Selecting Ions by Size in a Calcium Channel: The Ryanodine Receptor Case Study

Many calcium channels can distinguish between ions of the same charge but different size. For example, when cations are in direct competition with each other, the ryanodine receptor (RyR) calcium channel preferentially conducts smaller cations such as Li⁺ and Na⁺ over larger ones such as K⁺ and Cs⁺. Here, we analyze the physical basis for this preference using a previously established model of RyR permeation and selectivity. Like other calcium channels, RyR has four aspartate residues in its GGGIGDE selectivity filter. These aspartates have their terminal carboxyl group in the pore lumen, which take up much of the available space for permeating ions. We find that small ions are preferred by RyR because they can fit into this crowded environment more easily.     

Calcium-potassium selectivity: kinetic analysis of current-voltage relationships of the open, slowly activating channel in the vacuolar membrane of Vicia faba guard-cells

Single-channel current-voltage (IV ) relationships of the open, slowly activating vacuolar (SV) channel of Vicia faba L. were recorded in solutions with different activities of Ca²⁺ and K⁺, and have been analyzed for Ca²⁺/K⁺ selectivity. Two models with one binding site have been examined. A rigid-pore model with a main binding site between two energy barriers (nine free parameters) provides fair fits. Slightly better fits are obtained with an alternative, dynamic-pore model, where the selectivity filter is located between two Mitchellian ion wells of the cytoplasmic and luminal pore sections, and where the selectivity filter alternates the orientation of the binding site between the two faces of the pore (ten free parameters). Using sets of IV-relationships with only Ca²⁺ or only K⁺ as transportable substrates, both models consistently predict open-channel IV-relationships in the presence of both substrates. Fits of both models to the entire ensemble of␣data yield very similar flux-voltage characteristics for␣Ca²⁺ and for K⁺ in experimental conditions, and consistently predict such flux-voltage characteristics over physiologically relevant ranges of voltage and substrate concentrations. In a very general sense, physiological Ca⁺ fluxes through the open SV channel are predominantly inward and about 50 times smaller than K⁺ fluxes. The ions Cl⁻, OH⁻, and H⁺, do not pass the SV channel at significant rates. Kinetic details of the SV channel with respect to binding and passage of Ca²⁺ and K⁺ are discussed on the basis of the consistent results of the reaction-kinetic analysis of the experimental data by the two models. Received: 14 July 1997 / Accepted: 26 September 1997     

Non-Equilibrium Dynamics Contribute to Ion Selectivity in the KcsA Channel

The ability of biological ion channels to conduct selected ions across cell membranes is critical for the survival of both animal and bacterial cells. Numerous investigations of ion selectivity have been conducted over more than 50 years, yet the mechanisms whereby the channels select certain ions and reject others are not well understood. Here we report a new application of Jarzynski’s Equality to investigate the mechanism of ion selectivity using non-equilibrium molecular dynamics simulations of Na⁺ and K⁺ ions moving through the KcsA channel. The simulations show that the selectivity filter of KcsA adapts and responds to the presence of the ions with structural rearrangements that are different for Na⁺ and K⁺. These structural rearrangements facilitate entry of K⁺ ions into the selectivity filter and permeation through the channel, and rejection of Na⁺ ions. A mechanistic model of ion selectivity by this channel based on the results of the simulations relates the structural rearrangement of the selectivity filter to the differential dehydration of ions and multiple-ion occupancy and describes a mechanism to efficiently select and conduct K⁺. Estimates of the K⁺/Na⁺ selectivity ratio and steady state ion conductance for KcsA from the simulations are in good quantitative agreement with experimental measurements. This model also accurately describes experimental observations of channel block by cytoplasmic Na⁺ ions, the “punch through” relief of channel block by cytoplasmic positive voltages, and is consistent with the knock-on mechanism of ion permeation.     

Molecular basis of ion permeability in a voltage‐gated sodium channel

Voltage‐gated sodium channels are essential for electrical signalling across cell membranes. They exhibit strong selectivities for sodium ions over other cations, enabling the finely tuned cascade of events associated with action potentials. This paper describes the ion permeability characteristics and the crystal structure of a prokaryotic sodium channel, showing for the first time the detailed locations of sodium ions in the selectivity filter of a sodium channel. Electrostatic calculations based on the structure are consistent with the relative cation permeability ratios (Na⁺ ≈ Li⁺ ≫ K⁺, Ca²⁺, Mg²⁺) measured for these channels. In an E178D selectivity filter mutant constructed to have altered ion selectivities, the sodium ion binding site nearest the extracellular side is missing. Unlike potassium ions in potassium channels, the sodium ions in these channels appear to be hydrated and are associated with side chains of the selectivity filter residues, rather than polypeptide backbones.     

