The Behaviour of Ions in Narrow Water-Filled Pores

Today, the equilibrium behavior of ions in solution may be predicted with some confidence, essentially because rapid ionic diffusion over small distances ensures homogeneity throughout the solution. Equilibrium concepts such as ionic strength and pH apply. However, when attempting to understand the behavior of ions passing rapidly through narrow pores such as ion channels, no such equilibrium state may be assumed. The passing solution may have been in equilibrium with conditions at the mouth of the pore but will not be in equilibrium with charged molecules on the pore wall. In addition, the water in narrow pores will be partially ordered by contact with the pore walls and will not behave like bulk water.To illustrate this difference, a simple equilibrium calculation of the ion concentrations near a plastic sheet penetrated by narrow pores and containing in its surface partially ionized carboxyl groups is shown to be in good agreement with experiment. However, to predict the non-equilibrium behavior within the narrow pores is much more difficult. To illustrate the difficulty, a Monte Carlo computer model is described which attempts to predict the rapid switching of ion current observed experimentally with these narrow pores.     

The proton ladder,a static mechanism for ion/proton coports and counterports

An ion/proton counterport is formed simply by locating a chain of ionizable residues connected by a proton conducting path near a passive ion pore which spans the membrane. The electric coupling between the ion in transit through the pore and the residues can ensure that for each ion passing through the pore in one direction a proton is driven along the chain of ionizable residues (the proton ladder) in the same or in the opposite direction. The mechanism is symmetrical in that a trans-membrane ion gradient may drive protons against their electrochemical potential gradient or a proton gradient may drive ions against theirs. The mechanism is applicable to cation or anion channels and to coports or counterports. No mechanical motion is required other than the motion of the ions and the protons. Monte Carlo computer simulations are performed on the model and its predicted properties are listed. The new type of counterport model is compared with currently used models. Offprint requests to: D. T Edmonds     

Ion transport in the simplest single file pore

A kinetic scheme is developed to describe single-file transport through pores containing up to two ions which may be of different species. The solution for the fluxes in terms of rate constants for entry, exit, and transfer is derived without specific assumptions about symmetry or the voltage and activity dependence of the constants. For a symmetrical pore the relation between the slope conductance at zero applied potential and ion activity can have two distinct regions in which the conductance increases linearly. Zero current or reversal potentials depend on the absolute values of the activities as well as their ratios. The use of this theory to describe the cation fluxes through the pores formed by gramicidin A will be considered in a subsequent paper. Here the model is discussed for a number of more specific assumptions, most extensively the following combination: (1) while entry to a pore is less likely when the pore is already occupied at the opposite end, this entry is still rapid; (2) exit is much more rapid when the pore is occupied by two ions; and (3) transfer from one end to the other of a singly occupied pore is rapid. With these assumptions and for a range of concentrations over which the fluxes are proportional to ion activities, the model predicts a flux ratio exponent nearly equal to 2, blocking by impermeant ions, rectification due to blocking particles on one side only, relief of block by increase in the permeant ion concentration on the opposite side, and anomalous variations of the conductance and zero current potential with mole ratio when the total concentration of the two permeants is held constant.     

Improved 3D continuum calculations of ion flux through membrane channels

A continuum model, based on the Poisson–Nernst–Planck (PNP) theory, is applied to simulate steady-state ion flux through protein channels. The PNP equations are modified to explicitly account (1) for the desolvation of mobile ions in the membrane pore and (2) for effects related to ion sizes. The proposed algorithm for a three-dimensional self-consistent solution of PNP equations, in which final results are refined by a focusing technique, is shown to be suitable for arbitrary channel geometry and arbitrary protein charge distribution. The role of the pore shape and protein charge distribution in formation of basic electrodiffusion properties, such as channel conductivity and selectivity, as well as concentration distributions of mobile ions in the pore region, are illustrated by simulations on model channels. The influence of the ionic strength in the bulk solution and of the externally applied electric field on channel properties are also discussed.     

Brownian dynamics study of flux ratios in sodium channels

Measurements of unidirectional fluxes in ion channels provide one of the experimental methods for studying the steps involved in ion permeation in biological pores. Conventionally, the number of ions in the pore is inferred by fitting the ratio of inward and outward currents to an exponential function with an adjustable parameter known as the flux ratio exponent. Here we investigate the relationship between the number of ions in the pore and the flux ratio exponent in a model sodium channel under a range of conditions. Brownian dynamics simulations enable us to count the precise number of ions in the channel and at the same time measure the currents flowing across the pore in both directions. We show here that the values of the flux ratio exponent n′ ranges between 1 and 3 and is highly dependent on the ionic concentrations in which measurements are made. This is a consequence of the fact that both inward and outward currents are susceptible to saturation with increasing concentration. These results indicate that measurements of the flux ratio exponent cannot be directly related to the number of ions in the pore and that interpretation of such experimental measurements requires careful consideration of the conditions in which the study is made.     

