Negative conductance caused by entry of sodium and cesium ions into the potassium channels of squid axons

Internal Cs⁺, Na⁺, Li⁺, and, to a lesser degree, Rb⁺ interfere with outward current through the K pores in voltage clamped squid axons. Addition of 100 mM NaF to the perfusion medium cuts outward current for large depolarizations about in half, and causes negative conductance over a range of membrane voltages. For example, suddenly reducing membrane potential from +100 to +60 mv increases the magnitude of the outward current. Internal Cs⁺ and, to a small extent, Li⁺, also cause negative conductance. Na⁺ ions permeate at least 17 times less well through the K pores than K⁺, and Cs⁺ does not permeate measurably. The results strongly suggest that K pores have a wide and not very selective inner mouth, which accepts K⁺, Na⁺, Li⁺, Cs⁺, tetraethylammonium ion (TEA⁺), and other ions. The diameter of the mouth must be at least 8 A, which is the diameter of a TEA⁺ ion. K⁺ ions in the mouths probably have full hydration shells. The remainder of the pore is postulated to be 2.6–3.0 A in diameter, large enough for K⁺ and Rb⁺ but too small for Cs⁺ and TEA⁺. We postulate that Na⁺ ions do not enter the narrower part of the pore because they are too small to fit well in the coordination cages provided by the pore as replacements for the water molecules surrounding an ion.     

An analysis of conductance changes in squid axon

The membrane of the squid axon is considered on the basis of a pore model in which the distribution of the pore sizes strongly favors K⁺ transfer when there is no potential. Electrical asymmetry causes non-penetrating ions on the membrane capacitor to exert a mechanical force on both membrane surfaces and this force results in a deformation of the membrane pore system such that it assumes a distribution of sizes favoring the ions exerting mechanical force. The ions involved appear to be Ca⁺⁺ on the outside of the membrane and isethionate^-, (i^-) on the inside; as Ca⁺⁺ is equivalent in size to Na⁺, the charged membrane is potentially able to transfer Na⁺, when the ions deforming the membrane pore distribution are removed. A depolarization of the membrane leads to an opening of pores that will allow Na⁺ penetration and a release of the membrane from deformation. The pores revert to the zero-potential pore size distribution hence the Na permeability change is a transient. Calculation shows that the potassium conductance vs. displacement of membrane potential curve for the squid axon and the "inactivation" function, h, can be obtained directly from the assumed membrane distortion without the introduction of arbitrary parameters. The sodium conductance, because it is a transient, requires assumptions about the time constants with which ions unblock pores at the outside and the inside of the membrane.     

Molecular Dynamics Simulation of Limiting Conductance for Na2+, Cl2−, Na°, and Cl° in Supercritical Water

Abstract

We report results of molecular dynamics simulations of the limiting conductance of Na²⁺, Cl^2?, Na°, and Cl° in supercritical water using the SPC/E model for water in conjuction with our previous study (Lee et al., Chem. Phys. Lett. 293, 289 (1998)). The behavior of the limiting conductances of Na²⁺ and Cl^2? in the whole range of water density shows almost the same trend as those of Na⁺ and Cl^?, but the deviation from the assumed linear dependence of limiting conductances of Na²⁺ and Cl^2? on the water density is smaller than that of Na⁺ and Cl^?. The ratio of the limiting conductance of the divalentions to that of the corresponding monovalentions over the whole range of water density is almost constant. In the cases of Na²⁺ and Cl^2?, the dominating factor of the number of hydration water molecules around ions in the higher-density region and the dominating factor of the interaction strength between the ions and the hydration water molecules in the lower-density region are also found as was the cases for Na⁺ and Cl^?. These factors, however, are not so strong as for the corresponding monovalent ions because the change in the energetics, structure, and dynamics are very small mainly due to the strong Coulomb interaction of the divalent ions with the hydration water molecules. The diffusion coefficient of Na° and Cl° monotonically increases with decreasing water density over the whole range of water density. The increase of the diffusion coefficient with decreasing water density is attributed only to the dramatic decrease of the hydration number of water in the first solvation shell around the uncharged species. Among the two important competing factors in the limiting conductance of Na⁺ and Cl^?, the effect of the number of hydration water molecules around the uncharged species is the only existing factor over the whole range of water density since the interaction strength between the uncharged species and the hydration water molecules very small through the LJ interaction. This result has confirmed the dominating factor of the number of hydration water molecules around ions in the higher-density region in the explanation of the limiting conductance of Na⁺ and Cl^? in supercritical water at 673 K.     