Kinetic Analysis of Ca2+/K+ Selectivity of an Ion Channel by Single-Binding-Site Models

Current-voltage relationships of a cation channel in the tonoplast of Beta vulgaris, as recorded in solutions with different activities of Ca²⁺ and K⁺ (from Johannes & Sanders 1995, J. Membrane Biol. 146:211–224), have been reevaluated for Ca²⁺/K⁺ selectivity. Since conversion of reversal voltages to permeability ratios by constant field equations is expected to fail because different ions do not move independently through a channel, the data have been analyzed with kinetic channel models instead. Since recent structural information on K⁺ channels show one short and predominant constriction, selectivity models with only one binding site are assumed here to reflect this region kinetically. The rigid-pore model with a main binding site between two energy barriers (nine free parameters) had intrinsic problems to describe the observed current-saturation at large (negative) voltages. The alternative, dynamic-pore model uses a selectivity filter in which the binding site alternates its orientation (empty, or occupied by either Ca²⁺ or K⁺) between the cytoplasmic side and the luminal side within a fraction of the electrical distance and in a rate-limiting fashion. Fits with this model describe the data well. The fits yield about a 10% electrical distance of the selectivity filter, located about 5% more cytoplasmic than the electrical center. For K⁺ translocation, reorientation of the unoccupied binding site (with a preference of about 6:5 to face the lumenal side) is rate limiting. For Ca²⁺, the results show high affinity to the binding site and low translocation rates (<1% of the K⁺ translocation rate). With the fitted model Ca²⁺ entry through the open channel has been calculated for physiological conditions. The model predicts a unitary open channel current of about 100 fA which is insensitive to cytoplasmic Ca²⁺ concentrations (between 0.1 and 1 μm) and which shows little sensitivity to the voltage across the tonoplast. Received: 19 February 1997/Revised: 19 May 1997     

Effects of the Protonation State of the EEEE Motif of a Bacterial Na-channel on Conduction and Pore Structure

A distinctive feature of prokaryotic Na⁺-channels is the presence of four glutamate residues in their selectivity filter. In this study, how the structure of the selectivity filter, and the free-energy profile of permeating Na⁺ ions are altered by the protonation state of Glu177 are analyzed. It was found that protonation of a single glutamate residue was enough to modify the conformation of the selectivity filter and its conduction properties. Molecular dynamics simulations revealed that Glu177 residues may adopt two conformations, with the side chain directed toward the extracellular entrance of the channel or the intracellular cavity. The likelihood of the inwardly directed arrangement increases when Glu177 residues are protonated. The presence of one glutamate residue with its chain directed toward the intracellular cavity increases the energy barrier for translocation of Na⁺ ions. These higher-energy barriers preclude Na⁺ ions to permeate the selectivity filter of prokaryotic Na⁺-channels when one or more Glu177 residues are protonated.     

Effects of the Protonation State of the EEEE Motif of a Bacterial Na+-channel on Conduction and Pore Structure

A distinctive feature of prokaryotic Na⁺-channels is the presence of four glutamate residues in their selectivity filter. In this study, how the structure of the selectivity filter, and the free-energy profile of permeating Na⁺ ions are altered by the protonation state of Glu177 are analyzed. It was found that protonation of a single glutamate residue was enough to modify the conformation of the selectivity filter and its conduction properties. Molecular dynamics simulations revealed that Glu177 residues may adopt two conformations, with the side chain directed toward the extracellular entrance of the channel or the intracellular cavity. The likelihood of the inwardly directed arrangement increases when Glu177 residues are protonated. The presence of one glutamate residue with its chain directed toward the intracellular cavity increases the energy barrier for translocation of Na⁺ ions. These higher-energy barriers preclude Na⁺ ions to permeate the selectivity filter of prokaryotic Na⁺-channels when one or more Glu177 residues are protonated.     

