Reinterpreting the Anomalous Mole Fraction Effect: The Ryanodine Receptor Case Study

The origin of the anomalous mole fraction effect (AMFE) in calcium channels is explored with a model of the ryanodine receptor. This model predicted and experiments verified new AMFEs in the cardiac isoform. In mole fraction experiments, conductance is measured in mixtures of ion species X and Y as their relative amounts (mole fractions) vary. This curve can have a minimum (an AMFE). The traditional interpretation of the AMFE is that multiple interacting ions move through the pore in a single file. Mole fraction curves without minima (no AMFEs) are generally interpreted as X displacing Y from the pore in a proportion larger than its bath mole fraction (preferential selectivity). We find that the AMFE is also caused by preferential selectivity of X over Y, if X and Y have similar conductances. This is a prediction applicable to any channel and provides a fundamentally different explanation of the AMFE that does not require single filing or multiple occupancy: preferential selectivity causes the resistances to current flow in the baths, channel vestibules, and selectivity filter to change differently with mole fraction, and produce the AMFE.     

Synthetic nanopores as a test case for ion channel theories: the anomalous mole fraction effect without single filing

The predictions of a theory for the anomalous mole fraction effect (AMFE) are tested experimentally with synthetic nanopores in plastic. The negatively charged synthetic nanopores under consideration are highly cation selective and 50 Å in diameter at their smallest point. These pores exhibit an AMFE in mixtures of Ca²⁺ and monovalent cations. An AMFE occurs when the conductance through a pore is lower in a mixture of salts than in the pure salts at the same concentration. For ion channels, the textbook interpretation of the AMFE is that multiple ions move through the pore in coordinated, single-file motion. However, because the synthetic nanopores are so wide, their AMFE shows that single filing is not necessary for the AMFE. It is shown that the AMFE in the synthetic nanopores is explained by a theory of preferential ion selectivity. The unique properties of the synthetic nanopores allow us to experimentally confirm several predictions of this theory. These same properties make synthetic nanopores an interesting new platform to test theories of ion channel permeation and selectivity in general.     

Anomalous mole fraction effect, electrostatics, and binding in ionic channels.

Ionic channels bathed in mixed solutions of two permeant electrolytes often conduct less current than channels bathed in pure solutions of either. For many years, this anomalous mole fraction effect (AMFE) has been thought to occur only in single-file pores containing two or more ions at a time. Most thinking about channels incorporates this view. We show here that the AMFE arises naturally, as an electrostatic consequence of localized ion specific binding, if the average current through a channel is described by a theory (Poisson-Nernst-Planck, PNP) that computes the average electric field from the average concentration of charges in and near the channel. The theory contains only those ion-ion interactions mediated by the mean field, and it does not enforce single filing. The AMFE is predicted by PNP over a wide range of mean concentrations of ions in the channel; for example, it is predicted when (on the average) less, or much less, than one ion is found in the channel's pore. In this treatment, the AMFE arises, in large measure, from a depletion layer produced near a region of ion-specific binding. The small excess concentration of ions in the binding region repels all nearby ions of like charge, thereby creating a depletion layer. The overall conductance of the channel arises in effect from resistors in series, one from the binding region, one from the depletion zone, and one from the unbinding region. The highest value resistor (which occurs in the depletion zone) limits the overall series conductance. Here the AMFE is not the result of single filing or multiple occupancy, and so previous views of permeation need to be revised: the presence of an AMFE does not imply that ions permeate single file through a multiply occupied pore.     

Mechanisms of permeation and selectivity in calcium channels

The mechanisms underlying ion transport and selectivity in calcium channels are examined using electrostatic calculations and Brownian dynamics simulations. We model the channel as a rigid structure with fixed charges in the walls, representing glutamate residues thought to be responsible for ion selectivity. Potential energy profiles obtained from multi-ion electrostatic calculations provide insights into ion permeation and many other observed features of L-type calcium channels. These qualitative explanations are confirmed by the results of Brownian dynamics simulations, which closely reproduce several experimental observations. These include the current-voltage curves, current-concentration relationship, block of monovalent currents by divalent ions, the anomalous mole fraction effect between sodium and calcium ions, attenuation of calcium current by external sodium ions, and the effects of mutating glutamate residues in the amino acid sequence.     

