Brownian dynamics simulation of ion flow through porin channels

Dynamics accelerate the kinetics of ion diffusion through channels: Continuous-time random walk models beyond the mean field approximation

Ion channels are proteins that play a significant role in physiological processes, including neuronal excitability and signal transduction. However, the precise mechanisms by which these proteins facilitate ion diffusion through cell membranes are not well understood. This is because experimental techniques to characterize ion channel activity operate on a time scale too large to understand the role of the various protein conformations on diffusion. Meanwhile, computational approaches operate on a time scale too short to rationalize the observed behavior at the microscopic scale. In this paper, we present a continuous-time random walk model that aims to bridge the scales between the atomistic models of ion channels and the experimental measurement of their conductance. We show how diffusion slows down in complex systems by using 3D lattices that map out the pore geometry of two channels: Nav1.7 and gramicidin. We also introduce spatial and dynamic site disorder to account for system heterogeneity beyond the mean field approximation. Computed diffusion coefficients show that an increase in spatial disorder slows down diffusion kinetics, while dynamic disorder has the opposite effect. Our results imply that microscopic or phenomenological models based on the potential of mean force data overlook the functional importance of protein dynamics on ion diffusion through channels.

Accurate modeling of a biological nanopore with an extended continuum framework

Despite the broad success of biological nanopores as powerful instruments for the analysis of proteins and nucleic acids at the single-molecule level, a fast simulation methodology to accurately model their nanofluidic properties is currently unavailable. This limits the rational engineering of nanopore traits and makes the unambiguous interpretation of experimental results challenging. Here, we present a continuum approach that can faithfully reproduce the experimentally measured ionic conductance of the biological nanopore Cytolysin A (ClyA) over a wide range of ionic strengths and bias potentials. Our model consists of the extended Poisson-Nernst-Planck and Navier-Stokes (ePNP-NS) equations and a computationally efficient 2D-axisymmetric representation for the geometry and charge distribution of the nanopore. Importantly, the ePNP-NS equations achieve this accuracy by self-consistently considering the finite size of the ions and the influence of both the ionic strength and the nanoscopic scale of the pore on the local properties of the electrolyte. These comprise the mobility and diffusivity of the ions, and the density, viscosity and relative permittivity of the solvent. Crucially, by applying our methodology to ClyA, a biological nanopore used for single-molecule enzymology studies, we could directly quantify several nanofluidic characteristics difficult to determine experimentally. These include the ion selectivity, the ion concentration distributions, the electrostatic potential landscape, the magnitude of the electro-osmotic flow field, and the internal pressure distribution. Hence, this work provides a means to obtain fundamental new insights into the nanofluidic properties of biological nanopores and paves the way towards their rational engineering.

Manipulation of charge distribution in the arginine and glutamate clusters of the OmpG pore alters sugar specificity and ion selectivity

OmpG is a general diffusion pore in the E. coli outer membrane with a molecular architecture comprising a 14-stranded β-barrel scaffold and unique structural features. In contrast to other non-specific porins, OmpG lacks a central constriction zone and has an exceptionally wide pore diameter of about 13 Å. The equatorial plane of OmpG harbors an annulus of four alternating basic and acidic patches whose function is only poorly characterized. We have investigated the role of charge distribution for ion selectivity and sugar transport with the help of OmpG variants mutated in the annulus. Substituting the glutamate residues of the annulus for histidines or alanines led to a strong reduction in cation selectivity. Replacement of the glutamates in the annulus by histidine residues also disfavored the passage of pentoses and hexoses relative to disaccharides. Our results demonstrate that despite the wide pore diameter, an annulus only consisting of two opposing basic patches confers reduced cation and monosaccharide transport compared to OmpG wild type. Furthermore, randomization of charged residues in the annulus had the potential to abolish pH-dependency of sugar transport. Our results indicate that E¹⁵, E³¹, R⁹², R¹¹¹ and R²¹¹ in the annulus form electrostatic interactions with R²²⁸, E²²⁹ and D²³² in loop L6 that influence pH-dependency of sugar transport.

Layer-by-layer Assembled Membranes with Immobilized Porins

With the synthesis and functionalization of membranes for selective separations, reactivity, and stimuli responsive behavior arises new and advanced opportunities. The integration of bio-based channels is one of these advancements in membrane technologies. By a layer-by-layer (LbL) assembly of polyelectrolytes, outer membrane protein F trimers (OmpF) or "porins" from Escherichia coli with a central pore of ~2 nm diameter at its opening and ~0.7 × 1.1 nm at its constricted region are immobilized within the pores of poly(vinylidene fluoride) microfiltration membranes, as opposed to traditional ruptured lipid bilayer or vesicles processes. These OmpF-membranes demonstrate selective rejections of non-charged organics over ionic solutes, allowing the passage of salts up to 2 times higher than traditional nanofiltration membranes starting with rejections of 84% for 0.4-1.0 kDa organics. The presence of charged groups in OmpF membranes also leads to pH-dependent salt rejection through Donnan exclusion. These OmpF-membranes also show exceptional durability and stability, delivering consistent and constant permeability and recovery for over 160 h of operation. Characterization of solutions containing OmpF, and membranes were conducted during each stage of the process, including detection by fluorescence labelling (FITC), zeta potential, pH responsiveness, flux changes, and rejections of organic-inorganic solutions.

