Chemical modification of the bacterial porin OmpF: gain of selectivity by volume reduction

Approaching Ideal Selectivity with Bioinspired and Biomimetic Membranes

The applications of polymeric membranes have grown rapidly compared to traditional separation technologies due to their energy efficiency and smaller footprint. However, their potential is not fully realized due, in part, to their heterogeneity, which results in a "permeability-selectivity" trade-off for most membrane applications. Inspired by the intricate architecture and excellent homogeneity of biological membranes, bioinspired and biomimetic membranes (BBMs) aim to emulate biological membranes for practical applications. This Review highlights the potential of BBMs to overcome the limitations of polymeric membranes by utilizing the "division of labor" between well-defined permeable pores and impermeable matrix molecules seen in biological membranes. We explore the exceptional performance of membranes in biological organisms, focusing on their two major components: membrane proteins (biological channels) and lipid matrix molecules. We then discuss how these natural materials can be replaced with artificial mimics for enhanced properties and how macro-scale BBMs are developed. We highlight key demonstrations in the field of BBMs that draw upon the factors responsible for transport through biological membranes. Additionally, current state-of-the-art methods for fabrication of BBMs are reviewed with potential challenges and prospects for future applications. Finally, we provide considerations for future research that could enable BBMs to progress toward scale-up and enhanced applicability.

Supralinear scaling behavior of ionic transport in membrane nanochannels regulated by outer-surface charges

The peculiarity of ion transport at the nanoscale is revealed through electrophysiological studies of two biological ion channels: the cation-selective bacterial porin-OmpF and the mitochondrial voltage-dependent anion channel (VDAC). We provide evidence of an unprecedented scaling behavior in the power-law relationship between conductivity and concentration G ∼ c α with α > 1 when functional groups attached to the pore inner wall have opposite charges to those located in the nanochannel's outer surface. Indeed, we find α ∼ 1.4 both for OmpF in positively charged membranes and for VDAC in negatively charged ones. The experiments are analyzed using different levels of theoretical models, starting with an equivalent circuit where total electrical current is described as the sum of ionic currents. Subsequently, we show that electrical circuits incorporating simplifying assumptions such as local electroneutrality and Donnan equilibrium consistently account for the measured G-c relationships yielding extremely similar results to the numerical results of structure-based Poisson-Nernst-Planck equations computed without these assumptions. We demonstrate that unexpected scaling exponents do not correspond to deviations from these classical equilibrium/electroneutrality assumptions, but rather to the structural features of the pore that are not included in oversimplified models in terms of shape and/or charge distribution. In contrast to the predictions of widely accepted models, we demonstrate both experimentally and theoretically that the conductance of ion-selective nanochannels can be drastically reduced in dilute solutions through a mechanism in which membrane charges and pore charges do not compensate for each other but act as interacting sites of opposite charge. Our insights into the critical role of external surface charges aim to open new conceptual avenues for developing nanofluidic devices with enhanced capabilities for energy conversion and sensing properties.

Protein engineering of pores for separation, sensing, and sequencing

Proteins are critical to cellular function and survival. They are complex molecules with precise structures and chemistries, which allow them to serve diverse functions for maintaining overall cell homeostasis. Since the discovery of the first enzyme in 1833, a gamut of advanced experimental and computational tools has been developed and deployed for understanding protein structure and function. Recent studies have demonstrated the ability to redesign/alter natural proteins for applications in industrial processes of interest and to make customized, novel synthetic proteins in the laboratory through protein engineering. We comprehensively review the successes in engineering pore-forming proteins and correlate the amino acid-level biochemistry of different pore modification strategies to the intended applications limited to nucleotide/peptide sequencing, single-molecule sensing, and precise molecular separations.

