Coupling between fluxes in one-particle pores with fluctuating energy profiles. A theoretical study.

We show theoretically that extending pore models to allow for fluctuations between configurations with different energy profiles results in the prediction of coupling between fluxes and forces of different species diffusing through singly occupied pores. Considering the case of a one-site, two-barrier pore capable of existing in two states, and using Eyring rate theory to describe the translocation of two permeant species, the flux of each is found to be linked to the driving force of the other via cross coefficients that are given as explicit functions of concentrations and potential, and that obey Onsager's relations when the system is near equilibrium. Conditions for the existence of coupling are that both states of the channel be permeable to both diffusing species and that the peaks of the two energy barrier shift by different amounts during the state transition of the pore. Some implications of this model on phenomena of biological interest are discussed briefly.     

Protonophore anion permeability of the human red cell membrane determined in the presence of valinomycin

Summary A transport model for translocation of the protonophore CCCP across the red cell membrane has been established and cellular CCCP binding parameters have been determined. The time course of the CCCP redistribution across the red cell membrane, following a jump in membrane potential induced by valinomycin addition, has been characterized by fitting values of preequilibrium extracellular pHvs. time to the transport model. It is demonstrated, that even in the presence of valinomycin, the CCCP-anion is well behaved, in that the translocation can be described by simple electrodiffusion. The translocation kinetics conform to an Eyring transport model, with a single activation energy barrier, contrary to translocation across lipid bilayers, that is reported to follow a transport model with a plateau in the activation energy barrier. The CCCP anion permeability across the red cell membrane has been calculated to be close to 2.0×10^–4 cm/sec at 37°C with small variations between donors. Thus the permeability of CCCP in the human red cell membrane deviates from that found in black lipid membranes, in which the permeability is found to be a factor of 10 higher.     

Modulation of gramicidin A open channel lifetime by ion occupancy.

The hypothesis that the gramicidin A channel stability depends on the level of ion occupancy of the channel was used to derive a mathematical model relating channel lifetime to channel occupancy. Eyring barrier permeation models were examined for their ability to fit the zero-voltage conductance, current-voltage, as well as lifetime data. The simplest permeation model required to explain the major features of the experimental data consists of three barriers and four sites (3B4S) with a maximum of two ions occupying the channel. The average lifetime of the channel was calculated from the barrier model by assuming the closing rate constant to be proportional to the probability of the internal channel sites being empty. The link between permeation and lifetime has as its single parameter the experimentally determined averaged lifetime of gramicidin A channels in the limit of infinitely dilute solutions and has therefore no adjustable parameters. This simple assumption that one or more ions inside the channel completely stabilize the dimer conformation is successful in explaining the experimental data considering the fact that this model for stabilization is independent of ion species and configurational occupancy. The model is used to examine, by comparison with experimental data, the asymmetrical voltage dependence of the lifetime in asymmetrical solutions, the effects of blockers, and the effects of elevated osmotic pressure.     

Interactions of amiloride and small monovalent cations with the epithelial sodium channel. Inferences about the nature of the channel pore.

The voltage dependence of amiloride-induced inhibition of current flow through apical membrane sodium channels in toad urinary bladder was studied at different ionic conditions. The "inert" salt N-methyl-D-glucamine HCl (NMDG HCl) affected neither the apparent inhibition constant (Kl) for the amiloride-induced current inhibition nor the apparent fraction of the transmembrane voltage that falls between the mucosal solution and the amiloride-binding site (delta). When NMDG+ was replaced with Na+, Kl increased, reflecting amiloride-Na+ competition, whereas delta was unchanged. Similar results were obtained with another permeant cation, Li+. When NMDG+ was replaced by K+, an impermeant but channel-blocking cation, Kl increased whereas delta decreased. Similar results were obtained using another impermeant, channel-blocking cation guanidinium. The results are interpreted on the premise that Na+ and K+ compete with amiloride by binding to cation binding sites within the channel lumen such that ion occupancy of these sites vary with voltage. Occupancy by K+, which cannot traverse the channel, will increase as the mucosal solution becomes positive, relative to the serosal solution. Occupancy by Na+, which can traverse the channel, is comparatively voltage independent. Ion movement through the channels was simulated using discrete-state kinetic models. Two types of models could describe the shape of the current-voltage relationship and the voltage dependence of the amiloride-induced channel block. One model had a single ion-binding site with a broad energy barrier at the inner (cytoplasmic) side of the site. The other model had two binding sites separated from each other and from the aqueous solutions by sharp energy barriers.     