Multi-Dielectric Brownian Dynamics and Design-Space-Exploration Studies of Permeation in Ion Channels

This paper proposes a multi-dielectric Brownian dynamics simulation framework for design-space-exploration (DSE) studies of ion-channel permeation. The goal of such DSE studies is to estimate the channel modeling-parameters that minimize the mean-squared error between the simulated and expected "permeation characteristics." To address this computational challenge, we use a methodology based on statistical inference that utilizes the knowledge of channel structure to prune the design space. We demonstrate the proposed framework and DSE methodology using a case study based on the KcsA ion channel, in which the design space is successfully reduced from a 6-D space to a 2-D space. Our results show that the channel dielectric map computed using the framework matches with that computed directly using molecular dynamics with an error of 7%. Finally, the scalability and resolution of the model used are explored, and it is shown that the memory requirements needed for DSE remain constant as the number of parameters (degree of heterogeneity) increases.

Modulation of Asymmetric Flux in Heterotypic Gap Junctions by Pore Shape, Particle Size and Charge

Gap junction channels play a vital role in intercellular communication by connecting cytoplasm of adjoined cells through arrays of channel-pores formed at the common membrane junction. Their structure and properties vary depending on the connexin isoform(s) involved in forming the full gap junction channel. Lack of information on the molecular structure of gap junction channels has limited the development of computational tools for single channel studies. Currently, we rely on cumbersome experimental techniques that have limited capabilities. We have earlier reported a simplified Brownian dynamics gap junction pore model and demonstrated that variations in pore shape at the single channel level can explain some of the differences in permeability of heterotypic channels observed in in vitro experiments. Based on this computational model, we designed simulations to study the influence of pore shape, particle size and charge in homotypic and heterotypic pores. We simulated dye diffusion under whole cell voltage clamping. Our simulation studies with pore shape variations revealed a pore shape with maximal flux asymmetry in a heterotypic pore. We identified pore shape profiles that match the in silico flux asymmetry results to the in vitro results of homotypic and heterotypic gap junction formed out of Cx43 and Cx45. Our simulation results indicate that the channel's pore-shape established flux asymmetry and that flux asymmetry is primarily regulated by the sizes of the conical and/or cylindrical mouths at each end of the pore. Within the set range of particle size and charge, flux asymmetry was found to be independent of particle size and directly proportional to charge magnitude. While particle charge was vital to creating flux asymmetry, charge magnitude only scaled the observed flux asymmetry. Our studies identified the key factors that help predict asymmetry. Finally, we suggest the role of such flux asymmetry in creating concentration imbalances of messenger molecules in cardiomyocytes. We also assess the potency of fibroblasts in aggravating such imbalances through Cx43-Cx45 heterotypic channels in fibrotic heart tissue.

Computational simulations of asymmetric fluxes of large molecules through gap junction channel pores

Gap junction channels are formed out of connexin isoforms, which enable molecule and ion selective diffusion amongst neighboring cells. HeLa cells expressing distinct connexins (Cx) allow the formation of heterotypic channels, where we observed a molecular charge-independent preferential flux of large fluorescent molecules in the Cx45 to Cx43 direction. We hypothesize that the pore's shape is a significant factor along-side charge and transjunctional voltages for this asymmetric flux. To test this hypothesis, we developed a 3D computational model simulating Brownian diffusion of large molecules in a gap junction channel pore. The basic pore contour was derived from x-ray crystallographic structures of Cx43 and Cx26 and approximated using basic geometric shapes. Lucifer yellow dye molecules and cesium counter-ions were modeled as spheres using their respective Stokes radii. Our simulation results from simple diffusion and constant concentration gradient experiments showed that only charged particles yield asymmetric fluxes in heterotypic pores. While increasing the inner mouth size resulted in a near-quadratic rise in flux, the rise was asymptotic for outer mouth radii increase. Probability maps and average force per particle per pore section explain the asymmetric flux with variation in pore shape. Furthermore, the simulation results are in agreement with our in vitro experimental results with HeLa cells in Cx43-Cx45 heterotypic configurations. The presence of asymmetric fluxes can help us to understand effects of the molecular structure of the pore and predict potential differences in vivo.

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.

How do the protonation states of E296 and D312 in OmpF and D299 and D315 in homologous OmpC affect protein structure and dynamics? Simulation studies

In this study, the structural and dynamic properties of two major porins (OmpF and OmpC) in Escherichia coli are investigated using molecular dynamics (MD) simulations. Both porins have the extracellular loop L3 folded halfway through the pore to form a constriction area. The solute influx and efflux are controlled by the L3 movement. E296 and D312 in OmpF and homologous D299 and D315 in OmpC located on the barrel wall are found to play a key role in L3 gating activity. All possible charged states of both E296(D299) and D312(315) are applied in this study to observe changes in overall structure and especially L3 movement. The results show that different protonation states of both residues cause the large-scale deviations in structure and pore cavity especially in OmpF. Fully charged E296(D299) and D312(315) increase the protein flexibility significantly. Deprotonating at least one of E296(D299) and D312(315) helps to fasten L3 to the barrel wall and maintain pore size. Lacking of interactions with D312(315) can lead to the pore closure in OmpF. Comparing with OmpC, not only is OmpF less stable, but it is also more sensitive to the charge states of both E296(D299) and D312(315).

A structural study of ion permeation in OmpF porin from anomalous X-ray diffraction and molecular dynamics simulations

OmpF, a multiionic porin from Escherichia coli, is a useful protypical model system for addressing general questions about electrostatic interactions in the confinement of an aqueous molecular pore. Here, favorable anion locations in the OmpF pore were mapped by anomalous X-ray scattering of Br(–) ions from four different crystal structures and compared with Mg(2+) sites and Rb(+) sites from a previous anomalous diffraction study to provide a complete picture of cation and anion transfer paths along the OmpF channel. By comparing structures with various crystallization conditions, we find that anions bind in discrete clusters along the entire length of the OmpF pore, whereas cations find conserved binding sites with the extracellular, surface-exposed loops. Results from molecular dynamics simulations are consistent with the experimental data and help highlight the critical residues that preferentially contact either cations or anions during permeation. Analysis of these results provides new insights into the molecular mechanisms that determine ion selectivity in OmpF porin.