Deamidated Human Triosephosphate Isomerase is a Promising Druggable Target

Therapeutic strategies for the treatment of any severe disease are based on the discovery and validation of druggable targets. The human genome encodes only 600-1500 targets for small-molecule drugs, but posttranslational modifications lead to a considerably larger druggable proteome. The spontaneous conversion of asparagine (Asn) residues to aspartic acid or isoaspartic acid is a frequent modification in proteins as part of the process called deamidation. Triosephosphate isomerase (TIM) is a glycolytic enzyme whose deamidation has been thoroughly studied, but the prospects of exploiting this phenomenon for drug design remain poorly understood. The purpose of this study is to demonstrate the properties of deamidated human TIM (HsTIM) as a selective molecular target. Using in silico prediction, in vitro analyses, and a bacterial model lacking the tim gene, this study analyzed the structural and functional differences between deamidated and nondeamidated HsTIM, which account for the efficacy of this protein as a druggable target. The highly increased permeability and loss of noncovalent interactions of deamidated TIM were found to play a central role in the process of selective enzyme inactivation and methylglyoxal production. This study elucidates the properties of deamidated HsTIM regarding its selective inhibition by thiol-reactive drugs and how these drugs can contribute to the development of cell-specific therapeutic strategies for a variety of diseases, such as COVID-19 and cancer.

Electroosmosis Dominates Electrophoresis of Antibiotic Transport Across the Outer Membrane Porin F

We report that the dynamics of antibiotic capture and transport across a voltage-biased OmpF nanopore is dominated by the electroosmotic flow rather than the electrophoretic force. By reconstituting an OmpF porin in an artificial lipid bilayer and applying an electric field across it, we are able to elucidate the permeation of molecules and their mechanism of transport. This field gives rise to an electrophoretic force acting directly on a charged substrate but also indirectly via coupling to all other mobile ions, causing an electroosmotic flow. The directionality and magnitude of this flow depends on the selectivity of the channel. Modifying the charge state of three different substrates (norfloxacin, ciprofloxacin, and enoxacin) by varying the pH between 6 and 9 while the charge and selectivity of OmpF is conserved allows us to work under conditions in which electroosmotic flow and electrophoretic forces add or oppose. This configuration allows us to identify and distinguish the contributions of the electroosmotic flow and the electrophoretic force on translocation. Statistical analysis of the resolvable dwell times reveals rich kinetic details regarding the direction and the stochastic movement of antibiotics inside the nanopore. We quantitatively describe the electroosmotic velocity component experienced by the substrates and their diffusion coefficients inside the porin with an estimate of the energy barrier experienced by the molecules caused by the interaction with the channel wall, which slows down the permeation by several orders of magnitude.

On the different sources of cooperativity in pH titrating sites of a membrane protein channel

Cooperative interactions play a central role in the regulation of protein functions. Here we show that in multi-site systems like ion channels the application of the Hill formalism could require a combination of different experiments, even involving site-directed mutagenesis, to identify the different sources of cooperativity and to discriminate between genuine and apparent cooperativity. We discuss the implications for the channel function in the bacterial porins PorA (N. meningitidis) and OmpF (E. coli) and the viroporin SARS-CoV E.

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.

Lipid charge regulation of non-specific biological ion channels

Lipid charge regulation effects in different protein–lipid conformations highlight the role of electrostatic interactions in conductance and selectivity of non-specific biological ion channels.

Electrostatic interactions drive the nonsteric directional block of OmpF channel by La3+

Ion channels regulate the transport of molecules and the electric signal transduction in living cells by means of complex and even highly sophisticated mechanisms. We focus here on the crucial role that polyvalent ions, well-known modulators of many biological nanosystems, play in ion channel function. In particular, we show that trace amounts of lanthanum are able to block the bacterial porin OmpF, a large biological pore of Escherichia coli wide enough to exchange antibiotics and other larger molecules. The underlying mechanism has a strong directional character: it is sensitive to the sign of the applied voltage and to the side of the blocker addition. We explore these channel features by combining planar lipid bilayer electrophysiology at the single channel level, site-directed mutagenesis, and inductively coupled plasma mass spectrometry (ICP-MS). In contrast to other well-described channel blockers, which seem to occlude the narrower part of the pore, we envisage a nonsteric mechanism based on electrostatic interactions.