Interpretation of steady-state current-voltage curves: Consequences and implications of current subtraction in transport studies

Summary A problem often confronted in analyses of chargecarrying transport processesin vivo lies in identifying porterspecific component currents and their dependence on membrane potential. Frequently, current-voltage (I–V)—or more precisely, difference-current-voltage (dI-V)—relations, both for primary and for secondary transport processes, have been extracted from the overall membrane current-voltage profiles by subtracting currents measured before and after experimental manipulations expected to alter the porter characteristics only. This paper examines the consequences of current subtraction within the context of a generalized kinetic carrier model for Class I transport mechanisms (U.-P. Hansen, D. Gradmann, D. Sanders and C.L. Slayman, 1981,J. Membrane Biol. 63:165–190). Attention is focused primarily ondI-V profiles associated with ion-driven secondary transport for which external solute concentrations usually serve as the experimental variable, but precisely analogous results and the same conclusions are indicated in relation to studies of primary electrogenesis. The model comprises a single transport loop linkingn (3 or more) discrete states of a carrier molecule. State transitions include one membrane chargetransport step and one solute-binding step. Fundamental properties ofdI-V relations are derived analytically for alln-state formulations by analogy to common experimental designs. Additional features are revealed through analysis of a reduced 2-state empirical form, and numerical examples, computed using this and a minimum 4-state formulation, illustratedI-V curves under principle limiting conditions. Class I models generate a wide range ofdI-V profiles which can accommodate essentially all of the data now extant for primary and secondary transport systems, including difference current relations showing regions of negative slope conductance. The particular features exhibited by the curves depend on the relative magnitudes and orderings of reaction rate constants within the transport loop. Two distinct classes ofdI-V curves result which reflect the relative rates of membrane charge transit and carrier recycling steps. Also evident in difference current relations are contributions from hidden carrier states not directly associated with charge translocation in circumstances which can give rise to observations of counterflow or exchange diffusion. Conductance-voltage relations provide a semi-quantitative means to obtaining pairs of empirical rate parameters. It is demonstrated thatdI-V relationscannot yield directly meaningful transport reversal potentials in most common experimental situations. Well-defined arramgements of reaction constants are shown to givedI-V curves which exhibit little or no voltage sensitivity and finite currents over many tens to hundreds of millivoltsincluding the true reversal potential. Furthermore, difference currents show apparent Michaelian kinetics with solute concentration atall membrane potentials. These findings bring into question several previous reports of reversal potentials, stoichiometries and apparent current-source behavior based primarily on difference current analysis. They also provide a coherent explanation for anomolous and shallow conductances and paradoxical situations in which charge stoichiometry varies with membrane potential.     

Single-salt behavior of a symmetrical 4-site channel with barriers at its middle and ends

The theory of a symmetrical 3-barrier, 4-site, single-filing ionic channel is developed. The model goes beyond earlier models by including additional sites, as well as barriers which need not be symmetrical in the applied field, and contains the earlier models as special cases. It is itself a special case of the most general 4-site model, which has 5 barriers. By considering the barriers at the mouth and middle of the channel to be sufficiently larger than the barriers separating the sites in each channel half, these barriers can be neglected; thus this case reduces to a 3-barrier model where the sites in each channel half can then be assumed to be in equilibrium with each other. The alternative 3-barrier, 4-site case, where the barrier between the sites is considered to be larger than that at the mouth of the channel, is considered elsewhere. Pure cation permeation is considered and only single-salt properties of the system are analyzed, namely occupancy, conductance, flux ratio exponent and current-voltage relation. The concentration dependences of these properties are computed and interrelated and, where possible, also given in analytical form. The mathematical relations are obtained for a channel which is symmetrical around its middle, which is the appropriate assumption for the gramicidin channel. However, the barriers themselves are allowed to be asymmetric with respect to the potential dependence, which has been found to be essential for gramicidin. Mathematically, a straight-forward matrix formulation is used; but a general theoretical method is presented for reducing a complex model (with more than 2 sites) to a simpler cases when equilibrium exists across one or several barriers, as is often the cases. This method is a prototype which makes analytical solutions of complex barrier models possible in many cases.     

Symmetry and asymmetry of permeation through toxin-modified Na+ channels.