Ca2+-activated K+ permeability in human erythrocytes: Modulation of single-channel events

Elevated levels of intracellular Ca²⁺ activate a K⁺-selective permeability in the membrane of human erythrocytes. Currents through single channels were analysed in excised inside-out membrane patches. The effects of several ions that are known to inhibit K⁺ fluxes are described with respect to the single-channel events. The results suggest that the blocking ions can partly move into the channels (but cannot penetrate) and interact with other ions inside the pore. The reduction of single-channel conductance by Cs⁺, tetraethylammonium and Ba²⁺ and of single-channel activity by quinine and Ba²⁺ is referred to different rates of access to the channel. The concentration- and voltage-dependent inhibition by ions with measurable permeability (Na⁺ and Rb⁺) can be explained by their lower permeability, with single-file movement and ionic interactions inside the pore.     

Molecular dynamics of water and monovalent‐ions transportation mechanisms of pentameric sarcolipin

The Sarcolipin (SLN) is a transmembrane protein that can form a self‐assembled pentamer. In this work, the homology modeling and all‐atom molecular dynamic (MD) simulation was performed to study the model of SLN pentamer in POPC (1‐palmitoyl‐2‐oleoyl‐sn‐glycero‐3‐phosphocholine) membrane. The potential of mean force (PMF) was calculated for transmembrane transportation of Na⁺, Cl^? and water molecule along the pore channel of penta‐SLN complex. The root mean square deviation (RMSD) of the SLN pentamer in POPC membrane showed that the stabilized SLN protein complex could exist in the membrane and that the Na⁺ and Cl^? could not permeate through the channel when the pore was under the vacuum state, but the water could permeate through from cytoplasm to lumen. Under the aqueous state, our simulation demonstrated that hydrated state of Na⁺ and Cl^? could pass through the channel. The PMF and radii of the pore showed that the channel had a gate at Leu²¹ that is a key hydrophobicity residue in the channel. Our simulations help to clarify and to understand better the SLN pentamer channel that had a hydrophobic gate and could switch Na⁺ and Cl^? ion permeability by hydrated and vacuum states. Proteins 2016; 84:73–81. © 2015 Wiley Periodicals, Inc.     

Transport of ions across peritoneal membrane

The electrical conductance of ions across the peritoneal membrane of young buffalo (approximately 18-24 months old) has been recorded. Aqueous solutions of NaF, NaNO₃, NaCl, Na₂SO₄, KF, KNO₃, KCl, K₂SO₄, MgCl₂, CaCl₂, CrCl₃, MnCl₂, FeCl₃, CoCl₂, and CuCl₂ were used. The conductance values have been found to increase with increase in concentration as well as with temperature (15 to 35 °C) in these cases. The slope of plots of specific conductance, κ, versus concentration exhibits a decrease in its values at relatively higher concentrations compared to those in extremely dilute solutions. Also, such slopes keep on increasing with increase in temperature. In addition, the conductance also attains a maximum limiting value at higher concentrations in the said cases. This may be attributed to a progressive accumulation of ionic species within the membrane. The κ values of electrolytes follow the sequence for the anions: SO₄²⁻>Cl⁻>NO₃⁻>F⁻ while that for the cations: K⁺>Na⁺>Ca²⁺>Mn²⁺>Co²⁺>Cu²⁺>Mg²⁺>Cr³⁺>Fe³⁺. In addition, the diffusion of ions depends upon the charge on the membrane and its porosity. The membrane porosity in relation to the size of the hydrated species diffusing through the membrane appears to determine the above sequence. As the diffusional paths in the membrane become more difficult in aqueous solutions, the mobility of large hydrated ions gets impeded by the membrane framework and the interaction with the fixed charge groups on the membrane matrix. Consequently, the membrane pores reduce the conductance of small ions, which are much hydrated. An increase in conductance with increase in temperature may be due to the state of hydration, which implies that the energy of activation for the ionic transport across the membrane follows the sequence of crystallographic radii of ions accordingly. The Eyring's equation, κ=(RT/Nh)exp[−ΔH*/RT]exp[ΔS*/R], has been found suitable for explaining the temperature dependence of conductance in the said cases. This is apparent from the linear plots of log[κNh/RT] versus 1/T. The results indicate that the permeation of ions through the membrane giving negative values of ΔS* suggest that there may be formation of either covalent linkage between the penetrating ions and the membrane material or else the permeation may not be the rate-determining step. On the one hand, a high ΔS* value associated with the high value of energy of activation, E_a, for diffusion may suggest the existence of either a large zone of activation or loosening of more chain segments of the membrane. On the other hand, low value of ΔS* implies that converse is true in such cases, i.e., either a small zone of activation or no loosening of the membrane structure upon permeation.     