Interacting ions in biophysics: real is not ideal

Ions in water are important throughout biology, from molecules to organs. Classically, ions in water were treated as ideal noninteracting particles in a perfect gas. Excess free energy of each ion was zero. Mathematics was not available to deal consistently with flows, or interactions with other ions or boundaries. Nonclassical approaches are needed because ions in biological conditions flow and interact. The concentration gradient of one ion can drive the flow of another, even in a bulk solution. A variational multiscale approach is needed to deal with interactions and flow. The recently developed energetic variational approach to dissipative systems allows mathematically consistent treatment of the bio-ions Na(+), K(+), Ca(2+), and Cl(-) as they interact and flow. Interactions produce large excess free energy that dominate the properties of the high concentration of ions in and near protein active sites, ion channels, and nucleic acids: the number density of ions is often >10 M. Ions in such crowded quarters interact strongly with each other as well as with the surrounding protein. Nonideal behavior found in many experiments has classically been ascribed to allosteric interactions mediated by the protein and its conformation changes. The ion-ion interactions present in crowded solutions-independent of conformation changes of the protein-are likely to change the interpretation of many allosteric phenomena. Computation of all atoms is a popular alternative to the multiscale approach. Such computations involve formidable challenges. Biological systems exist on very different scales from atomic motion. Biological systems exist in ionic mixtures (like extracellular and intracellular solutions), and usually involve flow and trace concentrations of messenger ions (e.g., 10(-7) M Ca(2+)). Energetic variational methods can deal with these characteristic properties of biological systems as we await the maturation and calibration of all-atom simulations of ionic mixtures and divalents.

Ionic Interactions Are Everywhere

Ionic solutions are dominated by interactions because they must be electrically neutral, but classical theory assumes no interactions. Biological solutions are rather like seawater, concentrated enough so that the diameter of ions also produces important interactions. In my view, the theory of complex fluids is needed to deal with the interacting reality of biological solutions.

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.

Ionizable side chains at catalytic active sites of enzymes

Catalytic active sites of enzymes of known structure can be well defined by a modern program of computational geometry. The CASTp program was used to define and measure the volume of the catalytic active sites of 573 enzymes in the Catalytic Site Atlas database. The active sites are identified as catalytic because the amino acids they contain are known to participate in the chemical reaction catalyzed by the enzyme. Acid and base side chains are reliable markers of catalytic active sites. The catalytic active sites have 4 acid and 5 base side chains, in an average volume of 1,072 Å(3). The number density of acid side chains is 8.3 M (in chemical units); the number density of basic side chains is 10.6 M. The catalytic active site of these enzymes is an unusual electrostatic and steric environment in which side chains and reactants are crowded together in a mixture more like an ionic liquid than an ideal infinitely dilute solution. The electrostatics and crowding of reactants and side chains seems likely to be important for catalytic function. In three types of analogous ion channels, simulation of crowded charges accounts for the main properties of selectivity measured in a wide range of solutions and concentrations. It seems wise to use mathematics designed to study interacting complex fluids when making models of the catalytic active sites of enzymes.

Single-channel measurements of an N-acetylneuraminic acid-inducible outer membrane channel in Escherichia coli

NanC is an Escherichia coli outer membrane protein involved in sialic acid (Neu5Ac, i.e., N-acetylneuraminic acid) uptake. Expression of the NanC gene is induced and controlled by Neu5Ac. The transport mechanism of Neu5Ac is not known. The structure of NanC was recently solved (PDB code: 2WJQ) and includes a unique arrangement of positively charged (basic) side chains consistent with a role in acidic sugar transport. However, initial functional measurements of NanC failed to find its role in the transport of sialic acids, perhaps because of the ionic conditions used in the experiments. We show here that the ionic conditions generally preferred for measuring the function of outer-membrane porins are not appropriate for NanC. Single channels of NanC at pH 7.0 have: (1) conductance 100 pS to 800 pS in 100 mM: KCl to 3 M: KCl), (2) anion over cation selectivity (V (reversal) = +16 mV in 250 mM: KCl || 1 M: KCl), and (3) two forms of voltage-dependent gating (channel closures above ± 200 mV). Single-channel conductance decreases by 50% when HEPES concentration is increased from 100 μM: to 100 mM: in 250 mM: KCl at pH 7.4, consistent with the two HEPES binding sites observed in the crystal structure. Studying alternative buffers, we find that phosphate interferes with the channel conductance. Single-channel conductance decreases by 19% when phosphate concentration is increased from 0 mM: to 5 mM: in 250 mM: KCl at pH 8.0. Surprisingly, TRIS in the baths reacts with Ag|AgCl electrodes, producing artifacts even when the electrodes are on the far side of agar-KCl bridges. A suitable baseline solution for NanC is 250 mM: KCl adjusted to pH 7.0 without buffer.

