Permeation properties of an engineered bacterial OmpF porin containing the EEEE-locus of Ca2+ channels

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.

The application of single molecule nanopore sensing for quantitative analysis

Nanopore-based sensors typically work by monitoring transient pulses in conductance via current-time traces as molecules translocate through the nanopore. The unique property of being able to monitor single molecules gives nanopore sensors the potential as quantitative sensors based on the counting of single molecules. This review provides an overview of the concepts and fabrication of nanopore sensors as well as nanopore sensing with a view toward using nanopore sensors for quantitative analysis. We first introduce the classification of nanopores and highlight their applications in molecular identification with some pioneering studies. The review then shifts focus to recent strategies to extend nanopore sensors to devices that can rapidly and accurately quantify the amount of an analyte of interest. Finally, future prospects are provided and briefly discussed. The aim of this review is to aid in understanding recent advances, challenges, and prospects for nanopore sensors for quantitative analysis.

Modeling the Device Behavior of Biological and Synthetic Nanopores with Reduced Models

Biological ion channels and synthetic nanopores are responsible for passive transport of ions through a membrane between two compartments. Modeling these ionic currents is especially amenable to reduced models because the device functions of these pores, the relation of input parameters (e.g., applied voltage, bath concentrations) and output parameters (e.g., current, rectification, selectivity), are well defined. Reduced models focus on the physics that produces the device functions (i.e., the physics of how inputs become outputs) rather than the atomic/molecular-scale physics inside the pore. Here, we propose four rules of thumb for constructing good reduced models of ion channels and nanopores. They are about (1) the importance of the axial concentration profiles, (2) the importance of the pore charges, (3) choosing the right explicit degrees of freedom, and (4) creating the proper response functions. We provide examples for how each rule of thumb helps in creating a reduced model of device behavior.

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.

Fosfomycin Permeation through the Outer Membrane Porin OmpF

Fosfomycin is a frequently prescribed drug in the treatment of acute urinary tract infections. It enters the bacterial cytoplasm and inhibits the biosynthesis of peptidoglycans by targeting the MurA enzyme. Despite extensive pharmacological studies and clinical use, the permeability of fosfomycin across the bacterial outer membrane is largely unexplored. Here, we investigate the fosfomycin permeability across the outer membrane of Gram-negative bacteria by electrophysiology experiments as well as by all-atom molecular dynamics simulations including free-energy and applied-field techniques. Notably, in an electrophysiological zero-current assay as well as in the molecular simulations, we found that fosfomycin can rapidly permeate the abundant Escherichia coli porin OmpF. Furthermore, two triple mutants in the constriction region of the porin have been investigated. The permeation rates through these mutants are slightly lower than that of the wild type but fosfomycin can still permeate. Altogether, this work unravels molecular details of fosfomycin permeation through the outer membrane porin OmpF of E. coli and moreover provides hints for understanding the translocation of phosphonic acid antibiotics through other outer membrane pores.

Extracellular and Intracellular Biomineralization Induced by Bacillus licheniformis DB1-9 at Different Mg/Ca Molar Ratios

Biomineralization has become a research hotspot and attracted widespread attention in the field of carbonate sedimentology. In this study, precipitation of carbonate minerals was induced by Bacillus licheniformis DB1-9 bacteria, (identity confirmed with its phylogenetic tree), to further explore the biomineralization mechanisms. During experiments, lasting up to 24 days with varying Mg/Ca molar ratios and regular monitoring of conditions, ammonia and carbonic anhydrase are released by the bacteria, resulting in a pH increase. Carbonic anhydrase could have promoted carbon dioxide hydration to produce bicarbonate and carbonate ions, and so promoted supersaturation to facilitate the precipitation of carbonate minerals. These include rhombohedral, dumbbell-shaped, and elongated calcite crystals; aragonite appears in the form of mineral aggregates. In addition, spheroidal and fusiform minerals are precipitated. FTIR results show there are organic functional groups, such as C–O–C and C=O, as well as the characteristic peaks of calcite and aragonite; these indicate that there is a close relationship between the bacteria and the minerals. Ultrathin slices of the bacteria analyzed by HRTEM, SAED, EDS, and STEM show that precipitate within the extracellular polymeric substances (EPS) has a poor crystal structure, and intracellular granular areas have no crystal structure. Fluorescence intensity and STEM results show that calcium ions can be transported from the outside to the inside of the cells. This study provides further insights to our understanding of biomineralization mechanisms induced by microorganisms.

