Effect of pore structure on energy barriers and applied voltage profiles. I. Symmetrical channels.

This paper presents calculations of the image potential for an ion in an aqueous pore spanning a lipid membrane and for the electric field produced in such a pore when a transmembrane potential is applied. The pore diameter may be variable. As long as the length-to-radius ratio in the narrow portion of a channel is large enough, the image potential for an ion in or near the mouth of a channel is determined by the geometry of the mouth. Within the constriction, the image potential of the ion-pore system may be reasonably approximated by constructing an "equivalent pore" of uniform diameter spanning a somewhat thinner membrane. When a transmembrane potential is applied the electric field within a constricted, constant radius, section of the model pore is constant. If the length-to-radius ratio of the narrow part of the channel is not too large or the channel ensemble has wide mouths, the field extends a significant distance into the aqueous region. The method is used to model features of the gramicidin A channel. The energy barrier for hydration (for exiting the channel) is identified with the activation energy for gramicidin conductance (Bamberg and Läuger, 1974, Biochim. Biophys. Acta. 367:127).     

Electrostatic modeling of ion pores. Energy barriers and electric field profiles

This paper presents calculations of the image potential for an ion in an aqueous pore through lipid membrane and the electric field produced in such a pore when a transmembrane potential is applied. The method used is one introduced by Levitt (1978, Biophys. J. 22:209), who solved an equivalent problem, in which a surface charge density is placed at the dielectric boundary. It is shown that there are singularities in this surface charge density if the model system has sharp corners. Numerically accurate calculations require exact treatment of these singularities. The major result of this paper is the development of a projection method that explicitly accounts for this behavior. It is shown how this technique can be used to compute, both reliably and efficiently, the electrical potential within a model pore in response to any electrical source. As the length of a channel with fixed radius is increased, the peak in the image potential approaches that of an infinitely long channel more rapidly than previously believed. When a transmembrane potential is applied the electric field within a pore is constant over most of its length. Unless the channel is much longer than its radius, the field extends well into the aqueous domain. For sufficiently dissimilar dielectrics the calculated values for the peak in the image potential and for the field well within the pore can be summarized by simple empirical expressions that are accurate to within 5%.     

Effective pore radius of the gramicidin channel. Electrostatic energies of ions calculated by a three-dielectric model.

Electrostatic calculation of the gramicidin channel is performed on the basis of a three-dielectric model in which the peptide backbone of the channel is added as a third dielectric region to the conventional two-dielectric channel model (whose pore radius is often referred to as the effective pore radius reff). A basic principle for calculating electrostatic fields in three-dielectric models is introduced. It is shown that the gramicidin channel has no unique value of reff. The reff with respect to the "self-image energy" (i.e., the image energy in the presence of a single ion) is 2.6-2.7 A, slightly depending upon the position of the ion (the least-square value over the whole length of the pore is 2.6 A). In contrast, the reff with respect to the electric potential due to an ion (and hence the reff with respect to the interaction energy between two ions) is dependent upon the distance s of separation; it ranges from 2.6 to greater than 5 A, increasing with an increase in s. However, for the purpose of rough estimation, the reff with respect to the self-image energy can also be used in calculating the electric potential and the interaction energy, because the error introduced by this approximation is an overestimation of the order of 30% at most. It is also shown that the apparent dielectric constant for the interaction between two charges depends markedly upon the positions of the charges. In the course of this study, the dielectric constant and polarizability of the peptide backbone in the beta-sheet structure is estimated to be 10 and 8.22 A3.     

Electrostatic modeling of ion pores. II. Effects attributable to the membrane dipole potential.

This paper presents calculations of the shielded dipole potential in the interior of a pore piercing a lipid membrane that is at a potential V0 with respect to the aqueous solution. Except in the case of long narrow pores, there is substantial shielding of the membrane dipole potential. The associated dipole field never extends a significant distance into the aqueous region. The fact that the single-channel conductance of gramicidin B is only twice as large in glyceryl monooleate membranes as in phosphatidyl choline (PC) membranes, even though PC is approximately 120 mV more positive with respect to water, is interpreted in terms of the potential energy profile calculated for a gramicidin-like channel. It is demonstrated that the membrane dipole potential can significantly affect channel conductance only if the pore is narrow and if the peak in the potential energy profile occurs in the pore interior.     