Assessing the efficacy of vesicle fusion with planar membrane arrays using a mitochondrial porin as reporter

Reconstitution of functionally active membrane protein into artificially made lipid bilayers is a challenge that must be overcome to create a membrane-based biomimetic sensor and separation device. In this study we address the efficacy of proteoliposome fusion with planar membrane arrays. We establish a protein incorporation efficacy assay using the major non-specific porin of Fusobacterium nucleatum (FomA) as reporter. We use electrical conductance measurements and fluorescence microscopy to characterize proteoliposome fusion with an array of planar membranes. We show that protein reconstitution in biomimetic membrane arrays may be quantified using the developed FomA assay. Specifically, we show that FomA vesicles are inherently fusigenic. Optimal FomA incorporation is obtained with a proteoliposome lipid-to-protein molar ratio (LPR)=50 more than 10(5) FomA proteins could be incorporated in a bilayer array with a total membrane area of 2mm(2) within 20 min. This novel assay for quantifying protein delivery into lipid bilayers may be a useful tool in developing biomimetic membrane applications.

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.

Multiple Scales in the Simulation of Ion Channels and Proteins

Computation of living processes creates great promise for the everyday life of mankind and great challenges for physical scientists. Simulations molecular dynamics have great appeal to biologists as a natural extension of structural biology. Once a biologist sees a structure, she/he wants to see it move. Molecular biology has shown that a small number of atoms, sometimes even one messenger ion, like Ca(2+), can control biological function on the scale of cells, organs, tissues, and organisms. Enormously concentrated ions-at number densities of ~20 M-in protein channels and enzymes are responsible for many of the characteristics of living systems, just as highly concentrated ions near electrodes are responsible for many of the characteristics of electrochemical systems. Here we confront the reality of the scale differences of ions. We show that the scale differences needed to simulate all the atoms of biological cells are 10(7) in linear dimension, 10(21) in three dimensions, 10(9) in resolution, 10(11) in time, and 10(13) in particle number (to deal with concentrations of Ca(2+)). These scales must be dealt with simultaneously if the simulation is to deal with most biological functions. Biological function extends across all of them, all at once in most cases. We suggest a computational approach using explicit multiscale analysis instead of implicit simulation of all scales. The approach is based on an energy variational principle EnVarA introduced by Chun Liu to deal with complex fluids. Variational methods deal automatically with multiple interacting components and scales. When an additional component is added to the system, the resulting Euler Lagrange field equations change form automatically-by algebra alone-without additional unknown parameters. Multifaceted interactions are solutions of the resulting equations. We suggest that ionic solutions should be viewed as complex fluids with simple components. Highly concentrated solutions-dominated by interactions of components-are easily computed by EnVarA. Successful computation of ions concentrated in special places may be a significant step to understanding the defining characteristics of biological and electrochemical systems. Indeed, computing ions near proteins and nucleic acids may prove as important to molecular biology and chemical technology as computing holes and electrons has been to our semiconductor and digital technology.

