Selectivity and permeation in calcium release channel of cardiac muscle: alkali metal ions

Luminal Ca2+ regulation of RyR1 Ca2+ channel leak activation and inactivation in sarcoplasmic reticulum membrane vesicles

In this study, we tested the hypothesis that the RyR1 Ca²⁺ channel closure is sensitive to outward trans-SR membrane Ca²⁺ gradients established by SERCA1 pumping. To perform these studies, we employed stopped-flow rapid-kinetic fluorescence methods to measure and assess how variation in trans-SR membrane Ca²⁺ distribution affects evolution of RyR1 Ca²⁺ leaks in RyR1/ CASQ1/SERCA1-rich membrane vesicles. Our studies showed that rapid filling of a Mag-Fura-2-sensitive free Ca²⁺ pool during SERCA1-mediated Ca²⁺ sequestration appears to be a crucial condition allowing RyR1 Ca²⁺ channels to close once reloading of luminal Ca²⁺ stores is complete. Disruption in the filling of this pool caused activation of Ruthenium Red inhibitable RyR1 Ca²⁺ leaks, suggesting that SERCA1 pump formation of outward Ca²⁺ gradients is an important aspect of Ca²⁺ flux control channel opening and closing. In addition, our observed ryanodine-induced shift in luminal Ca²⁺ from free to a CTC-Ca⁺-sensitive, CASQ1-associated bound compartment underscores the complex organization and regulation of SR luminal Ca²⁺. Our study provides strong evidence that RyR1 functional states directly and indirectly influence the compartmentation of luminal Ca²⁺. This, in turn, is influenced by the activity of SERCA1 pumps to fill luminal pools while synchronously reducing Ca²⁺ levels on the cytosolic face of RyR1 channels.

Multiscale modeling of a rectifying bipolar nanopore: Comparing Poisson-Nernst-Planck to Monte Carlo

In the framework of a multiscale modeling approach, we present a systematic study of a bipolar rectifying nanopore using a continuum and a particle simulation method. The common ground in the two methods is the application of the Nernst-Planck (NP) equation to compute ion transport in the framework of the implicit-water electrolytemodel. The difference is that the Poisson-Boltzmann theory is used in the Poisson-Nernst-Planck (PNP) approach, while the Local Equilibrium Monte Carlo (LEMC) method is used in the particle simulation approach (NP+LEMC) to relate the concentration profile to the electrochemical potential profile. Since we consider a bipolar pore which is short and narrow, we perform simulations using two-dimensional PNP. In addition, results of a non-linear version of PNP that takes crowding of ions into account are shown. We observe that the mean field approximation applied in PNP is appropriate to reproduce the basic behavior of the bipolar nanopore (e.g., rectification) for varying parameters of the system (voltage, surface charge,electrolyte concentration, and pore radius). We present current data that characterize the nanopore's behavior as a device, as well as concentration, electrical potential, and electrochemical potential profiles.

Structural insights into Ca(2+)-activated long-range allosteric channel gating of RyR1

Ryanodine receptors (RyRs) are a class of giant ion channels with molecular mass over 2.2 mega-Daltons. These channels mediate calcium signaling in a variety of cells. Since more than 80% of the RyR protein is folded into the cytoplasmic assembly and the remaining residues form the transmembrane domain, it has been hypothesized that the activation and regulation of RyR channels occur through an as yet uncharacterized long-range allosteric mechanism. Here we report the characterization of a Ca²⁺-activated open-state RyR1 structure by cryo-electron microscopy. The structure has an overall resolution of 4.9 Å and a resolution of 4.2 Å for the core region. In comparison with the previously determined apo/closed-state structure, we observed long-range allosteric gating of the channel upon Ca²⁺ activation. In-depth structural analyses elucidated a novel channel-gating mechanism and a novel ion selectivity mechanism of RyR1. Our work not only provides structural insights into the molecular mechanisms of channel gating and regulation of RyRs, but also sheds light on structural basis for channel-gating and ion selectivity mechanisms for the six-transmembrane-helix cation channel family.

