrophobic LS specific proteins (SP-B and SP-C), in contrast to HF-B. Monolayers spread in a Langmuir trough were formed at the air/water interface of both fractions and the rate of adsorption-desorption and the respreading potential of the LS constituents was studied during six consecutive compression/decompression cycles of the monolayers. By drawing a comparison between the behavior of HF-A and HF-B monolayers on the subphase of 150 mm NaCl, either with or without additional Ca²⁺, we estimated the role of hydrophobic LS proteins and Ca²⁺ ions for LS surface activity. The results demonstrated much higher ability of the HF-A sample, compared to HF-B, to maintain lower surface tension (γ) during monolayer compression and its better respreading capacity during decompression. For instance, at a surface concentration corresponding to 80 Ų per phospholipid molecule, the HF-A monolayers showed a much lower γ _max value (surface tension at 100% of the trough area), being ca. 31.0 mN/m, compared to the HF-B monolayers (γ _max? 62.0 mN/m). The surface tension after compression to 20% of the initial area (γ _min) reached ca. 7.0 and 19.0 mN/m in the HF-A and HF-B monolayers, respectively. Better respreading of the HF-A monolayers compared to the HF-B monolayers was due to the faster adsorption and spreading of LS phospholipids during decompression, facilitated by the hydrophobic proteins. As the phospholipid composition of both fractions was similar, we showed that the hydrophobic surfactant proteins were responsible also for the prevention of the irreversible loss of material from the surface during monolayer compression/decompression. The effects observed demonstrated also that the hydrophobic surfactant proteins were the stronger determinant, compared with Ca²⁺ ions, for the surface tension decrease and respreading of the monolayers during film compression/decompression. For instance, when the HF-A monolayers were spread on a subphase with an additional 5 mm Ca²⁺ ion content, no significant changes were detected in the γ _min and γ _max values between the first and sixth cycle, compared to the monolayers spread on a subphase of 150 mm NaCl only. However, in the absence of positively charged SP-B and SP-C (HF-B sample) in highly compressed monolayers, Ca²⁺ ions were able to cause the effects shown by SP-B and SP-C, although to a less extent. The role of the electrostatic and hydrophobic interactions is discussed for the better respreading of LS components in the presence of LS proteins and Ca²⁺ ions.     

Hydrophobic Surfactant Proteins Strongly Induce Negative Curvature

The hydrophobic surfactant proteins SP-B and SP-C greatly accelerate the adsorption of vesicles containing the surfactant lipids to form a film that lowers the surface tension of the air/water interface in the lungs. Pulmonary surfactant enters the interface by a process analogous to the fusion of two vesicles. As with fusion, several factors affect adsorption according to how they alter the curvature of lipid leaflets, suggesting that adsorption proceeds via a rate-limiting structure with negative curvature, in which the hydrophilic face of the phospholipid leaflets is concave. In the studies reported here, we tested whether the surfactant proteins might promote adsorption by inducing lipids to adopt a more negative curvature, closer to the configuration of the hypothetical intermediate. Our experiments used x-ray diffraction to determine how the proteins in their physiological ratio affect the radius of cylindrical monolayers in the negatively curved, inverse hexagonal phase. With binary mixtures of dioleoylphosphatidylethanolamine (DOPE) and dioleoylphosphatidylcholine (DOPC), the proteins produced a dose-related effect on curvature that depended on the phospholipid composition. With DOPE alone, the proteins produced no change. With an increasing mol fraction of DOPC, the response to the proteins increased, reaching a maximum 50% reduction in cylindrical radius at 5% (w/w) protein. This change represented a doubling of curvature at the outer cylindrical surface. The change in spontaneous curvature, defined at approximately the level of the glycerol group, would be greater. Analysis of the results in terms of a Langmuir model for binding to a surface suggests that the effect of the lipids is consistent with a change in the maximum binding capacity. Our findings show that surfactant proteins can promote negative curvature, and support the possibility that they facilitate adsorption by that mechanism.