Hierarchical approach to predicting permeation in ion channels

A hierarchical computational strategy combining molecular modeling, electrostatics calculations, molecular dynamics, and Brownian dynamics simulations is developed and implemented to compute electrophysiologically measurable properties of the KcsA potassium channel. Models for a series of channels with different pore sizes are developed from the known x-ray structure, using insights into the gating conformational changes as suggested by a variety of published experiments. Information on the pH dependence of the channel gating is incorporated into the calculation of potential profiles for K(+) ions inside the channel, which are then combined with K(+) ion mobilities inside the channel, as computed by molecular dynamics simulations, to provide inputs into Brownian dynamics simulations for computing ion fluxes. The open model structure has a conductance of approximately 110 pS under symmetric 250 mM K(+) conditions, in reasonable agreement with experiments for the largest conducting substate. The dimensions of this channel are consistent with electrophysiologically determined size dependence of quaternary ammonium ion blocking from the intracellular end of this channel as well as with direct structural evidence that tetrabutylammonium ions can enter into the interior cavity of the channel. Realistic values of Ussing flux ratio exponents, distribution of ions within the channel, and shapes of the current-voltage and current-concentration curves are obtained. The Brownian dynamics calculations suggest passage of ions through the selectivity filter proceeds by a "knock-off" mechanism involving three ions, as has been previously inferred from functional and structural studies of barium ion blocking. These results suggest that the present calculations capture the essential nature of K(+) ion permeation in the KcsA channel and provide a proof-of-concept for the integrated microscopic/mesoscopic multitiered approach for predicting ion channel function from structure, which can be applied to other channel structures.     

Residue ionization and ion transport through OmpF channels

Single trimeric channels of the general bacterial porin, OmpF, were reconstituted into planar lipid membranes and their conductance, selectivity, and open-channel noise were studied over a wide range of proton concentrations. From pH 1 to pH 12, channel transport properties displayed three characteristic regimes. First, in acidic solutions, channel conductance is a strong function of pH; it increases by approximately threefold as the proton concentration decreases from pH 1 to pH 5. This rise in conductance is accompanied by a sharp increase in cation transport number and by pronounced open-channel low-frequency current noise with a peak at ~pH 2.5. Random stepwise transients with amplitudes at ~1/5 of the monomer conductance are major contributors to this noise. Second, over the middle range (pH 5 ÷ pH 9), channel conductance and selectivity stay virtually constant; open channel noise is at its minimum. Third, over the basic range (pH 9 ÷ pH 12), channel conductance and cation selectivity start to grow again with an onset of a higher frequency open-channel noise. We attribute these effects to the reversible protonation of channel residues whose pH-dependent charge influences transport by direct interactions with ions passing through the channel.     

Superposition properties of interacting ion channels.

Quantitative analysis of patch clamp data is widely based on stochastic models of single-channel kinetics. Membrane patches often contain more than one active channel of a given type, and it is usually assumed that these behave independently in order to interpret the record and infer individual channel properties. However, recent studies suggest there are significant channel interactions in some systems. We examine a model of dependence in a system of two identical channels, each modeled by a continuous-time Markov chain in which specified transition rates are dependent on the conductance state of the other channel, changing instantaneously when the other channel opens or closes. Each channel then has, e.g., a closed time density that is conditional on the other channel being open or closed, these being identical under independence. We relate the two densities by a convolution function that embodies information about, and serves to quantify, dependence in the closed class. Distributions of observable (superposition) sojourn times are given in terms of these conditional densities. The behavior of two channel systems based on two- and three-state Markov models is examined by simulation. Optimized fitting of simulated data using reasonable parameters values and sample size indicates that both positive and negative cooperativity can be distinguished from independence.     

