Permeation through an open channel: Poisson-Nernst-Planck theory of a synthetic ionic channel.

The synthetic channel [acetyl-(LeuSerSerLeuLeuSerLeu)3-CONH2]6 (pore diameter approximately 8 A, length approximately 30 A) is a bundle of six alpha-helices with blocked termini. This simple channel has complex properties, which are difficult to explain, even qualitatively, by traditional theories: its single-channel currents rectify in symmetrical solutions and its selectivity (defined by reversal potential) is a sensitive function of bathing solution. These complex properties can be fit quantitatively if the channel has fixed charge at its ends, forming a kind of macrodipole, bracketing a central charged region, and the shielding of the fixed charges is described by the Poisson-Nernst-Planck (PNP) equations. PNP fits current voltage relations measured in 15 solutions with an r.m.s. error of 3.6% using four adjustable parameters: the diffusion coefficients in the channel's pore DK = 2.1 x 10(-6) and DCl = 2.6 x 10(-7) cm2/s; and the fixed charge at the ends of the channel of +/- 0.12e (with unequal densities 0.71 M = 0.021e/A on the N-side and -1.9 M = -0.058e/A on the C-side). The fixed charge in the central region is 0.31e (with density P2 = 0.47 M = 0.014e/A). In contrast to traditional theories, PNP computes the electric field in the open channel from all of the charges in the system, by a rapid and accurate numerical procedure. In essence, PNP is a theory of the shielding of fixed (i.e., permanent) charge of the channel by mobile charge and by the ionic atmosphere in and near the channel's pore. The theory fits a wide range of data because the ionic contents and potential profile in the channel change significantly with experimental conditions, as they must, if the channel simultaneously satisfies the Poisson and Nernst-Planck equations and boundary conditions. Qualitatively speaking, the theory shows that small changes in the ionic atmosphere of the channel (i.e., shielding) make big changes in the potential profile and even bigger changes in flux, because potential is a sensitive function of charge and shielding, and flux is an exponential function of potential.     

Removal of the outermost arginine in IVS4 segment of the Ca(V)3.1 channel affects amplitude but not voltage dependence of gating current

Positively charged amino acids in S4 segments of voltage-dependent Ca(V)3.1 channel form putative voltage sensor. Previously we have shown that exchange of uppermost positively charged arginine in IVS4 segment for cysteine (mutation R1717C) affected deactivation and inactivation, but not activation of macroscopic current. Now we compared gating currents from both channels. Maximal amplitude of charge movement in R1717C channel decreased but voltage-dependent characteristics of charge movement were not significantly altered. We concluded that mutation of R1717C affects the coupling between S4 activation and pore opening, but not the S4 activation itself.     

The role of the dielectric barrier in narrow biological channels: a novel composite approach to modeling single-channel currents

A composite continuum theory for calculating ion current through a protein channel of known structure is proposed, which incorporates information about the channel dynamics. The approach is utilized to predict current through the Gramicidin A ion channel, a narrow pore in which the applicability of conventional continuum theories is questionable. The proposed approach utilizes a modified version of Poisson-Nernst-Planck (PNP) theory, termed Potential-of-Mean-Force-Poisson-Nernst-Planck theory (PMFPNP), to compute ion currents. As in standard PNP, ion permeation is modeled as a continuum drift-diffusion process in a self-consistent electrostatic potential. In PMFPNP, however, information about the dynamic relaxation of the protein and the surrounding medium is incorporated into the model of ion permeation by including the free energy of inserting a single ion into the channel, i.e., the potential of mean force along the permeation pathway. In this way the dynamic flexibility of the channel environment is approximately accounted for. The PMF profile of the ion along the Gramicidin A channel is obtained by combining an equilibrium molecular dynamics (MD) simulation that samples dynamic protein configurations when an ion resides at a particular location in the channel with a continuum electrostatics calculation of the free energy. The diffusion coefficient of a potassium ion within the channel is also calculated using the MD trajectory. Therefore, except for a reasonable choice of dielectric constants, no direct fitting parameters enter into this model. The results of our study reveal that the channel response to the permeating ion produces significant electrostatic stabilization of the ion inside the channel. The dielectric self-energy of the ion remains essentially unchanged in the course of the MD simulation, indicating that no substantial changes in the protein geometry occur as the ion passes through it. Also, the model accounts for the experimentally observed saturation of ion current with increase of the electrolyte concentration, in contrast to the predictions of standard PNP theory.     