Aspartate residues of the Glu-Glu-Asp-Asp (EEDD) pore locus control selectivity and permeation of the T-type Ca(2+) channel alpha(1G)

The structural determinant of the permeation and selectivity properties of high voltage-activated (HVA) Ca(2+) channels is a locus formed by four glutamate residues (EEEE), one in each P-region of the domains I-IV of the alpha(1) subunit. We tested whether the divergent aspartate residues of the EEDD locus of low voltage-activated (LVA or T-type) Ca(2+) channels account for the distinctive permeation and selectivity features of these channels. Using the whole-cell patch-clamp technique in the HEK293 expression system, we studied the properties of the alpha(1G) T-type, the alpha(1C) L-type Ca(2+) channel subunits, and alpha(1G) pore mutants, containing aspartate-to-glutamate conversions in domain III, domain IV, or both. Three characteristic features of HVA Ca(2+) channel permeation, i.e. (a) Ba(2+) over Ca(2+) permeability, (b) Ca(2+)/Ba(2+) anomalous mole fraction effect (AMFE), and (c) high Cd(2+) sensitivity, were conferred on the domain III mutant (EEED) of alpha(1G). In contrast, the relative Ca(2+)/Ba(2+) permeability and the lack of AMFE of the alpha(1G) wild type channel were retained in the domain IV mutant (EEDE). The double mutant (EEEE) displayed AMFE and a Cd(2+) sensitivity similar to that of alpha(1C), but currents were larger in Ca(2+)- than in Ba(2+)-containing solutions. The mutation in domain III, but not that in domain IV, consistently displayed outward fluxes of monovalent cations. H(+) blocked Ca(2+) currents in all mutants more efficiently than in alpha(1G). In addition, activation curves of all mutants were displaced to more positive voltages and had a larger slope factor than in alpha(1G) wild type. We conclude that the aspartate residues of the EEDD locus of the alpha(1G) Ca(2+) channel subunit not only control its permeation properties, but also affect its activation curve. The mutation of both divergent aspartates only partially confers HVA channel permeation properties to the alpha(1G) Ca(2+) channel subunit.     

The cardiac ryanodine receptor: Looking for anomalies in permeation properties

Anomalies in the permeation properties of the cardiac RyR channel reconstituted into bilayer lipid membranes were investigated systematically. We tested the presence of the anomalous mole fraction effect (AMFE) for the ion conductance and the reversal potential with varying mole fractions of two permeant ions, while the total ion concentration was lower, as in previous studies, to avoid the masking effect of the channel pore saturation with ions. Mixtures of Ba²⁺ with other divalents (Ca²⁺, Sr²⁺), of Ca²⁺ with monovalents (Li⁺, Cs⁺), and of Na⁺ with other monovalents (Cs⁺, Li⁺) were used. We revealed a clear anomaly only for the ion conductance measured in the Na⁺-Cs⁺ and Ca²⁺-Li⁺ mixtures as computed by a Poisson-Nernst-Planck/density functional theory (PNP/DFT) model. Furthermore, we found a significant minimum in the concentration dependence of the reversal potential determined under Li⁺/Ca²⁺ bi-ionic conditions. Our study led to new observations that may have important implications for understanding the mechanisms involved in ion handling in the RyR channel pore; furthermore our results could be useful for further validation of ion permeation models developed for the RyR channel.     

Anomalous mole-fraction effects in recombinant and native cyclic nucleotide-gated channels in rat olfactory receptor neurons.

Anomalous mole-fraction effects (AMFE) were studied, using the inside-out configuration of the patchclamp technique, in both recombinant wild-type alpha-homomeric rat olfactory adenosine 3',5'-cyclic monophosphate (cAMP)-gated channels (rOCNC1) expressed in human embryonic kidney cells (HEK 293) and native cyclic nucleotide-gated (CNG) channels in acutely isolated rat olfactory receptor neurons. Single-channel and macroscopic currents were activated by 200 microM and 500 microM cAMP, respectively. Macroscopic currents, measured with mixtures of Na(+)-NH(4)(+) or Cs(+)-Li(+) in the cytoplasmic bathing solution, displayed AMFE in the rOCNC1 channels at both positive and negative membrane potentials. The rOCNC1 single-channel conductance showed a distinct minimum (or maximum) in an 80% Na(+)-20% NH(4)(+) mixture (or a 60% Cs(+)-40% Li(+) mixture), but only at positive membrane potentials. Macroscopic measurements in native olfactory CNG channels with mixtures of Na(+)-NH(4)(+) indicated similar AMFE. These results suggest that both native CNG channels and recombinant alpha-homomeric channels allow several ions to be present simultaneously within the channel pore. They also further validate the dominant role of the alpha-subunit in permeation through these channels, provide the first evidence to suggest that rOCNC1 channels have multi-ion properties and further justify the use of the rOCNC1 channel as an effective model for structure-function studies of ion permeation and selectivity in olfactory CNG channels.     

