Transbilayer pores formed by beta-barrels: molecular modeling of pore structures and properties

Transmembrane β-barrel proteins of bacteria: From structure to function

The outer membrane of Gram-negative bacteria is a specialized organelle conferring protection to the cell against various environmental stresses and resistance to many harmful compounds. The outer membrane has a number of unique features, including an asymmetric lipid bilayer, the presence of lipopolysaccharides and an individual proteome. The vast majority of the integral transmembrane proteins in the outer membrane belongs to the family of β-barrel proteins. These evolutionarily related proteins share a cylindrical, anti-parallel β-sheet core fold spanning the outer membrane. The loops and accessory domains attached to the β-barrel allow for a remarkable versatility in function for these proteins, ranging from diffusion pores and transporters to enzymes and adhesins. We summarize the current knowledge on β-barrel structure and folding and give an overview of their functions, evolution, and potential as drug targets.

Voltage Gating of a Biomimetic Nanopore: Electrowetting of a Hydrophobic Barrier

It is desirable that nanopores that are components of biosensors are gated, i.e., capable of controllable switching between closed (impermeable) and open (permeable) states. A central hydrophobic barrier within a nanopore may act as a voltage-dependent gate via electrowetting, i.e., changes in nanopore surface wettability by application of an electric field. We use "computational electrophysiology" simulations to demonstrate and characterize electrowetting of a biomimetic nanopore containing a hydrophobic gate. We show that a hydrophobic gate in a model β-barrel nanopore can be functionally opened by electrowetting at voltages that do not electroporate lipid bilayers. During the process of electrowetting, voltage-induced alignment of water dipoles occurs within the hydrophobic gate region of the nanopore, with water entry preceding permeation of ions through the opened nanopore. When the ionic imbalance that generates a transbilayer potential is dissipated, water is expelled from the hydrophobic gate and the nanopore recloses. The open nanopore formed by electrowetting of a "featureless" β-barrel is anionic selective due to the transmembrane dipole potential resulting from binding of Na⁺ ions to the headgroup regions of the surrounding lipid bilayer. Thus, hydrophobic barriers can provide voltage-dependent gates in designed biomimetic nanopores. This extends our understanding of hydrophobic gating in synthetic and biological nanopores, providing a framework for the design of functional nanopores with tailored gating functionality.

Computational Methods for Structural and Functional Studies of Alzheimer's Amyloid Ion Channels

Aggregation can be studied by a range of methods, experimental and computational. Aggregates form in solution, across solid surfaces, and on and in the membrane, where they may assemble into unregulated leaking ion channels. Experimental probes of ion channel conformations and dynamics are challenging. Atomistic molecular dynamics (MD) simulations are capable of providing insight into structural details of amyloid ion channels in the membrane at a resolution not achievable experimentally. Since data suggest that late stage Alzheimer's disease involves formation of toxic ion channels, MD simulations have been used aiming to gain insight into the channel shapes, morphologies, pore dimensions, conformational heterogeneity, and activity. These can be exploited for drug discovery. Here we describe computational methods to model amyloid ion channels containing the β-sheet motif at atomic scale and to calculate toxic pore activity in the membrane.

Designing a hydrophobic barrier within biomimetic nanopores

Nanopores in membranes have a range of potential applications. Biomimetic design of nanopores aims to mimic key functions of biological pores within a stable template structure. Molecular dynamics simulations have been used to test whether a simple β-barrel protein nanopore can be modified to incorporate a hydrophobic barrier to permeation. Simulations have been used to evaluate functional properties of such nanopores, using water flux as a proxy for ionic conductance. The behavior of these model pores has been characterized as a function of pore size and of the hydrophobicity of the amino acid side chains lining the narrow central constriction of the pore. Potential of mean force calculations have been used to calculate free energy landscapes for water and for ion permeation in selected models. These studies demonstrate that a hydrophobic barrier can indeed be designed into a β-barrel protein nanopore, and that the height of the barrier can be adjusted by modifying the number of consecutive rings of hydrophobic side chains. A hydrophobic barrier prevents both water and ion permeation even though the pore is sterically unoccluded. These results both provide insights into the nature of hydrophobic gating in biological pores and channels, and furthermore demonstrate that simple design features may be computationally transplanted into β-barrel membrane proteins to generate functionally complex nanopores.