Ionic partition and transport in multi-ionic channels: a molecular dynamics simulation study of the OmpF bacterial porin

We performed all-atom molecular dynamics simulations studying the partition of ions and the ionic current through the bacterial porin OmpF and two selected mutants. The study is motivated by new, interesting experimental findings concerning their selectivity and conductance behavior at neutral pH. The mutations considered here are designed to study the effect of removal of negative charges present in the constriction zone of the wild-type OmpF channel (which contains, on one side, a cluster with three positive residues, and on the other side, two negatively charged residues). Our results show that these mutations induce an exclusion of cations from the constriction zone of the channel, substantially reducing the flow of cations. In fact, the partition of ions inside the mutant channels is strongly inhomogeneous, with regions containing an excess of cations and regions containing an excess of anions. Interestingly, the overall number of cations inside the channel is larger than the number of anions, this excess being different for each protein channel. We found that the differences in ionic charge inside these channels are justified by the differences in electric charge between the wild-type OmpF and the mutants, following an electroneutral balance.

Energy variational analysis of ions in water and channels: Field theory for primitive models of complex ionic fluids

Ionic solutions are mixtures of interacting anions and cations. They hardly resemble dilute gases of uncharged noninteracting point particles described in elementary textbooks. Biological and electrochemical solutions have many components that interact strongly as they flow in concentrated environments near electrodes, ion channels, or active sites of enzymes. Interactions in concentrated environments help determine the characteristic properties of electrodes, enzymes, and ion channels. Flows are driven by a combination of electrical and chemical potentials that depend on the charges, concentrations, and sizes of all ions, not just the same type of ion. We use a variational method EnVarA (energy variational analysis) that combines Hamilton's least action and Rayleigh's dissipation principles to create a variational field theory that includes flow, friction, and complex structure with physical boundary conditions. EnVarA optimizes both the action integral functional of classical mechanics and the dissipation functional. These functionals can include entropy and dissipation as well as potential energy. The stationary point of the action is determined with respect to the trajectory of particles. The stationary point of the dissipation is determined with respect to rate functions (such as velocity). Both variations are written in one Eulerian (laboratory) framework. In variational analysis, an "extra layer" of mathematics is used to derive partial differential equations. Energies and dissipations of different components are combined in EnVarA and Euler-Lagrange equations are then derived. These partial differential equations are the unique consequence of the contributions of individual components. The form and parameters of the partial differential equations are determined by algebra without additional physical content or assumptions. The partial differential equations of mixtures automatically combine physical properties of individual (unmixed) components. If a new component is added to the energy or dissipation, the Euler-Lagrange equations change form and interaction terms appear without additional adjustable parameters. EnVarA has previously been used to compute properties of liquid crystals, polymer fluids, and electrorheological fluids containing solid balls and charged oil droplets that fission and fuse. Here we apply EnVarA to the primitive model of electrolytes in which ions are spheres in a frictional dielectric. The resulting Euler-Lagrange equations include electrostatics and diffusion and friction. They are a time dependent generalization of the Poisson-Nernst-Planck equations of semiconductors, electrochemistry, and molecular biophysics. They include the finite diameter of ions. The EnVarA treatment is applied to ions next to a charged wall, where layering is observed. Applied to an ion channel, EnVarA calculates a quick transient pile-up of electric charge, transient and steady flow through the channel, stationary "binding" in the channel, and the eventual accumulation of salts in "unstirred layers" near channels. EnVarA treats electrolytes in a unified way as complex rather than simple fluids. Ad hoc descriptions of interactions and flow have been used in many areas of science to deal with the nonideal properties of electrolytes. It seems likely that the variational treatment can simplify, unify, and perhaps derive and improve those descriptions.

Simulations of calcium channel block by trivalent cations: Gd(3+) competes with permeant ions for the selectivity filter

Current through L-type calcium channels (Ca(V)1.2 or dihydropyridine receptor) can be blocked by micromolar concentrations of trivalent cations like the lanthanide gadolinium (Gd(3+)). It has been proposed that trivalent block is due to ions competing for a binding site in both the open and closed configuration, but possibly with different trivalent affinities. Here, we corroborate this general view of trivalent block by computing conductance of a model L-type calcium channel. The model qualitatively reproduces the Gd(3+) concentration dependence and the effect that substantially more Gd(3+) is required to produce similar block in the presence of Sr(2+) (compared to Ba(2+)) and even more in the presence of Ca(2+). Trivalent block is explained in this model by cations binding in the selectivity filter with the charge/space competition mechanism. This is the same mechanism that in the model channel governs other selectivity properties. Specifically, selectivity is determined by the combination of ions that most effectively screen the negative glutamates of the protein while finding space in the midst of the closely packed carboxylate groups of the glutamate residues.