Modeling squid axon Na+ channel by a nucleation and growth kinetic mechanism

A kinetic model accounting for all salient features of the Na⁺ channel of the squid giant axon is provided. The model furnishes explanations for the Cole-Moore-like effect, the rising phase of the ON gating current and the slow ‘intermediate component’ of its decaying phase, as well as the gating charge immobilization. Experimental ON ionic currents are semi-quantitatively simulated by the use of only three free parameters, upon assuming that the Na⁺ channel opening proceeds along with the stepwise aggregation of its four domains, while they are moving their gating charge outward under depolarizing conditions. The inactivation phase of the ON ionic current is interpreted by a progressive electrostatic attraction between the positively charged ‘hinged lid’ containing the hydrophobic IFM triad and its receptor inside the channel pore, as the stepwise outward movement of the S4 segments of the Na⁺ channel progressively increases the negative charge attracting the triad to its receptor. The Na⁺ channel closing is assumed to proceed by repolarization-induced disaggregation of its domains, accompanied by inward movement of their gating charge. The phenomenon of ‘gating charge immobilization’ can be explained by assuming that gradual structural changes of the receptor over the time course of depolarization strengthen the interaction between the IFM triad and its receptor, causing a slow release of the gating charge during the subsequent repolarization.     

A physical model of potassium channel activation: from energy landscape to gating kinetics

We have developed a method for rapidly computing gating currents from a multiparticle ion channel model. Our approach is appropriate for energy landscapes that can be characterized by a network of well-defined activation pathways with barriers. To illustrate, we represented the gating apparatus of a channel subunit by an interacting pair of charged gating particles. Each particle underwent spatial diffusion along a bistable potential of mean force, with electrostatic forces coupling the two trajectories. After a step in membrane potential, relaxation of the smaller barrier charge led to a time-dependent reduction in the activation barrier of the principal gate charge. The resulting gating current exhibited a rising phase similar to that measured in voltage-dependent ion channels. Reduction of the two-dimensional diffusion landscape to a circular Markov model with four states accurately preserved the time course of gating currents on the slow timescale. A composite system containing four subunits leading to a concerted opening transition was used to fit a series of gating currents from the Shaker potassium channel. We end with a critique of the model with regard to current views on potassium channel structure.     

Chemical modification of the bacterial porin OmpF: gain of selectivity by volume reduction

OmpF is an essentially nonselective porin isolated from the outer membrane of Escherichia coli. Here we report on the manipulation of the ion selectivity of OmpF by chemical modification with MTS reagents (MTSET, MTSEA, and MTSES) and the (rather bulky) tripeptide glutathione, all cysteine specific. When recorded in a gradient of 0.1//1 M CaCl2 or 0.1//1 M NaCl, pH 7.4 solutions, measured reversal potentials of the most cation-selective modified mutants were (virtually) identical to the Nernst potential of Ca2+ or Na+. Compared to this full cation selectivity, the anion-selective modified mutants performed somewhat less but nevertheless showed high anion selectivity. We conclude that a low permanent charge in combination with a narrow pore can render the same selectivity as a highly charged but wider pore. These results favor the view that both the electrostatic potential arising form the fixed charge in the pore and the space available at the selectivity filter contribute to the charge selection (i.e., cation versus anion selectivity) of a biological ion channel.     

Contributions of charged residues in a cytoplasmic linking region to Na channel gating

Na channels inactivate quickly after opening, and the very highly positively charged cytoplasmic linking region between homologous domains III and IV of the channel molecule acts as the inactivation gate. To test the hypothesis that the charged residues in the domain III to domain IV linker have a role in channel function, we measured currents through wild-type and two mutant skeletal muscle Na channels expressed in Xenopus oocytes, each lacking two or three charged residues in the inactivation gate. Microscopic current measures showed that removing charges hastened activation and inactivation. Macroscopic current measures showed that removing charges altered the voltage dependence of inactivation, suggesting less coupling of the inactivation and activation processes. Reduced intracellular ionic strength shifted the midpoint of equilibrium activation gating to a greater extent, and shifted the midpoint of equilibrium inactivation gating to a lesser extent in the mutant channels. The results allow the possibility that an electrostatic mechanism contributes to the role of charged residues in Na channel inactivation gating.     