Gating processes of channels induced by colicin A,its C-terminal fragment and colicin E1 in planar lipid bilayers

The dependence on pH and membrane potential of the pore formed by colicin A and its C-terminal 20 kDa fragment has been measured using planar lipid bilayers. The single channel conductance of the pore formed by both colicin A and the fragment increases with pH with an apparent pK of 6.0. At pH 5.0 the gating by membrane potential of the channels formed by either colicin A or its fragment is identical. At the same pH, quite similar pore properties were found when using the related bacteriocin, colicin E₁. In agreement with previous studies, these data indicate that the protein structure containing the lumen of the pore resides in the 20 kDa C-terminal part of the colicin A and favours the recently proposed model, based on protein sequence analysis, which proposes that colicin A, E₁ and I_B C-terminal domains are folded in the same three-dimensional structure. However, it is also shown that colicin A and not its C-terminal fragment undergoes a pH dependent transition between an acidic and a basic form of the pore with an apparent pK of 5.3. The two forms of the pore differ by their gating charge but not by the channel size. These results suggest that there is a pH dependent association between the C-terminal domain carrying the lumen of the pore and another domain of the molecule which affect the pore sensitivity to membrane potential.     

Ion effects on gating of the Ca(2+)-activated K+ channel correlate with occupancy of the pore.

We studied the effects of permeant ions on the gating of the large conductance Ca(2+)-activated K+ channel from rat skeletal muscle. Rb+ blockade of inward K+ current caused an increase in the open probability as though Rb+ occupancy of the pore interferes with channel closing. In support of this hypothesis, we directly measured the occupancy of the pore by the impermeant ion Cs+ and found that it strongly correlates with its effect on gating. This is consistent with the "foot-in-the-door" model of gating, which states that channels cannot close with an ion in the pore. However, because Rb+ and Cs+ not only slow the closing rate (as predicted by the model), but also speed the opening rate, our results are more consistent with a modified version of the model in which the channel can indeed close while occupied, but the occupancy destabilizes the closed state. Increasing the occupancy of the pore by the addition of other permeant (K+ and Tl+) and impermeant (tetraethylammonium) ions did not affect the open probability. To account for this disparity, we used a two-site permeation model in which only one of the sites influenced gating. Occupancy of this "gating site" interferes with channel closing and hastens opening. Ions that directly or indirectly increase the occupancy of this site will increase the open probability.     

Atomic scale structure and functional models of voltage-gated potassium channels.

Recent mutagenesis experiments have confirmed our hypothesis that a segment between S5 and S6 forms the ion selective portion of voltage-gated ion channels. Based on these and other new data, we have revised previous models of the general folding pattern of voltage-gated channel proteins and have developed atomic scale models of the entire transmembrane region of the Shaker A K+ channel. In these models, the ion selective region is a beta-barrel that spans the outer half of the membrane. The inner half of the pore is larger. The voltage-dependent conformational changes of activation gating are modeled to occur by the "helical screw" mechanism, in which the four S4 segments move along and rotate about their axes. These changes are followed by a voltage-independent conformational change, in which the segments linking S4 to S5 move from blocking the intracellular entrance of the pore to forming part of the lining of the large inner portion of the pore. The NH2-terminal of the protein was modeled as an alpha-helix that plugs the intracellular half of the pore to inactivate the channel.     

Simplified bacterial "pore" channel provides insight into the assembly, stability, and structure of sodium channels

Eukaryotic sodium channels are important membrane proteins involved in ion permeation, homeostasis, and electrical signaling. They are long, multidomain proteins that do not express well in heterologous systems, and hence, structure/function and biochemical studies on purified sodium channel proteins have been limited. Bacteria produce smaller, homologous tetrameric single domain channels specific for the conductance of sodium ions. They consist of N-terminal voltage sensor and C-terminal pore subdomains. We designed a functional pore-only channel consisting of the final two transmembrane helices, the intervening P-region, and the C-terminal extramembranous region of the sodium channel from the marine bacterium Silicibacter pomeroyi. This sodium "pore" channel forms a tetrameric, folded structure that is capable of supporting sodium flux in phospholipid vesicles. The pore-only channel is more thermally stable than its full-length counterpart, suggesting that the voltage sensor subdomain may destabilize the full-length channel. The pore subdomains can assemble, fold, and function independently from the voltage sensor and exhibit similar ligand-blocking characteristics as the intact channel. The availability of this simple pore-only construct should enable high-level expression for the testing of potential new ligands and enhance our understanding of the structural features that govern sodium selectivity and permeability.     

