Human PIEZO1: Removing Inactivation

PIEZO1 is an inactivating eukaryotic cation-selective mechanosensitive ion channel. Two sites have been located in the channel that when individually mutated lead to xerocytotic anemia by slowing inactivation. By introducing mutations at two sites, one associated with xerocytosis and the other artificial, we were able to remove inactivation. The double mutant (DhPIEZO1) has a substitution of arginine for methionine (M2225R) and lysine for arginine (R2456K). The loss of inactivation was accompanied by ∼30-mmHg shift of the activation curve to lower pressures and slower rates of deactivation. The slope sensitivity of gating was the same for wild-type and mutants, indicating that the dimensional changes between the closed and open state are unaffected by the mutations. The unitary channel conductance was unchanged by mutations, so these sites are not associated with pore. DhPIEZO1 was reversibly inhibited by the peptide GsMTx4 that acted as a gating modifier. The channel kinetics were solved using complex stimulus waveforms and the data fit to a three-state loop in detailed balance. The reaction had two pressure-dependent rates, closed to open and inactivated to closed. Pressure sensitivity of the opening rate with no sensitivity of the closing rate means that the energy barrier between them is located near the open state. Mutant cycle analysis of inactivation showed that the two sites interacted strongly, even though they are postulated to be on opposite sides of the membrane.     

Human PIEZO1: Removing Inactivation

PIEZO1 is an inactivating eukaryotic cation-selective mechanosensitive ion channel. Two sites have been located in the channel that when individually mutated lead to xerocytotic anemia by slowing inactivation. By introducing mutations at two sites, one associated with xerocytosis and the other artificial, we were able to remove inactivation. The double mutant (DhPIEZO1) has a substitution of arginine for methionine (M2225R) and lysine for arginine (R2456K). The loss of inactivation was accompanied by ∼30-mmHg shift of the activation curve to lower pressures and slower rates of deactivation. The slope sensitivity of gating was the same for wild-type and mutants, indicating that the dimensional changes between the closed and open state are unaffected by the mutations. The unitary channel conductance was unchanged by mutations, so these sites are not associated with pore. DhPIEZO1 was reversibly inhibited by the peptide GsMTx4 that acted as a gating modifier. The channel kinetics were solved using complex stimulus waveforms and the data fit to a three-state loop in detailed balance. The reaction had two pressure-dependent rates, closed to open and inactivated to closed. Pressure sensitivity of the opening rate with no sensitivity of the closing rate means that the energy barrier between them is located near the open state. Mutant cycle analysis of inactivation showed that the two sites interacted strongly, even though they are postulated to be on opposite sides of the membrane.     

Ion Permeation and Selectivity of Wild-Type Recombinant Rat CNG (rOCNC1) Channels Expressed in HEK293 Cells

The permeation properties of adenosine 3′, 5′-cyclic monophosphate (cAMP)-activated recombinant rat olfactory cyclic nucleotide-gated channels (rOCNC1) in human embryonic kidney (HEK 293) cells were investigated using inside-out excised membrane patches. The relative permeability of these rOCNC1 channels to monovalent alkali cations and organic cations was determined from measurements of the changes in reversal potential upon replacing sodium in the bathing solution with different test cations. The permeability ratio of Cl⁻ relative to Na⁺ (P _Cl /P _Na ) was about 0.14, confirming that these channels are mainly permeable to cations. The sequence of relative permeabilities of monovalent alkali metal ions in these channels was P _Na ≥P _K > P _Li > P _Cs ≥P _Rb , which closely corresponds to a high-strength field sequence as previously determined for native rat olfactory receptor neurons (ORNs). The permeability sequence for organic cations relative to sodium was P _NH3OH > P _NH4 > P _Na > P _Tris > P _Choline > P _TEA , again in good agreement with previous permeability ratios obtained in native rat ORNs. Single-channel conductance sequences agreed surprisingly well with permeability sequences. These conductance measurements also indicated that, even in asymmetric bi-ionic cation solutions, the conductance was somewhat independent of current direction and dependent on the composition of both solutions. These results indicate that the permeability properties of rOCNC1 channels are similar to those of native rat CNG channels, and provide a suitable reference point for exploring the molecular basis of ion selectivity in recombinant rOCNC1 channels using site-directed mutagenesis. Received: 3 July 2000/Revised: 29 August 2000     