Mechanism of membrane permeation induced by synthetic β-hairpin peptides

We have investigated the membrane destabilizing properties of synthetic amphiphilic cationic peptides, MAX1 and MAX35, which have the propensity to form β-hairpin structures under certain conditions, and a control non-β-hairpin-forming peptide MAX8V16E. All three peptides bind to liposomes containing a mixture of zwitterionic POPC and negatively charged POPS lipids as determined by Zeta potential measurements. Circular dichroism measurements indicated folding of MAX1 and MAX35 in the presence of the POPC/POPS liposomes, whereas no such folding was observed with MAX8V16E. There was no binding or folding of these peptides to liposomes containing only POPC. MAX1 and MAX35 induced release of contents from negatively charged liposomes, whereas MAX8V16E failed to promote solute release under identical conditions. Thus, MAX1 and MAX35 bind to, and fold at the surface of negatively charged liposomes adopting a lytic conformation. We ruled out leaky fusion as a mechanism of release by including 2 mol % PEG-PE in the liposomes, which inhibits aggregation/fusion but not folding of MAX or MAX-induced leakage. Using a concentration-dependent quenching probe (calcein), we determined that MAX-induced leakage of liposome contents was an all-or-none process. At MAX1 concentrations, which cause release of ~50% of the liposomes that contain small (R(h) <1.5 nm) markers, only ~15% of those liposomes release a fluorescent dextran of 40 kDa. A multimeric model of the pore is presented based on these results. Atomistic molecular dynamics simulations show that barrels consisting of 10 β-hairpin MAX1 and MAX35 peptides are relatively more stable than MAX8V16E barrels in the bilayer, suggesting that barrels of this size are responsible for the peptides lytic action.

Disulfide-bond scanning reveals assembly state and β-strand tilt angle of the PFO β-barrel

Perfringolysin O (PFO), a bacterial cholesterol-dependent cytolysin, binds a mammalian cell membrane, oligomerizes into a circular prepore complex (PPC) and forms a 250-Å transmembrane β-barrel pore in the cell membrane. Each PFO monomer has two sets of three short α-helices that unfold and ultimately refold into two transmembrane β-hairpin (TMH) components of the membrane-embedded β-barrel. Interstrand disulfide-bond scanning revealed that β-strands in a fully assembled PFO β-barrel were strictly aligned and tilted at 20° to the membrane perpendicular. In contrast, in a low temperature-trapped PPC intermediate, the TMHs were unfolded and had sufficient freedom of motion to interact transiently with each other, yet the TMHs were not aligned or stably hydrogen bonded. The PFO PPC-to-pore transition therefore converts TMHs in a dynamic folding intermediate far above the membrane into TMHs that are hydrogen bonded to those of adjacent subunits in the bilayer-embedded β-barrel.

Structure of the food-poisoning Clostridium perfringens enterotoxin reveals similarity to the aerolysin-like pore-forming toxins

Clostridium perfringens enterotoxin (CPE) is a major cause of food poisoning and antibiotic-associated diarrhea. Upon its release from C. perfringens spores, CPE binds to its receptor, claudin, at the tight junctions between the epithelial cells of the gut wall and subsequently forms pores in the cell membranes. A number of different complexes between CPE and claudin have been observed, and the process of pore formation has not been fully elucidated. We have determined the three-dimensional structure of the soluble form of CPE in two crystal forms by X-ray crystallography, to a resolution of 2.7 and 4.0 Å, respectively, and found that the N-terminal domain shows structural homology with the aerolysin-like β-pore-forming family of proteins. We show that CPE forms a trimer in both crystal forms and that this trimer is likely to be biologically relevant but is not the active pore form. We use these data to discuss models of pore formation.

Prediction of the exposure status of transmembrane beta barrel residues from protein sequence

We present BTMX (Beta barrel TransMembrane eXposure), a computational method to predict the exposure status (i.e. exposed to the bilayer or hidden in the protein structure) of transmembrane residues in transmembrane beta barrel proteins (TMBs). BTMX predicts the exposure status of known TM residues with an accuracy of 84.2% over 2,225 residues and provides a confidence score for all predictions. Predictions made are in concert with the fact that hydrophobic residues tend to be more exposed to the bilayer. The biological relevance of the input parameters is also discussed. The highest prediction accuracy is obtained when a sliding window comprising three residues with similar C(α)-C(β) vector orientations is employed. The prediction accuracy of the BTMX method on a separate unseen non-redundant test dataset is 78.1%. By employing out-pointing residues that are exposed to the bilayer, we have identified various physico-chemical properties that show statistically significant differences between the beta strands located at the oligomeric interfaces compared to the non-oligomeric strands. The BTMX web server generates colored, annotated snake-plots as part of the prediction results and is available under the BTMX tab at http://service.bioinformatik.uni-saarland.de/tmx-site/. Exposure status prediction of TMB residues may be useful in 3D structure prediction of TMBs.