Three-dimensional models of non-NMDA glutamate receptors.

Structural models have been produced for three types of non-NMDA inotropic glutamate receptors: an AMPA receptor, GluR1, a kainate receptor, GluR6; and a low-molecular-weight kainate receptor from goldfish, GFKAR alpha. Modeling was restricted to the domains of the proteins that bind the neurotransmitter glutamate and that form the ion channel. Model building combined homology modeling, distance geometry, molecular mechanics, interactive modeling, and known constraints. The models indicate new potential interactions in the extracellular domain between protein and agonists, and suggest that the transition from the "closed" to the "open" state involves the movement of a conserved positive residue away from, and two conserved negative residues into, the extracellular entrance to the pore upon binding. As a first approximation, the ion channel domain was modeled with a structure comprising a central antiparallel beta-barrel that partially crosses the membrane, and against which alpha-helices from each subunit are packed; a third alpha-helix packs against these two helices in each subunit. Much, but not all, of the available data were consistent with this structure. Modifying the beta-barrel to a loop-like topology produced a model consistent with available data.     

Charges, currents, and potentials in ionic channels of one conformation.

Flux through an open ionic channel is analyzed with Poisson-Nernst-Planck (PNP) theory. The channel protein is described as an unchanging but nonuniform distribution of permanent charge, the charge distribution observed (in principle) in x-ray diffraction. Appropriate boundary conditions are derived and presented in some generality. Three kinds of charge are present: (a) permanent charge on the atoms of the protein, the charge independent of the electric field; (b) free or mobile charge, carried by ions in the pore as they flux through the channel; and (c) induced (sometimes called polarization) charge, in the pore and protein, created by the electric field, zero when the electric field is zero. The permanent charge produces an offset in potential, a built-in Donnan potential at both ends of the channel pore. The system is completely solved for bathing solutions of two ions. Graphs describe the distribution of potential, concentration, free (i.e., mobile) and induced charge, and the potential energy associated with the concentration of charge, as well as the unidirectional flux as a function of concentration of ions in the bath, for a distribution of permanent charge that is uniform. The model shows surprising complexity, exhibiting some (but not all) of the properties usually attributed to single filing and exchange diffusion. The complexity arises because the arrangement of free and induced charge, and thus of potential and potential energy, varies, sometimes substantially, as conditions change, even though the channel structure and conformation (of permanent charge) is strictly constant. Energy barriers and wells, and the concomitant binding sites and binding phenomena, are outputs of the PNP theory: they are computed, not assumed. They vary in size and location as experimental conditions change, while the conformation of permanent charge remains constant, thus giving the model much of its interesting behavior.     

The Outer Pore and Selectivity Filter of TRPA1

TRPA1 (transient-receptor-potential-related ion channel with ankyrin domains) is a direct receptor or indirect effector for a wide variety of nociceptive signals, and thus is a compelling target for development of analgesic pharmaceuticals such as channel blockers. Recently, the structure of TRPA1 was reported, providing insights into channel assembly and pore architecture. Here we report whole-cell and single-channel current recordings of wild-type human TRPA1 as well as TRPA1 bearing point mutations of key charged residues in the outer pore. These measurements demonstrate that the glutamate at position 920 plays an important role in collecting cations into the mouth of the pore, by changing the effective surface potential by ~16 mV, while acidic residues further out have little effect on permeation. Electrophysiology experiments also confirm that the aspartate residue at position 915 represents a constriction site of the TRPA1 pore and is critical in controlling ion permeation.     

Ion-channel entrances influence permeation. Net charge, size, shape, and binding considerations.