Single Na+ channels from rat skeletal muscle were inserted into planar lipid bilayers in the presence of either 200 nM batrachotoxin (BTX) or 50 microM veratridine (VT). These toxins, in addition to their ability to shift inactivation of voltage-gated Na+ channels, may be used as probes of ion conduction in these channels. Channels modified by either of the toxins have qualitatively similar selectivity for the alkali cations (Na+ approximately Li+ greater than K+ greater than Rb+ greater than Cs+). Biionic reversal potentials, for example, were concentration independent for all ions studied. Na+/K+ and Na+/Rb+ reversal potentials, however, were dependent on the orientation of the ionic species with respect to the intra- or extracellular face of the channel, whereas Na+/Li+ biionic reversal potentials were not orientation dependent. A simple, four-barrier, three-well, single-ion occupancy model was used to generate current-voltage relationships similar to those observed in symmetrical solutions of Na, K, or Li ions. The barrier profiles for Na and Li ions were symmetric, whereas that for K ions was asymmetric. This suggests the barrier to ion permeation for K ions may be different than that for Na and Li ions. With this model, these hypothetical energy barrier profiles could predict the orientation-dependent reversal potentials observed for Na+/K+ and Na+/Rb+. The energy barrier profiles, however, were not capable of describing biionic Na/Li ion permeation. Together these results support the hypothesis that Na ions have a different rate determining step for ion permeation than that of K and Rb ions.     

Weak acid transport across bilayer lipid membrane in the presence of buffers. Theoretical and experimental pH profiles in the unstirred layers.

This paper presents a simple model to describe experimental data on weak acid transport across planar bilayer lipid membrane separating two buffered solutions. The model takes into account multiple proton-transfer reactions occurring in the unstirred layers (ULs) adjacent to the membrane. Differential equations of the model are shown to be reduced to a set of nonlinear algebraic equations. Since the latter equations depend monotonically on unknown variables, they can be easily solved numerically, using bisection method. For the particular system studied experimentally (with acetate as the weak acid and TRIS+MES as the buffer mixture) pH profiles in the ULs are calculated from the model. These results are compared with experimental data obtained using pH microelectrode. The agreement between theoretical and experimental pH profiles is found to be satisfactory. The most pronounced deviations are observed at the UL/bulk solution boundary. To obtain a better correlation between the theoretical and experimental results, two other, less idealized models are considered. They take into account, respectively, (a) the electric field arising in the ULs from ion diffusion and (b) finiteness of the rates of proton-transfer reactions. However, both acetate membrane fluxes and pH profiles in the ULs computed from these models are found to be close to those of the simple model. One can thus conclude that the difference between experimental and theoretical pH profiles is due to the inconsistency of the generally accepted model of the "unstirred layer", assuming the existence of a strict boundary between the regions of "pure diffusion" and "ideal stirring".     

Interpretation of current-voltage relationships for “active” ion transport systems: I. Steady-state reaction-kinetic analysis of class-I mechanisms

Summary This paper develops a simple reaction-kinetic model to describe electrogenic pumping and co- (or counter-) transport of ions. It uses the standard steady-state approach for cyclic enzyme- or carrier-mediated transport, but does not assume rate-limitation by any particular reaction step. Voltage-dependence is introduced, after the suggestion of Läuger and Stark (Biochim. Biophys. Acta 211:458–466, 1970), via a symmetric Eyring barrier, in which the charge-transit reaction constants are written ask ₁₂=k ₁₂ ⁰ exp(zF/2RT) andk ₂₁=k ₂₁ ⁰ exp(–zF/2RT). For interpretation of current-voltage relationships, all voltage-independent reaction steps are lumped together, so the model in its simplest form can be described as a pseudo-2-state model. It is characterized by the two voltage-dependent reaction constants, two lumped voltage-independent reaction constants (K ₁₂,K ₂₁), and two reserve factors (r _i,r ₀) which formally take account of carrier states that are indistinguishable in the current-voltage (I–V) analysis. The model generates a wide range ofI–V relationships, depending on the relative magnitudes of the four reaction constants, sufficient to describe essentially allI–V data now available on active ion-transport systems. Algebraic and numerical analysis of the reserve factors, by means of expanded pseudo-3-, 4-, and 5-state models, shows them to be bounded and not large for most combinations of reaction constants in the lumped pathway. The most important exception to this rule occurs when carrier decharging immediately follows charge transit of the membrane and is very fast relative to other constituent voltage-independent reactions. Such a circumstance generates kinetic equivalence of chemical and electrical gradients, thus providing a consistent definition of ion-motive forces (e.g., proton-motive force, PMF). With appropriate restrictions, it also yields both linear and log-linear relationships between net transport velocity and either membrane potential or PMF. The model thus accommodates many known properties of proton-transport systems, particularly as observed in chemiosmotic or energy-coupling membranes.     