Ion permeation in the NanC porin from Escherichia coli: free energy calculations along pathways identified by coarse-grain simulations

Using the X-ray structure of a recently discovered bacterial protein, the N-acetylneuraminic acid-inducible channel (NanC), we investigate computationally K(+) and Cl(-) ions' permeation. We identify ion permeation pathways that are likely to be populated using coarse-grain Monte Carlo simulations. Next, we use these pathways as reaction coordinates for umbrella sampling-based free energy simulations. We find distinct tubelike pathways connecting specific binding sites for K(+) and, more pronounced, for Cl(-) ions. Both ions permeate the porin preserving almost all of their first hydration shell. The calculated free energy barriers are G(#) ≈ 4 kJ/mol and G(#) ≈ 8 kJ/mol for Cl(-) and K(+), respectively. Within the approximations associated with these values, discussed in detail in this work, we suggest that the porin is slightly selective for Cl(-) versus K(+). Our suggestion is consistent with the experimentally observed weak Cl(-) over K(+) selectivity. A rationale for the latter is suggested by a comparison with previous calculations on strongly anion selective porins.

Quantitative imaging of the electrostatic field and potential generated by a transmembrane protein pore at subnanometer resolution

Elucidating the mechanisms by which proteins translocate small molecules and ions through transmembrane pores and channels is of great interest in biology, medicine, and nanotechnology. However, the characterization of pore forming proteins in their native state lacks suitable methods that are capable of high-resolution imaging (~1 nm) while simultaneously mapping physical and chemical properties. Here we report how force-distance (FD) curve-based atomic force microscopy (AFM) imaging can be applied to image the native pore forming outer membrane protein F (OmpF) at subnanometer resolution and to quantify the electrostatic field and potential generated by the transmembrane pore. We further observe the electrostatic field and potential of the OmpF pore switching "on" and "off" in dependence of the electrolyte concentration. Because electrostatic field and potential select for charged molecules and ions and guide them to the transmembrane pore the insights are of fundamental importance to understand the pore function. These experimental results establish FD-based AFM as a unique tool to image biological systems to subnanometer resolution and to quantify their electrostatic properties.

Molecular origin of VDAC selectivity towards inorganic ions: a combined molecular and Brownian dynamics study

The voltage-dependent anion channel (VDAC) serves as the major pore for metabolites and electrolytes in the outer mitochondrial membrane. To refine our understanding of ion permeation through this channel we performed an extensive Brownian (BD) and molecular dynamics (MD) study on the mouse VDAC isoform 1 wild-type and mutants (K20E, D30K, K61E, E158K and K252E). The selectivity and the conductance of the wild-type and of the variant channels computed from the BD trajectories are in agreement with experimental data. The calculated selectivity is shown to be very sensitive to slight conformational changes which may have some bearing on the variability of the selectivity values measured on the VDAC open state. The MD and BD free energy profiles of the ion permeation suggest that the pore region comprising the N-terminal helix and the barrel band encircling it predominantly controls the ion transport across the channel. The overall 12μs BD and 0.9μs MD trajectories of the mouse VDAC isoform 1 wild-type and mutants feature no distinct pathways for ion diffusion and no long-lived ion-protein interactions. The dependence of ion distribution in the wild-type channel with the salt concentration can be explained by an ionic screening of the permanent charges of the protein arising from the pore. Altogether these results bolster the role of electrostatic features of the pore as the main determinant of VDAC selectivity towards inorganic anions.

Divalent Metal Ion Transport across Large Biological Ion Channels and Their Effect on Conductance and Selectivity

Electrophysiological characterization of large protein channels, usually displaying multi-ionic transport and weak ion selectivity, is commonly performed at physiological conditions (moderate gradients of KCl solutions at decimolar concentrations buffered at neutral pH). We extend here the characterization of the OmpF porin, a wide channel of the outer membrane of E. coli, by studying the effect of salts of divalent cations on the transport properties of the channel. The regulation of divalent cations concentration is essential in cell metabolism and understanding their effects is of key importance, not only in the channels specifically designed to control their passage but also in other multiionic channels. In particular, in porin channels like OmpF, divalent cations modulate the efficiency of molecules having antimicrobial activity. Taking advantage of the fact that the OmpF channel atomic structure has been resolved both in water and in MgCl₂ aqueous solutions, we analyze the single channel conductance and the channel selectivity inversion aiming to separate the role of the electrolyte itself, and the counterion accumulation induced by the protein channel charges and other factors (binding, steric effects, etc.) that being of minor importance in salts of monovalent cations become crucial in the case of divalent cations.