Protonation of the Human PIEZO1 Ion Channel Stabilizes Inactivation

PIEZO1 is a recently cloned eukaryotic cation-selective channel that opens with mechanical force. We found that extracellular protonation inhibits channel activation by ≈90% by increased occupancy in the closed or the inactivated state. Titration between pH 6.3 and 8.3 exhibited a pK of ≈6.9. The steepness of the titration data suggests positive cooperativity, implying the involvement of at least two protonation sites. Whole-cell recordings yielded results similar to patches, and pH 6.5 reduced whole-cell currents by >80%. The effects were reversible. To assess whether pH acts on the open or the inactivated state, we tested a double-mutant PIEZO1 that does not inactivate. Cell-attached patches and whole-cell currents from this mutant channel were pH-insensitive. Thus, protonation appears to be associated with domain(s) of the channel involved with inactivation. pH also did not affect mutant channels with point mutations at position 2456 that are known to exhibit slow inactivation. To determine whether the physical properties of the membrane are altered by pH and thereby affect channel gating, we measured patch capacitance during mechanical stimuli at pH 6.5 and 7.3. The rate constants for changes in patch capacitance were independent of pH, suggesting that bilayer mechanics are not involved. In summary, low pH stabilizes the inactivated state. This effect may be important when channels are activated under pathological conditions in which the pH is reduced, such as during ischemia.     

Human PIEZO1 Ion Channel Functions as a Split Protein

PIEZO1 is a mechanosensitive eukaryotic cation-selective channel that rapidly inactivates in a voltage-dependent manner. We previously showed that a fluorescent protein could be encoded within the hPIEZO1 sequence without loss of function. In this work, we split the channel into two at this site and asked if coexpression would produce a functional channel or whether gating and permeation might be contained in either segment. The split protein was expressed in two segments by a bicistronic plasmid where the first segment spanned residues 1 to 1591, and the second segment spanned 1592 to 2521. When the “split protein” is coexpressed, the parts associate to form a normal channel. We measured the whole-cell, cell-attached and outside-out patch currents in transfected HEK293 cells. Indentation produced whole-cell currents monotonic with the stimulus. Single channel recordings showed voltage-dependent inactivation. The Boltzmann activation curve for outside-out patches had a slope of 8.6/mmHg vs 8.1 for wild type, and a small leftward shift in the midpoint (32 mmHg vs 41 mmHg). The association of the two channel domains was confirmed by FRET measurements of mCherry on the N-terminus and EGFP on the C-terminus. Neither of the individual protein segments produced current when expressed alone.     

Ionic Channels of the Sugar Beet Tonoplast are Regulated by a Multi-ion Single-file Permeation Mechanism

Ionic channels of the sugar beet tonoplast were studied using the patch-clamp technique. At micromolar concentrations of cytosolic calcium, several (at least four) distinct single-channel current levels were routinely identified. On the basis of channel voltage dependence, kinetic properties and conductance of single openings, the largest channel (103 ± 2 pS in symmetric 150 mm KCl) corresponds to the slow vacuolar (SV) channel already identified by Hedrich and Neher (1987). The majority of the whole-vacuole current was ascribed to this time-dependent slow-activating channel elicited by positive vacuolar potentials. The channel of intermediate amplitude (41 ± 1 pS in 150 mm KCl) did not show any voltage dependence and delay in the activation upon the application of voltage steps to both positive and negative transmembrane potentials. Owing to its voltage independence this channel was denominated FV1. The opening probability of the SV-type channel increased by increasing the cytoplasmic calcium concentration, while the activity of the FV1 channel did not increase appreciably by changing the calcium concentration in the range from 6 μm to 1 mm. All the channels identified showed a linear current-voltage characteristic in the range ±100 mV and at least the three most conductive ones displayed potassium selectivity properties. Substitution of potassium with tetramethylammonium (TMA) on the cytosolic side demonstrated that both the SV and FV1 channels are impermeable to TMA influx into the vacuole and support the potassium selectivity properties of these two channels. Moreover, the single channel conductances of all the channels identified increased as a function of the potassium concentration and reached a maximum conductivity at [K⁺] ∼0.5 m. This behavior can be explained by a multi-ion occupancy single-file permeation mechanism. Received: 26 December 1995/Revised: 10 July 1996     