Mitochondrial ion channels

Ion channels are proteins, which facilitate the ions flow throught biological membranes. In recent years the structure as well as the function of the plasma membrane ion channels have been well investigated. The knowledge of intracellular ion channels however is still poor. Up till now, the calcium channel described in endoplasmatic reticulum and mitochondrial porine are the examples of intracellular ion channels, which have been well characterized. The mitochondrial potassium channels: regulated by ATP (mitoK(ATP)) and of big conductance activated by Ca2+ (mitoBK(Ca)), which were described in inner mitochondrial membrane, play a key role in the protection of heart muscle against ischemia. In this review the last date concerning the mitochondrial ion channels as well as they function in cell metabolism have been presented.     

Multi-state, 4-aminopyridine-sensitive ion channels in human spermatozoa

Although ion channels are known to be pivotal to sperm function, the technical difficulty of applying electrophysiological techniques to spermatozoa has prevented significant progress in this area. This is due to the cell size and angular shape in combination with their motility. Using a refined technique, specifically for patch clamping spermatozoa, we have made recordings from human cells. This technique permitted approaches which enable functional analysis of sperm ion channels, including acquisition of inside-out patches, generation of averaged currents, and observation of the effects of pharmacological manipulation during prolonged recordings. As well as a low conductance (7 pS) channel and a 25-pS channel, the most striking finding was the presence of very high conductance, 4-aminopyridine-sensitive multistate channels resembling the non-selective cation channel of sea urchin and mouse spermatozoa. Application of 2 mM 4-aminopyridine (a dose sufficient to cause channel blockade) caused an instant and dramatic transition of motility in the sperm population increasing hyperactivated motility by more than 10-fold as assessed by computer-assisted semen analysis. Combined application of patch clamp and pharmacological investigation of mature sperm cells and will permit rapid advances in our understanding the role of ion channels in sperm function.     

Electrostatic tuning of ion conductance in potassium channels

Members of the K(+) channel family display remarkable conservation of sequence and structure of the ion selectivity filter, whereas the rates of K(+) turnover vary widely within the family. Here we show that channel conductance is strongly influenced by charge at the channel's intracellular mouth. Introduction of a ring of negative charges at this position in KcsA, a bacterial K(+) channel, augments the conductance in a pH-dependent manner. These results are explained by a simple electrostatic effect based on known channel structures, where the negative charges serve to alter the electrical potential at the inner mouth and, thus, to increase the local K(+) concentration. In addition, removal of the conserved negative charges at equivalent positions in a high-conductance eukaryotic K(+) channel leads to a decrease in conductance.     

Conductivity noise in transmembrane ion channels due to ion concentration fluctuations via diffusion.

A Green's function approach is developed from first principles to evaluate the power spectral density of conductance fluctuations caused by ion concentration fluctuations via diffusion in an electrolyte system. This is applied to simple geometric models of transmembrane ion channels to obtain an estimate of the magnitude of ion concentration fluctuation noise in the channel current. Pure polypeptide alamethicin forms stable ion channels with multiple conductance states in artificial phospholipid bilayers isolated onto tips of micropipettes with gigaohm seals. In the single-channel current recorded by voltage-clamp techniques, excess noise was found after the background instrumental noise and the intrinsic Johnson and shot noises were removed. The noise que to ion concentration fluctuations via diffusion was isolated by the dependence of the excess current noise on buffer ion concentration. The magnitude of the concentration fluctuation noise derived from experimental data lies within limits estimated using our simple geometric channel models. Variation of the noise magnitude for alamethicin channels in various conductance states agrees with theoretical prediction.     

Reservoir boundaries in Brownian dynamics simulations of ion channels

Brownian dynamics (BD) simulations provide a practical method for the calculation of ion channel conductance from a given structure. There has been much debate about the implementation of reservoir boundaries in BD simulations in recent years, with claims that the use of improper boundaries could have large effects on the calculated conductance values. Here we compare the simple stochastic boundary that we have been using in our BD simulations with the recently proposed grand canonical Monte Carlo method. We also compare different methods of creating transmembrane potentials. Our results confirm that the treatment of the reservoir boundaries is mostly irrelevant to the conductance properties of an ion channel as long as the reservoirs are large enough.     