The transport of potassium through lipid bilayer membranes by the neutral carriers valinomycin and monactin

Summary Stationary conductance experiments on neutral and negatively charged bilayer membranes in the presence of valinomycin or monactin agree with a recently proposed carrier transport model, which is common to both carrier types. This model assumes an interface reaction between a cation from the aqueous solution and a carrier molecule from the membrane phase to establish charge transport across the interface. The transport across the membrane interior is described by some kind of Eyring model. The discussion of the current-voltage characteristic, the dependence of membrane conductance on the carrier and K⁺ concentrations, and the comparison with appropriate experiments allow correlation of the different rate constants of the transport model. The results show that the rate constants partly depend on the surface charge of the membranes. This dependency can be described by introducing the Gouy-Chapman theory for charged surfaces into the transport model.It was found that the carrier molecules could be added either to the aqueous phase or to the membrane-forming solution. The quantitative treatment of this phenomenon gives an evaluation of the partition coefficient of the carrier molecules between the membrane bulk phase and water.     

(In)validity of the constant field and constant currents assumptions in theories of ion transport.

Constant electric fields and constant ion currents are often considered in theories of ion transport. Therefore, it is important to understand the validity of these helpful concepts. The constant field assumption requires that the charge density of permeant ions and flexible polar groups is virtually voltage independent. We present analytic relations that indicate the conditions under which the constant field approximation applies. Barrier models are frequently fitted to experimental current-voltage curves to describe ion transport. These models are based on three fundamental characteristics: a constant electric field, negligible concerted motions of ions inside the channel (an ion can enter only an empty site), and concentration-independent energy profiles. An analysis of those fundamental assumptions of barrier models shows that those approximations require large barriers because the electrostatic interaction is strong and has a long range. In the constant currents assumption, the current of each permeating ion species is considered to be constant throughout the channel; thus ion pairing is explicitly ignored. In inhomogeneous steady-state systems, the association rate constant determines the strength of ion pairing. Among permeable ions, however, the ion association rate constants are not small, according to modern diffusion-limited reaction rate theories. A mathematical formulation of a constant currents condition indicates that ion pairing very likely has an effect but does not dominate ion transport.     

Ionic selectivity, saturation, and block in sodium channels. A four- barrier model

Ionic fluxes in Na channels of myelinated axons show ionic competition, block, and deviations from simple flux independence. These phenomena are particularly evident when external Na+ ions are replaced by other permeant or impermeant ions. The observed currents require new flux equations not based on the concepts of free diffusion. A specific permeability model for the Na channel is developed from Eyring rate theory applied to a chain of saturable binding sites. There are four energy barriers in the pore and only one ion is allowed inside at a time. Deviations from independence arise from saturation. The model shows that ionic permeability ratios measured from zero-current potentials can differ from those measured from relative current amplitudes or conductances. The model can be fitted to experiments with various external sodium substitutes by varying only two parameters: For each ion the height of the major energy barrier (the selectivity filter) determines the biionic zero-current potential and the depth of the energy well (binding site) just external to that barrier then determines the current amplitudes. Voltage clamp measurements with myelinated nerve fibers are given showing numerous examples of deviations from independence in ionic fluxes. Strong blocks of ionic currents by guanidinium compounds and Tl+ ions are fitted by binding within the channel with apparent dissociation constants in the range 50-122 mM. A small block with high Na+ concentrations can be fitted by Na+ ion binding with a dissociation constant of 368 mM. The barrier model is given a molecular interpretation that includes stepwise dehydration of the permeating ion as it interacts with an ionized carboxylic acid.     

Delayed-exponential approximation of a linear homogeneous diffusion model of neuron

The diffusion models of neuronal activity are general yet conceptually simple and flexible enough to be useful in a variety of modeling problems. Unfortunately, even simple diffusion models lead to tedious numerical calculations. Consequently, the existing neural net models use characteristics of a single neuron taken from the pre-diffusion era of neural modeling. Simplistic elements of neural nets forbid to incorporate a single learning neuron structure into the net model. The above drawback cannot be overcome without the use of the adequate structure of the single neuron as an element of a net. A linear (not necessarily homogeneous) diffusion model of a single neuron is a good candidate for such a structure, it must, however, be simplified. In the paper the structure of the diffusion model of neuron is discussed and a linear homogeneous model with reflection is analyzed. For this model an approximation is presented, which is based on the approximation of the first passage time distribution of the Ornstein-Uhlenbeck process by the delayed (shifted) exponential distribution. The resulting model has a simple structure and has a prospective application in neural modeling and in analysis of neural nets.Work supported by Polish Academy of Sciences grant # CPBP 04.01     