Permeation Models and Structure-Function Relationships in Ion Channels

Recent determination of the molecular structures of potassium andmechanosensitive channels from x-ray crystallography has led to arenewed interest in ion channels. The challenge for permeation modelsis to understand the functional properties of channels from the availablestructural information. Here we give a critical review of the three maincontenders, namely, continuum theories, Brownian dynamics and moleculardynamics. Continuum theories are shown to be invalid in a narrow channel environment because they ignore the self-energy of ions arising from theinduced charges on the dielectric boundary. Brownian and moleculardynamics are thus the only physically valid methods for studying thestructure-function relations in ion channels. Applications of thesemethods to potassium and calcium channels are presented, which illustratethe multi-ion nature of the permeation mechanism in selective biologicalchannels.     

Separation of Gating Properties from Permeation and Block in mslo Large Conductance Ca-activated K+ Channels

In this and the following paper we have examined the kinetic and steady-state properties of macroscopic mslo Ca-activated K⁺ currents in order to interpret these currents in terms of the gating behavior of the mslo channel. To do so, however, it was necessary to first find conditions by which we could separate the effects that changes in Ca²⁺ concentration or membrane voltage have on channel permeation from the effects these stimuli have on channel gating. In this study we investigate three phenomena which are unrelated to gating but are manifest in macroscopic current records: a saturation of single channel current at high voltage, a rapid voltage-dependent Ca²⁺ block, and a slow voltage-dependent Ba²⁺ block. Where possible methods are described by which these phenomena can be separated from the effects that changes in Ca²⁺ concentration and membrane voltage have on channel gating. Where this is not possible, some assessment of the impact these effects have on gating parameters determined from macroscopic current measurements is provided. We have also found that without considering the effects of Ca²⁺ and voltage on channel permeation and block, macroscopic current measurements suggest that mslo channels do not reach the same maximum open probability at all Ca²⁺ concentrations. Taking into account permeation and blocking effects, however, we find that this is not the case. The maximum open probability of the mslo channel is the same or very similar over a Ca²⁺ concentration range spanning three orders of magnitude indicating that over this range the internal Ca²⁺ concentration does not limit the ability of the channel to be activated by voltage.     

Fast Inactivation in Shaker K+ Channels : Properties of Ionic and Gating Currents

Fast inactivating Shaker H4 potassium channels and nonconducting pore mutant Shaker H4 W434F channels have been used to correlate the installation and recovery of the fast inactivation of ionic current with changes in the kinetics of gating current known as “charge immobilization” (Armstrong, C.M., and F. Bezanilla. 1977. J. Gen. Physiol. 70:567–590.). Shaker H4 W434F gating currents are very similar to those of the conducting clone recorded in potassium-free solutions. This mutant channel allows the recording of the total gating charge return, even when returning from potentials that would largely inactivate conducting channels. As the depolarizing potential increased, the OFF gating currents decay phase at −90 mV return potential changed from a single fast component to at least two components, the slower requiring ∼200 ms for a full charge return. The charge immobilization onset and the ionic current decay have an identical time course. The recoveries of gating current (Shaker H4 W434F) and ionic current (Shaker H4) in 2 mM external potassium have at least two components. Both recoveries are similar at −120 and −90 mV. In contrast, at higher potentials (−70 and −50 mV), the gating charge recovers significantly more slowly than the ionic current. A model with a single inactivated state cannot account for all our data, which strongly support the existence of “parallel” inactivated states. In this model, a fraction of the charge can be recovered upon repolarization while the channel pore is occupied by the NH₂-terminus region.     