Characterization of ion channels in human preadipocytes

Ion channels participate in regulation of cell proliferation. However, though preadipocyte (the progenitor of fat cell) is a type of highly proliferating cells, ion channel expression and their role in proliferation is not understood in human preadipocytes. The present study was designed to characterize ion channels using whole-cell patch clamp technique, RT-PCR, and Western blotting. It was found that a 4-aminopyridine- (4-AP) sensitive transient outward K(+) current (I(to)) was present in a small population of (32.0%) cells, and an outward "noisy" big conductance Ca(2+)-activated K(+) current (I(KCa)) was present in most (92.7%) preadipocytes. The noisy current was inhibited by the big conductance I(KCa) channel blocker paxilline (1 microM), and enhanced by the Ca(2+) ionophore A23187 (5 microM) and the big conductance I(KCa) channel activator NS1619 (10 microM). RT-PCR and Western blot revealed the molecular identities (i.e., KCa1.1 and Kv4.2) of the functional ionic currents I(KCa) and I(to). Blockade of I(KCa) or I(to) with paxilline or 4-AP reduced preadipocyte proliferation, and similar results were obtained with specific siRNAs targeting to KCa1.1 and Kv4.2. Flow cytometric analysis showed ion channel blockade or knockdown of KCa1.1 or Kv4.2 with specific siRNA increased the cell number of G0/G1 phase. The present study demonstrates for the first time that two types of functional ion channel currents, I(to) and big conductance I(KCa), are present in human preadipocytes and that these two types of ion channels participate in regulating proliferation of human preadipocytes.     

The properties of ion channels formed by zervamicins

The zervamicins (Zrv) are a family of 16 residue peptaibol channel formers, related to the 20 residue peptaibol alamethicin (Alm), but containing a higher proportion of polar sidechains. Zrv-1113 forms multi-level channels in planar lipid (diphytanoyl phosphatidylcholine) bilayers in response to cis positive voltages. Analysis of the voltage and concentration dependence of macroscopic conductances induced by Zrv-IIB suggests that, on average, channels contain ca. 13 peptide monomers. Analysis of single channel conductance levels suggests a similar value. The pattern of successive conductance levels is consistent with a modified helix bundle model in which the higher order bundle are distorted within the plane of the bilayer towards a torpedo shaped cross-section. The kinetics of intro-burst switching between adjacent conductance levels are shown to be approximately an order of magnitude faster for Zrv-IIB than for Alm. The channel forming properties of the related naturally occurring peptaibols, Zrv-Leu and Zrv-IC, have also been demonstrated, as have those of the synthetic apolar analogue Zrv-Al-16. The experimental studies on channel formation are combined with the known crystallographic structures of Zrv-Al-16 and Zrv-Leu to develop a molecular model of Zrv-II3 channels.Abbreviations Alm Alamethicin - Zrv Zervamicin - CFP Channel forming peptide - Aib -aminoisobutyric acid Correspondence to: M. S. P. Sansom     

Ionic selectivity, saturation and block in gramicidin A channels: I. Theory for the electrical properties of ion selective channels having two pairs of binding sites and multiple conductance states.

A model for the gramicidin A channel is proposed which extends existing models by adding a specific cationic binding site at each entrance to the channel. The binding of ions to these outer channel sites is assumed to shift the energy levels of the inner sites and barriers and thereby alter the channel conductance. The resulting properties are analyzed theoretically for the simplest case of two inner sites and a single energy barrier. This for-site model (two outer and two inner) predicts that the membrane potential at zero current (Uo) should be a Goldman-Hodgkin-Katz equation with concentration-dependent permeability ratios. The coefficients of the concentration-dependent terms are shown to be related to the peak energy shifts of the barrier and to the binding constants of the outer sites. The thory also predicts the channel conductance in symmetrical solutions to exhibit three limiting behaviors, from which the properties of the outer and inner sites can be characterized. In two-cation symmetrical mixtures the conductance as a function of mole fraction is shown to have a minimum, and the related phenomenon of inhibition and block exerted by one ion on the other is explained explicitly by the theory. These various phenomena, having ion interactions in a multiply occupied channel as a common physical basis, are all related (by the theory) through a set of measurable parameters describing the properties of the system.     