Bacterial origin of a mitochondrial outer membrane protein translocase: new perspectives from comparative single channel electrophysiology

Mitochondria are of bacterial ancestry and have to import most of their proteins from the cytosol. This process is mediated by Tom40, an essential protein that forms the protein-translocating pore in the outer mitochondrial membrane. Tom40 is conserved in virtually all eukaryotes, but its evolutionary origin is unclear because bacterial orthologues have not been identified so far. Recently, it was shown that the parasitic protozoon Trypanosoma brucei lacks a conventional Tom40 and instead employs the archaic translocase of the outer mitochondrial membrane (ATOM), a protein that shows similarities to both eukaryotic Tom40 and bacterial protein translocases of the Omp85 family. Here we present electrophysiological single channel data showing that ATOM forms a hydrophilic pore of large conductance and high open probability. Moreover, ATOM channels exhibit a preference for the passage of cationic molecules consistent with the idea that it may translocate unfolded proteins targeted by positively charged N-terminal presequences. This is further supported by the fact that the addition of a presequence peptide induces transient pore closure. An in-depth comparison of these single channel properties with those of other protein translocases reveals that ATOM closely resembles bacterial-type protein export channels rather than eukaryotic Tom40. Our results support the idea that ATOM represents an evolutionary intermediate between a bacterial Omp85-like protein export machinery and the conventional Tom40 that is found in mitochondria of other eukaryotes.

Asymmetric pore occupancy in crystal structure of OmpF porin from Salmonella typhi

OmpF is a major general diffusion porin of Salmonella typhi, a Gram-negative bacterium, which is an obligatory human pathogen causing typhoid. The structure of S. typhi Ty21a OmpF (PDB Id: 3NSG) determined at 2.8 Å resolution by X-ray crystallography shows a 16-stranded β-barrel with three β-barrel monomers associated to form a trimer. The packing observed in S. typhi Ty21a rfOmpF crystals has not been observed earlier in other porin structures. The variations seen in the loop regions provide a starting point for using the S. typhi OmpF for structure-based multi-valent vaccine design. Along one side of the S. typhi Ty21a OmpF pore there exists a staircase arrangement of basic residues (20R, 60R, 62K, 65R, 77R, 130R and 16K), which also contribute, to the electrostatic potential in the pore. This structure suggests the presence of asymmetric electrostatics in the porin oligomer. Moreover, antibiotic translocation, permeability and reduced uptake in the case of mutants can be understood based on the structure paving the way for designing new antibiotics.

Exploring protein import pores of cellular organelles at the single molecule level using the planar lipid bilayer technique

Proteins of living cells carry out their specialized functions within various subcellular membranes or aqueous spaces. Approximately half of all the proteins of a typical cell are transported into or across membranes. Targeting and transport to their correct subcellular destinations are essential steps in protein biosynthesis. In eukaryotic cells secretory proteins are transported into the endoplasmic reticulum before they are transported in vesicles to the plasma membrane. Virtually all proteins of the endosymbiotic organelles, chloroplasts and mitochondria, are synthesized on cytosolic ribosomes and posttranslationally imported. Genetic and biochemical techniques led to rather detailed knowledge on the subunit composition of the various protein transport complexes which carry out the membrane transport of the preproteins. Conclusive concepts on targeting and cytosolic transport of polypeptides emerged, while still few details on the molecular nature and mechanisms of the channel moieties of protein translocation complexes have been achieved. In this paper we will describe the history of how the individual subunits forming the channel pores of the chloroplast, mitochondrial and endoplasmic reticulum protein import machineries were identified and characterized by single channel electrophysiological techniques in planar bilayers. We will also highlight recent developments in the exploration of the molecular properties of protein translocating channels and the regulation of the diverse protein translocation systems using the planar bilayer technique.

Concentration dependent ion selectivity in VDAC: a molecular dynamics simulation study

The voltage-dependent anion channel (VDAC) forms the major pore in the outer mitochondrial membrane. Its high conducting open state features a moderate anion selectivity. There is some evidence indicating that the electrophysiological properties of VDAC vary with the salt concentration. Using a theoretical approach the molecular basis for this concentration dependence was investigated. Molecular dynamics simulations and continuum electrostatic calculations performed on the mouse VDAC1 isoform clearly demonstrate that the distribution of fixed charges in the channel creates an electric field, which determines the anion preference of VDAC at low salt concentration. Increasing the salt concentration in the bulk results in a higher concentration of ions in the VDAC wide pore. This event induces a large electrostatic screening of the charged residues promoting a less anion selective channel. Residues that are responsible for the electrostatic pattern of the channel were identified using the molecular dynamics trajectories. Some of these residues are found to be conserved suggesting that ion permeation between different VDAC species occurs through a common mechanism. This inference is buttressed by electrophysiological experiments performed on bean VDAC32 protein akin to mouse VDAC.

First-passage-time analysis of atomic-resolution simulations of the ionic transport in a bacterial porin

We have studied the dynamics of chloride and potassium ions in the interior of the Outer membrane porin F (OmpF) under the influence of an external electric field. From the results of extensive all-atom molecular dynamics (MD) simulations of the system, we computed several first-passage-time (FPT) quantities to characterize the dynamics of the ions in the interior of the channel. Such FPT quantities obtained from MD simulations demonstrate that it is not possible to describe the dynamics of chloride and potassium ions inside the whole channel with a single constant diffusion coefficient. However, we showed that a valid, statistically rigorous description in terms of a constant diffusion coefficient D and an effective deterministic force F(eff) can be obtained after appropriate subdivision of the channel in different regions suggested by the x-ray structure. These results have important implications for popular simplified descriptions of channels based on the one-dimensional Poisson-Nernst-Planck equations. Also, the effect of entropic barriers on the diffusion of the ions is identified and briefly discussed.

Insights on the permeability of wide protein channels: measurement and interpretation of ion selectivity

Ion channels are hollow proteins that have evolved to exhibit discrimination between charged solutes. This property, known as ion selectivity is critical for several biological functions. By using the bacterial porin OmpF as a model system of wide protein channels, we demonstrate that significant insights can be gained when selectivity measurements are combined with electrodiffusion continuum models and simulations based on the atomic structure. A correct interpretation of the mechanisms ruling the many sources of channel discrimination is a first, indispensable step for the understanding of the controlled movement of ions into or out of cells characteristic of many physiological processes. We conclude that the scattered information gathered from several independent approaches should be appropriately merged to provide a unified and coherent picture of the channel selectivity.