Physical descriptions of experimental selectivity measurements in ion channels

Three experiments that quantify the amount of selectivity exhibited by a biological ion channel are examined with Poisson-Nernst-Planck (PNP) theory. Conductance ratios and the conductance mole fraction experiments are examined by considering a simple model ion channel for which an approximate solution to the PNP equations with Donnan boundary conditions is derived. A more general result is derived for the Goldman-Hodgkin-Katz permeability ratio. The results show that (1) the conductance ratio measures the ratio of the diffusion coefficients of the ions inside the channel, (2) the mole fraction experiment measures the difference of the excess chemical potentials of the ions inside the channel, and (3) the permeability ratio measures both diffusion coefficients and excess chemical potentials. The results are used to divide selectivity into two components: partitioning, an equilibrium measure of how well the ions enter the channel, and diffusion, a nonequilibrium measure of how well the ions move through the channel.     

Molecular modeling of benzothiazepine binding in the L-type calcium channel

Benz(othi)azepine (BTZ) derivatives constitute one of three major classes of L-type Ca(2+) channel ligands. Despite intensive experimental studies, no three-dimensional model of BTZ binding is available. Here we have built KvAP- and KcsA-based models of the Ca(v)1.2 pore domain in the open and closed states and used multiple Monte Carlo minimizations to dock representative ligands. In our open channel model, key functional groups of BTZs interact with BTZ-sensing residues, which were identified in previous mutational experiments. The bulky tricyclic moiety occupies interface between domains III and IV, while the ammonium group protrudes into the inner pore, where it is stabilized by nucleophilic C-ends of the pore helices. In the closed channel model, contacts with several ligand-sensing residues in the inner helices are lost, which weakens ligand-channel interactions. An important feature of the ligand-binding mode in both open and closed channels is an interaction between the BTZ carbonyl group and a Ca(2+) ion chelated by the selectivity filter glutamates in domains III and IV. In the absence of Ca(2+), the tricyclic BTZ moiety remains in the domain interface, while the ammonium group directly interacts with a glutamate residue in the selectivity filter. Our model suggests that the Ca(2+) potentiation involves a direct electrostatic interaction between aCa(2+) ion and the ligand rather than an allosteric mechanism. Energy profiles indicate that BTZs can reach the binding site from the domain interface, whereas access through the open activation gate is unlikely, because reorientation of the bulky molecule in the pore is hindered.     

Molecular dynamics study of the KcsA potassium channel

The structural, dynamical, and thermodynamic properties of a model potassium channel are studied using molecular dynamics simulations. We use the recently unveiled protein structure for the KcsA potassium channel from Streptomyces lividans. Total and free energy profiles of potassium and sodium ions reveal a considerable preference for the larger potassium ions. The selectivity of the channel arises from its ability to completely solvate the potassium ions, but not the smaller sodium ions. Self-diffusion of water within the narrow selectivity filter is found to be reduced by an order of magnitude from bulk levels, whereas the wider hydrophobic section of the pore maintains near-bulk self-diffusion. Simulations examining multiple ion configurations suggest a two-ion channel. Ion diffusion is found to be reduced to approximately (1)/(3) of bulk diffusion within the selectivity filter. The reduced ion mobility does not hinder the passage of ions, as permeation appears to be driven by Coulomb repulsion within this multiple ion channel.     

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.     

Ionic selectivity in L-type calcium channels by electrostatics and hard-core repulsion