Comparing the temperature-dependent conductance of the two structurally similar E. coli porins OmpC and OmpF

The temperature-dependent ion conductance of OmpC, a major outer membrane channel of Escherichia coli, is predicted using all-atom molecular dynamics simulations and experimentally verified. To generalize previous results, OmpC is compared to its structural homolog OmpF at different KCl concentrations, pH values, and a broad temperature range. At low salt concentrations and up to room temperature, the molecular modeling predicts the experimental conductance accurately. At high salt concentrations above 1 M KCl and above room temperature, the simulations underestimate the conductance. Moreover, the temperature dependence of the channel conductance is different from that of the bulk, both in experiment and simulation, indicating a strong contribution of surface effects to the ion conductance. With respect to OmpC, subconductance levels can be observed in experiments only. Subconductance and gating levels can be clearly distinguished by their differences in conductance values and temperature-dependent behavior. With increasing temperature, the probability of a subconductance state to occur, increases, while the dwell time is decreased. The open probability, frequency, and dwell time of such states is largely pH- and KCl concentration-independent, while their amplitudes show a lower increase with increasing salt concentration than gating amplitudes. Voltage dependence of subconductance has been found to be negligible within the uncertainty of the measurements.

Diffusion, exclusion, and specific binding in a large channel: a study of OmpF selectivity inversion

We find that moderate cationic selectivity of the general bacterial porin OmpF in sodium and potassium chloride solutions is inversed to anionic selectivity in concentrated solutions of barium, calcium, nickel, and magnesium chlorides. To understand the origin of this phenomenon, we consider several factors, which include the binding of divalent cations, electrostatic and steric exclusion of differently charged and differently sized ions, size-dependent hydrodynamic hindrance, electrokinetic effects, and significant "anionic" diffusion potential for bulk solutions of chlorides of divalent cations. Though all these factors contribute to the measured selectivity of this large channel, the observed selectivity inversion is mostly due to the following two. First, binding divalent cations compensates, or even slightly overcompensates, for the negative charge of the OmpF protein, which is known to be the main cause of cationic selectivity in sodium and potassium chloride solutions. Second, the higher anionic (versus cationic) transport rate expected for bulk solutions of chloride salts of divalent cations is the leading cause of the measured anionic selectivity of the channel. Interestingly, at high concentrations the binding of cations does not show any pronounced specificity within the divalent series because the reversal potentials measured in the series correlate well with the corresponding bulk diffusion potentials. Thus our study shows that, in contrast to the highly selective channels of neurophysiology that employ mostly the exclusion mechanism, quite different factors account for the selectivity of large channels. The elucidation of these factors is essential for understanding large channel selectivity and its regulation in vivo.

Overcharging below the nanoscale: multivalent cations reverse the ion selectivity of a biological channel

We report charge inversion within a nanoscopic biological protein ion channel in salts of multivalent ions. The presence of positive divalent and trivalent counterions reverses the cationic selectivity of the OmpF channel, a general diffusion porin located in the outer membrane of E. coli. We discuss the conditions under which charge inversion can be inferred from the change in sign of the measured quantity, the channel zero current potential. By comparing experimental results in protein channels whose charge has been modified after site-directed mutagenesis, the predictions of current theories of charge inversion are critically examined. It is emphasized that charge inversion does not necessarily increase with the bare surface charge density of the interface and that even this concept of surface charge density may become meaningless in some biological ion channels. Thus, any theory based on electrostatic correlations or chemical binding should explicitly take into account the particular structure of the charged interface.