Surface Potentials and the Calculated Selectivity of Ion Channels

Ion channels catalyze the transport of ions across biological membranes. A proper understanding of ion-channel functioning is essential to our knowledge of cell physiology, and, in this context, ion-channel selectivity is a key concept. The extent to which a channel permeates two ion species, a and b, is expressed by the permeability ratio, P_a/P_b. This paper addresses a complication in the calculation of P_a/P_b that is related to the existence of surface potentials (ψ) and that so far has not been fully appreciated. This paper shows the rather surprising effect of ψ on the calculated P_a/P_b of a channel that is permeable to two ion species of different valence. If we ignore ψ, we conclude, for instance, P_a > P_b. If we implement ψ in the calculation of P_a/P_b, we may, however, conclude exactly the reverse, i.e., P_a < P_b. Because electrostatic potentials arise at the surface of essentially all biological membranes, this paper argues for a more critical evaluation of ion channel selectivity measurements.     

Substrate Profile and Metal-ion Selectivity of Human Divalent Metal-ion Transporter-1

Divalent metal-ion transporter-1 (DMT1) is a H⁺-coupled metal-ion transporter that plays essential roles in iron homeostasis. DMT1 exhibits reactivity (based on evoked currents) with a broad range of metal ions; however, direct measurement of transport is lacking for many of its potential substrates. We performed a comprehensive substrate-profile analysis for human DMT1 expressed in RNA-injected Xenopus oocytes by using radiotracer assays and the continuous measurement of transport by fluorescence with the metal-sensitive PhenGreen SK fluorophore. We provide validation for the use of PhenGreen SK fluorescence quenching as a reporter of cellular metal-ion uptake. We determined metal-ion selectivity under fixed conditions using the voltage clamp. Radiotracer and continuous measurement of transport by fluorescence assays revealed that DMT1 mediates the transport of several metal ions that were ranked in selectivity by using the ratio I_max/K_0.5 (determined from evoked currents at −70 mV): Cd²⁺ > Fe²⁺ > Co²⁺, Mn²⁺ ≫ Zn²⁺, Ni²⁺, VO²⁺. DMT1 expression did not stimulate the transport of Cr²⁺, Cr³⁺, Cu⁺, Cu²⁺, Fe³⁺, Ga³⁺, Hg²⁺, or VO⁺. ⁵⁵Fe²⁺ transport was competitively inhibited by Co²⁺ and Mn²⁺. Zn²⁺ only weakly inhibited ⁵⁵Fe²⁺ transport. Our data reveal that DMT1 selects Fe²⁺ over its other physiological substrates and provides a basis for predicting the contribution of DMT1 to intestinal, nasal, and pulmonary absorption of metal ions and their cellular uptake in other tissues. Whereas DMT1 is a likely route of entry for the toxic heavy metal cadmium, and may serve the metabolism of cobalt, manganese, and vanadium, we predict that DMT1 should contribute little if at all to the absorption or uptake of zinc. The conclusion in previous reports that copper is a substrate of DMT1 is not supported.     

Mechanism of Ion Permeation in Skeletal Muscle Chloride Channels

Voltage-gated Cl⁻ channels belonging to the ClC family exhibit unique properties of ion permeation and gating. We functionally probed the conduction pathway of a recombinant human skeletal muscle Cl⁻ channel (hClC-1) expressed both in Xenopus oocytes and in a mammalian cell line by investigating block by extracellular or intracellular I⁻ and related anions. Extracellular and intracellular I⁻ exert blocking actions on hClC-1 currents that are both concentration and voltage dependent. Similar actions were observed for a variety of other halide (Br⁻) and polyatomic (SCN⁻, NO₃ ⁻, CH₃SO₃ ⁻) anions. In addition, I⁻ block is accompanied by gating alterations that differ depending on which side of the membrane the blocker is applied. External I⁻ causes a shift in the voltage-dependent probability that channels exist in three definable kinetic states (fast deactivating, slow deactivating, nondeactivating), while internal I⁻ slows deactivation. These different effects on gating properties can be used to distinguish two functional ion binding sites within the hClC-1 pore. We determined K _D values for I⁻ block in three distinct kinetic states and found that binding of I⁻ to hClC-1 is modulated by the gating state of the channel. Furthermore, estimates of electrical distance for I⁻ binding suggest that conformational changes affecting the two ion binding sites occur during gating transitions. These results have implications for understanding mechanisms of ion selectivity in hClC-1, and for defining the intimate relationship between gating and permeation in ClC channels.     