β-Barrel topology of Alzheimer's β-amyloid ion channels

Emerging evidence supports the ion channel mechanism for Alzheimer's disease pathophysiology wherein small β-amyloid (Aβ) oligomers insert into the cell membrane, forming toxic ion channels and destabilizing the cellular ionic homeostasis. Solid-state NMR-based data of amyloid oligomers in solution indicate that they consist of a double-layered β-sheets where each monomer folds into β-strand-turn-β-strand and the monomers are stacked atop each other. In the membrane, Aβ peptides are proposed to be β-type structures. Experimental structural data available from atomic force microscopy (AFM) imaging of Aβ oligomers in membranes reveal heterogeneous channel morphologies. Previously, we modeled the channels in a non-tilted organization, parallel with the cross-membrane normal. Here, we modeled a β-barrel-like organization. β-Barrels are common in transmembrane toxin pores, typically consisting of a monomeric chain forming a pore, organized in a single-layered β-sheet with antiparallel β-strands and a right-handed twist. Our explicit solvent molecular dynamics simulations of a range of channel sizes and polymorphic turns and comparisons of these with AFM image dimensions support a β-barrel channel organization. Different from the transmembrane β-barrels where the monomers are folded into a circular β-sheet with antiparallel β-strands stabilized by the connecting loops, these Aβ barrels consist of multimeric chains forming double β-sheets with parallel β-strands, where the strands of each monomer are connected by a turn. Although the Aβ barrels adopt the right-handed β-sheet twist, the barrels still break into heterogeneous, loosely attached subunits, in good agreement with AFM images and previous modeling. The subunits appear mobile, allowing unregulated, hence toxic, ion flux.

Self-consistent analytic solution for the current and the access resistance in open ion channels

A self-consistent analytic approach is introduced for the estimation of the access resistance and the current through an open ion channel for an arbitrary number of species. For an ion current flowing radially inward from infinity to the channel mouth, the Poisson-Boltzmann-Nernst-Planck equations are solved analytically in the bulk with spherical symmetry in three dimensions, by linearization. Within the channel, the Poisson-Nernst-Planck equation is solved analytically in a one-dimensional approximation. An iterative procedure is used to match the two solutions together at the channel mouth in a self-consistent way. It is shown that the current-voltage characteristics obtained are in good quantitative agreement with experimental measurements.

Structure and energetics of channel-forming protein-polysaccharide complexes inferred via computational statistical thermodynamics

The ion channel protein alpha-hemolysin (alphaHL) forms supramolecular complexes with the polysaccharide beta-cyclodextrin (betaCD). This system has potential uses in nanoscale device engineering. It has been found recently that betaCD formed longer- or shorter-lived complexes with some engineered alphaHL mutants then with a wild type protein (Gu et al. J. Gen. Physiol. 2001, 118, 481-493). However, how changes in the protein sequence affect complex lifetime was not completely understood in part due to the lack of knowledge of structures of these metastable complexes. In this paper, we present an extensive molecular modeling study of the betaCD-alphaHL and selected mutant complexes to gain insights into the betaCD-alphaHL interaction mechanisms and to predict possible structures and energetics of the complexes. Thermodynamic integration (TI) and umbrella sampling (US) techniques (with the weighted histogram analysis method (WHAM)) were used to calculate the relative binding affinities of the complexes formed with the wild type alphaHL and the M113N, M113E, M113A, and M113V mutants. Our results are in excellent agreement with experiment. While betaCD-M113N and betaCD-M113A complexes were stable in the configuration of the wild type complex, the equilibrium configuration of the betaCD-M113V and betaCD-M113E complexes was significantly different. In these cases, TI alone was insufficient to accurately calculate the corresponding free energy differences. By utilizing a TI/US combination in a novel manner, we were able to accurately calculate free energy changes in these flexible systems. The betaCD-M113A and betaCD-M113E complexes, which exhibited shorter lifetimes than other complexes in an experiment, in simulations exhibited greater flexibility and higher water solvation of the betaCD adapter. MD simulations of the betaCD-M113N complex with betaCD in a downward orientation were also performed.