How to Properly Measure a Current-Voltage Relation?-Interpolation vs. Ramp Methods Applied to Studies of GABAA Receptors

The relation between current and voltage, I-V relation, is central to functional analysis of membrane ion channels. A commonly used method, since the introduction of the voltage-clamp technique, to establish the I-V relation depends on the interpolation of current amplitudes recorded at different steady voltages. By a theoretical computational approach as well as by experimental recordings from GABA_A-receptor mediated currents in mammalian central neurons, we here show that this interpolation method may give reversal potentials and conductances that do not reflect the properties of the channels studied under conditions when ion flux may give rise to concentration changes. Therefore, changes in ion concentrations may remain undetected and conclusions on changes in conductance, such as during desensitization, may be mistaken. In contrast, an alternative experimental approach, using rapid voltage ramps, enable I-V relations that much better reflect the properties of the studied ion channels.

Selecting ions by size in a calcium channel: the ryanodine receptor case study

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

Characterization of ryanodine receptor type 1 single channel activity using "on-nucleus" patch clamp

In this study, we provide the first description of the biophysical and pharmacological properties of ryanodine receptor type 1 (RyR1) expressed in a native membrane using the on-nucleus configuration of the patch clamp technique. A stable cell line expressing rabbit RyR1 was established (HEK-RyR1) using the FLP-in 293 cell system. In contrast to untransfected cells, RyR1 expression was readily demonstrated by immunoblotting and immunocytochemistry in HEK-RyR1 cells. In addition, the RyR1 agonists 4-CMC and caffeine activated Ca(2+) release that was inhibited by high concentrations of ryanodine. On nucleus patch clamp was performed in nuclei prepared from HEK-RyR1 cells. Raising the [Ca(2+)] in the patch pipette resulted in the appearance of a large conductance cation channel with well resolved kinetics and the absence of prominent subconductance states. Current versus voltage relationships were ohmic and revealed a chord conductance of ∼750pS or 450pS in symmetrical 250mM KCl or CsCl, respectively. The channel activity was markedly enhanced by caffeine and exposure to ryanodine resulted in the appearance of a subconductance state with a conductance ∼40% of the full channel opening with a Po near unity. In total, these properties are entirely consistent with RyR1 channel activity. Exposure of RyR1 channels to cyclic ADP ribose (cADPr), nicotinic acid adenine dinucleotide phosphate (NAADP) or dantrolene did not alter the single channel activity stimulated by Ca(2+), and thus, it is unlikely these molecules directly modulate RyR1 channel activity. In summary, we describe an experimental platform to monitor the single channel properties of RyR channels. We envision that this system will be influential in characterizing disease-associated RyR mutations and the molecular determinants of RyR channel modulation.

Control of flux by narrow passages and hidden targets in cellular biology

Critical biological processes, such as synaptic plasticity and transmission, activation of genes by transcription factors, or double-strained DNA break repair, are controlled by diffusion in structures that have both large and small spatial scales. These may be small binding sites inside or on the surface of the cell, or narrow passages between subcellular compartments. The great disparity in spatial scales is the key to controlling cell function by structure. We report here recent progress on resolving analytical and numerical difficulties in extracting properties from experimental data, from biophysical models, and from Brownian dynamics simulations of diffusion in multi-scale structures. This progress is achieved by developing an analytical approximation methodology for solving the model equations. The reported results are applied to analysis and simulations of subcellular processes and to the quantification of their biological functions.

Interacting ions in biophysics: real is not ideal

Ions in water are important throughout biology, from molecules to organs. Classically, ions in water were treated as ideal noninteracting particles in a perfect gas. Excess free energy of each ion was zero. Mathematics was not available to deal consistently with flows, or interactions with other ions or boundaries. Nonclassical approaches are needed because ions in biological conditions flow and interact. The concentration gradient of one ion can drive the flow of another, even in a bulk solution. A variational multiscale approach is needed to deal with interactions and flow. The recently developed energetic variational approach to dissipative systems allows mathematically consistent treatment of the bio-ions Na(+), K(+), Ca(2+), and Cl(-) as they interact and flow. Interactions produce large excess free energy that dominate the properties of the high concentration of ions in and near protein active sites, ion channels, and nucleic acids: the number density of ions is often >10 M. Ions in such crowded quarters interact strongly with each other as well as with the surrounding protein. Nonideal behavior found in many experiments has classically been ascribed to allosteric interactions mediated by the protein and its conformation changes. The ion-ion interactions present in crowded solutions-independent of conformation changes of the protein-are likely to change the interpretation of many allosteric phenomena. Computation of all atoms is a popular alternative to the multiscale approach. Such computations involve formidable challenges. Biological systems exist on very different scales from atomic motion. Biological systems exist in ionic mixtures (like extracellular and intracellular solutions), and usually involve flow and trace concentrations of messenger ions (e.g., 10(-7) M Ca(2+)). Energetic variational methods can deal with these characteristic properties of biological systems as we await the maturation and calibration of all-atom simulations of ionic mixtures and divalents.