Nonlinear charge movement in mammalian cardiac ventricular cells. Components from Na and Ca channel gating [published erratum appears in J Gen Physiol 1989 Aug;94(2):401]

Intramembrane charge movement was recorded in rat and rabbit ventricular cells using the whole-cell voltage clamp technique. Na and K currents were eliminated by using tetraethylammonium as the main cation internally and externally, and Ca channel current was blocked by Cd and La. With steps in the range of -110 to -150 used to define linear capacitance, extra charge moves during steps positive to approximately -70 mV. With holding potentials near -100 mV, the extra charge moving outward on depolarization (ON charge) is roughly equal to the extra charge moving inward on repolarization (OFF charge) after 50-100 ms. Both ON and OFF charge saturate above approximately +20 mV; saturating charge movement is approximately 1,100 fC (approximately 11 nC/muF of linear capacitance). When the holding potential is depolarized to -50 mV, ON charge is reduced by approximately 40%, with little change in OFF charge. The reduction of ON charge by holding potential in this range matches inactivation of Na current measured in the same cells, suggesting that this component might arise from Na channel gating. The ON charge remaining at a holding potential of -50 mV has properties expected of Ca channel gating current: it is greatly reduced by application of 10 muM D600 when accompanied by long depolarizations and it is reduced at more positive holding potentials with a voltage dependence similar to that of Ca channel inactivation. However, the D600-sensitive charge movement is much larger than the Ca channel gating current that would be expected if the movement of channel gating charge were always accompanied by complete opening of the channel.     

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

Current was measured from single open channels of the calcium release channel (CRC) of cardiac sarcoplasmic reticulum (over the range +/-180 mV) in pure and mixed solutions (e.g., biionic conditions) of the alkali metal ions Li+, K+, Na+, Rb+, Cs+, ranging in concentration from 25 mM to 2 M. The current-voltage (I-V) relations were analyzed by an extension of the Poisson-Nernst-Planck (PNP) formulation of electrodiffusion, which includes local chemical interaction described by an offset in chemical potential, which likely reflects the difference in dehydration/solvation/rehydration energies in the entry/exit steps of permeation. The theory fits all of the data with few adjustable parameters: the diffusion coefficient of each ion species, the average effective charge distribution on the wall of the pore, and an offset in chemical potential for lithium and sodium ions. In particular, the theory explains the discrepancy between "selectivities" defined by conductance sequence and "selectivities" determined by the permeability ratios (i.e., reversal potentials) in biionic conditions. The extended PNP formulation seems to offer a successful combined treatment of selectivity and permeation. Conductance selectivity in this channel arises mostly from friction: different species of ions have different diffusion coefficients in the channel. Permeability selectivity of an ion is determined by its electrochemical potential gradient and local chemical interaction with the channel. Neither selectivity (in CRC) seems to involve different electrostatic interaction of different ions with the channel protein, even though the ions have widely varying diameters.     

Effects of membrane surface charge and calcium on the gating of rat brain sodium channels in planar bilayers [published erratum appears in J Gen Physiol 1989 Apr;93(4):following 760]

The voltage-dependent gating of single, batrachotoxin-activated Na channels from rat brain was studied in planar lipid bilayers composed of negatively charged or neutral phospholipids. The relationship between the probability of finding the Na channel in the open state and the membrane potential (Po vs. Vm) was determined in symmetrical NaCl, both in the absence of free Ca2+ and after the addition of Ca2+ to the extracellular side of the channel, the intracellular side, or both. In the absence of Ca2+, neither the midpoint (V0.5) of the Po vs. Vm relation, nor the steepness of the gating curve, was affected by the charge on the bilayer lipid. The addition of 7.5 mM Ca2+ to the external side caused a depolarizing shift in V0.5. This depolarizing shift was approximately 17 mV in neutral bilayers and approximately 25 mV in negatively charged bilayers. The addition of the same concentration of Ca2+ to only the intracellular side caused hyperpolarizing shifts in V0.5 of approximately 7 mV (neutral bilayers) and approximately 14 mV (negatively charged bilayers). The symmetrical addition of Ca2+ caused a small depolarizing shift in Po vs. Vm. We conclude that: (a) the Na channel protein possesses negatively charged groups on both its inner and outer surfaces. Charges on both surfaces affect channel gating but those on the outer surface exert a stronger influence. (b) Negative surface charges on the membrane phospholipid are close enough to the channel's gating machinery to substantially affect its operation. Charges on the inner and outer surfaces of the membrane lipid affect gating symmetrically. (c) Effects on steady-state Na channel activation are consistent with a simple superposition of contributions to the local electrostatic potential from charges on the channel protein and the membrane lipid.     