The versatile beta-barrel membrane protein

The beta-barrel membrane protein is found in the outer membranes of bacteria, mitochondria and chloroplasts. Approximately 2-3% of the genes in Gram-negative bacterial genomes encode beta-barrels. Whereas there are fewer than 20 known three-dimensional beta-barrel structures, genomic databases currently contain thousands of beta-barrels belonging to dozens of families. New research is revealing the variety of beta-barrel structures and the variety of functions performed by these versatile proteins.

Geometrical modelling of Ohmic conductance in ion channels

In an Ohmic model, channel conductivity can be described in terms of the geometry of a conducting cable. The essential features of such devices are the arc length of the curve describing the channel's longitudinal path, and the cross-sectional areas transversal to this curve. In a first approximation, conducting channels can be represented by an average molecular shape with estimated lengths and cross-sectional areas. Whereas the physical shortcomings of this approach are known, its accuracy limitations in practice have not been established. In this work, we discuss an improved model for the channel's shape, one that allows us to gauge how much of the Ohmic conductivity can be assigned purely to geometrical features. In the present algorithm, we investigate all regions inside the pore that are accessible to ions using various choices for the molecular surface of the inner channel. We discuss the agreement with experimental conductances in the case of 12 channels (cholera toxin B-subunit pentamer, Staphylococcus aureus alpha-hemolysin, Streptomyces lividans KcsA channel, seven porins, gramicidin A, and phospholamban). Our results can be regarded as a benchmark for the best performance that can be expected from a geometrical model of conductance. Consequently, significant deviations from experimental trends can safely be assigned to non-geometrical factors, namely the specific composition of the ion channel and the detailed electrostatic interactions between the channel and a particular ion.

Toward genomic identification of beta-barrel membrane proteins: composition and architecture of known structures

The amino acid composition and architecture of all beta-barrel membrane proteins of known three-dimensional structure have been examined to generate information that will be useful in identifying beta-barrels in genome databases. The database consists of 15 nonredundant structures, including several novel, recent structures. Known structures include monomeric, dimeric, and trimeric beta-barrels with between 8 and 22 membrane-spanning beta-strands each. For this analysis the membrane-interacting surfaces of the beta-barrels were identified with an experimentally derived, whole-residue hydrophobicity scale, and then the barrels were aligned normal to the bilayer and the position of the bilayer midplane was determined for each protein from the hydrophobicity profile. The abundance of each amino acid, relative to the genomic abundance, was calculated for the barrel exterior and interior. The architecture and diversity of known beta-barrels was also examined. For example, the distribution of rise-per-residue values perpendicular to the bilayer plane was found to be 2.7 +/- 0.25 A per residue, or about 10 +/- 1 residues across the membrane. Also, as noted by other authors, nearly every known membrane-spanning beta-barrel strand was found to have a short loop of seven residues or less connecting it to at least one adjacent strand. Using this information we have begun to generate rapid screening algorithms for the identification of beta-barrel membrane proteins in genomic databases. Application of one algorithm to the genomes of Escherichia coli and Pseudomonas aeruginosa confirms its ability to identify beta-barrels, and reveals dozens of unidentified open reading frames that potentially code for beta-barrel outer membrane proteins.

Prediction of the transmembrane regions of beta-barrel membrane proteins with a neural network-based predictor

A method based on neural networks is trained and tested on a nonredundant set of beta-barrel membrane proteins known at atomic resolution with a jackknife procedure. The method predicts the topography of transmembrane beta strands with residue accuracy as high as 78% when evolutionary information is used as input to the network. Of the transmembrane beta-strands included in the training set, 93% are correctly assigned. The predictor includes an algorithm of model optimization, based on dynamic programming, that correctly models eight out of the 11 proteins present in the training/testing set. In addition, protein topology is assigned on the basis of the location of the longest loops in the models. We propose this as a general method to fill the gap of the prediction of beta-barrel membrane proteins.

Crystal structure of the F component of the Panton-Valentine leucocidin

Leucocidins and gamma-hemolysins are bi-component staphylococcal toxins that form lytic transmembrane pores. Their cytotoxic activities involve the synergistic association of a class S and a class F component, produced as water-soluble monomers which assemble on the surface of specific cells. The structure of the F protein from Panton-Valentine leucocidin, solved at 2.0 A resolution, and sequence alignment suggest that it represents the fold of any secreted protein in this family of toxins. The comparison of this structure to that of the homoheptameric alpha-hemolysin provides some insights into the molecular events that may occur during pore formation.