Ion leakage through transient water pores in protein-free lipid membranes driven by transmembrane ionic charge imbalance

We have employed atomic-scale molecular dynamics simulations to address ion leakage through transient water pores in protein-free phospholipid membranes. Our results for phospholipid membranes in aqueous solution with NaCl and KCl salts show that the formation of transient water pores and the consequent ion leakage can be induced and be driven by a transmembrane ionic charge imbalance, an inherent feature in living cells. These processes take place if the gradient is large enough to develop a sufficiently significant potential difference across the membrane. The transport of cations and anions through the water pores is then seen; it discharges the transmembrane potential, considerably reduces the size of a water pore, and makes the water pore metastable, leading eventually to its sealing. The ion transport is found to be sensitive to the type of ions. It turns out that Na(+) and Cl(-) ions leak through a membrane at approximately the same ratio despite the fact that Na(+) ions are expected to experience a lower potential barrier for the permeation through the pore. This is because of strong interactions of sodium ions with the carbonyl region of a phospholipid membrane as well as with lipid headgroups forming pore "walls," considerably slowing down the permeation of sodium ions. In contrast, we observed a pronounced selectivity of a phospholipid membrane to the permeation of potassium ions as compared to chloride ions: Potassium ions, being larger than sodium ions, interact only weakly with phospholipid headgroups, so that these interactions are not able to compensate for a large difference in free-energy barriers for permeation of K(+) and Cl(-) ions. These findings are found to be robust to a choice of force-field parameters for ions (tested by Gromacs and Charmm force-fields for ions). What is more, a potassium ion is found to be able to permeate a membrane along an alternate, "water-defect-mediated" pathway without actual formation of a pore. The "water-defect-mediated" leakage involves formation of a single water defect only and is found to be at least one order of magnitude faster than the pore-mediated ion leakage.     

A simple method for the determination of the pore radius of ion channels in planar lipid bilayer membranes

Abstract A new method of pore size determination is presented. The results of applying this simple method to ion channels formed by staphylococcal α-toxin and its N-terminal fragment as well as to cholera toxin channels are shown. The advantages and the difficulties of this method are discussed. It was found that (i) the mobility of ions in solutions depends only on the percentage of concentration of added non-electrolytes and practically not on their chemical nature (sugars or polyglycols) and molecular size; (ii) the proportional change of both ion channel conductance and bulk solution conductivity by low M . non-electrolytes may be used as an indication of a diffusion mechanism of ion transport through channels; (iii) the slope of the dependence of the ion channel conductance on the bulk conductivity of solutions containing different concentrations of non-electrolyte is a good measure of channel permeability for non-electrolytes.     

Possible existence of ion pairs at the mouths of ion channels

An electrostatic calculation suggests that when an ion is bound near the mouth of a channel penetrating a low-dielectric membrane, a counter ion may form an ion pair with this ion. The tendency towards ion-pair formation is remarkably enhanced at channel mouths by forces (image forces) arising from the charges induced on the boundaries between different dielectrics. The binding constant for the formation of ion-pairs of monovalent ions is estimated under the assumption that local interactions between the counter ion and the channel wall are negligibly small. It is of the order of 1–10 molal^?1 or more for the binding of a Cl^? (F^?) counter ion to an $\text{Na}{}^{\mathrm{+}}$ ($\text{Li}{}^{\mathrm{+}}$) ion if appropriate conditions are fulfilled. The binding constant depends on the position of the binding site, the dimensions and geometries of the channel and channel mouth, and the state of ion loading of the channel, as well as the ionic species. The present results also indicate that when cation (anion) channels have anionic (cationic) groups as integrant parts of their channel walls, interactions between these charged groups and permeant ions are markedly enhanced by the image forces.     