A physical model of selective “ion binding” in the L-type calcium channel is constructed, and consequences of the model are compared with experimental data. This reduced model treats only ions and the carboxylate oxygens of the EEEE locus explicitly and restricts interactions to hard-core repulsion and ion–ion and ion–dielectric electrostatic forces. The structural atoms provide a flexible environment for passing cations, thus resulting in a self-organized induced-fit model of the selectivity filter. Experimental conditions involving binary mixtures of alkali and/or alkaline earth metal ions are computed using equilibrium Monte Carlo simulations in the grand canonical ensemble. The model pore rejects alkali metal ions in the presence of biological concentrations of Ca²⁺ and predicts the blockade of alkali metal ion currents by micromolar Ca²⁺. Conductance patterns observed in varied mixtures containing Na⁺ and Li⁺, or Ba²⁺ and Ca²⁺, are predicted. Ca²⁺ is substantially more potent in blocking Na⁺ current than Ba²⁺. In apparent contrast to experiments using buffered Ca²⁺ solutions, the predicted potency of Ca²⁺ in blocking alkali metal ion currents depends on the species and concentration of the alkali metal ion, as is expected if these ions compete with Ca²⁺ for the pore. These experiments depend on the problematic estimation of Ca²⁺ activity in solutions buffered for Ca²⁺ and pH in a varying background of bulk salt. Simulations of Ca²⁺ distribution with the model pore bathed in solutions containing a varied amount of Li⁺ reveal a “barrier and well” pattern. The entry/exit barrier for Ca²⁺ is strongly modulated by the Li⁺ concentration of the bath, suggesting a physical explanation for observed kinetic phenomena. Our simulations show that the selectivity of L-type calcium channels can arise from an interplay of electrostatic and hard-core repulsion forces among ions and a few crucial channel atoms. The reduced system selects for the cation that delivers the largest charge in the smallest ion volume.     

Current and selectivity in a model sodium channel under physiological conditions: Dynamic Monte Carlo simulations

A reduced model of a sodium channel is analyzed using Dynamic Monte Carlo simulations. These include the first simulations of ionic current under approximately physiological ionic conditions through a model sodium channel and an analysis of how mutations of the sodium channel's DEKA selectivity filter motif transform the channel from being Na(+) selective to being Ca(2+) selective. Even though the model of the pore, amino acids, and permeant ions is simplified, the model reproduces the fundamental properties of a sodium channel (e.g., 10 to 1 Na(+) over K(+) selectivity, Ca(2+) exclusion, and Ca(2+) selectivity after several point mutations). In this model pore, ions move through the pore one at a time by simple diffusion and Na(+) versus K(+) selectivity is due to both the larger K(+) not fitting well into the selectivity filter that contains amino acid terminal groups and K(+) moving more slowly (compared to Na(+)) when it is in the selectivity filter.     

Homology modeling and molecular dynamics simulation studies of an inward rectifier potassium channel

A homology model has been generated for the pore-forming domain of Kir6.2, a component of an ATP-sensitive K channel, based on the x-ray structure of the bacterial channel KcsA. Analysis of the lipid-exposed and pore-lining surfaces of the model reveals them to be compatible with the known features of membrane proteins and Kir channels, respectively. The Kir6.2 homology model was used as the starting point for nanosecond-duration molecular dynamics simulations in a solvated phospholipid bilayer. The overall drift from the model structure was comparable to that seen for KcsA in previous similar simulations. Preliminary analysis of the interactions of the Kir6.2 channel model with K(+) ions and water molecules during these simulations suggests that concerted single-file motion of K(+) ions and water through the selectivity filter occurs. This is similar to such motion observed in simulations of KcsA. This suggests that a single-filing mechanism is conserved between different K channel structures and may be robust to changes in simulation details. Comparison of Kir6.2 and KcsA suggests some degree of flexibility in the filter, thus complicating models of ion selectivity based upon a rigid filter.     

Proteins,channels and crowded ions

Ion channels are proteins with a hole down their middle that control a vast range of biological function in health and disease. Selectivity is an important biological function determined by the open channel, which does not change conformation on the biological time scale. The challenge is to predict the function—the current of ions of different types and concentrations through a variety of channels—from structure, given fundamental physical laws. Walls of ion channels, like active sites of enzymes, often contain several fixed charges. Those fixed charges demand counter ions nearby, and the density of those counter ions is very high, greater than 5 molar, because of the tiny volumes of the channel's pore. Physical chemists can now calculate the free energy per mole of salt solutions (e.g. the activity coefficient) from infinite dilution to saturation, even in ionic melts. Such calculations of a model of the L-type calcium channel show that the large energies needed to crowd charges into the channel can account for the substantial selectivity and complex properties found experimentally. The properties of such crowded charge are likely to be an important determinant of the properties of proteins in general because channels are nearly enzymes.     

Ion solvation and structural stability in a sodium channel investigated by molecular dynamics calculations

The stability and ion binding properties of the homo-tetrameric pore domain of a prokaryotic, voltage-gated sodium channel are studied by extensive all-atom molecular dynamics simulations, with the channel protein being embedded in a fully hydrated lipid bilayer. It is found that Na(+) ion presents in a mostly hydrated state inside the wide pore of the selectivity filter of the sodium channel, in sharp contrast to the nearly fully dehydrated state for K(+) ions in potassium channels. Our results also indicate that Na(+) ions make contact with only one or two out of the four polypeptide chains forming the selectivity filter, and surprisingly, the selectivity filter exhibits robust stability for various initial ion configurations even in the absence of ions. These findings are quite different from those in potassium channels. Furthermore, an electric field above 0.5V/nm is suggested to be able to induce Na(+) permeation through the selectivity filter.     