Recent Progress in Micro/Nanoreactors toward the Creation of Artificial Organelles

Artificial organelles created from a bottom up approach are a new type of engineered materials, which are not designed to be living but, instead, to mimic some specific functions inside cells. By doing so, artificial organelles are expected to become a powerful tool in biomedicine. They can act as nanoreactors to convert a prodrug into a drug inside the cells or as carriers encapsulating therapeutic enzymes to replace malfunctioning organelles in pathological conditions. For the design of artificial organelles, several requirements need to be fulfilled: a compartmentalized structure that can encapsulate the synthetic machinery to perform an enzymatic function, as well as a means to allow for communication between the interior of the artificial organelle and the external environment, so that substrates and products can diffuse in and out the carrier allowing for continuous enzymatic reactions. The most recent and exciting advances in architectures that fulfill the aforementioned requirements are featured in this review. Artificial organelles are classified depending on their constituting materials, being lipid and polymer-based systems the most prominent ones. Finally, special emphasis will be put on the intracellular response of these newly emerging systems.

Outer membrane protein design

Membrane proteins are the gateway to the cell. These proteins are also a control center of the cell, as information from the outside is passed through membrane proteins as signals to the cellular machinery. The design of membrane proteins seeks to harness the power of these gateways and signal carriers. This review will focus on the design of the membrane proteins that are in the outer membrane, a membrane which only exists for gram negative bacteria, mitochondria, and chloroplasts. Unlike other membrane proteins, outer membrane proteins are uniquely shaped as β-barrels. Herein, I describe most known examples of membrane β-barrel design to date, focusing particularly on categorizing designs as: Firstly, structural deconstruction; secondly, structural changes; thirdly, chemical function design; and finally, the creation of new folds.

Stimuli-Triggered Activity of Nanoreactors by Biomimetic Engineering Polymer Membranes

The development of advanced stimuli-responsive systems for medicine, catalysis, or technology requires compartmentalized reaction spaces with triggered activity. Only very few stimuli-responsive systems preserve the compartment architecture, and none allows a triggered activity in situ. We present here a biomimetic strategy to molecular transmembrane transport by engineering synthetic membranes equipped with channel proteins so that they are stimuli-responsive. Nanoreactors with triggered activity were designed by simultaneously encapsulating an enzyme inside polymer compartments, and inserting protein "gates" in the membrane. The outer membrane protein F (OmpF) porin was chemically modified with a pH-responsive molecular cap to serve as "gate" producing pH-driven molecular flow through the membrane and control the in situ enzymatic activity. This strategy provides complex reaction spaces necessary in "smart" medicine and for biomimetic engineering of artificial cells.

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.

Structure-based engineering of a minimal porin reveals loop-independent channel closure

Porins, like outer membrane protein G (OmpG) of Escherichia coli, are ideal templates among ion channels for protein and chemical engineering because of their robustness and simple architecture. OmpG shows fast transitions between open and closed states, which were attributed to loop 6 (L6). As flickering limits single-channel-based applications, we pruned L6 by either 8 or 12 amino acids. While the open probabilities of both L6 variants resemble that of native OmpG, their gating frequencies were reduced by 63 and 81%, respectively. Using the 3.2 Å structure of the shorter L6 variant in the open state, we engineered a minimal porin (220 amino acids), where all remaining extramembranous loops were truncated. Unexpectedly, this minimized porin still exhibited gating, but it was 5-fold less frequent than in OmpG. The residual gating of the minimal pore is hence independent of L6 rearrangements and involves narrowing of the ion conductance pathway most probably driven by global stretching-flexing deformations of the membrane-embedded β-barrel.

Energetics of discrete selectivity bands and mutation-induced transitions in the calcium-sodium ion channels family

We use Brownian dynamics (BD) simulations to study the ionic conduction and valence selectivity of a generic electrostatic model of a biological ion channel as functions of the fixed charge Q(f) at its selectivity filter. We are thus able to reconcile the discrete calcium conduction bands recently revealed in our BD simulations, M0 (Q(f)=1e), M1 (3e), M2 (5e), with a set of sodium conduction bands L0 (0.5e), L1 (1.5e), thereby obtaining a completed pattern of conduction and selectivity bands vs Q(f) for the sodium-calcium channels family. An increase of Q(f) leads to an increase of calcium selectivity: L0 (sodium-selective, nonblocking channel) → M0 (nonselective channel) → L1 (sodium-selective channel with divalent block) → M1 (calcium-selective channel exhibiting the anomalous mole fraction effect). We create a consistent identification scheme where the L0 band is putatively identified with the eukaryotic sodium channel The scheme created is able to account for the experimentally observed mutation-induced transformations between nonselective channels, sodium-selective channels, and calcium-selective channels, which we interpret as transitions between different rows of the identification table. By considering the potential energy changes during permeation, we show explicitly that the multi-ion conduction bands of calcium and sodium channels arise as the result of resonant barrierless conduction. The pattern of periodic conduction bands is explained on the basis of sequential neutralization taking account of self-energy, as Q(f)(z,i)=ze(1/2+i), where i is the order of the band and z is the valence of the ion. Our results confirm the crucial influence of electrostatic interactions on conduction and on the Ca(2+)/Na(+) valence selectivity of calcium and sodium ion channels. The model and results could be also applicable to biomimetic nanopores with charged walls.