Polymorphism and interactions of a viral fusion peptide in a compressed lipid monolayer

With a view toward possible new insights into viral fusion mechanisms, we have investigated the HIV-1 gp41 fusion peptide in a monomolecular film of the biomembrane lipid palmitoyloleoylphosphatidylcholine. Its surface activity at an air/water interface was measured under equilibrium conditions, using the conventional Langmuir trough technique. Through a novel thermodynamic analysis, the partial molecular area of the peptide in the lipid moiety could be determined as a function of the lateral pressure and the interfacial peptide/lipid ratio. This indicates an orientation of the peptide backbone parallel to the lipid hydrocarbon tails. The molecular area decreases significantly upon monolayer compression, suggesting a conformational transition from a somewhat compact configuration to a more extended, presumably beta-strand structure when a lipid packing density is approached that is generally believed to mimic the physical state of a biological membrane. Up to a lateral pressure of approximately 15 mN/m, practically all peptide inserts into the lipid monolayer. At higher compression a distinct partitioning into the aqueous subphase is observed. Under these conditions the data also reflect a strong aggregation of the lipid-associated peptide. Beyond a critical peptide/lipid ratio, the peptide's area requirement was found to become substantially enhanced, possibly because of the formation of water-filled pores.

The structure of a Staphylococcus aureus leucocidin component (LukF-PV) reveals the fold of the water-soluble species of a family of transmembrane pore-forming toxins

BACKGROUND

Leucocidins and gamma-hemolysins are bi-component toxins secreted by Staphylococcus aureus. These toxins activate responses of specific cells and form lethal transmembrane pores. Their leucotoxic and hemolytic activities involve the sequential binding and the synergistic association of a class S and a class F component, which form hetero-oligomeric complexes. The components of each protein class are produced as non-associated, water-soluble proteins that undergo conformational changes and oligomerization after recognition of their cell targets.

RESULTS

The crystal structure of the monomeric water-soluble form of the F component of Panton-Valentine leucocidin (LukF-PV) has been solved by the multiwavelength anomalous dispersion (MAD) method and refined at 2.0 A resolution. The core of this three-domain protein is similar to that of alpha-hemolysin, but significant differences occur in regions that may be involved in the mechanism of pore formation. The glycine-rich stem, which undergoes a major rearrangement in this process, forms an additional domain in LukF-PV. The fold of this domain is similar to that of the neurotoxins and cardiotoxins from snake venom.

CONCLUSIONS

The structure analysis and a multiple sequence alignment of all toxic components, suggest that LukF-PV represents the fold of any water-soluble secreted protein in this family of transmembrane pore-forming toxins. The comparison of the structures of LukF-PV and alpha-hemolysin provides some insights into the mechanism of transmembrane pore formation for the bi-component toxins, which may diverge from that of the alpha-hemolysin heptamer.

Meningococcal PorA/C1, a channel that combines high conductance and high selectivity

Class 1 porins (PorA/C1) from Neisseria meningitidis achieve both high selectivity and high conductance. The channel is highly selective (24:1 Na+ over Cl-), suggesting a highly negatively charged selectivity filter. The trimeric nature of PorA/C1 accounts for part of the enormous conductance in 200 mM NaCl (0.97nS). However, the currents that can be achieved exceed the simple infinite-sink calculation for a pore 0.7 nm in radius (estimated from nonelectrolyte permeability). The conductance is linear with salt activity from 20 mM to 2.0 M NaCl with no sign of saturation at low salt. Impermeant polymers reduce the conductance in a manner consistent with their ability to reduce bulk conductivity. Extrapolating from the known structure of homologous porins, the selectivity filter is likely to be small and localized. If small and highly negatively charged ( approximately 9 charges), the predicted conductance would be an order of magnitude higher than that observed. The rate at which ions reach the selectivity filter seems to limit overall ionic flux. PorA/C1 rectifies strongly, and this rectification can be accounted for by calculated differences in the voltage and concentration profiles in the access regions. Thus, it appears that the conductance of this channel is determined by the access resistance and the selectivity by a highly-conductive filter.

Modelling and simulation of ion channels: applications to the nicotinic acetylcholine receptor

Molecular dynamics simulations with experimentally derived restraints have been used to develop atomic models of M2 helix bundles forming the pore-lining domains of the nicotinic acetylcholine receptor and related ligand-gated ion channels. M2 helix bundles have been used in microscopic simulations of the dynamics and energetics of water and ions within an ion channel. Translational and rotational motion of water are restricted within the pore, and water dipoles are aligned relative to the pore axis by the surrounding helix dipoles. Potential energy profiles for translation of a Na+ ion along the pore suggest that the protein and water components of the interaction energy exert an opposing effect on the ion, resulting in a relatively flat profile which favors cation permeation. Empirical conductance calculations based on a pore radius profile suggest that the M2 helix model is consistent with a single channel conductance of ca. 50 pS. Continuum electrostatics calculations indicate that a ring of glutamate residues at the cytoplasmic mouth of the alpha 7 nicotinic receptor M2 helix bundle may not be fully ionized. A simplified model of the remainder of the channel protein when added to the M2 helix bundle plays a significant role in enhancing the ion selectivity of the channel.