Ionic Interactions Are Everywhere

Ionic solutions are dominated by interactions because they must be electrically neutral, but classical theory assumes no interactions. Biological solutions are rather like seawater, concentrated enough so that the diameter of ions also produces important interactions. In my view, the theory of complex fluids is needed to deal with the interacting reality of biological solutions.

First-passage-time analysis of atomic-resolution simulations of the ionic transport in a bacterial porin

We have studied the dynamics of chloride and potassium ions in the interior of the Outer membrane porin F (OmpF) under the influence of an external electric field. From the results of extensive all-atom molecular dynamics (MD) simulations of the system, we computed several first-passage-time (FPT) quantities to characterize the dynamics of the ions in the interior of the channel. Such FPT quantities obtained from MD simulations demonstrate that it is not possible to describe the dynamics of chloride and potassium ions inside the whole channel with a single constant diffusion coefficient. However, we showed that a valid, statistically rigorous description in terms of a constant diffusion coefficient D and an effective deterministic force F(eff) can be obtained after appropriate subdivision of the channel in different regions suggested by the x-ray structure. These results have important implications for popular simplified descriptions of channels based on the one-dimensional Poisson-Nernst-Planck equations. Also, the effect of entropic barriers on the diffusion of the ions is identified and briefly discussed.

Insights on the permeability of wide protein channels: measurement and interpretation of ion selectivity

Ion channels are hollow proteins that have evolved to exhibit discrimination between charged solutes. This property, known as ion selectivity is critical for several biological functions. By using the bacterial porin OmpF as a model system of wide protein channels, we demonstrate that significant insights can be gained when selectivity measurements are combined with electrodiffusion continuum models and simulations based on the atomic structure. A correct interpretation of the mechanisms ruling the many sources of channel discrimination is a first, indispensable step for the understanding of the controlled movement of ions into or out of cells characteristic of many physiological processes. We conclude that the scattered information gathered from several independent approaches should be appropriately merged to provide a unified and coherent picture of the channel selectivity.

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.

Self-consistent analytic solution for the current and the access resistance in open ion channels

A self-consistent analytic approach is introduced for the estimation of the access resistance and the current through an open ion channel for an arbitrary number of species. For an ion current flowing radially inward from infinity to the channel mouth, the Poisson-Boltzmann-Nernst-Planck equations are solved analytically in the bulk with spherical symmetry in three dimensions, by linearization. Within the channel, the Poisson-Nernst-Planck equation is solved analytically in a one-dimensional approximation. An iterative procedure is used to match the two solutions together at the channel mouth in a self-consistent way. It is shown that the current-voltage characteristics obtained are in good quantitative agreement with experimental measurements.

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 Ba(2+) with other divalents (Ca(2+), Sr(2+)), of Ca(2+) 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 Ca(2+)-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(+)/Ca(2+) 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.

Energetics of divalent selectivity in a calcium channel: the ryanodine receptor case study

A model of the ryanodine receptor (RyR) calcium channel is used to study the energetics of binding selectivity of Ca(2+) versus monovalent cations. RyR is a calcium-selective channel with a DDDD locus in the selectivity filter, similar to the EEEE locus of the L-type calcium channel. While the affinity of RyR for Ca(2+) is in the millimolar range (as opposed to the micromolar range of the L-type channel), the ease of single-channel measurements compared to L-type and its similar selectivity filter make RyR an excellent candidate for studying calcium selectivity. A Poisson-Nernst-Planck/density functional theory model of RyR is used to calculate the energetics of selectivity. Ca(2+) versus monovalent selectivity is driven by the charge/space competition mechanism in which selectivity arises from a balance of electrostatics and the excluded volume of ions in the crowded selectivity filter. While electrostatic terms dominate the selectivity, the much smaller excluded-volume term also plays a substantial role. In the D4899N and D4938N mutations of RyR that are analyzed, substantial changes in specific components of the chemical potential profiles are found far from the mutation site. These changes result in the significant reduction of Ca(2+) selectivity found in both theory and experiments.