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 dynamics study of ion transport in transmembrane protein channels

Ion transport through biological membranes often takes place via pore-like protein channels. The elementary process of this transport can be described as a motion of the ion in a quasi-periodic multi-well potential. In this study molecular dynamics simulations of ion transport in a model channel were performed in order to test the validity of reaction-rate theory for this process. The channel is modelled as a hexagonal helix of infinite length, and the ligand groups interacting with the ion are represented by dipoles lining the central hole of the channel. The dipoles interact electrostatically with each other and are allowed to oscillate around an equilibrium orientation. The coupled equations of motion for the ion and the dipoles were solved simultaneously with the aid of a numerical integration procedure. From the calculated ion trajectories it is seen that, particularly at low temperatures, the ion oscillates back and forth in the trapping site many times before it leaves the site and jumps over the barrier. The observed oscillation frequency was found to be virtually temperature-independent (nu 0 approximately equal to 2 X 10(12) s-1) so that the strong increase of transport rate with temperature results almost exclusively from the Arrhenius-type exponential dependence of jump probability w on 1/T. At higher temperatures simultaneous jumps over several barriers occasionally occur. Although the exponential form of w(T) was in agreement with the predictions of rate theory, the activation energy Ea as determined from w(T) was different from the barrier height which was calculated from the static potential of the ion in the channel; the actual transport rate was 1 X 10(3) times higher than the rate predicted from the calculated barrier height. This observation was interpreted by the notion that ion transport in the channel is strongly influenced by thermal fluctuations in the conformation of the ligand system which in turn give rise to fluctuations of barrier height.     

Interactions of n-3 fatty acids with ion channels in excitable tissues

In summary, we have shown that the conventional explanation for the site of action of a ligand which alters the conductance of a membrane ion channel is that the ligand interacts or binds with the ion channel protein, changing its conductance, is inadequate to explain the primary site of action of the antiarrhythmic n-3 PUFAs. We have shown that when a neutral asparagine is replaced by a positively charged lysine in the N406 amino acid site in the alpha-subunit of the human cardiac sodium channel, the n-3 fatty acids lose their inhibitory action on the sodium current. The inadequacy of this finding to explain the primary site of action of the n-3 PUFAs is demonstrated by the inhibitory effect on all other cardiac ion channels, so far tested. We show that ion channels, which share no amino acid homology with the PUFAs, have their conductance also reduced in the presence of the PUFAs, Thus a more general conceptual framework or paradigm is needed to account for the broad action of the PUFAs on diverse different ion channels lacking amino acid homology. We have been testing the membrane tension hypothesis of Andersen and associates. According to this hypothesis, the fatty acids are not acting directly on the ion channel protein but accumulating in the phospholipid membrane in immediate juxtaposition to the site in the membrane where the ion channel protein penetrates the membrane phospholipid bilayer. This alters membrane tensions exerted by the phospholipid membrane on the ion channel, which in turn causes conformational changes in the ion channel, altering the conductance of the ion channel. Our preliminary data seem to support this membrane tension hypothesis.     

The conductance of single cardiac sodium channels from guinea pig depends on the intracellular sodium concentration.

Currents through DPI 201-106 modified single sodium channels have been measured in cell-free inside-out patches from guinea-pig ventricular myocytes. Single-channel conductance and reversal potential of the sodium channel have been calculated at different intracellular sodium concentrations [( Na+]i) from microscopic I-V curves, which were obtained by application of linear voltage ramps. The relation between the reversal potential and [Na+]i could be fitted with a modified Goldman-Hodgkin-Katz equation with a relative permeability for K+ over Na+ ions of 0.054. The zero-current conductance of the Na channel as a function of [Na+]i shows a plateau value at low Na concentrations, and increases in a sigmoidal manner at higher concentrations. It is concluded that the Na channel can carry outward currents and that its conductance depends on [Na+]i.     