The selectivity of K+ ion channels: testing the hypotheses

How K⁺ channels are able to conduct certain cations yet not others remains an important but unresolved question. The recent elucidation of the structure of NaK, an ion channel that conducts both Na⁺ and K⁺ ions, offers an opportunity to test the various hypotheses that have been put forward to explain the selectivity of K⁺ ion channels. We test the snug-fit, field-strength, and over-coordination hypotheses by comparing their predictions to the results of classical molecular dynamics simulations of the K⁺ selective channel KcsA and the less selective channel NaK embedded in lipid bilayers. Our results are incompatible with the so-called strong variant of the snug-fit hypothesis but are consistent with the over-coordination hypothesis and neither confirm nor refute the field-strength hypothesis. We also find that the ions and waters in the NaK selectivity filter unexpectedly move to a new conformation in seven K⁺ simulations: the two K⁺ ions rapidly move from site S4 to S2 and from the cavity to S4. At the same time, the selectivity filter narrows around sites S1 and S2 and the carbonyl oxygen atoms rotate 20°−40° inwards toward the ion. These motions diminish the large structural differences between the crystallographic structures of the selectivity filters of NaK and KcsA and appear to allow the binding of ions to S2 of NaK at physiological temperature.     

Preferential binding of K+ ions in the selectivity filter at equilibrium explains high selectivity of K+ channels

K⁺ channels exhibit strong selectivity for K⁺ ions over Na⁺ ions based on electrophysiology experiments that measure ions competing for passage through the channel. During this conduction process, multiple ions interact within the region of the channel called the selectivity filter. Ion selectivity may arise from an equilibrium preference for K⁺ ions within the selectivity filter or from a kinetic mechanism whereby Na⁺ ions are precluded from entering the selectivity filter. Here, we measure the equilibrium affinity and selectivity of K⁺ and Na⁺ ions binding to two different K⁺ channels, KcsA and MthK, using isothermal titration calorimetry. Both channels exhibit a large preference for K⁺ over Na⁺ ions at equilibrium, in line with electrophysiology recordings of reversal potentials and Ba²⁺ block experiments used to measure the selectivity of the external-most ion-binding sites. These results suggest that the high selectivity observed during ion conduction can originate from a strong equilibrium preference for K⁺ ions in the selectivity filter, and that K⁺ selectivity is an intrinsic property of the filter. We hypothesize that the equilibrium preference for K⁺ ions originates in part through the optimal spacing between sites to accommodate multiple K⁺ ions within the selectivity filter.     

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.     

Structural modeling of calcium binding in the selectivity filter of the L-type calcium channel

Calcium channels play crucial physiological roles. In the absence of high-resolution structures of the channels, the mechanism of ion permeation is unknown. Here we used a method proposed in an accompanying paper (Cheng and Zhorov in Eur Biophys J, 2009) to predict possible chelation patterns of calcium ions in a structural model of the L-type calcium channel. We compared three models in which two or three calcium ions interact with the four selectivity filter glutamates and a conserved aspartate adjacent to the glutamate in repeat II. Monte Carlo energy minimizations yielded many complexes with calcium ions bound to at least two selectivity filter carboxylates. In these complexes calcium-carboxylate attractions are counterbalanced by calcium-calcium and carboxylate-carboxylate repulsions. Superposition of the complexes suggests a high degree of mobility of calcium ions and carboxylate groups of the glutamates. We used the predicted complexes to propose a permeation mechanism that involves single-file movement of calcium ions. The key feature of this mechanism is the presence of bridging glutamates that coordinate two calcium ions and enable their transitions between different chelating patterns involving four to six oxygen atoms from the channel protein. The conserved aspartate is proposed to coordinate a calcium ion incoming to the selectivity filter from the extracellular side. Glutamates in repeats III and IV, which are most distant from the repeat II aspartate, are proposed to coordinate the calcium ion that leaves the selectivity filter to the inner pore. Published experimental data and earlier proposed permeation models are discussed in view of our model.     