Folding of beta-sheet membrane proteins: a hydrophobic hexapeptide model

Beta-sheets, in the form of the beta-barrel folding motif, are found in several constitutive membrane proteins (porins) and in several microbial toxins that assemble on membranes to form oligomeric transmembrane channels. We report here a first step towards understanding the principles of beta-sheet formation in membranes. In particular, we describe the properties of a simple hydrophobic hexapeptide, acetyl-Trp-Leu5 (AcWL5), that assembles cooperatively into beta-sheet aggregates upon partitioning into lipid bilayer membranes from the aqueous phase where the peptide is strictly monomeric and random coil. The aggregates, containing 10 to 20 monomers, undergo a relatively sharp and reversible thermal unfolding at approximately 60 degreesC. No pores are formed by the aggregates, but they do induce graded leakage of vesicle contents at very high peptide to lipid ratios. Because beta-sheet structure is not observed when the peptide is dissolved in n-octanol, trifluoroethanol or sodium dodecyl sulfate micelles, aggregation into beta-sheets appears to be an exclusive property of the peptide in the bilayer membrane interface. This is an expected consequence of the hypothesis that a reduction in the free energy of partitioning of peptide bonds caused by hydrogen bonding drives secondary structure formation in membrane interfaces. But, other features of interfacial partitioning, such as side-chain interactions and reduction of dimensionality, must also contribute. We estimate from our partitioning data that the free energy reduction per residue for aggregation is about 0.5 kcal mol-1. Although modest, its aggregate effect on the free energy of assembling beta-sheet proteins can be huge. This surprising finding, that a simple hydrophobic hexapeptide readily assembles into oligomeric beta-sheets in membranes, reveals the potent ability of membranes to promote secondary structure in peptides, and shows that the formation of beta-sheets in membranes is more facile than expected. Furthermore, it provides a basis for understanding the observation that membranes promote self-association of beta-amyloid peptides. AcWL5 and related peptides thus provide a good starting point for designing peptide models for exploring the principles of beta-sheet formation in membranes.

Protein-water-ion interactions in a model of the pore domain of a potassium channel: a simulation study

A model of the selectivity filter of a voltage-gated K+ (Kv) channel formed by an eight-stranded beta-barrel is compared with physiological properties of the channel. Continuum electrostatic calculations suggest that only two of the eight Asp sidechains at the extracellular mouth of the pore will ionise. A ring of four Tyr sidechains forms the narrowest region of the pore. Molecular dynamic simulations of the potential energy of a K+ ion as translated along the model pore indicate that the two ionised Asp sidechains and the hydroxyl groups of the Tyr sidechains stabilise the partially desolvated ion as it passes through the narrowest region.

Shear numbers of protein beta-barrels: definition refinements and statistics

The original definition of shear number for a beta-barrel is not unique if it contains one or more uneven beta-bulges. We define the shear number of a beta-barrel as the minimal change of residue numbers in the backbone direction for all closed paths on the beta-barrel. We also discuss how to overcome some computational difficulties. It is pointed out that some closed beta-sheets should not be considered as beta-barrels. The pertinent statistics obtained from a representative list of the Protein Data Bank entries are summarized. All beta-barrels have positive shear numbers, i.e. they are right-twisted. The shear numbers of most beta-barrels are even, but exceptions do exist. The sizes of beta-ladders in a beta-barrel vary significantly. Most beta-barrels contain uneven beta-bulges, which may have important biological functions.