Many ion channels have wide entrances that serve as transition zones to the more selective narrow region of the pore. Here some physical features of these vestibules are explored. They are considered to have a defined size, funnel shape, and net-negative charge. Ion size, ionic screening of the negatively charged residues, cation binding, and blockage of current are analyzed to determine how the vestibules influence transport. These properties are coupled to an Eyring rate theory model for the narrow length of the pore. The results include the following: Wide vestibules allow the pore to have a short narrow region. Therefore, ions encounter a shorter length of restricted diffusion, and the channel conductance can be greater. The potential produced by the net-negative charge in the vestibules attracts cations into the pore. Since this potential varies with electrolyte concentration, the conductance measured at low electrolyte concentrations is larger than expected from measurements at high concentrations. Net charge inside the vestibules creates a local potential that confers some cation vs. anion, and divalent vs. monovalent selectivity. Large cations are less effective at screening (diminishing) the net-charge potential because they cannot enter the pore as well as small cations. Therefore, at an equivalent bulk concentration the attractive negative potential is larger, which causes large cations to saturate sites in the pore at lower concentrations. Small amounts of large or divalent cations can lead to misinterpretation of the permeation properties of a small monovalent cation.     

CFTR: what's it like inside the pore?

The Cystic Fibrosis Conductance Regulator (CFTR) functions as a cAMP-activated, anion-selective channel, but the structural basis for anion permeation is not well understood. Here we summarize recent studies aimed at understanding how anions move through the CFTR channel, and the nature of the environment anions experience inside the pore. From these studies it is apparent that anion permeability selectivity and anion binding selectivity of the pore are consistent with a model based on a "dielectric tunnel." The selectivity pattern for halides and pseudohalides can be predicted if it is assumed that permeant anions partition between bulk water and a polarizable space that is characterized by an effective dielectric constant of about 19. Covalent labeling of engineered cysteines and pH titration of engineered cysteines and histidines lead to the conclusion that the CFTR anion conduction path includes a positively charged outer vestibule. A residue in transmembrane segment 6 (TM6) (R334) appears to reside in the outer vestibule of the CFTR pore where it creates a positive electrostatic potential that enhances anion conduction.     

State-dependent changes in the electrostatic potential in the pore of a GluR channel

The M2 loop and the M3 segment are the major pore-lining domains in the GluR channel. These domains determine ion permeation and channel block processes and are extensively involved in gating. To study the distribution of the membrane electric potential across the GluR channel pore, we recorded from alpha-amino-3-hydroxy-5-methylisoxazole-4-proprionic acid receptors containing M2 and M3 cysteine substitutions in the GluR-A subunit and measured the voltage dependence of the modification rate of these substituted cysteines by methanethiosulfonate reagents either in the presence or absence of glutamate. In the presence of glutamate, the voltage dependence became gradually stronger for positions located deeper in the pore suggesting that the electrostatic potential drops fairly uniformly across the pore in the open state. In contrast, in the absence of glutamate, the voltage dependence was biphasic. The difference in the electrostatic potential in the presence and absence of glutamate had an apparent maximum in the middle of the extracellular vestibule. We suggest that these state-dependent changes in the membrane electric potential reflect a reorientation of the dipoles of the M2 loop alpha-helices toward and away from the center of the channel pore during gating.     

The inactivation gate of the Shaker K+ channel behaves like an open-channel blocker.

Following voltage-dependent activation, Drosophila Shaker K+ channels enter a nonconducting, inactivated state. This process has been proposed to occur by a "ball-and-chain" mechanism, in which the N-terminus of the protein behaves like a blocker tethered to the cytoplasmic side of the channel and directly occludes the pore to cause inactivation. To complement the ample evidence for the involvement of the N-terminus, we sought evidence that it blocks the pore directly. We found that inactivation exhibits several distinctive properties of pore blockade. First, recovery was speeded by increased external K+ concentrations, just as blockade can be relieved by trans-permeant ions. Second, single-channel experiments show that the channel reopens from the inactivated state upon repolarization. These openings were usually required for recovery, as though the blocking particle must exit the pore before the channel can close.     

A novel type of internal barium block of a maxi-K+ channel from human vas deferens epithelial cells.

We have recently shown that a maxi-K+ channel from vas deferens epithelial cells contains two Ba2+-binding sites accessible from the external side: a "flickering" site located deep in the channel pore and a "slow" site located close to the extracellular mouth of the channel. Using the patch-clamp technique, we have now studied the effect of internal Ba2+ on this channel. Cytoplasmic Ba2+ produced a voltage- and concentration-dependent "slow" type of block with a dissociation constant of approximately 100 microM. However, based on its voltage dependence and sensitivity to K+ concentration, this block was clearly different from the external "slow" Ba2+ block previously described. Kinetic analysis also revealed a novel "fast flickering" block restricted to channel bursts, with an unblocking rate of approximately 310 s(-1), some 10-fold faster than the external "flickering" block. Taken together, these results show that this channel contains multiple Ba2+-binding sites within the conduction pore. We have incorporated this information into a new model of Ba2+ block, a novel feature of which is that internal "slow" block results from the binding of at least two Ba2+ ions. Our results suggest that current models for Ba2+ block of maxi-K+ channels need to be revised.     