Solution probing of metal ion binding by helix 27 from Escherichia coli 16S rRNA

Helix (H)27 from Escherichia coli 16S ribosomal (r)RNA is centrally located within the small (30S) ribosomal subunit, immediately adjacent to the decoding center. Bacterial 30S subunit crystal structures depicting Mg(2+) binding sites resolve two magnesium ions within the vicinity of H27: one in the major groove of the G886-U911 wobble pair, and one within the GCAA tetraloop. Binding of such metal cations is generally thought to be crucial for RNA folding and function. To ask how metal ion-RNA interactions in crystals compare with those in solution, we have characterized, using solution NMR spectroscopy, Tb(3+) footprinting and time-resolved fluorescence resonance energy transfer (tr-FRET), location, and modes of metal ion binding in an isolated H27. NMR and Tb(3+) footprinting data indicate that solution secondary structure and Mg(2+) binding are generally consistent with the ribosomal crystal structures. However, our analyses also suggest that H27 is dynamic in solution and that metal ions localize within the narrow major groove formed by the juxtaposition of the loop E motif with the tandem G894-U905 and G895-U904 wobble pairs. In addition, tr-FRET studies provide evidence that Mg(2+) uptake by the H27 construct results in a global lengthening of the helix. We propose that only a subset of H27-metal ion interactions has been captured in the crystal structures of the 30S ribosomal subunit, and that small-scale structural dynamics afforded by solution conditions may contribute to these differences. Our studies thus highlight an example for differences between RNA-metal ion interactions observed in solution and in crystals.     

Molecular dynamics of the KcsA K(+) channel in a bilayer membrane

Molecular dynamics (MD) simulations of an atomic model of the KcsA K(+) channel embedded in an explicit dipalmitoylphosphatidylcholine (DPPC) phospholipid bilayer solvated by a 150 mM KCl aqueous salt solution are performed and analyzed. The model includes the KcsA K(+) channel, based on the recent crystallographic structure of, Science. 280:69-77), 112 DPPC, K(+) and Cl(-) ions, as well as over 6500 water molecules for a total of more than 40,000 atoms. Three K(+) ions are explicitly included in the pore. Two are positioned in the selectivity filter on the extracellular side and one in the large water-filled cavity. Different starting configurations of the ions and water molecules in the selectivity filter are considered, and MD trajectories are generated for more than 4 ns. The conformation of KcsA is very stable in all of the trajectories, with a global backbone root mean square (RMS) deviation of less than 1.9 A with respect to the crystallographic structure. The RMS atomic fluctuations of the residues surrounding the selectivity filter on the extracellular side of the channel are significantly lower than those on the intracellular side. The motion of the residues with aromatic side chains surrounding the selectivity filter (Trp(67), Trp(68), Tyr(78), and Tyr(82)) is anisotropic with the smallest RMS fluctuations in the direction parallel to the membrane plane. A concerted dynamic transition of the three K(+) ions in the pore is observed, during which the K(+) ion located initially in the cavity moves into the narrow part of the selectivity filter, while the other two K(+) ions move toward the extracellular side. A single water molecule is stabilized between each pair of ions during the transition, suggesting that each K(+) cation translocating through the narrow pore is accompanied by exactly one water molecule, in accord with streaming potential measurements (, Biophys. J. 55:367-371). The displacement of the ions is coupled with the structural fluctuations of Val(76) and Gly(77), in the selectivity filter, as well as the side chains of Glu(71), Asp(80), and Arg(89), near the extracellular side. Thus the mechanical response of the channel structure at distances as large as 10-20 A from the ions in the selectivity filter appears to play an important role in the concerted transition.     

The nicotinic acetylcholine receptor: from molecular model to single-channel conductance

The nicotinic acetylcholine receptor (nAChR) is the archetypal ligand-gated ion channel. A model of the α7 homopentameric nAChR is described in which the pore-lining M2 helix bundle is treated atomistically and the remainder of the molecule is treated as a “low resolution” cylinder. The surface charge on the cylinder is derived from the distribution of charged amino acids in the amino acid sequence (excluding the M2 segments). This model is explored in terms of its predicted single-channel properties. Based on electrostatic potential profiles derived from the model, the one-dimensional Poisson-Nernst-Planck equation is used to calculate single-channel current/voltage curves. The predicted single-channel conductance is three times higher (ca. 150 pS) than that measured experimentally, and the predicted ion selectivity agrees with the observed cation selectivity of nAChR. Molecular dynamics (MD) simulations are used to estimate the self-diffusion coefficients (D) of water molecules within the channel. In the narrowest region of the pore, D is reduced ca. threefold relative to that of bulk water. Assuming that the diffusion of ions scales with that of water, this yields a revised prediction of the single-channel conductance (ca. 50 pS) in good agreement with the experimental value. We conclude that combining atomistic (MD) and continuum electrostatics calculations is a promising approach to bridging the gap between structure and physiology of ion channels. Received: 2 August 1999 / Revised version: 5 November 1999 / Accepted: 9 November 1999     

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.     