Estimating the dielectric constant of the channel protein and pore

When modelling biological ion channels using Brownian dynamics (BD) or Poisson-Nernst-Planck theory, the force encountered by permeant ions is calculated by solving Poisson's equation. Two free parameters needed to solve this equation are the dielectric constant of water in the pore and the dielectric constant of the protein forming the channel. Although these values can in theory be deduced by various methods, they do not give a reliable answer when applied to channel-like geometries that contain charged particles. To determine the appropriate values of the dielectric constants, here we solve the inverse problem. Given the structure of the MthK channel, we attempt to determine the values of the protein and pore dielectric constants that minimize the discrepancies between the experimentally-determined current-voltage curve and the curve obtained from BD simulations. Two different methods have been applied to determine these values. First, we use all possible pairs of the pore dielectric constant of water, ranging from 20 to 80 in steps of 10, and the protein dielectric constant of 2-10 in steps of 2, and compare the simulated results with the experimental values. We find that the best agreement is obtained with experiment when a protein dielectric constant of 2 and a pore water dielectric constant of 60 is used. Second, we employ a learning-based stochastic optimization algorithm to pick out the optimum combination of the two dielectric constants. From the algorithm we obtain an optimum value of 2 for the protein dielectric constant and 64 for the pore dielectric constant.

Electrostatic properties and macroscopic electrodiffusion in OmpF porin and mutants

The bacterial porin OmpF found in the outer membrane of E. coli is a wide channel, characterized by its poor selectivity and almost no ion specificity. It has an asymmetric structure, with relatively large entrances and a narrow constriction. By applying continuum electrostatic methods we determine the ionization states of titratable amino acid residues in the protein and calculate self-consistently the electric potential 3-D distribution within the channel. The average electrostatic properties are then represented by an effective fixed charge distribution along the pore which is the input for a macroscopic electrodiffusion model. The theoretical predictions agree with measurements performed under different salt gradients and pH. The sensitivity of reversal potential and conductance to the direction of the salt gradient and the solution pH is captured by the model. The theory is also able to explain the influence of the lipid membrane charge. The same methodology is satisfactorily applied to some OmpF mutants involving slight structural changes but a large number of net charges. The correlation found between atomic structure and ionic selectivity shows that the transport characteristics of wide channels like OmpF and its mutants are mainly regulated by the collective action of a large number of residues, rather than by the specific interactions of residues at particular locations.

The effect of calcium on the properties of charged phospholipid bilayers

We have performed molecular dynamics simulations to investigate the structure and dynamics of charged bilayers as well as the distribution of counterions at the bilayer interface. For this, we have considered the negatively charged di-myristoyl-phosphatidyl-glycerol (DMPG) and di-myristoyl-phosphatidyl-serine (DMPS) bilayers as well as a protonated di-myristoyl-phosphatidyl-serine (DMPSH) bilayer. We were particularly interested in calcium ions due to their important role in biological systems. Simulations performed in the presence of calcium ions (DMPG, DMPS) or sodium ions (DMPS) were run for 45-60 ns. Simulation results for DMPG are compared with fluorescence measurements. The average areas per molecule were 47.4+/-0.5 A2 (DMPG with calcium), 47.3+/-0.5 A2 (DMPS with calcium), 51.3+/-1.0 A2 (DMPS with sodium) and 45.3+/-0.5 A2 (DMPSH). The structure of the negatively charged lipids is significantly affected by the counterions, where calcium ions have a more pronounced effect than sodium ions. Calcium ions were found to be tightly bound to the anionic groups of the lipid molecules and as such appear to constitute an integral part of the membrane interface on nanoseconds time scales. In contrast to sodium ions, calcium ions are localised in a narrow (approximately 10 A) band around the phosphate group. The interaction of calcium with the lipid molecules enhances the molecular packing of the PG and PS lipids. This observation is in good agreement with emission spectra of the membrane partitioning probe Laurdan in DMPG multilamellar vesicles that indicate an increase in the ordering of the DMPG bilayer due to the presence of calcium. Our results indicate that calcium ions, which often function as a second messengers in living cells have a pronounced effect on membrane structures, which may have implications during signal transduction events.