Protein structure and ionic selectivity in calcium channels: selectivity filter size, not shape, matters

Calcium channels have highly charged selectivity filters (4 COO(-) groups) that attract cations in to balance this charge and minimize free energy, forcing the cations (Na(+) and Ca(2+)) to compete for space in the filter. A reduced model was developed to better understand the mechanism of ion selectivity in calcium channels. The charge/space competition (CSC) mechanism implies that Ca(2+) is more efficient in balancing the charge of the filter because it provides twice the charge as Na(+) while occupying the same space. The CSC mechanism further implies that the main determinant of Ca(2+) versus Na(+) selectivity is the density of charged particles in the selectivity filter, i.e., the volume of the filter (after fixing the number of charged groups in the filter). In this paper we test this hypothesis by changing filter length and/or radius (shape) of the cylindrical selectivity filter of our reduced model. We show that varying volume and shape together has substantially stronger effects than varying shape alone with volume fixed. Our simulations show the importance of depletion zones of ions in determining channel conductance calculated with the integrated Nernst-Planck equation. We show that confining the protein side chains with soft or hard walls does not influence selectivity.

Ions and inhibitors in the binding site of HIV protease: comparison of Monte Carlo simulations and the linearized Poisson-Boltzmann theory

Proteins can be influenced strongly by the electrolyte in which they are dissolved, and we wish to model, understand, and ultimately control such ionic effects. Relatively detailed Monte Carlo (MC) ion simulations are needed to capture biologically important properties of ion channels, but a simpler treatment of ions, the linearized Poisson-Boltzmann (LPB) theory, is often used to model processes such as binding and folding, even in settings where the LPB theory is expected to be inaccurate. This study uses MC simulations to assess the reliability of the LPB theory for such a system, the constrained, anionic active site of HIV protease. We study the distributions of ions in and around the active site, as well as the energetics of displacing ions when a protease inhibitor is inserted into the active site. The LPB theory substantially underestimates the density of counterions in the active site when divalent cations are present. It also underestimates the energy cost of displacing these counterions, but the error is not consequential because the energy cost is less than kBT, according to the MC calculations. Thus, the LPB approach will often be suitable for studying energetics, but the more detailed MC approach is critical when ionic distributions and fluxes are at issue.

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.

Mechanical compaction of smectite clays increases ion exchange selectivity for cesium

A key discussion in radioactive waste disposal is the question of whether adsorption behavior of radionuclides in dispersed and in highly compacted materials is similar. It is common practice to measure sorption data on dispersed systems and to use these data to predict the sorption in compacted systems. The latter represent the situation in a real, deep geological repository system. The discussions focus mainly on items such as the effect of compaction on the accessibility of sorption sites, that is, on sterical effects, and not on the effect of compaction on the thermodynamics of the sorption processes. Here we show that in the case of sorption of cesium on sodium bentonite, material compaction indeed affects the thermodynamics of the sorption process such that sorption increases. This increase is due to a reduction of the interlayer space, leading to a lower ability of the interlayer water for cation hydration. Cations with a low hydration tendency, such as cesium, therefore accumulate in the interlayer space, whereas highly hydrated cations such as sodium tends to accumulate in the bulk water where water is easily available for hydration. The fact that mechanical compaction affects the thermodynamics of ion exchange processes in clay is an important finding and brings in a new aspect in the discussion on the transferability of thermodynamic data from diluted to compacted systems. The common practice of applying chemical and thermodynamic concepts valid for diluted systems to compacted systems must be basically scrutinized.

Energetics of divalent selectivity in a calcium channel: the ryanodine receptor case study

A model of the ryanodine receptor (RyR) calcium channel is used to study the energetics of binding selectivity of Ca(2+) versus monovalent cations. RyR is a calcium-selective channel with a DDDD locus in the selectivity filter, similar to the EEEE locus of the L-type calcium channel. While the affinity of RyR for Ca(2+) is in the millimolar range (as opposed to the micromolar range of the L-type channel), the ease of single-channel measurements compared to L-type and its similar selectivity filter make RyR an excellent candidate for studying calcium selectivity. A Poisson-Nernst-Planck/density functional theory model of RyR is used to calculate the energetics of selectivity. Ca(2+) versus monovalent selectivity is driven by the charge/space competition mechanism in which selectivity arises from a balance of electrostatics and the excluded volume of ions in the crowded selectivity filter. While electrostatic terms dominate the selectivity, the much smaller excluded-volume term also plays a substantial role. In the D4899N and D4938N mutations of RyR that are analyzed, substantial changes in specific components of the chemical potential profiles are found far from the mutation site. These changes result in the significant reduction of Ca(2+) selectivity found in both theory and experiments.