Ionic channels through the axon membrane (a review)

Ionic channels are discrete sites at which the passive movement of ions takes place during nervous excitation. Three types of channels are distinguished. 1. Leakage channels that are permanently open to various cations. 2. Na channels that open promptly on depolarization but slowly close again (inactivate) on sustained depolarization and that are predominantly permeable to Na⁺ ions. 3. K channels that on depolarization open after some delay but stay open and that are mainly passed by K⁺ ions. The selectivity sequence of the Na channels of the squid axon (or frog nerve) is as follows: Na⁺ ≈ Li⁺>(T1+)>NH⁺ ₄?K⁺> Rb⁺, Cs⁺; that of K channels is: (T1+)>K⁺>Rb⁺>NH⁺ ₄?Na⁺, Cs⁺, Na channels are selectively blocked by tetrodotoxin (TTX) or saxitoxin (STX), K channels by tetraethylammonium ions (TEA). Either channel type is reversibly blocked when one drug molecule binds to one site per channel, the equilibrium dissociation constant of these reactions being about 3×10^?9 MTTX (or STX) and 4×10^?4 M TEA, respectively. Because of their specificity and high affinity, TTX and STX are used to “titrate” the Na channels whose density appears to be of the order of 100/Μm². The “gates” of the channels operate as a function of potential and time but independent of the permeating ion species. Drugs (e.g. veratridine) and enzymes (e.g. pronase, applied intraaxonally) cause profound changes in the gating function of the Na channels without influencing their selectivity. This points to separate structures for gating and ion discrimination. The latter is thought to be, in part, brought about by a “selectivity filter” of which detailed structural ideas exist. Recent experiments suggest that the gates of the Na channels are controlled by charged particles moving within the membrane under the influence of the electrical field.     

Permeation Redux: Thermodynamics and Kinetics of Ion Movement through Potassium Channels