Correlated ion flux through parallel pores: Application to channel subconductance states

Summary Many ion channels that normally gate fully open or shut have recently been observed occasionally to display well-defined subconductance states with conductances much less than those of the fully open channel. One model of this behavior is a channel consisting of several parallel pores with a strong correlation between the flux in each pore such that, normally, they all conduct together but, under special circumstances, the pores may transfer to a state in which only some of them conduct. This paper introduces a general technique for modeling correlated pores, and explores in detail by computer simulation a particular model based upon electric interaction between the pores. Correlation is obtained when the transient electric field of ions passing through the pores acts upon a common set of ionizable residues of the channel protein, causing transient changes in their effective pK and hence in their charged state. The computed properties of such a correlated parallel pore channel with single occupation of each pore are derived and compared to those predicted for a single pore that can contain more than one ion at a time and also to those predicted for a model pore with fluctuating barriers. Experiments that could distinguish between the present and previous models are listed.R.M.B. is grateful to the S.E.R.C. for the award of a graduate studentship.     

Gated pores in the ferritin protein nanocage

Properties of ferritin gated pores control rates of FMNH₂ reduction of ferric iron in hydrated oxide minerals inside the protein nanocage, and are discussed in terms of: (1) the conserved pore gate residues (ion pairs: arginine 72, aspartate 122, and a hydrophobic pair, leucine 110-leucine 134), (2) pore sensitivity to heat at temperatures 30 °C below that of the nanocage itself, and (3) pore sensitivity to physiological changes in urea (1-10 mM). Conditions which alter ferritin pore structure/function in solution, coupled with the high evolutionary conservation of the pore gates, suggest the presence of molecular regulators in vivo that recognize the pore gates and hold them either closed or open, depending on biological iron need. The apparent homology between ferrous ion transport through gated pores in the ferritin nanocage and ion transport through gated pores in ion channel proteins embedded in cell membranes, make studies of water soluble ferritin and the pore gating folding/unfolding a useful model for other gated pores.     

Ion coordination in the amphotericin B channel.

The antifungal polyene antibiotic amphotericin B forms channels in lipid membranes that are permeable to ions, water, and nonelectrolytes. Anion, cation, and ion pair coordination in the water-filled pore of the "barrel" unit of the channels was studied by molecular dynamics simulations. Unlike the case of the gramicidin A channel, the water molecules do not create a single-file configuration in the pore, and some cross sections of the channel contain three or four water molecules. Both the anion and cation are strongly bound to ligand groups and water molecules located in the channel. The coordination number of the ions is about six. The chloride has two binding sites in the pore. The binding with water is dominant; more than four water molecules are localized in the anion coordination sphere. Three motifs of the ion coordination were monitored. The dominant motif occurs when the anion is bound to one ligand group. The ion is bound to two or three ligand groups in the less favorable configurations. The strong affinity of cations to the channel is determined by the negatively charged ligand oxygens, whose electrostatic field dominates over the field of the hydrogens. The ligand contribution to the coordination number of the sodium ion is noticeably higher than in the case of the anion. As in the case of the anion, there are three motifs of the cation coordination. The favorable one occurs when the cation is bound to two ligand oxygens. In the less favorable cases, the cation is bound to three or four oxygens. In the contact ion pair, the cation and anion are bound to two ligand oxygens and one ligand hydrogen, respectively. There exist intermediate solvent-shared states of the ion pair. The average distances between ions in these states are twice as large as that of the contact ion pair. The stability of the solvent-shared state is defined by the water molecule oriented along the electrostatic field of both ions.     

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.     