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.     

A model for the generation of localized transient [Na] elevations in vascular smooth muscle

We present a stochastic computational model to study the mechanism of signaling between a source and a target ionic transporter, both localized on the plasma membrane (PM). In general this requires a nanometer-scale cytoplasmic space, or nanodomain, between the PM and a peripheral organelle to reflect ions back towards the PM. Specifically we investigate the coupling between Na⁺ entry via the transient receptor potential canonical channel 6 (TRPC6) and the Na⁺/Ca²⁺ exchanger (NCX), a process which is essential for reloading the sarcoplasmic reticulum (SR) via the sarco/endoplasmic reticulum Ca²⁺ATPase (SERCA) and maintaining Ca²⁺ oscillations in activated vascular smooth muscle. Having previously modeled the flow of Ca²⁺ between reverse NCX and SERCA during SR refilling, this quantitative approach now allows us to model the upstream linkage of Na⁺ entry through TRPC6 to reversal of NCX. We have implemented a random walk (RW) Monte Carlo (MC) model with simulations mimicking a diffusion process originating at the TRPC6 within PM-SR junctions. The model calculates the average Na⁺ in the nanospace and also produces profiles as a function of distance from the source. Our results highlight the necessity of a strategic juxtaposition of the relevant ion translocators as well as other physical structures within the nanospaces to permit adequate Na⁺ build-up to initiate NCX reversal and Ca²⁺ influx to refill the SR.     

Differences in the interaction of inorganic and organic (hydrophobic) cations with phosphatidylserine membranes

The interaction of phosphatidylserine dispersions with “hydrophobic”, organic cations (acetylcholine, tetraethylammonium ion) is compared with that of simple inorganic cations (Na⁺, Ca²⁺); differences in the hydration properties of the two classes of ions exist in the bulk phase as evident from spin-lattice relaxation time T₁, measurements. It is shown that the reaction products (cation-phospholipid) differ markedly in their physicochemical behaviour. With increasing concentration both classes of ions reduce the ζ-potential of phosphatidylserine surfaces, the monovalent inorganic cations being only slightly more effective than the hydrophobic cations. Inorganic cations cause precipitation of the lipid once the surface charge of the bilayer is reduced to a certain threshold value. This is not the case with the organic cations. The difference is probably associated with the different hydration properties of the resulting complexes. Thus binding of Ca²⁺ causes displacement of water of hydration and formation of an anhydrous, hydrophobic calcium-phosphatidylserine complex which is insoluble in water, whereas the product of binding of the organic cations is hydrated, hydrophilic and water soluble. The above findings are consistent with NMR results which show that the phosphodiester group is involved in the binding of both classes of cations as well as being the site of the primary hydration shell. Besides affecting interbilayer membrane interactions such as those involved in cell adhesion and membrane fusion, the binding of both classes of cation can affect the molecular packing within a bilayer.     

Cation diffusion selectivity in a pore model. The phosphatidylcholine/water lamellar phase

The diffusion coefficients $\text{D}$ (cm²/s), of four monovalent cations K⁺, Na⁺, Rb⁺ and Cs⁺ and of Ca²⁺ have been measured in phosphatidylcholine/water lamellar phase as a function of phase hydration and temperature and in the presence of divalent cations. Diffusion rates vary strongly with phase hydration, between 10^?7 and 10^?6 cm²/s for monovalent and 10^?8 and 10^?7 for Ca²⁺. The activation energies obtained are relatively small (5–10 kcal/mol). As the phase water content increases, a series of diffusion sequences is obtained, corresponding to the sequences predicted by Eisenman's theory of alkali ion equilibrium selectivity.This diffusionnal selectivity, which depends exclusively upon non-equilibrium parameters (mobility) within the hydrophilic path is discussed in respect to current theories of pore selectivity.     

Hydrophobic Gating of Ion Permeation in Magnesium Channel CorA

Ion channels catalyze ionic permeation across membranes via water-filled pores. To understand how changes in intracellular magnesium concentration regulate the influx of Mg²⁺ into cells, we examine early events in the relaxation of Mg²⁺ channel CorA toward its open state using massively-repeated molecular dynamics simulations conducted either with or without regulatory ions. The pore of CorA contains a 2-nm-long hydrophobic bottleneck which remained dehydrated in most simulations. However, rapid hydration or “wetting” events concurrent with small-amplitude fluctuations in pore diameter occurred spontaneously and reversibly. In the absence of regulatory ions, wetting transitions are more likely and include a wet state that is significantly more stable and more hydrated. The free energy profile for Mg²⁺ permeation presents a barrier whose magnitude is anticorrelated to pore diameter and the extent of hydrophobic hydration. These findings support an allosteric mechanism whereby wetting of a hydrophobic gate couples changes in intracellular magnesium concentration to the onset of ionic conduction.     