Critical assessment of OmpF channel selectivity: merging information from different experimental protocols

The ion selectivity of a channel can be quantified in several ways by using different experimental protocols. A wide, mesoscopic channel, the OmpF porin of the outer membrane of E. coli, serves as a case study for comparing and analysing several measures of the channel cation-anion permeability in chlorides of alkali metals (LiCl, NaCl, KCl, CsCl). We show how different insights can be gained and integrated to rationalize the global image of channel selectivity. To this end, reversal potential, channel conductance and bi-ionic potential (two different salts with a common anion on each side of the channel but with the same concentration) experiments are discussed in light of an electrodiffusion model based on the Poisson-Nernst-Planck formalism. Measurements and calculations based on the atomic crystal structure of the channel show that each protocol displays a particular balance between the different sources of selectivity.

Cation-selective pathway of OmpF porin revealed by anomalous X-ray diffraction

The OmpF porin from the Escherichia coli outer membrane folds into a trimer of beta-barrels, each forming a wide aqueous pore allowing the passage of ions and small solutes. A long loop (L3) carrying multiple acidic residues folds into the beta-barrel pore to form a narrow "constriction zone". A strong and highly conserved charge asymmetry is observed at the constriction zone, with multiple basic residues attached to the wall of the beta-barrel (Lys16, Arg42, Arg82 and Arg132) on one side, and multiple acidic residues of L3 (Asp107, Asp113, Glu117, Asp121, Asp126, Asp127) on the other side. Several computational studies have suggested that a strong transverse electric field could exist at the constriction zone as a result of such charge asymmetry, giving rise to separate permeation pathways for cations and anions. To examine this question, OmpF was expressed, purified and crystallized in the P6(3) space group and two different data sets were obtained at 2.6 A and 3.0 A resolution with K(+) and Rb(+), respectively. The Rb(+)-soaked crystals were collected at the rubidium anomalous wavelength of 0.8149 A and cation positions were determined. A PEG molecule was observed in the pore region for both the K(+) and Rb(+)-soaked crystals, where it interacts with loop L3. The results reveal the separate pathways of anions and cations across the constriction zone of the OmpF pore.

Understanding ion conductance on a molecular level: an all-atom modeling of the bacterial porin OmpF

All-atom molecular dynamics simulations of the ion current through OmpF, the major porin in the outer membrane of Escherichia coli, were performed. Starting from the crystal structure, the all-atom modeling allows us to calculate a parameter-free ion conductance in semiquantitative agreement with experiment. Discrepancies between modeling and experiment occur, e.g., at salt concentrations above 1 M KCl or at high temperatures. At lower salt concentrations, the ions have separate pathways along the channel surface. The constriction zone in the channel contains, on one side, a series of positively charges (R42, R82, R132), and on the opposite side, two negatively charged residues (D113, E117). Mutations generated in the constriction zone by removing cationic residues enhance the otherwise small cation selectivity, whereas removing the anionic residues reverses the selectivity. Reduction of the negatively charged residues decreases the conductance by half, whereas cationic residues enhance the conductance. Experiments on mutants confirm the results of the molecular-level simulations.

Reconstructing potentials of mean force from short steered molecular dynamics simulations of Vpu from HIV-1

Vpu from human immunodeficiency virus type-1 (HIV-1) is an 81 amino acid type I integral membrane protein. Vpu forms ion conducting homooligomeric assemblies. To assess the energy landscape of an ion traversing the channel or pore single ion potentials of mean force (PMF) are reconstructed from short (1.2 ns) steered molecular dynamics (SMD) simulations using the Langevin equation of motion. For the simulations a section of the first 32 amino acids including the transmembrane domain of the Vpu protein is used. The values for the friction coefficient are estimated as a function of time using the velocity autocorrelation method. The PMFs of K(+), Na(+), and C(-) adopt a wave like pattern with a maximum around the hydrophobic stretch of the pore and a minimum at the hydrophilic site (C terminus). Independent of the pore size the amplitude of the PMF of at least one cation is always the lowest.

The outer membrane protein VhOmp of Vibrio harveyi: pore-forming properties in black lipid membranes

Vibrio harveyi is known to cause fatal vibriosis in marine animals. Here, an outer membrane protein from V. harveyi, namely, VhOmp, was isolated and functionally characterized in terms of pore-forming contact with artificial lipid membranes. The native VhOmp exists as a trimer of a molecular weight similar to that of the porin OmpF from Escherichia coli. Reconstitution of VhOmp into black lipid membranes demonstrated its ability to form ion channels. The average pore conductance of VhOmp was revealed to be about 0.9 and 2 nS in 0.2 and 1 M KCl, respectively. Within transmembrane potentials of +/-100 mV, VhOmp pores behaved as ohmic conduits, and their conductance scaled linearly with voltage. Nonlinear plots of the pore conductance versus symmetrical salt concentrations at either side of the protein-incorporating membrane suggested the influence of interior channel functionalities on the passage of charged species. In the presence of Omp-specific polyclonal antibodies, the pore-forming property of VhOmp was modulated so that the usual step-like current increments were replaced by random transitory current fluctuations. VhOmp exhibited a strong biological activity by causing hemolysis of human red blood cells, indicating that VhOmp may act as a crucial determinant during bacterial infection to animal host cells.