Channels formed by the transmembrane helix of phospholamban: a simulation study

Phospholamban is a small membrane protein which can form cation selective ion channels in lipid bilayers. Each subunit contains a single, largely hydrophobic transmembrane helix. The helices are thought to assemble as a pentameric and approximately parallel bundle surrounding a central pore. A model of this assembly (PDB code IPSL) has been used as the starting point for molecular dynamics (MD) simulations of a system consisting of the pentameric helix bundle, plus 217 water molecules located within and at either mouth of the pore. Interhelix distance restraints were employed to maintain the integrity of the helix bundle during a 500 ps MD simulation. Water molecules within the pore exhibited reduced diffusional and rotational mobility. Interactions between the alpha-helix dipoles and the water dipoles, the latter aligned anti-parallel to the former, contribute to the stability of the system. Analysis of the potential energy of interaction of a K+ ion as it was moved through the pore suggested that unfavourable interactions of the cation with the aligned helix dipoles at the N-terminal mouth were overcome by favourable ion-water interactions. Comparable analysis for a Cl ion revealed that the ion-(pore + water) interactions were unfavourable along the whole of the pore, increasingly so from the N- to the C-terminal mouth. Overall, the interaction energy profiles were consistent with a pore selective for cations over anions. Pore radius profiles were used to predict a channel conductance of 50 to 70 ps in 0.2 M KCl, which compares well with an experimental value of 100 ps.

Secondary structure of an isolated P-region from the voltage-gated sodium channel: a molecular modelling/dynamics study

Conformational studies of synthetic peptides corresponding to the pore-forming regions of voltage-gated sodium channels show a high tendency for beta-sheet conformation when interacting with lipid vesicles, as revealed by circular dichroism and infrared spectroscopy. These observations have guided our choice of possible molecular models for the P-region peptide of domain II of voltage-gated sodium channels: three alternative beta-hairpins, with differing turn assignments, or an alpha-helical hairpin. After generation of models by distance geometry-based methods, molecular dynamics (MD) simulations were run. in the absence of explicit solvent molecules but employing three different dielectric constants, to explore possible conformational preferences. The simulations in the different dielectric environments suggest that a 4-residue turn with the sequence LCGE yields more stable beta-hairpins. The MD results suggest that the SS1 part of the peptide may be more stable as an alpha-helix, whereas the SS2 part tends to adopt a beta-conformation.

The pore-lining region of shaker voltage-gated potassium channels: comparison of beta-barrel and alpha-helix bundle models

Although there is a large body of site-directed mutagenesis data that identify the pore-lining sequence of the voltage-gated potassium channel, the structure of this region remains unknown. We have interpreted the available biochemical data as a set of topological and orientational restraints and employed these restraints to produce molecular models of the potassium channel pore region, H5. The H5 sequence has been modeled either as a tetramer of membrane-spanning beta-hairpins, thus producing an eight-stranded beta-barrel, or as a tetramer of incompletely membrane-spanning alpha-helical hairpins, thus producing an eight-staved alpha-helix bundle. In total, restraints-directed modeling has produced 40 different configurations of the beta-barrel model, each configuration comprising an ensemble of 20 structures, and 24 different configurations of the alpha-helix bundle model, each comprising an ensemble of 24 structures. Thus, over 1300 model structures for H5 have been generated. Configurations have been ranked on the basis of their predicted pore properties and on the extent of their agreement with the biochemical data. This ranking is employed to identify particular configurations of H5 that may be explored further as models of the pore-lining region of the voltage-gated potassium channel pore.

Shaker pore structure as predicted by annealed atomic simulation using symmetry and novel geometric restraints

Recent studies making use of channel-blocking peptides as molecular calipers have revealed the architecture of the pore-forming region of Shaker-type potassium channels. Here we show that the low-resolution, experimentally derived geometric information can be incorporated as restraints within the context of an annealed molecular dynamics simulation to predict an atomic structure for the channel pore which, by virtue of restraints, conforms to the experimental evidence. The simulation is reminiscent of the computational method employed by nuclear magnetic resonance (NMR) spectroscopists to resolve solution structures of biological macromolecules, but in lieu of restraints conventionally derived from NMR spectra, novel restraints are developed that include side-chain orientation of amino acid residues and assumed symmetry of protein subunits. The method presented here offers the possibility of expanding cooperation between simulation and experiment in developing structural models, especially for systems such as ion channels whose three-dimensional structures may not be amenable to determination by direct methods at the present time.

Alamethicin channels - modelling via restrained molecular dynamics simulations

Alamethicin channels have been modelled as approximately parallel bundles of transbilayer helices containing between N = 4 and 8 helices per bundle. Initial models were generated by in vacuo restrained molecular dynamics (MD) simulations, and were refined by 60 ps MD simulations with water molecules present within and at the mouths of the central pore. The helix bundles were stabilized by networks of H-bonds between intra-pore water molecules and Gln-7 side-chains. Channel conductances were predicted on the basis of pore radius profiles, and suggested that the N = 4 bundle formed an occluded pore, whereas pores with N > or = 5 helices per bundle were open. Continuum electrostatics calculations suggested that the N = 6 pore is cation-selective, whereas pores with N > or = 7 helices per bundle were predicted to be somewhat less ion-selective.