Optimization of 3D Poisson-Nernst-Planck model for fast evaluation of diverse protein channels

We show the accuracy and applicability of our fast algorithmic implementation of a three-dimensional Poisson-Nernst-Planck (3D-PNP) flow model for characterizing different protein channels. Due to its high computational efficiency, our model can predict the full current-voltage characteristics of a channel within minutes, based on the experimental 3D structure of the channel or its computational model structure. Compared with other methods, such as Brownian dynamics, which currently needs a few weeks of the computational time, or even much more demanding molecular dynamics modeling, 3D-PNP is the only available method for a function-based evaluation of very numerous tentative structural channel models. Flow model tests of our algorithm and its optimal parametrization are provided for five native channels whose experimental structures are available in the protein data bank (PDB) in an open conductive state, and whose experimental current-voltage characteristics have been published. The channels represent very different geometric and structural properties, which makes it the widest test to date of the accuracy of 3D-PNP on real channels. We test whether the channel conductance, rectification, and charge selectivity obtained from the flow model, could be sufficiently sensitive to single-point mutations, related to unsignificant changes in the channel structure. Our results show that the classical 3D-PNP model, under proper parametrization, is able to achieve a qualitative agreement with experimental data for a majority of the tested characteristics and channels, including channels with narrow and irregular conductivity pores. We propose that although the standard PNP model cannot provide insight into complex physical phenomena due to its intrinsic limitations, its semiquantitative agreement is achievable for rectification and selectivity at a level sufficient for the bioinformatical purpose of selecting the best structural models with a great advantage of a very short computational time.

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.

Identification of a cation transport pathway in Neisseria meningitidis PorB

Neisseria meningitidis is the main causative agent of bacterial meningitis. In its outer membrane, the trimeric Neisserial porin PorB is responsible for the diffusive transport of essential hydrophilic solutes across the bilayer. Previous molecular dynamics simulations based on the recent crystal structure of PorB have suggested the presence of distinct solute translocation pathways through this channel. Although PorB has been electrophysiologically characterized as anion-selective, cation translocation through nucleotide-bound PorB during pathogenesis is thought to be instrumental for host cell death. As a result, we were particularly interested in further characterizing cation transport through the pore. We combined a structural approach with additional computational analysis. Here, we present two crystal structures of PorB at 2.1 and 2.65 Å resolution. The new structures display additional electron densities around the protruding loop 3 (L3) inside the pore. We show that these electron densities can be identified as monovalent cations, in our case Cs(+), which are tightly bound to the inner channel. Molecular dynamics simulations reveal further ion interactions and the free energy landscape for ions inside PorB. Our results suggest that the crystallographically identified locations of Cs(+) form a cation transport pathway inside the pore. This finding suggests how positively charged ions are translocated through PorB when the channel is inserted into mitochondrial membranes during Neisserial infection, a process which is considered to dissipate the mitochondrial transmembrane potential gradient and thereby induce apoptosis.

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.

Divalent base cations hamper Hg(II) uptake

Despite the alarming trends of declining base cation concentrations in boreal lakes, no studies have attempted to predict the consequences of this decline on the geochemical cycle of mercury, a top priority contaminant worldwide. In this study, we used a whole-cell gram-negative bioreporter to evaluate the direction and magnitude of changes in net accumulation of Hg(II) by bacteria in response to changing base cation concentrations. We show that regardless of the speciation of Hg(II) in solution, increasing divalent base cation concentrations decrease net Hg(II) accumulation by the bioreporter, suggesting a protective effect of these cations. Our work suggests that the complexity of the cell wall of gram-negative bacteria must be considered when modeling Hg uptake pathways; we propose that base divalent cations contribute to hamper net Hg(II) accumulation by decreasing outer membrane permeability and, therefore, the passive diffusion of Hg(II) species to the periplasmic space. This work points to an unsuspected and likely harmful consequence of a delay in recovering from acidification in boreal lakes, in that uptake of Hg(II) by bacteria is not only enhanced by the reduced pH but can also be enhanced by a decline in base cation levels.

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.

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.