Hexahydrated Mg2+ Binding and Outer-Shell Dehydration on RNA Surface

The interaction between metal ions, especially Mg²⁺ ions, and RNA plays a critical role in RNA folding. Upon binding to RNA, a metal ion that is fully hydrated in bulk solvent can become dehydrated. Here we use molecular dynamics simulation to investigate the dehydration of bound hexahydrated Mg²⁺ ions. We find that a hydrated Mg²⁺ ion in the RNA groove region can involve significant dehydration in the outer hydration shell. The first or innermost hydration shell of the Mg²⁺ ion, however, is retained during the simulation because of the strong ion-water electrostatic attraction. As a result, water-mediated hydrogen bonding remains an important form for Mg²⁺-RNA interaction. Analysis for ions at different binding sites shows that the most pronounced water deficiency relative to the fully hydrated state occurs at a radial distance of around 11 Å from the center of the ion. Based on the independent 200 ns molecular dynamics simulations for three different RNA structures (Protein Data Bank: 1TRA, 2TPK, and 437D), we find that Mg²⁺ ions overwhelmingly dominate over monovalent ions such as Na⁺ and K⁺ in ion-RNA binding. Furthermore, application of the free energy perturbation method leads to a quantitative relationship between the Mg²⁺ dehydration free energy and the local structural environment. We find that $\text{ΔΔ}{G}_{\text{hyd}},$ the change of the Mg²⁺ hydration free energy upon binding to RNA, varies linearly with the inverse distance between the Mg²⁺ ion and the nearby nonbridging oxygen atoms of the phosphate groups, and $\text{ΔΔ}{G}_{\text{hyd}}$ can reach ?2.0 kcal/mol and ?3.0 kcal/mol for an Mg²⁺ ion bound to the surface and to the groove interior, respectively. In addition, the computation results in an analytical formula for the hydration ratio as a function of the average inverse Mg²⁺-O distance. The results here might be useful for further quantitative investigations of ion-RNA interactions in RNA folding.     

Nonequilibrium Statistical Model of Active Transport of Ions and ATP Production in Mitochondria

A model of the active transport of ions through internal membranes of mitochondria is proposed. If concentrations of ions in a cell are known, this model allows calculating concentrations of all main ions (H⁺, Ca⁺², K⁺, Mg²⁺, Na⁺, Cl⁻) in the mitochondrion matrix and the resting potential across the membrane. The theoretical values satisfactorily agree with available experimental data on the concentrations and the potentials, including different operating regimes of the adenosine triphosphate (ATP) synthetase (the main regime, short circuiting or ATP synthetase blocking). The active transport of Mg²⁺ ions in exchange for protons was assumed. In accordance with the model, the ATP synthetase operation is possible only if the stoichiometric coefficient of protons is 3.     

A permeability change of myelin membrane vesicles towards cations is induced by MgATP but not by phosphorylation of myelin basic protein

The existence of an endogenous protein kinase activity and protein phosphatase activity in myelin membrane from mammalian brain has now been well established. We found that under all conditions tested the myelin basic protein is almost the only substrate of the endogenous protein kinase in myelin of bovine brain. The protein kinase activity is stimulated by Ca²⁺ in the micromolar range. Optimal activity is reached at a free Ca²⁺ concentration of about 2 μM. Myelin membrane vesicles were prepared and then shown to be sealed by a light-scattering technique. After preloading with ⁴⁵Ca²⁺, ⁸⁶Rb⁺, or ²²Na⁺, the self-diffusion (passive outflux) of these ions from myelin membrane vesicles was measured. Ionophores induced a rapid, concentration-dependent outflux of 80–90% of the cations, indicating that only a small fraction of the trapped ions was membrane bound. There was no difference in the diffusion rates of the three cations whether phosphorylated (about 1 mol phosphate per myelin basic protein) or non-phosphorylated vesicles were tested. In contrast, a small but significant decrease in permeability for Rb⁺ and Na⁺ was measured, when the vesicles were pretreated with ATP and Mg²⁺.     