Three computational methods for studying permeation, selectivity and dynamics in biological ion channels

The cell membrane, confining some ions and molecules on one side and exchanging others with the other side, is the ultimate unit of the physiology of life. The delicate task of regulating the transport of ions across the membrane is carried out by biological nanotubes called 'ion channels'. Recently, there have been enormous strides in our understanding of the structure-function relationships of biological ion channels. The molecular structures of several ion channels have been determined from crystallographic analysis, including potassium channels, mechanosensitive channels, a chloride channel, as well as gramicidin channels and porins. It is expected that the X-ray structures of other ion channels will soon follow these discoveries, ushering in a new era of ion channel studies in which predicting the function of channels from their atomic structures will become the main quest. In parallel to these experimental findings, there have been important advances in computational biophysics. Here we summarize three theoretical approaches that have been utilized to understand the dynamics of ion permeation across bio-nanotubes, highlighting their advantages and shortcomings, and briefly describe some of the salient properties of ion channels uncovered through computational studies.

Molecular regulation of cardiac ryanodine receptor ion channel

The release of Ca(2+) ions from intracellular stores is a key step in a wide variety of cellular functions. In striated muscle, the release of Ca(2+) from the sarcoplasmic reticulum (SR) leads to muscle contraction. Ca(2+) release occurs through large, high-conductance Ca(2+) release channels, also known as ryanodine receptors (RyRs) because they bind the plant alkaloid ryanodine with high affinity and specificity. The RyRs are isolated as 30S protein complexes comprised of four 560 kDa RyR2 subunits and four 12 kDa FK506 binding protein (FKBP12) subunits. Multiple endogenous effector molecules and posttranslational modifications regulate the RyRs. This review focuses on current research toward understanding the control of the isolated cardiac Ca(2+) release channel/ryanodine receptor (RyR2) by Ca(2+), calmodulin, thiol oxidation/reduction and nitrosylation, and protein phosphorylation.

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.

Unitary Ca2+ current through mammalian cardiac and amphibian skeletal muscle ryanodine receptor Channels under near-physiological ionic conditions

Ryanodine receptor (RyR) channels from mammalian cardiac and amphibian skeletal muscle were incorporated into planar lipid bilayers. Unitary Ca2+ currents in the SR lumen-to-cytosol direction were recorded at 0 mV in the presence of caffeine (to minimize gating fluctuations). Currents measured with 20 mM lumenal Ca2+ as exclusive charge carrier were 4.00 and 4.07 pA, respectively, and not significantly different. Currents recorded at 1-30 mM lumenal Ca2+ concentrations were attenuated by physiological [K+] (150 mM) and [Mg2+] (1 mM), in the same proportion (approximately 55%) in mammalian and amphibian channels. Two amplitudes, differing by approximately 35%, were found in amphibian channel studies, probably corresponding to alpha and beta RyR isoforms. In physiological [Mg2+], [K+], and lumenal [Ca2+] (1 mM), the Ca2+ current was just less than 0.5 pA. Comparison of this value with the Ca2+ flux underlying Ca2+ sparks suggests that sparks in mammalian cardiac and amphibian skeletal muscles are generated by opening of multiple RyR channels. Further, symmetric high concentrations of Mg2+ substantially reduced the current carried by 10 mM Ca2+ (approximately 40% at 10 mM Mg2+), suggesting that high Mg2+ may make sparks smaller by both inhibiting RyR gating and reducing unitary current.

The electrical behaviour of rat connexin46 gap junction channels expressed in transfected HeLa cells

Pairs of human HeLa cells expressing rat connexin46 were used to study the electrical properties of gap junction channels with the dual voltage-clamp method. The steady-state conductance ( g(j,ss)) had a bell-shaped dependence on transjunctional voltage ( V(j)). The parameters of the Boltzmann fit were: V(j,0)=42 mV, g(j,min)=0.12, z=2.5 (pipette solution: K(+) aspartate(-); 27 degrees C). The Boltzmann parameters were sensitive to the ionic composition of the pipette solution (KCl, K(+) aspartate(-), TEA(+) Cl(-), TEA(+) aspartate(-)). The V(j)-dependent inactivation of the junctional current I(j) was approximated by single exponentials (exceptions: two exponentials with KCl at V(j)>or=75 mV and K(+) aspartate(-) at V(j)=125 mV). The time constant of inactivation (tau(i)) decreased with increasing V(j) and was sensitive to the pipette solution. The larger the ions, the slower the inactivation. Recovery from inactivation followed a single exponential. The time constant of recovery (tau(r)) increased with increasing V(j). Single-channel currents showed a main state, several substates and a residual state. The corresponding conductances gamma(j,main) and gamma(j,residual) decreased slightly with increasing V(j); extrapolation to V(j)=0 mV yielded values of 152 and 28 pS, respectively (K(+) aspartate(-); 37 degrees C). The values of gamma(j,main) and gamma(j,residual) were dependent on pipette solution. The ratio gamma(j,main)/gamma(j,residual) increased with increasing ionic size, suggesting that the residual state impairs ion permeation more severely than the main state. The gamma(j,main) data suggest that the ionic selectivity of Cx46 channels may be controlled primarily by ionic size. Compared with hemichannel results, docking of connexons may modify the channel structure and thereby affect the ionic selectivity of gap junction channels. The open channel probability at steady state ( P(o)) decreased with increasing V(j). The parameters of the Boltzmann fit were: V(j,0)=41 mV, z=2.2 (K(+) aspartate(-); 27 degrees C).