A molecular dynamics study of an L-type calcium channel model

In this work, we propose a molecular model of the L-type calcium channel pore from the human cardiac alpha1 subunit. Four glutamic acid residues, the EEEE locus, located at highly conserved P loops (also called SS1-SS2 segments) of the alpha1 subunit, molecularly express the calcium channel selectivity. The proposed alpha-helix structure for the SS1 segment, analyzed through molecular dynamics simulations in aqueous-phase, was validated by the plotting of Ramachandran diagrams for the averaged structures and by the analysis of i and i + 4 helical hydrogen bonding between the amino acid residues. The results of the simulation of the calcium channel model with one and two Ca2+ ions at the binding site are in accordance with mutation studies which suggest that the EEEE locus in the L-type calcium channel must form a single high-affinity binding site. These results suggest that the Ca2+ permeation through the channel would be derived from competition between two ions for the only high-affinity binding site. Furthermore, the experimentally observed blocking of the Na+ flux at micromolar Ca2+ concentrations, probably due to the occupancy of the single high-affinity binding site for one Ca2+, was also reproduced by our model.     

Ion permeation and glutamate residues linked by Poisson-Nernst-Planck theory in L-type calcium channels.

L-type Ca channels contain a cluster of four charged glutamate residues (EEEE locus), which seem essential for high Ca specificity. To understand how this highly charged structure might produce the currents and selectivity observed in this channel, a theory is needed that relates charge to current. We use an extended Poisson-Nernst-Planck (PNP2) theory to compute (mean) Coulombic interactions and thus to examine the role of the mean field electrostatic interactions in producing current and selectivity. The pore was modeled as a central cylinder with tapered atria; the cylinder (i.e., "pore proper") contained a uniform volume density of fixed charge equivalent to that of one to four carboxyl groups. The pore proper was assigned ion-specific, but spatially uniform, diffusion coefficients and excess chemical potentials. Thus electrostatic selection by valency was computed self-consistently, and selection by other features was also allowed. The five external parameters needed for a system of four ionic species (Na, Ca, Cl, and H) were determined analytically from published measurements of thre limiting conductances and two critical ion concentrations, while treating the pore as a macroscopic ion-exchange system in equilibrium with a uniform bath solution. The extended PNP equations were solved with these parameters, and the predictions were compared to currents measured in a variety of solutions over a range of transmembrane voltages. The extended PNP theory accurately predicted current-voltage relations, anomalous mole fraction effects in the observed current, saturation effects of varied Ca and Na concentrations, and block by protons. Pore geometry, dielectric permittivity, and the number of carboxyl groups had only weak effects. The successful prediction of Ca fluxes in this paper demonstrates that ad hoc electrostatic parameters, multiple discrete binding sites, and logistic assumptions of single-file movement are all unnecessary for the prediction of permeation in Ca channels over a wide range of conditions. Further work is needed, however, to understand the atomic origin of the fixed charge, excess chemical potentials, and diffusion coefficients of the channel. The Appendix uses PNP2 theory to predict ionic currents for published "barrier-and-well" energy profiles of this channel.     

Thiocyanate as a probe of the cystic fibrosis transmembrane conductance regulator chloride channel pore

Immediately following exposure to thiocyanate (SCN-)-containing solutions, the cystic fibrosis conductance regulator Cl- channel exhibits high unitary SCN conductance and anomalous mole fraction behaviour, suggesting the presence of multiple anion binding sites within the channel pore. However, under steady-state conditions SCN-conductance is very low. Here I show, using patch clamp recording from CFTR-transfected mammalian cell lines, that under steady-state conditions neither SCN- conductance nor SCN- permeability show anomalous mole fraction behaviour. Instead, SCN conductance, permeability, and block of Cl- permeation can all be reproduced by a rate theory model that assumes only a single intrapore anion binding site. These results suggest that under steady-state conditions the interaction between SCN- and the CFTR channel pore can be understood by a simple model whereby SCN- ions enter the pore more easily than Cl-, and bind within the pore more tightly than Cl-. The implications of these findings for investigating and understanding the mechanism of anion permeation are discussed.