The third transmembrane segment of orai1 protein modulates Ca2+ release-activated Ca2+ (CRAC) channel gating and permeation properties

Orai1, the pore subunit of Ca(2+) release-activated Ca(2+) channels, has four transmembrane segments (TMs). The first segment, TMI, lines the pore and plays an important role in channel activation and ion permeation. TMIII, on the other hand, does not line the pore but still regulates channel gating and permeation properties. To understand the role of TMIII, we have mutated and characterized several residues in this domain. Mutation of Trp-176 to Cys (W176C) and Gly-183 to Ala (G183A) had dramatic effects. Unlike wild-type channels, which exhibit little outward current and are activated by STIM1, W176C mutant channels exhibited a large outward current at positive potentials and were constitutively active in the absence of STIM1. G183A mutant channels also exhibited substantial outward currents but were active only in the presence of 2-aminoethoxydiphenyl borate (2-APB), irrespective of STIM1. With W176C mutant channels inward, monovalent currents were blocked by Ca(2+) with a high affinity similar to the wild type, but the Ca(2+)-dependent blocking of outward currents differed in the two cases. Although a 50% block of the WT outward current required 250 μm Ca(2+), more than 6 mm was necessary to have the same effect on W176C mutant channels. In the presence of extracellular Ca(2+), W176C and G183A outward currents developed slowly in a voltage-dependent manner, whereas they developed almost instantaneously in the absence of Ca(2+). These changes in permeation and gating properties mimic the changes induced by mutations of Glu-190 in TMIII and Asp-110/Asp-112 in the TMI/TMII loop. On the basis of these data, we propose that TMIII maintains negatively charged residues at or near the selectivity filter in a conformation that facilitates Ca(2+) inward currents and prevents outward currents of monovalent cations. In addition, to controlling selectivity, TMIII may also stabilize channel gating in a closed state in the absence of STIM1 in a Trp-176-dependent manner.     

Charges, currents, and potentials in ionic channels of one conformation.

Flux through an open ionic channel is analyzed with Poisson-Nernst-Planck (PNP) theory. The channel protein is described as an unchanging but nonuniform distribution of permanent charge, the charge distribution observed (in principle) in x-ray diffraction. Appropriate boundary conditions are derived and presented in some generality. Three kinds of charge are present: (a) permanent charge on the atoms of the protein, the charge independent of the electric field; (b) free or mobile charge, carried by ions in the pore as they flux through the channel; and (c) induced (sometimes called polarization) charge, in the pore and protein, created by the electric field, zero when the electric field is zero. The permanent charge produces an offset in potential, a built-in Donnan potential at both ends of the channel pore. The system is completely solved for bathing solutions of two ions. Graphs describe the distribution of potential, concentration, free (i.e., mobile) and induced charge, and the potential energy associated with the concentration of charge, as well as the unidirectional flux as a function of concentration of ions in the bath, for a distribution of permanent charge that is uniform. The model shows surprising complexity, exhibiting some (but not all) of the properties usually attributed to single filing and exchange diffusion. The complexity arises because the arrangement of free and induced charge, and thus of potential and potential energy, varies, sometimes substantially, as conditions change, even though the channel structure and conformation (of permanent charge) is strictly constant. Energy barriers and wells, and the concomitant binding sites and binding phenomena, are outputs of the PNP theory: they are computed, not assumed. They vary in size and location as experimental conditions change, while the conformation of permanent charge remains constant, thus giving the model much of its interesting behavior.     