The fundamental biophysics underlying the selective movement of ions through ion channels was launched by George Eisenman in the 1960s, using glass electrodes. This minireview examines the insights from these early studies and the explosive progress made since then.The recent passing of George Eisenman (December 18, 2013) inspired us to revisit the topic most associated with his passionate input, namely how the membrane proteins known as ion channels control passive movements of ions across biological membranes. Ion permeation has captivated biophysicists for more than half a century, and only now, with the combined advent of atomic-level structures and sophisticated computational wizardry, are the secrets of this amazing process beginning to be revealed. Why “amazing”? For example, because K⁺-selective ion channels can discriminate between K⁺ and Na⁺ ions, which differ in radius by a mere 0.38 Ångstrom, and do so with 1000:1 reliability and at lightning speed near the diffusion limit, the dwell time of an ion in the pore of a channel is as fleeting as ∼10⁻⁸ s. Understanding this remarkably-tuned process in K⁺ channels requires attention to two perspectives: the ability of specific channels to discriminate between the ions they might encounter (i.e., selectivity); and the kinetics of ion movement across the channel pore (i.e., conduction).The classical thermodynamic explanation of ion selectivity is that the relative free energy difference of ions in the pore relative to the bulk solution is the critical quantity to consider (1–4). Some of the earliest insights into thermodynamic selectivity derive from studies of ion binding to aluminosilicate glass electrodes (5,6). Depending on the composition of the glass, these electrodes, originally developed for their proton sensitivity, can exhibit a dramatic range of selectivities among the five alkali metal cations. In rank order, one might expect as many as 5 × 4 × 3 × 2 × 1 = 120 different sequences of selectivities among these five cations. Remarkably, however, in the vast literature of selectivity in biological membranes, typically only 11 sequences are observed (with some exceptions). These became known as the “Eisenman sequences”. The exact same selectivity sequences are observed in glass electrodes of various compositions.Why are the free energy differences the way they are for a given system? To answer this question, one needs a physical mechanism. For Eisenman, numerical calculations stood as a critical component of the process of better understanding Nature. In other words, proposing a physical mechanism that is qualitatively reasonable is not enough—one must also test it by constructing atomic models leading to actual quantitative predictions (Fig. 1). In the early days, the concept of the anionic field strength of a binding site was formulated and tested with direct calculations based on exceedingly simple atomic hard-sphere models of ions, water molecules, and coordinating ligands such as shown in Fig. 1 A (2,5). Remarkably, these simple calculations led to the Eisenman selectivity sequences. Eisenman was able to account for the limited class of sequences by considering the equilibrium binding of cations to the glass, and the energetic competition between water and glass for the ions. The critical factor that determines the selectivity sequence of a given glass is the anionic field strength of the binding site on the glass. Briefly, the smallest group Ia cation, Li⁺, holds water most tenaciously, so it will only dehydrate and bind in the presence of a strongly negative electrostatic potential.Open in a separate windowFigure 1Structural models used in theoretical studies of ion selectivity. (A) Simple model used to introduce the concept of field strength leading to 11 cationic selectivity sequences (2,5,6). Ions, water, and ligands are represented by simple hard-spheres with embedded point charges. Selectivity arises from the difference in the interaction energy of the cation with a water molecule (top) and an anionic coordinating ligand (bottom). (B) Ion-selective transfer process is depicted with atomic models incorporating all molecular details in the case of solvation in liquid water (top) and binding to the K⁺-selective ionophore valinomycin (bottom). Such atomic models were used to carry out some of the earliest MD free energy simulations on ion binding selectivity (12,13,15).By contrast, the largest cation, Cs⁺, holds water least tenaciously. It cannot bind readily to a strongly negative site because the site itself greedily clings to water molecules, and thus prevents Cs⁺ binding. However, Cs⁺ is more willing, relative to the smaller cations, to dehydrate and bind in the presence of a weakly negative electrostatic potential. At the extremes, the highest anionic field strength glass shows a selectivity sequence ofLi⁺ > Na⁺ > K⁺ > Rb⁺ > Cs⁺(sequence XI), and the lowest anionic field strength glass shows a selectivity sequence ofCs⁺ > Rb⁺ > K⁺ > Na⁺ > Li⁺(sequence I).A very simple model, based on the relative Gibbs’ free energies of binding and hydration, explains why there are only 11 sequences (5–7). The critical factor underlying the pattern of these selectivity sequences is that the “ion-site interaction energies fall off as a function of cation size as a lower power of the cation radius than do ion-water interaction energies” (5,6). The icing on the cake is that ion selectivity of channels in membranes appears to follow similar principles (7). The thermodynamic principles are evidently analogous. Moreover, Eisenman’s contributions went far beyond the monovalent cation selectivity of potassium channels. His theoretical approach was seminal in understanding both cation and anion selectivity in a diverse range of physical and biological systems (8,9).The advent of molecular dynamics (MD) simulations around this period was of critical importance to the field. This made it possible to construct increasingly realistic models of proteins (10), including ion channels (11), and examine the ion selectivity of carriers using the alchemical free energy perturbation (FEP) technique (12,13). With no experimental structures yet available for the ion-selective regions of biological K⁺ channels, an important step forward was Eisenman’s realization that other ion-selective systems could be used to computationally test the structural basis of his selectivity theory. Both peptidelike small ionophores, such as valinomycin and nonactin, and the ion-coordinating fivefold symmetry sites in icosahedral virus structures, thus caught his attention (13). As it turned out, these types of structures were indeed very relevant for the selectivity problem, because K⁺-channel filters were eventually shown to be lined likewise by carbonyl groups (14). With the crystallographically determined valinomycin structure at hand, its selectivity could be energetically analyzed by atomistic computer simulations, as illustrated in Fig. 1 B (12,15). The anionic field strength (represented by the carbonyl ligand dipole moment) could then be varied artificially, and the successive progression through the different selectivity sequences, as a function of field strength, directly observed. Likewise, Eisenman and Alvarez (13) made computational predictions for the binding energetics and selectivity of the Ca²⁺ binding site at the fivefold symmetry axis of satellite tobacco necrosis virus, and they subsequently showed experimentally that this binding site had a marked rare-earth ion size selectivity (16). To this day, the general computational FEP/MD framework based on equilibrium thermodynamics used in these studies continues to be a critical tool to understand ion channels (17), transporters (18), and pumps (19).Despite these early insights, it was always clear to Eisenman that explanations of selectivity solely based on thermodynamic equilibrium were too simple to account for the detailed properties observed in biological systems. Since the halcyon days of equilibrium binding studies on glass electrodes, the permeation landscape presented by the pores of ion channels has emerged as richer than anticipated. One important realization is that binding and conduction of ions through a channel may act as contradictory processes, because although an ion has to leave the comfort of its hydration shells to selectively enter the mouth of a channel pore, if it binds the channel too tightly, it cannot move rapidly through it. This mini-conundrum is most apparent, perhaps, for K⁺-channels, which attract K⁺ ions much more forcefully than Na⁺ ions, yet conduct K⁺ ions much faster than Na⁺ ions.Another factor evident in early studies of permeation is that ions encounter a series of obstacles (i.e., energy barriers) and binding sites (i.e., energy wells) as they wend their way through the pore. One approach to understanding permeation is to consider that ions hopscotch from one well to the next over a series of barriers. When the number of barriers is rather limited, say <5, one can use so-called “rate theory” (20) to analyze and formulate the free energy profile experienced by an ion crossing the membrane. Hille (21) proposed that selectivity derives largely from the selectivities of the barriers, not the wells. Eisenman and Horn (7) later considered the possibility that binding sites and barriers within a particular channel might have different selectivity sequences. For example, if a channel presents two barriers, one of which has selectivity sequence I and the other has selectivity sequence XI, the channel as a whole will have an intermediate selectivity sequence that is not an Eisenman sequence at all. Rather, it is a so-called “polarizability sequence” (7). Interestingly, contemporary studies indicate that successive binding sites along K⁺-selective channels display different selectivities (22). Another concept based on Eyring barrier models is that the energy levels for wells and barriers may not be static, and may therefore fluctuate on a timescale relevant to ion permeation (23). Finally, the biophysics of ion permeation and later structural studies show that multiple ions may cohabit the same channel simultaneously, and the interactions among these ions have profound consequences for ion conduction and selectivity.Fast forward to the 21st century: atomic-level structures and all-atom simulations seem to have blown the permeation field wide open, as suggested by recent reviews (24–27). Once the KcsA channel structure was solved (14), the structural origin of K⁺-ion permeation could finally be addressed by computer simulations of the “real structure” and a number MD simulation studies provided novel insight (22,28–31). Needless to say, George Eisenman took great interest in these simulations even though he had by then retired. Also, in the case of KcsA, the initial work largely revolved around calculations of equilibrium ion binding and selectivity, barrier heights, and energy landscape mapping (22,31), because direct all-atom simulations of spontaneous permeation were not possible. However, the general type of knock-on mechanism with multiion occupancy of the channel selectivity filter, involving key distinct states (22,31), and a surprisingly flat energy landscape (22), appear to be robust features of these channels.Even with the advent of MD simulations, the concept of field strength has kept its relevance. For example, the selectivity filter in MD simulations of the KcsA channel displayed a range of atomic flexibility that seemed somewhat shocking at the time because a traditional host-guest mechanism of selectivity would require a fairly rigid cavity-size. Yet, free energy computations indicated that this was not strictly necessary to establish the thermodynamic free energy differences needed to support ion selectivity (32). The resilience of Eisenman’s ideas is not entirely surprising because, as foreseen early on by Bertil Hille (21), the concept of field strength remains “useful if the dipoles of the channel are free to move and can be pulled in by small ions and pushed back by large ones”.Nevertheless, despite the exciting progress, the chapter on ion selectivity in K⁺ channels is far from closed. Very recently, a number of studies have revealed some extremely intriguing multiion aspects of selectivity in K⁺ channels that appear to stand squarely outside the realm of equilibrium thermodynamics. By examining the properties of MthK (33) and NaK (34) mutants, Liu and Lockless (35) and Sauer et al. (36) showed that the channel becomes K⁺-selective only if there are four consecutive binding sites along the filter. This has culminated more recently with studies of two engineered mutants of the NaK channel, referred to as “NaK2K” and “NaK2CNG”. According to reversal potential measurements from single-channel electrophysiology, the NaK2K construct is K⁺-selective and the NaK2CNG construct is nonselective. Remarkably, despite being nonselective in ion permeation, the NaK2CNG filter displays an equilibrium preference for binding K⁺ over Na⁺, as indicated by measurements with isothermal titration calorimetry and concentration-dependent ion replacement within the filter observed through crystallographic titration experiments.K⁺-selective channels bind two or more K⁺ ions in the narrow filter, whereas the nonselective channels bind fewer ions. Based on the crystallographic titration experiments, the NaK2K construct has two high-affinity K⁺ sites whereas the NaK2CNG construct has only one K⁺-selective site. These experiments show that both K⁺-selective and nonselective channels select K⁺ over Na⁺ ions at equilibrium, implying that equilibrium selectivity is insufficient to determine the selectivity of ion permeation (35,36). The data indicate that having multiple K⁺ ions bound simultaneously is required for selective K⁺ conduction, and that a reduction in the number of bound K⁺ ions destroys the multiion selectivity mechanism utilized by K⁺ channels. Although these experimental results are intriguing, the underlying microscopic mechanisms remain unclear. The implication is that the multiion character of the permeation process must, somehow, be a critical element for establishing selective ion conduction through K⁺ channels.The progress made, and the challenges that remain, are perhaps best illustrated by returning to computational studies of the simplest membrane spanning structure known, namely the gramicidin A channel. Before detailed studies of selectivity and conductance of K⁺-channels were launched, computational work on ion conduction through membrane channels was largely focused on this simple channel (37–41). In this case the permeation selectivity was monotonically size-dependent (Eisenman sequence I) and, in this respect, less interesting than K⁺-selective channels. However, from an energetic point of view it was puzzling how this single helical structure could yield free energy barriers low enough to permit high conductivity (7,42). Computer simulations of increasing complexity in this case established that the combined effect of several contributions to ion stabilization along the pore (from the protein, membrane, single-file waters, and bulk solution) indeed results in low barriers to permeation (11,39,40). Furthermore, the most realistic model comes in close agreement with experimental measurements (11,43), although it is clear that work is still needed.     