Structure of the squid axon membrane as derived from charge-pulse relaxation studies in the presence of absorbed lipophilic ions

Summary Charge-pulse relaxation studies were performed on squid giant axons in the presence of membrane absorbed lipophilic anions, dipicrylamine (DPA) and tetraphenylborate (TPhB), and of specific blockers of sodium and potassium active currents. With the instrumentation used in this work a time resolution of 5 to 10 sec was easily obtained without any averaging, although the voltage relaxations were always smaller than 5 mV in amplitude in order to keep the membrane voltage in a range where the used theory cyn be linearized. Two well distinguishable linear relaxations were invariably observed in the presence of the lipophilic anions. With DPA the fast relaxation (time constants between 8 and 70 sec) was attributed to the redistribution of the lipophilic ions within the membrane following the change in membrane potential. The long relaxation process (time constant in the millisecond range) corresponds to the normal voltage relaxation of the passive squid axon membrane slightly modified by the process of redistribution of the extrinsic ions.The results support the same model for the translocation of lipophilic ions within the nerve membrane proposed earlier for artificial lipid bilayers. The fit of the data with a single barrier model yields the translocation rate constant,K, and the total concentration,N _t , of membrane absorbed ions, from which the membrane-solution partition coefficient, , can be derived. Both for DPA and TPhB,K had values close to those measured for solvent-free artificial lipid bilayers. The axon membrane appears as fluid mosaic membrane with a thickness of about 2.5 nm for the lipid bilayer part.In axons treated with DPA the dependence of relaxation data upon the holding membrane potential, , provided information on the asymmetry of the membrane structure. The data were best fitted by assuming that nearly 100% of the membrane potential drops between the two free energy minima where the extrinsic ions are located, indicating that these minima lie very close to the membrane-solution interfaces, in the region of the phospholipid polar heads. The asymmetry voltage,E _o, at which the extrinsic ions are expected to be equally distributed between the two sides of the membrane was found to range between –35 and –65 mV (inside negative), depending on the assumed shape of the free energy barrier describing the ion translocation process. This voltage is of the same sign and of the same order of magnitude as the equilibrium voltages for the open-close transitions of the gates of sodium and potassium channels, suggesting that all these voltages result from the same membrane asymmetry. A similar analogy was found between the asymmetry of the free energy barrier which best fitted DPA relaxation data and the asymmetrical voltage dependence of the gating of ionic channels. Our data were best fitted by assuming that about 70% of the potential drop occurs between the free energy minimum on the intracellular membrane face and the top of the barrier.     

Modeling ion permeation through batrachotoxin-modified Na+ channels from rat skeletal muscle with a multi-ion pore.

The mechanism of ion permeation through Na+ channels that have been modified by batrachotoxin (BTX) and inserted into planar bilayers has been generally described by models based on single-ion occupancy, with or without an influence of negative surface charge, depending on the tissue source. For native Na+ channels there is evidence suggestive of a multi-ion conduction mechanism. To explore the question of ion occupancy, we have reexamined permeation of Na+, Li+, and K+ through BTX-modified Na+ channels from rat skeletal muscle. Single-channel current-voltage (I-V) behavior was studied in neutral lipid bilayers in the presence of symmetrical Na+ concentrations ranging from 0.5 to 3,000 mM. The dependence of unitary current on the mole fraction of Na+ was also examined in symmetrical mixtures of Na(+)-Li+ and Na(+)-K+ at a constant total ionic strength of 206 and 2,006 mM. The dependence of unitary conductance on symmetrical Na+ concentration does not exhibit Michaelis-Menten behavior characteristic of single-ion occupancy but can be simulated by an Eyring-type model with three barriers and two sites (3B2S) that includes double occupancy and ion-ion repulsion. Best-fit energy barrier profiles for Na+, Li+, and K+ were obtained by nonlinear curve fitting of I-V data using the 3B2S model. The Na(+)-Li+ and Na(+)-K+ mole-fraction experiments do not exhibit an anomalous mole-fraction effect. However, the 3B2S model is able to account for the biphasic dependence of unitary conductance on symmetrical [Na+] that is suggestive of multiple occupancy and the monotonic dependence of unitary current on the mole fraction of Na+ that is compatible with single or multiple occupancy. The best-fit 3B2S barrier profiles also successfully predict bi-ionic reversal potentials for Na(+)-Li+ and Na(+)-K+ in both orientations across the channel. Our experimental and modeling results reconcile the dual personality of ion permeation through Na+ channels, which can display features of single or multiple occupancy under various conditions. To a first approximation, the 3B2S model developed for this channel does not require corrections for vestibule surface charge. However, if negative surface charges of the protein do influence conduction, the conductance behavior in the limit of low [Na+] does not correspond to a Gouy-Chapman model of planar surface charge.     