Elucidating in vivo structural dynamics in integral membrane protein by hydroxyl radical footprinting

We describe here a novel footprinting technique to probe the in vivo structural dynamics of membrane protein. This method utilized in situ generation of hydroxyl radicals to oxidize and covalently modify biomolecules on living Escherichia coli cell surface. After enriching and purifying the membrane proteome, the modified amino acid residues of the protein were identified with tandem mass spectrometry to map the solvent-accessible surface of the protein that will form the footprint of in vivo structure of the protein. Of about 100 outer membrane proteins identified, we investigated the structure details of a typical beta-barrel structure, the porin OmpF. We found that six modified tryptic peptides of OmpF were reproducibly detected with 19 amino acids modified under the physiological condition. The modified amino acid residues were widely distributed in the external loop area, beta-strands, and periplasmic turning area, and all of them were validated as solvent-accessible according to the crystallography data. We further extended this method to study the dynamics of the voltage gating of OmpF in vivo using mimic changes of physiological circumstance either by pH or by ionic strength. Our data showed the voltage gating of porin OmpF in vivo for the first time and supported the proposed mechanism that the local electrostatic field changes in the eyelet region may alter the porin channels to switch. Thus, this novel method can be a potentially efficient method to study the structural dynamics of the membrane proteins of a living cell.

Altered pore properties and kinetic changes in mutants of the Vibrio cholerae porin OmpU

The electrophysiological technique of patch-clamp was used to characterize the pore properties of site-directed mutants in the Vibrio cholerae general diffusion porin OmpU. Changes in conductance and selectivity were observed, thus confirming the predicted pore location of these residues, based on homology with the Escherichia coli porins OmpF and OmpC. Some mutants acquire a weak selectivity for cations, which mirrors the properties of the homologous, deoxycholic acid sensitive, OmpT porin of V. cholerae. However, the mutants remain insensitive to deoxycholic acid, like wildtype OmpU. This result suggests that channel selectivity is not an important determinant in the sensitivity to this drug, and is in agreement with our finding that the neutral deoxycholic acid, and not deoxycholate, is the actual active form in channel block. Modifications in the kinetics of spontaneous closures were also noted, and are similar to those found for the E. coli channels. In addition, mutants at the D116 residue on the L3 loop display marked transitions to sub-conductance states. The results reported here are compared to a phenotypical characterization of the mutants in terms of permeability to maltodextrins and beta-lactam antibiotic sensitivity. No strict correlations are observed, suggesting that distinct, but somewhat overlapping, molecular determinants control electrophysiological properties and substrate permeability.

Non-Markovian noise mediated through anomalous diffusion within ion channels

It is evident from a wide range of experimental findings that ion channel gating is inherently stochastic. The issue of "memory effects" (diffusional retardation due to local changes in water viscosity) in ionic flow has been recently addressed using Brownian dynamics simulations. The results presented indicate such memory effects are negligible, unless the diffusional barrier is much higher than that of free solute. In this paper using differential stochastic methods we conclude that the Markovian property of exponential dwell times gives rise to a high barrier, resulting in diffusional memory effects that cannot be ignored in determining ionic flow through channels. We have addressed this question using a generalized Langevin equation that contains a combination of Markovian and non-Markovian processes with different time scales. This approach afforded the development of an algorithm that describes an oscillatory ionic diffusional sequence. The resulting oscillatory function behavior, with exponential decay, was obtained at the weak non-Markovian limit with two distinct time scales corresponding to the processes of ionic diffusion and drift. This will be analyzed further in future studies using molecular dynamics simulations. We propose that the rise of time scales and memory effects is related to differences of shear viscosity in the cytoplasm and extracellular matrix.

A biological porin engineered into a molecular, nanofluidic diode

We changed the nonrectifying biological porin OmpF into a nanofluidic diode. To that end, we engineered a pore that possesses two spatially separated selectivity filters of opposite charge where either cations or anions accumulate. The observed current inhibition under applied reverse bias voltage reflects, we believe, the creation of a zone depleted of charge carriers, in a sense very similar to what happens at the np junction of a semiconductor device.

Electrostatic properties and macroscopic electrodiffusion in OmpF porin and mutants

The bacterial porin OmpF found in the outer membrane of E. coli is a wide channel, characterized by its poor selectivity and almost no ion specificity. It has an asymmetric structure, with relatively large entrances and a narrow constriction. By applying continuum electrostatic methods we determine the ionization states of titratable amino acid residues in the protein and calculate self-consistently the electric potential 3-D distribution within the channel. The average electrostatic properties are then represented by an effective fixed charge distribution along the pore which is the input for a macroscopic electrodiffusion model. The theoretical predictions agree with measurements performed under different salt gradients and pH. The sensitivity of reversal potential and conductance to the direction of the salt gradient and the solution pH is captured by the model. The theory is also able to explain the influence of the lipid membrane charge. The same methodology is satisfactorily applied to some OmpF mutants involving slight structural changes but a large number of net charges. The correlation found between atomic structure and ionic selectivity shows that the transport characteristics of wide channels like OmpF and its mutants are mainly regulated by the collective action of a large number of residues, rather than by the specific interactions of residues at particular locations.

Crystal Structure of Osmoporin OmpC from E. coli at 2.0 Å

Porins form transmembrane pores in the outer membrane of Gram-negative bacteria with matrix porin OmpF and osmoporin OmpC from Escherichia coli being differentially expressed depending on environmental conditions. The three-dimensional structure of OmpC has been determined to 2.0 A resolution by X-ray crystallography. As expected from the high sequence similarity, OmpC adopts the OmpF-like 16-stranded hollow beta-barrel fold with three beta-barrels associated to form a tight trimer. Unlike in OmpF, the extracellular loops form a continuous wall at the perimeter of the vestibule common to the three pores, due to a 14-residues insertion in loop L4. The pore constriction and the periplasmic outlet are very similar to OmpF with 74% of the pore lining residues being conserved. Overall, only few ionizable residues are exchanged at the pore lining. The OmpC structure suggests that not pore size, but electrostatic pore potential and particular atomic details of the pore linings are the critical parameters that physiologically distinguish OmpC from OmpF.