Steric selectivity in Na channels arising from protein polarization and mobile side chains

Monte Carlo simulations of equilibrium selectivity of Na channels with a DEKA locus are performed over a range of radius R and protein dielectric coefficient epsilon(p). Selectivity arises from the balance of electrostatic forces and steric repulsion by excluded volume of ions and side chains of the channel protein in the highly concentrated and charged (approximately 30 M) selectivity filter resembling an ionic liquid. Ions and structural side chains are described as mobile charged hard spheres that assume positions of minimal free energy. Water is a dielectric continuum. Size selectivity (ratio of Na+ occupancy to K+ occupancy) and charge selectivity (Na+ to Ca2+) are computed in concentrations as low as 10(-5) M Ca2+. In general, small R reduces ion occupancy and favors Na+ over K+ because of steric repulsion. Small epsilon(p) increases occupancy and favors Na+ over Ca2+ because protein polarization amplifies the pore's net charge. Size selectivity depends on R and is independent of epsilon(p); charge selectivity depends on both R and epsilon(p). Thus, small R and epsilon(p) make an efficient Na channel that excludes K+ and Ca2+ while maximizing Na+ occupancy. Selectivity properties depend on interactions that cannot be described by qualitative or verbal models or by quantitative models with a fixed free energy landscape.

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.

The effect of protein dielectric coefficient on the ionic selectivity of a calcium channel

Calcium-selective ion channels are known to have carboxylate-rich selectivity filters, a common motif that is primarily responsible for their high Ca(2+) affinity. Different Ca(2+) affinities ranging from micromolar (the L-type Ca channel) to millimolar (the ryanodine receptor channel) are closely related to the different physiological functions of these channels. To understand the physical mechanism for this range of affinities given similar amino acids in their selectivity filters, we use grand canonical Monte Carlo simulations to assess the binding of monovalent and divalent ions in the selectivity filter of a model Ca channel. We use a reduced model where the electolyte is modeled by hard-sphere ions embedded in a continuum dielectric solvent, while the interior of protein surrounding the channel is allowed to have a dielectric coefficient different from that of the electrolyte. The induced charges that appear on the protein/lumen interface are calculated by the induced charge computation method [Boda et al., Phys. Rev. E 69, 046702 (2004)]. It is shown that decreasing the dielectric coefficient of the protein attracts more cations into the pore because the protein's carboxyl groups induce negative charges on the dielectric boundary. As the density of the hard-sphere ions increases in the filter, Ca(2+) is absorbed into the filter with higher probability than Na(+) because Ca(2+) provides twice the charge to neutralize the negative charge of the pore (both structural carboxylate oxygens and induced charges) than Na(+) while occupying about the same space (the charge/space competition mechanism). As a result, Ca(2+) affinity is improved an order of magnitude by decreasing the protein dielectric coefficient from 80 to 5. Our results indicate that adjusting the dielectric properties of the protein surrounding the permeation pathway is a possible way for evolution to regulate the Ca(2+) affinity of the common four-carboxylate motif.

Ion hydration in nanopores and the molecular basis of selectivity

Using a simple model, it is shown that the cost of constraining a hydrated potassium ion inside a narrow pore is smaller than the cost of constraining hydrated sodium or lithium ions in pores of radius around 1.5 A. The opposite is true for pores of radius around 2.5 A. The reason for the selectivity in the first region is that the potassium ion allows for a greater distortion of its hydration shell and can therefore maintain a better coordination, and the reason for the reverse selectivity in the second region is that the smaller ions retain their hydration shells in these pores. This is relevant to the molecular basis of ion selective channels, and since this mechanism does not depend on the molecular details of the pore, it could also operate in all sorts of nanotubes.

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.