A novel method for structure-based prediction of ion channel conductance properties

A rapid and easy-to-use method of predicting the conductance of an ion channel from its three-dimensional structure is presented. The method combines the pore dimensions of the channel as measured in the HOLE program with an Ohmic model of conductance. An empirically based correction factor is then applied. The method yielded good results for six experimental channel structures (none of which were included in the training set) with predictions accurate to within an average factor of 1.62 to the true values. The predictive r2 was equal to 0.90, which is indicative of a good predictive ability. The procedure is used to validate model structures of alamethicin and phospholamban. Two genuine predictions for the conductance of channels with known structure but without reported conductances are given. A modification of the procedure that calculates the expected results for the effect of the addition of nonelectrolyte polymers on conductance is set out. Results for a cholera toxin B-subunit crystal structure agree well with the measured values. The difficulty in interpreting such studies is discussed, with the conclusion that measurements on channels of known structure are required.

HOLE: a program for the analysis of the pore dimensions of ion channel structural models

A method (HOLE) that allows the analysis of the dimensions of the pore running through a structural model of an ion channel is presented. The algorithm uses a Monte Carlo simulated annealing procedure to find the best route for a sphere with variable radius to squeeze through the channel. Results can be displayed in a graphical fashion or visualized with most common molecular graphical packages. Advances include a method to analyze the anisotropy within a pore. The method can also be used to predict the conductance of channels using a simple empirically corrected ohmic model. As an example the program is applied to the cholera toxin B-subunit pentamer. The compatibility of the crystal structure and conductance data is established.

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.

Molecular dynamics simulations of water within models of ion channels

The transbilayer pores formed by ion channel proteins contain extended columns of water molecules. The dynamic properties of such waters have been suggested to differ from those of water in its bulk state. Molecular dynamics simulations of ion channel models solvated within and at the mouths of their pores are used to investigate the dynamics and structure of intra-pore water. Three classes of channel model are investigated: a) parallel bundles of hydrophobic (Ala20) alpha-helices; b) eight-stranded hydrophobic (Ala10) antiparallel beta-barrels; and c) parallel bundles of amphipathic alpha-helices (namely, delta-toxin, alamethicin, and nicotinic acetylcholine receptor M2 helix). The self-diffusion coefficients of water molecules within the pores are reduced significantly relative to bulk water in all of the models. Water rotational reorientation rates are also reduced within the pores, particularly in those pores formed by alpha-helix bundles. In the narrowest pore (that of the Ala20 pentameric helix bundle) self-diffusion coefficients and reorientation rates of intra-pore waters are reduced by approximately an order of magnitude relative to bulk solvent. In Ala20 helix bundles the water dipoles orient antiparallel to the helix dipoles. Such dipole/dipole interaction between water and pore may explain how water-filled ion channels may be formed by hydrophobic helices. In the bundles of amphipathic helices the orientation of water dipoles is modulated by the presence of charged side chains. No preferential orientation of water dipoles relative to the pore axis is observed in the hydrophobic beta-barrel models.

Water in channel-like cavities: structure and dynamics

Ion channels contain narrow columns of water molecules. It is of interest to compare the structure and dynamics of such intrapore water with those of the bulk solvent. Molecular dynamics simulations of modified TIP3P water molecules confined within channel-like cavities have been performed and the orientation and dynamics of the water molecules analyzed. Channels were modeled as cylindrical cavities with lengths ranging from 15 to 60 A and radii from 3 to 12 A. At the end of the molecular dynamics simulations water molecules were observed to be ordered into approximately concentric cylindrical shells. The waters of the outermost shell were oriented such that their dipoles were on average perpendicular to the normal of the wall of the cavity. Water dynamics were analyzed in terms of self-diffusion coefficients and rotational reorientation rates. For cavities of radii 3 and 6 A, water mobility was reduced relative to that of simulated bulk water. For 9- and 12-A radii confined water molecules exhibited mobilities comparable with that of the bulk solvent. If water molecules were confined within an hourglass-shaped cavity (with a central radius of 3 A increasing to 12 A at either end) a gradient of water mobility was observed along the cavity axis. Thus, water within simple models of transbilayer channels exhibits perturbations of structure and dynamics relative to bulk water. In particular the reduction of rotational reorientation rate is expected to alter the local dielectric constant within a transbilayer pore.