Single-file diffusion and neurotransmitter transporters: Hodgkin and Keynes model revisited

Norepinephrine transporters (NETs) use the Na gradient to remove norepinephrine (NE) from the synaptic cleft of adrenergic neurons following NE release from the presynaptic terminal. By coupling NE to the inwardly directed Na gradient, it is possible to concentrate NE inside cells. This mechanism, which is referred to as co-transport or secondary transport (L?uger, 1991, Electrogenic Ion Pumps, Sinauer Associates) is apparently universal: Na coupled transport applies to serotonin transporters (SERTs), dopamine transporters (DATs), glutamate transporters, and many others, including transporters for osmolites, metabolites and substrates such as sugar. Recently we have shown that NETs and SERTs transport norepinephrine or serotonin as if Na and the transmitter permeated through an ion channel together 'Galli et al., 1998, PNAS 95, 13260-13265; Petersen and DeFelice, 1999, Nature Neurosci. 2, 605-610'. These data are paradoxical because it has been difficult to envisage how NE, for example, would couple to Na if these ions move passively through an open pore. An 'alternating access' model is usually evoked to explain coupling: in such models NE and Na bind to NET, which then undergoes a conformational change to release NE and Na on the inside. The empty transporter then turns outward to complete the cycle. Alternating-access models never afford access to an open channel. Rather, substrates and co-transported ions are occluded in the transporter and carried across the membrane. The coupling mechanism we propose is fundamentally different than the coupling mechanism evoked in the alternating access model. To explain coupling in co-transporters, we use a mechanism first evoked by 'Hodgkin and Keynes (1955) J. Physiol. 128, 61-88' to explain ion interactions in K-selective channels. In the Hodgkin and Keynes model, K ions move single-file through a long narrow pore. Their model accounted for the inward/outward flux ratio if they assumed that two K ions queue within the pore. We evoke a similar model for the co-transport of transmitter and Na. In our case, however, coupling occurs not only between like ions but also between unlike ions (i.e. the transmitter and Na ). We made a replica of the Hodgkin and Keynes mechanical model to test our ideas, and we extended the model with computer simulations using Monte Carlo methods. We also developed an analytic formula for Na coupled co-transport that is analogous to the single-file Ussing equation for channels. The model shows that stochastic diffusion through a long narrow pore can explain coupled transport. The length of the pore amplifies the Na gradient that drives co-transport.     

Ion binding properties and structure stability of the NaK channel

Ion distribution in the selectivity filter and ion-water and ion-protein interactions of NaK channel are systematically investigated by all-atom molecular dynamics simulations, with the tetramer channel protein being embedded in a solvated phospholipid bilayer. Analysis of the simulation results indicates that K⁺ ions prefer to bind within the sites formed by two adjacent planes of oxygen atoms from the selectivity filter, while Na⁺ ions are inclined to bind to a single plane of four oxygen atoms. At the same time, both K⁺ and Na⁺ ions can diffuse in the vestibule, accompanying with movements of the water molecules confined in a complex formed by the vestibule together with four small grottos connecting to it. As a result, K⁺ ions show a wide range of coordination numbers (6-8), while Na⁺ ions display a constant coordination number of ∼ 6 in the selectivity filter, which may result in the loss of selectivity of NaK. It is also found that a Ca²⁺ can bind at the extracellular site as reported in the crystal structure in a partially hydrated state, or at a higher site in a full hydration state. Furthermore, the carbonyl group of Asp66 can reorient to point towards the center pore when an ion exists in the vestibule, while that of Gly65 always aligns tangentially to the channel axis, as in the crystallographic structures.     

Uptake and long-distance transport of phosphate,potassium and chloride in relation to internal ion concentrations in barley: evidence of non-allosteric regulation

The extent to which uptake and transport of either phosphate, potassium or chloride are controlled by the concentration of these ions within the root, perhaps through an allosteric mechanism, was investigated with young barley plants in nutrient solution culture. Plants were grown with their roots divided between two containers, such that a single seminal root was continuously supplied with all the required nutrient ions, while the remaining four or five seminal roots were either supplied with the same solution (controls) or, temporarily, a solution lacking a particular nutrient ion (nutrient-deficient treatment). Compared with controls, there was a marked stimulation of uptake and transport of labelled ions by the single root following 24 h or more of nutrient dificiency to the remainder of the root system. This stimulation, which comprised an increased transport to the shoot and, for all ions except Cl^-, increased transport to the remainder of the root system, took place without appreciable change in the concentration of particular ions within the single root. However, nutrient deficiency quickly caused a lower concentration of ions in the shoot and the remaining roots. The results are discussed in relation to various mechanisms, proposed in the literature, by which the coordination of ion uptake and transport may be maintained within the plant. We suggest that under our conditions any putative allosteric control of uptake and transport by root cortical cells was masked by an alternative mechanism, in which ion influx appears to be regulated by ion efflux to the xylem, perhaps controlled by the concentration of particular ions recycled in the phloem to the root from the shoot.