Structure based computational assessment of channel properties of assembled ORF‐8a from SARS‐CoV

ORF 8a is a short 39 amino acid bitopic membrane protein encoded by severe acute respiratory syndrome causing corona virus (SARS‐CoV). It has been identified to increase permeability of the lipid membrane for cations. Permeability is suggested to occur due to the assembly of helical bundles. Computational models of a pentameric assembly of 8a peptides are generated using the first 22 amino acids, which include the transmembrane domain. Low energy structures reveal a hydrophilic pore mantled by residues Thr‐8, and ?18, Ser‐11, Cys‐13, and Arg‐22. Potential of mean force (PMF) profiles for mono (Na⁺, K⁺, Cl^?) and divalent (Ca²⁺) ions along the pore are calculated. The data support experimental findings of a weak cation selectivity of the channel. Calculations on 8a are compared to data derived for a pentameric bundle consisting of the M2 helices of the bacterial pentameric ligand gated ion channel GLIC (3EHZ). PMF curves of both, bundles 8a and M2, show sigmoidal shaped profiles. In comparison to the data for the M2‐GLIC model, data of the 8a bundle show lower amplitude of the PMF values between maximum and minimum and less discrimination amongst ions. Proteins 2015; 83:300–308. © 2014 Wiley Periodicals, Inc.     

Stochastic binding of Ca2+ ions in the dyadic cleft; continuous versus random walk description of diffusion

Ca²⁺ signaling in the dyadic cleft in ventricular myocytes is fundamentally discrete and stochastic. We study the stochastic binding of single Ca²⁺ ions to receptors in the cleft using two different models of diffusion: a stochastic and discrete Random Walk (RW) model, and a deterministic continuous model. We investigate whether the latter model, together with a stochastic receptor model, can reproduce binding events registered in fully stochastic RW simulations. By evaluating the continuous model goodness-of-fit for a large range of parameters, we present evidence that it can. Further, we show that the large fluctuations in binding rate observed at the level of single time-steps are integrated and smoothed at the larger timescale of binding events, which explains the continuous model goodness-of-fit. With these results we demonstrate that the stochasticity and discreteness of the Ca²⁺ signaling in the dyadic cleft, determined by single binding events, can be described using a deterministic model of Ca²⁺ diffusion together with a stochastic model of the binding events, for a specific range of physiological relevant parameters. Time-consuming RW simulations can thus be avoided. We also present a new analytical model of bimolecular binding probabilities, which we use in the RW simulations and the statistical analysis.     

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.     

A Single-File Model for Potassium Transport in Squid Giant Axon: Simulation of Potassium Currents at Normal Ionic Concentrations

A physical model for potassium transport in squid giant axon is proposed. The model is designed to explain the empirical data given by the Hodgkin-Huxley model and related experiments. It is assumed that K⁺ moves across the axon membrane by single-file diffusion through narrow pores. In the model a pore has three negatively charged sites that can be occupied alternatively by K⁺ or by a gating particle, GP⁺⁺, coming from the external surface. GP⁺⁺ is considered to be part of the membrane rather than a diffusible component of the surrounding solutions. A high activation barrier for GP⁺⁺ is supposed at the inner membrane border so that it cannot change over to the internal surface. Therefore potassium diffusion can be blocked by GP⁺⁺ penetrating into the pores. This mechanism controls the dynamic behaviour of the model. The time-dependent probabilities of the pore states are described by a system of differential equations. The rate constants in these equations depend on the ionic concentrations, the membrane voltage, and the electrostatic interaction between ions in a single pore. Detailed computational tests for normal composition of external and internal solutions show that the model agrees remarkably well with the stationary and dynamic behaviour of the Hodgkin-Huxley model. However, the hyperpolarization delay is not reproduced. A structural modification, concerning this delay and the way in which GP⁺⁺ is attached to the membrane, is proposed, and the qualitative behavior of the model at varied external and internal concentrations is discussed.     

Cation Selectivity in Biological Cation Channels Using Experimental Structural Information and Statistical Mechanical Simulation

Cation selective channels constitute the gate for ion currents through the cell membrane. Here we present an improved statistical mechanical model based on atomistic structural information, cation hydration state and without tuned parameters that reproduces the selectivity of biological Na⁺ and Ca²⁺ ion channels. The importance of the inclusion of step-wise cation hydration in these results confirms the essential role partial dehydration plays in the bacterial Na⁺ channels. The model, proven reliable against experimental data, could be straightforwardly used for designing Na⁺ and Ca²⁺ selective nanopores.