Improved 3D continuum calculations of ion flux through membrane channels

A continuum model, based on the Poisson–Nernst–Planck (PNP) theory, is applied to simulate steady-state ion flux through protein channels. The PNP equations are modified to explicitly account (1) for the desolvation of mobile ions in the membrane pore and (2) for effects related to ion sizes. The proposed algorithm for a three-dimensional self-consistent solution of PNP equations, in which final results are refined by a focusing technique, is shown to be suitable for arbitrary channel geometry and arbitrary protein charge distribution. The role of the pore shape and protein charge distribution in formation of basic electrodiffusion properties, such as channel conductivity and selectivity, as well as concentration distributions of mobile ions in the pore region, are illustrated by simulations on model channels. The influence of the ionic strength in the bulk solution and of the externally applied electric field on channel properties are also discussed.     

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

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

Glutamate substitution in repeat IV alters divalent and monovalent cation permeation in the heart Ca2+ channel.

In voltage-gated ion channels, residues responsible for ion selectivity were identified in the pore-lining SS1-SS2 segments. Negatively charged glutamate residues (E393, E736, E1145, and E1446) found in each of the four repeats of the alpha 1C subunit were identified as the major determinant of selectivity in Ca2+ channels. Neutralization of glutamate residues by glutamine in repeat I (E393Q), repeat III (E1145Q), and repeat IV (E1446Q) decreased the channel affinity for calcium ions 10-fold from the wild-type channel. In contrast, neutralization of glutamate residues in repeat II failed to significantly alter Ca2+ affinity. Likewise, mutation of neighboring residues in E1149K and D1450N did not affect the channel affinity, further supporting the unique role of glutamate residues E1145 in repeat III and E1446 in repeat IV in determining Ca2+ selectivity. Conservative mutations E1145D and E1446D preserved high-affinity Ca2+ binding, which suggests that the interaction between Ca2+ and the pore ligand sites is predominantly electrostatic and involves charge neutralization. Mutational analysis of E1446 showed additionally that polar residues could achieve higher Ca2+ affinity than small hydrophobic residues could. The role of high-affinity calcium binding sites in channel permeation was investigated at the single-channel level. Neutralization of glutamate residue in repeats I, II, and III did not affect single-channel properties measured with 115 mM BaCl2. However, mutation of the high-affinity binding site E1446 was found to significantly affect the single-channel conductance for Ba2+ and Li+, providing strong evidence that E1446 is located in the narrow region of the channel outer mouth. Side-chain substitutions at 1446 in repeat IV were used to probe the nature of divalent cation-ligand interaction and monovalent cation-ligand interaction in the calcium channel pore. Monovalent permeation was found to be inversely proportional to the volume of the side chain at position 1446, with small neutral residues such as alanine and glycine producing higher Li+ currents than the wild-type channel. This suggests that steric hindrance is a major determinant for monovalent cation conductance. Divalent permeation was more complex. Ba2+ single-channel conductance decreased when small neutral residues such as glycine were replaced by bulkier ones such as glutamine. However, negatively charged amino acids produced single-channel conductance higher than predicted from the size of their side chain. Hence, negatively charged residues at position 1446 in repeat IV are required for divalent cation permeation.     

Ion permeation and selectivity of OmpF porin: a theoretical study based on molecular dynamics,Brownian dynamics,and continuum electrodiffusion theory