Biological effects of oscillating electric fields: Role of voltage-sensitive ion channels

An alternating component of potential across the membrane of an excitable cell may change the membrane conductance by interacting with the voltagesensing charged groups of the protein macromolecules that form voltage-sensitive ion channels. Because the probability that a voltage sensor is in a given state is a highly nonlinear function of the applied electric field, the average occupancy of a particular state will change in an oscillating electric field of sufficient magnitude. This “rectification” at the level of the voltage sensors could result in conformational changes (gating) that would modify channel conductance. A simplified two-state model is examined where the relaxation time of the voltage sensor is assumed to be considerably faster than the fastest changes of ionic conductance. Significant changes in the occupancy of voltage sensor states in response to an applied oscillating electric field are predicted by the model.     

Brownian dynamics simulation of ion flow through porin channels

Bacterial porins, which allow the passage of solutes across the outer bacterial membrane, are structurally well characterized. They therefore lend themselves to detailed studies of the determinants of ion flow through transmembraneous channels. In a comparative study, we have performed Brownian dynamics simulations to obtain statistically significant transfer efficiencies for cations and anions through matrix porin OmpF, osmoporin OmpK36, phosphoporin PhoE and two OmpF charge mutants.The simulations show that the electrostatic potential at the highly charged channel constriction serves to enhance ion permeability of either cations or anions, dependent on the type of porin. At the same time translocation of counterions is not severely impeded. At the constriction, cations and anions follow distinct trajectories, due to the segregation of basic and acidic protein residues.Simulated ion selectivity and relative conductance agree well with experimental values, and are dependent crucially on the charge constellation at the pore constriction. The experimentally observed decrease in ion selectivity and single channel conductance with increasing ionic strength is well reproduced and can be attributed to electrostatic shielding of the pore lining.     

Cooperative mechanosensitive ion channels in Escherichia coli.

A patch-clamp investigation was carried out on giant Escherichia coli spheroplasts. The membrane exhibited stretch-induced as well as "spontaneous" activity, with similar characteristics, i.e., a large number of conductance values arising from the cooperative behavior of channels in functional clusters. It appears likely that the same molecular species are responsible for both stretch-induced and "spontaneous" current conduction; the channel multiplexes can either respond to membrane stretch or function in an activate state, presumably brought about by the previous application of the mechanical stimulus.     

Interactions of protons with single open L-type calcium channels. Location of protonation site and dependence of proton-induced current fluctuations on concentration and species of permeant ion

We further investigated the rapid fluctuations between two different conductance levels promoted by protons when monovalent ions carry current through single L-type Ca channels. We tested for voltage dependence of the proton-induced current fluctuations and for accessibility of the protonation site from both sides of the membrane patch. The results strongly suggest an extracellular location of the protonation site. We also studied the dependence of the kinetics of the fluctuations and of the two conductance levels on the concentration of permeant ion and on external ionic strength. We find that saturation curves of channel conductance vs. [K] are similar for the two conductance levels. This provides evidence that protonation does not appreciably change the surface potential near the entry of the permeation pathway. The proton-induced conduction change must therefore result from an indirect interaction between the protonation site and the ion-conducting pathway. Concentration of permeant ion and ionic strength also affect the kinetics of the current fluctuations, in a manner consistent with our previous hypothesis that channel occupancy destabilizes the low conductance channel conformation. We show that the absence of measurable fluctuations with Li and Ba as charge carriers can be explained by significantly higher affinities of these ions for permeation sites. Low concentrations of Li reduce the Na conductance and abbreviate the lifetimes of the low conductance level seen in the presence of Na. We use whole-cell recordings to extrapolate our findings to the physiological conditions of Ca channel permeation and conclude that in the presence of 1.8 mM Ca no proton-induced fluctuations occur between pH 7.5 and 6.5. Finally, we propose a possible physical interpretation of the formal model of the protonation cycle introduced in the companion paper.