Ca2+ selectivity of a chemically modified OmpF with reduced pore volume

We studied an E. coli OmpF mutant (LECE) containing both an EEEE-like locus, typical of Ca(2+) channels, and an accessible and reactive cysteine. After chemical modification with the cysteine-specific, negatively charged (-1e) reagents MTSES or glutathione, this LECE mutant was tested for Ca(2+) versus alkali metal selectivity. Selectivity was measured by conductance and zero-current potential. Conductance measurements showed that glutathione-modified LECE had reduced conductance at Ca(2+) mole fractions <10(-3). MTSES-modified LECE did not. Apparently, the LECE protein is (somehow) a better Ca(2+) chelator after modification with the larger glutathione. Zero-current potential measurements revealed a Ca(2+) versus monovalent cation selectivity that was highest in the presence of Li(+) and lowest in the presence of Cs(+). Our data clearly show that after the binding of Ca(2+) the LECE pore (even with the bulky glutathione present) is spacious enough to allow monovalent cations to pass. Theoretical computations based on density functional theory combined with Poisson-Nernst-Planck theory and a reduced pore model suggest a functional separation of ionic pathways in the pore, one that is specific for small and highly charged ions, and one that accepts preferentially large ions, such as Cs(+).

Conductance and selectivity fluctuations in D127 mutants of the bacterial porin OmpF

A recent molecular dynamics study questioned the protonation state and physiological role of aspartate 127 (D127) of E. coli porin OmpF. To address that question we isolated two OmpF mutants with D127 either neutralized (D127N) or replaced by a positively charged lysine (D127K). The charge state of the residue at position 127 has clear effects on both conductance and selectivity. The D127K but not the D127N mutant expresses resilient conductance and selectivity fluctuations. These fluctuations reflect, we think, either changes in the ionization state of K127 and/or transitions between unstable subconformations as induced by the electrostatic repulsion between two positively charged residues, K127 and the nearby R167. Our results slightly favor the view that in WT OmpF residue D127 is deprotonated. As for the role of D127 in OmpF functionality, the gating of both mutants shows very similar sensitivity toward voltage as WT OmpF. Moreover, the current fluctuations of the D127K mutant were observed also in the absence of an applied electric field. We therefore dismiss D127 as a key residue in the control mechanism of the voltage-dependent gating of OmpF.

OEP37 Is a New Member of the Chloroplast Outer Membrane Ion Channels

The chloroplast outer envelope protein OEP37 is a member of the growing beta-barrel protein family of the outer chloroplast membrane. The reconstituted recombinant protein OEP37 from pea forms a rectifying high conductance channel with a main conductance (lambda) of Lambda= 500 picosiemens (symmetrical 250 mm KCl). The OEP37 channel is cation-selective (P(K+)/P(K-) = 14:1) with a voltage-dependent open probability maximal at V(mem) = 0 mV. The channel pore reveals an hourglass-shaped form with different diameters for the vestibule and restriction zone. The diameters of the vestibule at the high conductance side were estimated by d = 3.0 nm and the restriction zone by d = 1.5 nm. The OEP37 channel displayed a nanomolar affinity for the precursor of the chloroplast inner membrane protein Tic32, which is imported into the chloroplast through a yet unknown pathway. Pre-proteins imported through the usual Toc pathway and synthetic control peptides, however, did not show a comparable block of the OEP37 channel. In addition to the electrophysiological characterization, we studied the gene expression of OEP37 in the model plant Arabidopsis thaliana. Here, transcripts of AtOEP37 are ubiquitously expressed throughout plant development and accumulate in early germinating seedlings as well as in late embryogenesis. The plastid intrinsic protein could be detected in isolated chloroplasts of cotyledons and rosette leaves. However, the knock-out mutant oep37-1 shows that the proper function of this single copy gene is not essential for development of the mature plant. Moreover, import of Tic32 into chloroplasts of oep37-1 was not impaired when compared with wild type. Thus, OEP37 may constitute a novel peptide-sensitive ion channel in the outer envelope of plastids with function during embryogenesis and germination.

Electrostatic properties of the mechanosensitive channel of small conductance MscS

The mechanosensitive channel of small conductance (MscS) belongs to a family of membrane proteins that are gated in response to changes in membrane tension, thereby protecting the cell from hypo-osmotic shock. Here we report on passive ion transport simulations of MscS in a POPC bilayer using a coarse-grained particle-based description based on the Boltzmann transport Monte Carlo method. Single channel current-voltage curves are computed over hundreds of nanoseconds for channel conformations derived from all-atom molecular dynamics simulations reaching an overall simulation time of over 5 micros. Channel conformations similar to that of the crystal structure exhibit low conductance, whereas conformations reached after opening the channel by means of steered molecular dynamics simulations match experimentally determined conductances. However, while experiments indicate a slight preference for anionic currents, the simulated channel strongly selects anions over cations and the direction of rectification at high voltages is opposite to what is observed in experiments. Three-dimensional maps of time-averaged ion distribution and equilibrium occupancy profiles constructed from trajectory data indicate separation of anions and cations inside and in the immediate vicinity of the large cytoplasmic domain of MscS, in accordance with earlier molecular dynamics simulations. This separation arises from the distribution of ionizable residues of MscS and suggests a specific, yet unknown, functional purpose.