The Gating and Conductance Properties of CaV3.2 Low-Voltage-Activated T-Type Calcium Channels

Calcium channels are essential for excitation-contraction coupling and pacemaker potentials in cardiac muscle cells. Whereas L-type Ca(2+) channels have been extensively studied, T-type channels have been poorly characterized in cardiac myocytes. We describe here the functional properties of recombinant Ca(V)3.2 T-type Ca(2+) channels expressed in mammalian cell lines. The T-type Ca(2+) current showed a rapid activation and an inactivation phase in response to depolarization, and it displayed a window current over the voltage range from -60 to -40 mV in 1 to 10 mM external Ca(2+). Barium (Ba(2+)) and strontium (Sr(2+)) permeate the channel with similar activation kinetics. On the other hand, monovalent cations, Li(+) and Na(+), permeate the T-type Ca(2+) channel more easily than the L-type Ca(2+) channel. The permeability order of the Ca(V)3.2 T-type Ca(2+) channel among monovalent and divalent cations was determined as Ba(2+)>Mn(2+)>Ca(2+)>Sr(2+)>Li(+1)>Na(+) with the permeability order of 1.39:1.25:1.00:0.95:0.55:0.29. The ionic conductance sequence for cations relative to calcium was Sr(2+)>Ba(2+)>Ca(2+)>Li(+1)>Mn(2+)>Na(+) with the conductance ratio of 1.39:1.21:1.00:0.40:0.23:0.11. The permeation profile of manganese (Mn(2+)) is complex. Mn(2+) permeates the Ca(2+) channel with a permeability similar to Ca(2+) or Ba(2+), but with a much smaller current density, resulting in a much smaller conductance. The properties relating to progression and recovery from inactivation in the Ca(V)3.2 channel are substantially identical with either Ca(2+) or Ba(2+) as the charge carrier.

Model channel ion currents in NaCl-extended simple point charge water solution with applied-field molecular dynamics

Using periodic boundary conditions and a constant applied field, we have simulated current flow through an 8.125-A internal diameter, rigid, atomistic channel with polar walls in a rigid membrane using explicit ions and extended simple point charge water. Channel and bath currents were computed from 10 10-ns trajectories for each of 10 different conditions of concentration and applied voltage. An electric field was applied uniformly throughout the system to all mobile atoms. On average, the resultant net electric field falls primarily across the membrane channel, as expected for two conductive baths separated by a membrane capacitance. The channel is rarely occupied by more than one ion. Current-voltage relations are concentration dependent and superlinear at high concentrations.

Modified Donnan potentials for ion transport through biological ion channels

In the classical study of ion transport through charged membranes, Donnan potentials are used to approximate the difference between the applied electrostatic potential and the potential at the liquid/membrane interface. For very thin membranes (e.g., biological lipid bilayers), this discontinuous approximation of the potential is not sufficient. Here we derive a modification to the classic Donnan potential for ion transport through a biological ion channel embedded in a lipid bilayer. We also show how to derive the classic Donnan potential without the usual assumptions and estimate the amount of space charge at the liquid/membrane interface.