How electrolyte shielding influences the electrical potential in transmembrane ion channels.

The electrical potential due to fixed charge distributions is strongly altered in the vicinity of a membrane and notably dependent on aqueous electrolyte concentration. We present an efficient way to solve the nonlinear Poisson-Boltzmann equation applicable to general cylindrically symmetric dielectric geometries. It generalizes Gouy-Chapman theory to systems containing transmembrane channels. The method is applied to three channel systems: gramicidin, gap junction, and porin. We find that for a long, narrow channel such as gramicidin concentration variation has little influence on the electrical image barrier to ion permeation. However, electrolyte shielding reduces the image induced contribution to the energy required for multiple occupancy. In addition, the presence of electrolyte significantly affects the voltage profile due to an applied potential, substantially compressing the electric field to the immediate vicinity of the pore itself. In the large diameter channels, where bulk electrolyte may be assumed to enter the pore, the electrolyte greatly reduces the image barrier to ion permeation. At physiological ionic strengths this barrier is negligible and the channel may be readily multiply occupied. At all ionic strengths considered (l greater than 0.005 M) the image barrier saturates rapidly and is essentially constant more than one channel radius from the entrance to the pore. At lower ionic strengths (l less than 0.016 M) there are noticeable (greater than 20 mV) energy penalties associated with multiple occupancy.     

Histidines 13 and 14 in the Abeta sequence are targets for inhibition of Alzheimer's disease Abeta ion channel and cytotoxicity

The fact that Alzheimer's beta amyloid (Abeta) peptides forms cation channels in lipid bilayers was discovered during the course of our experiments in the laboratory of "Guayo" Rojas at NIH in Bethesda, Maryland (USA). Recently, we found that the Abeta ion channel could be blocked selectively with small peptides that copy the amino acid sequence of the predicted mouth region of the Abeta channel pore. We now have searched for the essential amino acid residues required for this blocking effect by mutations. We found that the ability of peptides to block Abeta channel activity could be lost by replacement of histidines 13 and 14 by alanine or lysine. The amino acid substitution also resulted in the loss of the capacity of the peptides to protect cells from Abeta cytotoxicity. These data thus contribute to the definition of the region of the Abeta sequence that participates in the formation of the channel pore. Additionally, these data support the hypothesis that the ion channel activity of Ab contributes significantly to the cytotoxic properties of Abeta. These data also emphasize the potential value in using inhibition of Abeta ion channel activity as an end point for Alzheimer's disease drug discovery.     

Probing distance and electrical potential within a protein pore with tethered DNA

DNA molecules tethered inside a protein pore can be used as a tool to probe distance and electrical potential. The approach and its limitations were tested with alpha-hemolysin, a pore of known structure. A single oligonucleotide was attached to an engineered cysteine to allow the binding of complementary DNA strands inside the wide internal cavity of the extramembranous domain of the pore. The reversible binding of individual oligonucleotides produced transient current blockades in single channel current recordings. To probe the internal structure of the pore, oligonucleotides with 5' overhangs of deoxyadenosines and deoxythymidines up to nine bases in length were used. The characteristics of the blockades produced by the oligonucleotides indicated that single-stranded overhangs of increasing length first approach and then thread into the transmembrane beta-barrel. The distance from the point at which the DNA was attached and the internal entrance to the barrel is 43 A, consistent with the lengths of the DNA probes and the signals produced by them. In addition, the tethered DNAs were used to probe the electrical potential within the protein pore. Binding events of oligonucleotides with an overhang of five bases or more, which threaded into the beta-barrel, exhibited shorter residence times at higher applied potentials. This finding is consistent with the idea that the main potential drop is across the alpha-hemolysin transmembrane beta-barrel, rather than the entire length of the lumen of the pore. It therefore explains why the kinetics and thermodynamics of formation of short duplexes within the extramembranous cavity of the pore are similar to those measured in solution, and bolsters the idea that a "DNA nanopore" provides a useful means for examining duplex formation at the single molecule level.