Three different theoretical approaches are used and compared to refine our understanding of ion permeation through the channel formed by OmpF porin from Escherichia coli. Those approaches are all-atom molecular dynamics (MD) in which ions, solvent, and lipids are represented explicitly, Brownian dynamics (BD) in which ions are represented explicitly, while solvent and lipids are represented as featureless dielectrics, and Poisson-Nernst-Planck (PNP) electrodiffusion theory in which both solvent and local ion concentrations are represented as a continuum. First, the ability of the different theoretical approaches in reproducing the equilibrium average ion density distribution in OmpF porin bathed by a 1M KCl symmetric salt solution is examined. Under those conditions the PNP theory is equivalent to the non-linear Poisson-Boltzmann (PB) theory. Analysis shows that all the three approaches are able to capture the important electrostatic interactions between ions and the charge distribution of the channel that govern ion permeation and selectivity in OmpF. The K(+) and Cl(-) density distributions obtained from the three approaches are very consistent with one another, which suggests that a treatment on the basis of a rigid protein and continuum dielectric solvent is valid in the case of OmpF. Interestingly, both BD and continuum electrostatics reproduce the distinct left-handed twisted ion pathways for K(+) and Cl(-) extending over the length of the pore which were observed previously in MD. Equilibrium BD simulations in the grand canonical ensemble indicate that the channel is very attractive for cations, particularly at low salt concentration. On an average there is 1.55 K(+) inside the pore in 10mM KCl. Remarkably, there is still 0.17 K(+) on average inside the pore even at a concentration as low as 1microM KCl. Secondly, non-equilibrium ion flow through OmpF is calculated using BD and PNP and compared with experimental data. The channel conductance in 0.2M and 1M KCl calculated using BD is in excellent accord with the experimental data. The calculations reproduce the experimentally well-known conductance-concentration relation and also reveal an asymmetry in the channel conductance (a larger conductance is observed under a positive transmembrane potential). Calculations of the channel conductance for three mutants (R168A, R132A, and K16A) in 1M KCl suggest that the asymmetry in the channel conductance arises mostly from the permanent charge distribution of the channel rather than the shape of the pore itself. Lastly, the calculated reversal potential in a tenfold salt gradient (0.1:1M KCl) is 27.4(+/-1.3)mV (BD) and 22.1(+/-0.6)mV (PNP), in excellent accord with the experimental value of 24.3mV. Although most of the results from PNP are qualitatively reasonable, the calculated channel conductance is about 50% higher than that calculated from BD probably because of a lack of some dynamical ion-ion correlations.     

Ionic currents and ion channels of lobster olfactory receptor neurons

The role of the soma of spiny lobster olfactory receptor cells in generating odor-evoked electrical signals was investigated by studying the ion channels and macroscopic currents of the soma. Four ionic currents; a tetrodotoxin-sensitive Na+ current, a Ca++ current, a Ca(++)-activated K+ current, and a delayed rectifier K+ current, were isolated by application of specific blocking agents. The Na+ and Ca++ currents began to activate at -40 to -30 mV, while the K+ currents began to activate at -30 to -20 mV. The size of the Na+ current was related to the presence of a remnant of a neurite, presumably an axon, and not to the size of the soma. No voltage-dependent inward currents were observed at potentials below those activating the Na+ current, suggesting that receptor potentials spread passively through the soma to generate action potentials in the axon of this cell. Steady-state inactivation of the Na+ current was half-maximal at -40 mV. Recovery from inactivation was a single exponential function that was half-maximal at 1.7 ms at room temperature. The K+ currents were much larger than the inward currents and probably underlie the outward rectification observed in this cell. The delayed rectifier K+ current was reduced by GTP-gamma-S and AIF-4, agents which activate GTP-binding proteins. The channels described were a 215-pS Ca(++)-activated K+ channel, a 9.7-pS delayed rectifier K+ channel, and a 35-pS voltage-independent Cl- channel. The Cl- channel provides a constant leak conductance that may be important in stabilizing the membrane potential of the cell.     

Charge dissociation and the rising phase of gating currents

Gating currents from voltage-sensitive channels are generally attributed to the translocation or redistribution of ionic charge associated with the channel molecule. Such charge moves in the direction of the applied field to produce a decreasing current in the external circuit. An early rising phase for the gating current is observed for a number of channel systems and might be either some special kinetic redistribution of charge or an experimental artifact. A model that produces net charge in the channel through sequential molecular dissociation of a charged channel segment gives a rising phase for the gating current. Translocation of the charged segment produces the decay phase for a biphasic gating current. This kinetic molecular explanation constitutes a physical explanation for the biphasic gating currents that is consistent with present views of channel structure.     

Lipid-mediated inactivation of colicin E1 channels by calcium ions

Based on the model of a toroidal protein-lipid pore, the effect of calcium ions on colicin E1 channel was predicted. In electrophysiological experiments Ca2+ suppressed the activity of colicin E1 channels in membranes formed of diphytanoylphosphatidylglycerol, whereas no desorption of the protein occurred from the membrane surface. The effect of Ca2+ was not observed on membranes formed of diphytanoylphosphatidylcholine. Single-channel measurements revealed that Ca2+-induced reduction of the colicin-induced current across the negatively charged membrane was due to a decrease in the number of open colicin channels and not changes in their properties. In line with the toroidal model, the effect of Ca2+ on the colicin E1 channel-forming activity is explained by alteration of the membrane lipid curvature caused by electrostatic interaction of Ca2+ with negatively charged lipid head groups.