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 Ca²⁺ 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 Ca²⁺ 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. Ca²⁺ 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 Ca²⁺ selectivity found in both theory and experiments.     

Simulation of the effect of an external GHz electric field on the potential energy profile of Ca2+ ions in the selectivity filter of the CaVAb channel

Ca_V channels are transmembrane proteins that mediate and regulate ion fluxes across cell membranes, and they are activated in response to action potentials to allow Ca²⁺ influx. Since ion channels are composed of charge or polar groups, an external alternating electric field may affect the ion‐selective membrane transport and the performance of the channel. In this article, we have investigated the effect of an external GHz electric field on the dynamics of calcium ions in the selectivity filter of the Ca_VAb channel. Molecular dynamics (MD) simulations and the potential of mean force (PMF) calculations were carried out, via the umbrella sampling method, to determine the free energy profile of Ca²⁺ ions in the Ca_VAb channels in presence and absence of an external field. Exposing Ca_VAb channel to 1, 2, 3, 4, and 5 GHz electric fields increases the depth of the potential energy well and this may result in an increase in the affinity and strength of Ca²⁺ ions to binding sites in the selectivity filter the channel. This increase of strength of Ca²⁺ ions binding in the selectivity filter may interrupt the mechanism of Ca²⁺ ion conduction, and leads to a reduction of Ca²⁺ ion permeation through the Ca_VAb channel.     

Alkali metal ion selectivity of the hemocyanin channel

Summary The selectivity of the hemocyanin channel was measured for alkali metal ions and ammonium. Permeability ratios relative to K⁺ measured from biionic potentials were: NH ₄ ⁺ (1.52)>Rb⁺ (1.05)>K⁺ (1.0)>Cs⁺ (0.89)>Na⁺ (0.81)>Li⁺ (0.35). Single-channel ion conductance was a saturating function of ion concentration regardless of the cation present in the bathing medium. Maximal conductances were 270, 267, 215, 176, 170 and 37 ps for K⁺, Rb⁺, NH ₄ ⁺ , Cs⁺, Na⁺ and Li⁺, respectively. Current-voltage curves for the different monovalent cations were measured and described using a threebarrier model previously used to explain the voltage dependence of the instantaneous channel conductance (Cecchi, Alvarez & Latorre, 1981). In this way, binding and peak energies were estimated for the different ions. Considering the energy peaks as transition states between the ion and the channel, it is concluded that they follow Eisenman's selectivity sequences XI (cis peak, i.e., Li⁺>Na⁺>K⁺>Rb⁺>Cs⁺; highest field strength), VII (central peak) and II (trans peak). The cis side was that to which hemocyanin was added and was electrically ground. The binding energies, on the other hand, follow Eisenman's series XI for strong electric field sites. Binding of NH ₄ ⁺ to the cis-well suggests that the orientation of the ligands in the site is tetrahedric.     