Ionic Blockage of Sodium Channels in Nerve

Increasing the hydrogen ion concentration of the bathing medium reversibly depresses the sodium permeability of voltage-clamped frog nerves. The depression depends on membrane voltage: changing from pH 7 to pH 5 causes a 60% reduction in sodium permeability at +20 mV, but only a 20% reduction at +180 mV. This voltage-dependent block of sodium channels by hydrogen ions is explained by assuming that hydrogen ions enter the open sodium channel and bind there, preventing sodium ion passage. The voltage dependence arises because the binding site is assumed to lie far enough across the membrane for bound ions to be affected by part of the potential difference across the membrane. Equations are derived for the general case where the blocking ion enters the channel from either side of the membrane. For H⁺ ion blockage, a simpler model, in which H⁺ enters the channel only from the bathing medium, is found to be sufficient. The dissociation constant of H⁺ ions from the channel site, 3.9 x 10^-6 M (pK_a 5.4), is like that of a carboxylic acid. From the voltage dependence of the block, this acid site is about one-quarter of the way across the membrane potential from the outside. In addition to blocking as described by the model, hydrogen ions also shift the responses of sodium channel "gates" to voltage, probably by altering the surface potential of the nerve. Evidence for voltage-dependent blockage by calcium ions is also presented.     

Selectivity Changes during Activation of Mutant Shaker Potassium Channels

Mutations of the pore-region residue T442 in Shaker channels result in large effects on channel kinetics. We studied mutations at this position in the backgrounds of NH₂-terminal–truncated Shaker H4 and a Shaker -NGK2 chimeric channel having high conductance (Lopez, G.A., Y.N. Jan, and L.Y. Jan. 1994. Nature (Lond.). 367: 179–182). While mutations of T442 to C, D, H, V, or Y resulted in undetectable expression in Xenopus oocytes, S and G mutants yielded functional channels having deactivation time constants and channel open times two to three orders of magnitude longer than those of the parental channel. Activation time courses at depolarized potentials were unaffected by the mutations, as were first-latency distributions in the T442S chimeric channel. The mutant channels show two subconductance levels, 37 and 70% of full conductance. From single-channel analysis, we concluded that channels always pass through the larger subconductance state on the way to and from the open state. The smaller subconductance state is traversed in ∼40% of activation time courses. These states apparently represent kinetic intermediates in channel gating having voltage-dependent transitions with apparent charge movements of ∼1.6 e₀. The fully open T442S chimeric channel has the conductance sequence Rb⁺ > NH₄ ⁺ > K⁺. The opposite conductance sequence, K⁺ > NH₄ ⁺ > Rb⁺, is observed in each of the subconductance states, with the smaller subconductance state discriminating most strongly against Rb⁺.     

Functional Reconstitution of Purified Human Hv1 H Channels

Voltage-dependent H⁺ (Hv) channels mediate proton conduction into and out of cells under the control of membrane voltage. Hv channels are unusual compared to voltage-dependent K⁺, Na⁺, and Ca²⁺ channels in that Hv channel genes encode a voltage sensor domain (VSD) without a pore domain. The H⁺ currents observed when Hv channels are expressed heterologously suggest that the VSD itself provides the pathway for proton conduction. In order to exclude the possibility that the Hv channel VSD assembles with an as yet unknown protein in the cell membrane as a requirement for H⁺ conduction, we have purified Hv channels to homogeneity and reconstituted them into synthetic lipid liposomes. The Hv channel VSD by itself supports H⁺ flux.     

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.     

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.