A barrier model for current flow in lipid bilayer membranes

Summary Theshape of the energy barrier inside thin, insulating membranes can be an important factor in determining the detailed behavior of transmembrane ionic flows. In particular, a model is developed in which the shape of the barrier is expected to have direct influence on such experimentally important membrane properties as: (a) the shape of the current-voltage relation; (b) the dependence of zero current conductivity on asymmetric concentrations; (c) the dependence of the rectification ratio on the concentration ratio.Current-voltage curves were measured for a wide range of symmetrical and asymmetrical concentrations in black lipid (phosphatidyl ethanolamine) films in the presence of nonactin and potassium. A single barrier shape was found to describe accurately the experimental results in terms of the model.     

Exploration of the structural features defining the conduction properties of a synthetic ion channel.

The finite-difference Poisson-Boltzmann methodology was applied to a series of parallel, alpha-helical bundle models of the designed ion channel peptide Ac-(LSSLLSL)3-CONH2. This method is able to fully describe the current-voltage curves for this channel and quantitatively explains their cation selectivity and rectification. We examined a series of energy-minimized models representing different aggregation states, side-chain rotamers, and helical rotations, as well as an ensemble of structures from a molecular dynamics trajectory. Potential energies were computed for single, permeating K+ and Cl- ions at a series of positions along a central pathway through the models. A variable-electric-field Nernst-Planck electrodiffusion model was used, with two adjustable parameters representing the diffusion coefficients of K+ and Cl- to scale the individual ion current magnitudes. The ability of a given DelPhi potential profile to fit the experimental data depended strongly on the magnitude of the desolvation of the permeating ion. Below a pore radius of 3.8 A, the predicted profiles showed large energy barriers, and the experimental data could be fit only with unrealistically high values for the K+ and Cl- diffusion coefficients. For pore radii above 3.8 A, the desolvation energies were 2kT or less. The electrostatic calculations were sensitive to positioning of the Ser side chains, with the best fits associated with maximum exposure of the Ser side-chain hydroxyls to the pore. The backbone component was shown to be the major source of asymmetry in the DelPhi potential profiles. Only two of the energy-minimized structures were able to explain the experimental data, whereas an average of the dynamics structures gave excellent agreement with experimental results. Thus this method provides a promising approach to prediction of current-voltage curves from three-dimensional structures of ion channel proteins.     

Ion conduction in substates of the batrachotoxin-modified Na+ channel from toad skeletal muscle.

Batrachotoxin-modified Na+ channels from toad muscle were inserted into planar lipid bilayers composed of neutral phospholipids. Single-channel conductances were measured for [Na+] ranging between 0.4 mM and 3 M. When membrane preparations were made in the absence of protease inhibitors, two open conductance states were identified: a fully open state (16.6 pS in 200 mM symmetrical NaCl) and a substate that was 71% of the full conductance. The substate was predominant at [Na+] > 65 mM, whereas the presence of the fully open state was predominant at [Na+] < 15 mM. Addition of protease inhibitors during membrane preparation stabilized the fully open state over the full range of [Na+] studied. In symmetrical Na+ solutions and in biionic conditions, the ratio of amplitudes remained constant and the two open states exhibited the same permeability ratios of PLi/PNa and PCs/PNa. The current-voltage relations for both states showed inward rectification only at [Na+] < 10 mM, suggesting the presence of asymmetric negative charge densities at both channel entrances, with higher charge density in the external side. An energy barrier profile that includes double ion occupancy and asymmetric charge densities at the channel entrances was required to fit the conductance-[Na+] relations and to account for the rectification seen at low [Na+]. Energy barrier profiles differing only in the energy peaks can give account of the differences between both conductance states. Estimation of the surface charge density at the channel entrances is very dependent on the ion occupancy used and the range of [Na+] tested. Independent evidence for the existence of a charged external vestibule was obtained at low external [Na+] by identical reduction of the outward current induced by micromolar additions of Mg2+ and Ba2+.