Ion–protein interactions of a potassium ion channel studied by attenuated total reflection Fourier transform infrared spectroscopy

An understanding of ion–protein interactions is key to a better understanding of the molecular mechanisms of proteins, such as enzymes, ion channels, and ion pumps. A potassium ion channel, KcsA, has been extensively studied in terms of ion selectivity. Alkali metal cations in the selectivity filter were visualized by X-ray crystallography. Infrared spectroscopy has an intrinsically higher structural sensitivity due to frequency changes in molecular vibrations interacting with different ions. In this review article, I attempt to summarize ion-exchange-induced differences in Fourier transform infrared spectroscopy, as applied to KcsA, to explain how this method can be utilized to study ion–protein interactions in the KcsA selectivity filter. A band at 1680 cm^?1 in the amide I region would be a marker band for the ion occupancy of K⁺, Rb⁺, and Cs⁺ in the filter. The band at 1627 cm^?1 observed in both Na⁺ and Li⁺ conditions suggests that the selectivity filter similarly interacts with these ions. In addition to the structural information, the results show that the titration of K⁺ ions provides quantitative information on the ion affinity of the selectivity filter.     

The conserved potassium channel filter can have distinct ion binding profiles: Structural analysis of rubidium,cesium, and barium binding in NaK2K

Potassium channels are highly selective for K⁺ over the smaller Na⁺. Intriguingly, they are permeable to larger monovalent cations such as Rb⁺ and Cs⁺ but are specifically blocked by the similarly sized Ba²⁺. In this study, we used structural analysis to determine the binding profiles for these permeant and blocking ions in the selectivity filter of the potassium-selective NaK channel mutant NaK2K and also performed permeation experiments using single-channel recordings. Our data revealed that some ion binding properties of NaK2K are distinct from those of the canonical K⁺ channels KcsA and MthK. Rb⁺ bound at sites 1, 3, and 4 in NaK2K, as it does in KcsA. Cs⁺, however, bound predominantly at sites 1 and 3 in NaK2K, whereas it binds at sites 1, 3, and 4 in KcsA. Moreover, Ba²⁺ binding in NaK2K was distinct from that which has been observed in KcsA and MthK, even though all of these channels show similar Ba²⁺ block. In the presence of K⁺, Ba²⁺ bound to the NaK2K channel at site 3 in conjunction with a K⁺ at site 1; this led to a prolonged block of the channel (the external K⁺-dependent Ba²⁺ lock-in state). In the absence of K⁺, however, Ba²⁺ acts as a permeating blocker. We found that, under these conditions, Ba²⁺ bound at sites 1 or 0 as well as site 3, allowing it to enter the filter from the intracellular side and exit from the extracellular side. The difference in the Ba²⁺ binding profile in the presence and absence of K⁺ thus provides a structural explanation for the short and prolonged Ba²⁺ block observed in NaK2K.     

Energy distribution and ion selectivity of the bacterial potassium channel

The ion selectivity of the bacterial potassium channel K_CSA is explained upon comparing the energy characteristics of the interaction of cations (Li⁺, Na⁺, K⁺) with atoms of the selectivity filter of the protein pore. Quantum-chemical calculations reveal a deeper potential well for potassium ions, which accounts for preferred K⁺ permeation. It is shown that the conventional methods with AMBER, CHARMM, OPLS force fields in standard parametrization as well as partial re-parametrization give incorrect estimates of ion energy distribution in the channel.     

Dynamics, Energetics, and Selectivity of the Low-K KcsA Channel Structure

Potassium channels are a diverse family of integral membrane proteins through which K⁺ can pass selectively. There is ongoing debate about the nature of conformational changes associated with the opening/closing and conductive/nonconductive states of potassium channels. The channels partly exert their function by varying their conductance through a mechanism known as C-type inactivation. Shortly after the activation of K⁺ channels, their selectivity filter stops conducting ions at a rate that depends on various stimuli. The molecular mechanism of C-type inactivation has not been fully understood yet. However, the X-ray structure of the KcsA channel obtained in the presence of low K⁺ concentration is thought to be representative of a K⁺ channel in the C-type inactivated state. Here, extensive, fully atomistic molecular dynamics and free-energy simulations of the low-K⁺ KcsA structure in an explicit lipid bilayer are performed to evaluate the stability of this structure and the selectivity of its binding sites. We find that the low-K⁺ KcsA structure is stable on the timescale of the molecular dynamics simulations performed, and that ions preferably remain in S1 and S4. In the absence of ions, the selectivity filter evolves toward an asymmetric architecture, as already observed in other computations of the high-K⁺ structure of KcsA and KirBac. The low-K⁺ KcsA structure is not permeable by Na⁺, K⁺, or Rb⁺, and the selectivity of its binding sites is different from that of the high-K⁺ structure.