The first extracellular loop domain is a major determinant of charge selectivity in connexin46 channels

Intercellular channels formed of members of the gene family of connexins (Cxs) vary from being substantially cation selective to being anion selective. We took advantage of the ability of Cx46 to function as an unopposed hemichannel to examine the basis of Cx charge selectivity. Previously we showed Cx46 hemichannels to be large pores that predominantly conduct cations and inwardly rectify in symmetric salts, properties suggesting selectivity is influenced by fixed negative charges located toward the extracellular end of the pore. Here we demonstrate that high ionic strength solutions applied to the extracellular, but not the intracellular, side of Cx46 hemichannels substantially reduce the ratio of cation to anion permeability. Substitution of the first extracellular loop (E1) domain of Cx32, an anion-preferring Cx, reduces conductance, converts Cx46 from cation to anion preferring, and changes the I-V relation form inwardly to outwardly rectifying. These data suggest that fixed negative charges influencing selectivity in Cx46 are located in E1 and are substantially reduced and/or are replaced with positive charges from the Cx32 E1 sequence. Extending studies to Cx46 cell-cell channels, we show that they maintain a strong preference for cations, have a conductance nearly that expected by the series addition of hemichannels, but lack rectification in symmetric salts. These properties are consistent with preservation of the fixed charge region in E1 of hemichannels, which upon docking, become symmetrically placed near the center of the cell-cell channel pore. Furthermore, heterotypic cell-cell channels formed by pairing Cx46 with Cx32 or Cx43 rectify in symmetric salts in accordance with the differences in the charges we ascribed to E1. These data are consistent with charged residues in E1 facing the channel lumen and playing an important role in determining Cx channel conductance and selectivity.

Molecular dynamics estimates of ion diffusion in model hydrophobic and KcsA potassium channels

Molecular dynamics simulations are carried out to obtain estimates of diffusion coefficients of biologically important Na+, K+, Ca2+ and Cl- ions in hydrophobic cylindrical channels with varying radii and large reservoirs. Calculations for the cylindrical channels are compared to those for the KcsA potassium channel, for which the protein structure has recently been determined from X-ray diffraction experiments. Our results show that ion diffusion is maintained at reasonably high levels even within narrow channels, and does not support the very small diffusion coefficients used in some continuum models in order to fit experimental data. The present estimates of ion diffusion coefficients are useful in the calculation of channel conductance using the Poisson-Nernst-Planck theory, or Brownian dynamics.

Tests of continuum theories as models of ion channels. II. Poisson-Nernst-Planck theory versus brownian dynamics

We test the validity of the mean-field approximation in Poisson-Nernst-Planck theory by contrasting its predictions with those of Brownian dynamics simulations in schematic cylindrical channels and in a realistic potassium channel. Equivalence of the two theories in bulk situations is demonstrated in a control study. In simple cylindrical channels, considerable differences are found between the two theories with regard to the concentration profiles in the channel and its conductance properties. These differences are at a maximum in narrow channels with a radius smaller than the Debye length and diminish with increasing radius. Convergence occurs when the channel radius is over 2 Debye lengths. These tests unequivocally demonstrate that the mean-field approximation in the Poisson-Nernst-Planck theory breaks down in narrow ion channels that have radii smaller than the Debye length.

Accelerated diffusion of Na+ in a hydrophobic region revealed by molecular dynamics simulations of a synthetic ion channel

To get insight into the significance of the hydrophobic lining on the ion permeation, we performed molecular dynamics simulations on a Na(+) permeation through a de novo synthetic hydrophobic channel. Electrophysiological study has suggested that the channel is formed from a tail-to-tail associated dimer of a cyclic octa-peptide coupled with hydrophobic acyl chains. The acyl chains line the channel pore while the cyclic peptide forms the channel entrance [Z. Qi, M. Sokabe, K. Donowaki, H. Ishida, Biophys. J. 76 (1999) 631]. Molecular dynamics simulation of water in the channel indicated that the inferred structure is physically reasonable [Z. Qi, M. Sokabe, Biophys. Chem. 71 (1998) 35]. In the present study, the potential energy profile of the Na(+) and the energy contributions from each component of the system at different positions along the channel axis were calculated. An energy well instead of a peak is located at the central hydrophobic cavity of the channel, due to its ability of accommodating at least five water molecules to hydrate the ion. Interestingly, the ion diffuses much faster in the hydrophobic acyl chain region, particularly in the central hydrophobic cavity, than it does in the peptide ring region and even surprisingly faster than that in the bulk phase. These results provide a physical basis for an idea that the hydrophobic lining of the K(+) channel [D.A. Doyle, J.M. Cabral, R.A. Pfuetzner, A. Kuo, J.M. Gulbis, S.L. Cohen, B.T. Chait, R. MacKinnon, Science 280 (1998) 69] plays an active role to facilitate the ion permeation through the channel pore.