The influence of amino acid protonation states on molecular dynamics simulations of the bacterial porin OmpF

Several groups, including our own, have found molecular dynamics (MD) calculations to result in the size of the pore of an outer membrane bacterial porin, OmpF, to be reduced relative to its size in the x-ray crystal structure. At the narrowest portion of its pore, loop L3 was found to move toward the opposite face of the pore, resulting in decreasing the cross-section area by a factor of approximately 2. In an earlier work, we computed the protonation states of titratable residues for this system and obtained values different from those that had been used in previous MD simulations. Here, we show that MD simulations carried out with these recently computed protonation states accurately reproduce the cross-sectional area profile of the channel lumen in agreement with the x-ray structure. Our calculations include the investigation of the effect of assigning different protonation states to the one residue, D(127), whose protonation state could not be modeled in our earlier calculation. We found that both assumptions of charge states for D(127) reproduced the lumen size profile of the x-ray structure. We also found that the charged state of D(127) had a higher degree of hydration and it induced greater mobility of polar side chains in its vicinity, indicating that the apparent polarizability of the D(127) microenvironment is a function of the D(127) protonation state.

Ion transit pathways and gating in ClC chloride channels

ClC chloride channels possess a homodimeric structure in which each monomer contains an independent chloride ion pathway. ClC channel gating is regulated by chloride ion concentration, pH and voltage. Based on structural and physiological evidence, it has been proposed that a glutamate residue on the extracellular end of the selectivity filter acts as a fast gate. We utilized a new search algorithm that incorporates electrostatic information to explore the ion transit pathways through wild-type and mutant bacterial ClC channels. Examination of the chloride ion permeation pathways supports the importance of the glutamate residue in gating. An external chloride binding site previously postulated in physiological experiments is located near a conserved basic residue adjacent to the gate. In addition, access pathways are found for proton migration to the gate, enabling pH control at hyperpolarized membrane potentials. A chloride ion in the selectivity filter is required for the pH-dependent gating mechanism.

Computing numerically the access resistance of a pore

The access resistance (AR) of a channel is an important component of the conductance of ion channels, particularly in wide and short channels, where it accounts for a substantial fraction of the total resistance to the movement of ions. The AR is usually calculated by using a classical and simple expression derived by Hall from electrostatics (J.E. Hall 1975 J. Gen. Phys. 66:531-532), though other expressions, both analytical and numerical, have been proposed. Here we report some numerical results for the AR of a channel obtained by solving the Poisson-Nernst-Planck equations at the entrance of a circular pore. Agreement is found between numerical calculations and analytical results from Hall's equation for uncharged pores in neutral membranes. However, for channels embedded in charged membranes, Hall's expression overestimates the AR, which is much lower and can even be neglected in some cases. The weak dependence of AR on the pore radius for charged membranes at low salt concentration can be exploited to separate the channel and the access contributions to the measured conductance.

Permeation of particle through a four-helix-bundle model channel

By using molecular dynamics simulation, the dynamic behaviors of particle permeation through a four-helix-bundle model channel are studied. The interior cavity of the four-helix-bundle provides the "routes" for particle permeation. The main structural properties of the model channel are similar to those that appear in natural four-helix-bundle proteins. It is found that the interior structure of the model channel may greatly influence the permeation process. At the narrow necks of the model channel, the particle would be trapped during the permeation. There is a threshold value for the driving force. When the driving force is larger than this threshold value, the mean first permeation time decreases sharply and tends to be saturated. Increasing the temperature of either the model channel or the particle reservoir can also facilitate the permeation. Enhancing the interaction strength between the particle and monomer on the four-helix-bundle model chain will hinder the permeation. Hence, the electrical current which is induced by the particle permeation is a function of the driving force and temperature. It is found that this current increases monotonically as the strength of the driving force or the temperature increases, but decreases as the interaction strength between the particle and monomer increases. It is also found that the larger the friction coefficient, the slower the permeation is. In addition, the multiparticle (or multi-ion) permeation process is also studied. The permeation of multiparticle is usually quicker than that of the single particle. The permeation of particle through a five-helix-bundle shows similar properties as that through a four-helix-bundle.

Salting out the ionic selectivity of a wide channel: the asymmetry of OmpF

Although the crystallographic structure of the bacterial porin OmpF has been known for a decade, the physical mechanisms of its ionic selectivity are still under investigation. We address this issue in a series of experiments with varied pH, salt concentrations, inverted salt gradient, and charged and uncharged lipids. Measuring reversal potential, we show that OmpF selectivity (traditionally regarded as slightly cationic) depends strongly on pH and salt concentration and is conditionally asymmetric, that is, the calculated selectivity is sensitive to the direction of salt concentration gradient. At neutral pH and subdecimolar salt concentrations the channel exhibits nearly ideal cation selectivity (t(G)(+)=0.98+/-0.01). Substituting neutral DPhPC with DPhPS, we demonstrate that the fixed charge of the host lipid has a small but measurable effect on the channel reversal potential. The available structural information allows for a qualitative explanation of our experimental findings. These findings now lead us to re-examine the ionization state of 102 titratable sites of the OmpF channel. Using standard methods of continuum electrostatics tailored to our particular purpose, we find the charge distribution in the channel as a function of solution acidity and relate the pH-dependent asymmetry in channel selectivity to the pH-dependent asymmetry in charge distribution. In an attempt to find a simple phenomenological description of our results, we also discuss different macroscopic models of electrodiffusion through large channels.