Computational studies of membrane proteins: models and predictions for biological understanding

We discuss recent progresses in computational studies of membrane proteins based on physical models with parameters derived from bioinformatics analysis. We describe computational identification of membrane proteins and prediction of their topology from sequence, discovery of sequence and spatial motifs, and implications of these discoveries. The detection of evolutionary signal for understanding the substitution pattern of residues in the TM segments and for sequence alignment is also discussed. We further discuss empirical potential functions for energetics of inserting residues in the TM domain, for interactions between TM helices or strands, and their applications in predicting lipid-facing surfaces of the TM domain. Recent progresses in structure predictions of membrane proteins are also reviewed, with further discussions on calculation of ensemble properties such as melting temperature based on simplified state space model. Additional topics include prediction of oligomerization state of membrane proteins, identification of the interfaces for protein-protein interactions, and design of membrane proteins. This article is part of a Special Issue entitled: Protein Folding in Membranes.

Selectivity sequences in a model calcium channel: role of electrostatic field strength

The energetics that give rise to selectivity sequences of ionic binding selectivity of Li(+), Na(+), K(+), Rb(+), and Cs(+) in a model of a calcium channel are considered. This work generalizes Eisenman's classic treatment (Biophys J 2(Suppl. 2):259, 1962) by including multiple, mobile binding site oxygens that coordinate many permeating ions (all modeled as charged, hard spheres). The selectivity filter of the model calcium channel allows the carboxyl terminal groups of glutamate and aspartate side chains to directly interact with and coordinate the permeating ions. Ion dehydration effects are represented with a Born energy between the dielectric coefficients of the selectivity filter and the bath. High oxygen concentration creates a high field strength site that prefers small ions, as in Eisenman's model. On the other hand, a low filter dielectric constant also creates a high field strength site, but this site prefers large ions, contrary to Eisenman's model. These results indicate that field strength does not have a unique effect on ionic binding selectivity sequences once entropic, electrostatic, and dehydration forces are included in the model. Thus, Eisenman's classic relationship between field strength and selectivity sequences must be supplemented with additional information about selectivity filters such as the calcium channel that has amino acid side chains mixing with ions to make a crowded permeation pathway.

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.

Crowding effects in non-equilibrium transport through nano-channels

Transport through nano-channels plays an important role in many biological processes and industrial applications. Gaining insights into the functioning of biological transport processes and the design of man-made nano-devices requires an understanding of the basic physics of such transport. A simple exclusion process has proven to be very useful in explaining the properties of several artificial and biological nano-channels. It is particularly useful for modeling the influence of inter-particle interactions on transport characteristics. In this paper, we explore several models of the exclusion process using a mean field approach and computer simulations. We examine the effects of crowding inside the channel and in its immediate vicinity on the mean flux and the transport times of single molecules. Finally, we discuss the robustness of the theory's predictions with respect to the crucial characteristics of the hindered diffusion in nano-channels that need to be included in the model.

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.

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.

Sieving experiments and pore diameter: it's not a simple relationship

The classic sieving experiment for estimating an ion channel's diameter with successively larger ions is re-examined. Using a very reduced model of a calcium channel, it is shown that sieving experiments measure a combination of three mechanisms: the cross-sectional area available to the sieving ions (the classic interpretation), the exclusion of the sieving ions from a pore crowded with amino acid side chains that protrude into the permeation pathway, and competitive selectivity of the sieving ions with other ions in the bath (even if those are present only at trace concentrations). The latter two can be called sieving-by-crowding because they stem from the excluded volume of the amino acids in the permeation pathway. The model shows that--to a first--order approximation-sieving experiments measure the available volume inside a selectivity filter, rather than the available cross-sectional area. The two are only the same if the narrow part of the pore does not have flexible amino acid side chains interacting directly with the permeant ions; this may be true of potassium channels, but not calcium, sodium, and other channels with "crowded" selectivity filters.

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.

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.

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.

The anomalous mole fraction effect in calcium channels: a measure of preferential selectivity

The cause of the anomalous mole fraction effect (AMFE) in calcium-selective ion channels is studied. An AMFE occurs when the conductance through a channel is lower in a mixture of salts than in the pure salts at the same concentration. The textbook interpretation of the AMFE is that multiple ions move through the pore in coordinated, single-file motion. Instead of this, we find that at its most basic level an AMFE reflects a channel's preferential binding selectivity for one ion species over another. The AMFE is explained by considering the charged and uncharged regions of the pore as electrical resistors in series: the AMFE is produced by these regions of high and low ion concentration changing differently with mole fraction due to the preferential ion selectivity. This is demonstrated with simulations of a model L-type calcium channel and a mathematical analysis of a simplistic point-charge model. The particle simulations reproduce the experimental data of two L-type channel AMFEs. Conditions under which an AMFE may be found experimentally are discussed. The resistors-in-series model provides a fundamentally different explanation of the AMFE than the traditional theory and does not require single filing, multiple occupancy, or momentum-correlated ion motion.

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.