Calculation of ion currents from energy profiles and energy profiles from ion currents in multibarrier, multisite, multioccupancy channel model.
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Biomedical subjects
Publications and source records attributed to G Eisenman.
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Satellite tobacco necrosis virus (STNV) is an icosahedral virus which contains three classes of Ca2+ binding site. One of these classes, a five-fold carbonyl site which is believed to exist in a Ca2+ channel, has been investigated using laser-induced Eu3+ luminescence spectroscopy. These twelve identical sites are rather rigid, as evidenced by the single narrow (full width at half-maximum is 6.5 cm-1) band observed at 579.58 nm in the 7F0----5D0 excitation spectrum of the Eu(3+)-STNV complex. Lifetimes of 270 microseconds in H2O and 1620 microseconds in D2O indicate that there are three water molecules bound to the Eu3+ at this site. Ligand field splitting of the 7F0----5D1 and 7F0----5D2 excitation spectra show that this site possesses fairly high symmetry (less than or equal to C5V). The Eu3+ complex of nitrilotriacetic acid was determined via titration to have a dissociation constant, Kd, of 20 +/- 2 nM; this value has been used in competition experiments to deduce that the virus site class binds Eu3+ with a Kd of 1.1 +/- 0.3 nM. This putative ion channel demonstrates remarkable size selectivity, with lanthanide affinities varying by more than one order of magnitude.
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.
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The environments of metal ions (Li+, Na+, K+, Ag+, Cs+, Mg2+, Ca2+, Mn2+, Cu2+, Zn2+) in proteins and other metal-host molecules have been examined. Regardless of the metal and its precise pattern of ligation to the protein, there is a common qualitative feature to the binding site: the metal is ligated by a shell of hydrophilic atomic groups (containing oxygen, nitrogen, or sulfur atoms) and this hydrophilic shell is embedded within a larger shell of hydrophobic atomic groups (containing carbon atoms). That is, metals bind at centers of high hydrophobicity contrast. This qualitative observation can be described analytically by the hydrophobicity contrast function, C, evaluated from the structure. This function is large and positive for a sphere of hydrophilic atomic groups (characterized by atomic solvation parameters, delta sigma, having values less than 0) at the center of a larger sphere of hydrophobic atomic groups (characterized by delta sigma greater than 0). In the 23 metal-binding molecules we have examined, the maximum values of the contrast function lie near to observed metal binding sites. This suggests that the hydrophobicity contrast function may be useful for locating, characterizing, and designing metal binding sites in proteins.
Single channel patch-clamp techniques were used to study nicotinic acetylcholine receptors in cultured rat myotubes. The single channel conductance in pure cesium and sodium levels off at high concentrations, as if a binding site within the channel were saturating. The conductances at very low concentrations, however, are larger than predicted by the simplest one-site transport model fitted to the high-concentration data. At low concentrations, the current-voltage relations are inwardly rectifying, but they become more ohmic if a small amount of divalent cations is added externally. Magnesium and barium are good permeants that have rather high affinities for the channel. Upon adding low millimolar concentrations of these divalent cations externally to a membrane bathed in pure cesium, the inward current carried by cesium is decreased. As more divalent cations are added, the inward-going currents continued to decrease and the divalent cation replaces cesium as the main current carrier. The ion transport data are described by considering the size, shape, and possible net charge of the channel. In that way, even the complex features of transport are explained in a realistic physical framework. The results are consistent with the channel having long, wide, multiply occupied vestibules that serve as transition zones to the short, selective, singly occupied narrow region of the channel. A small amount of net negative charge within the pore could produce concentration-dependent potentials that provide a simple explanation for the more complicated aspects of the permeation properties.
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Open-channel ion permeation properties were investigated for Ca++-activated K+ (CaK) channels in solutions of K+ and its analogues T1+, Rb+, and NH4+. Single CaK channels were inserted into planar lipid bilayers composed of neutral phospholipids, and open-channel current-voltage (I-V) relations were measured in symmetrical and asymmetrical solutions of each of these individual ions. For all concentrations studied, the zero-voltage conductance falls in the sequence K+ greater than T1+ greater than NH4+ greater than Rb+. The shape of the I-V curve in symmetrical solutions of a single permeant ion is non-ohmic and is species-dependent. The I-V shape is sublinear for K+ and T1+ and superlinear for Rb+ and NH4+. As judged by reversal potentials under bi-ionic conditions with K+ on one side of the bilayer and the test cation on the other, the permeability sequence is T1+ greater than K+ greater than Rb+ greater than NH4+ at 300 mM, which differs from the conductance sequence. Symmetrical mixtures of K+ or NH4+ with Rb+ show a striking anomalous mole fraction behavior, i.e., a minimum in single-channel conductance when the composition of a two-ion mixture is varied at constant total ion concentration. This result is incompatible with present models that consider the CaK channel a single-ion pore. In total, the results show that the CaK channel finely discriminates among K+-like ions, exhibiting different energy profiles among these species, and that several such ions can reside simultaneously within the conduction pathway.
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A procedure is developed for dealing with multioccupancy in single-filing channels having any number of sites internal to the barriers at the channel ends but having the outermost sites in equilibrium with the bathing solutions. Using this procedure, a general theory is developed for a single-filing channel having three barriers and four sites, the outermost of which are in equilibrium with the bathing solutions. By introducing a vectorial representation, it is shown that the four-site model can be reduced to an equivalent two-site model with respect to the number of possible transitions, thereby simplifying the algebraic steps required to solve transport equations for the system. The transport coefficients are derived and expressed in terms of the energy levels of the peaks and the wells for the different occupancy configurations. An explicit solution to the transport equations is given in a comprised form for a single permeable species. The solution allows some important properties for the system to be deduced, specifically with regard to the conductance at zero current, the correlation factor between electrical conductance and tracer flux, and the current-voltage relationship. Examples are given for the use of the present results in a physical interpretation of the data from the gramicidin A channel.
By introducing external driving forces in rate-theory models of transport we show how the Eyring rate equations can be transformed into Ohm's law with potentials that obey Kirchhoff's second law. From such a formalism the state diagram of a multioccupancy multicomponent system can be directly converted into linear network with resistors connecting nodal (branch) points and with capacitances connecting each nodal point with a reference point. The external forces appear as emf or current generators in the network. This theory allows the algebraic methods of linear network theory to be used in solving the flux equations for multistate models and is particularly useful for making proper simplifying approximation in models of complex membrane structure. Some general properties of linear network representation are also deduced. It is shown, for instance, that Maxwell's reciprocity relationships of linear networks lead directly to Onsager's relationships in the near equilibrium region. Finally, as an example of the procedure, the equivalent circuit method is used to solve the equations for a few transport models.
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The conductance-voltage (G-V) characteristic of a single-filing, multi-barrier, multi-occupancy channel depends in the limit of low ion concentration upon only two parameters: the voltage dependence of the entry step and the ratio of the rate constant for leaving the channel to that for crossing its middle (14,17,20). We show that the G-V shape in this low concentration limit can be measured accurately using a triangular wave, many-channel technique and demonstrate that the observed shape is incompatible with that expected if the only important rate limiting barrier at low concentration were at the channel mouth. Instead the central barrier turns out, surprisingly, in view of the markedly sublinear I-V shape at low concentration, to be even slightly larger than the exit barrier. Additionally, we find that it is not possible to fit both the G-V shape and the concentration dependence of the zero-current conductance simultaneously with a 3-barrier 2-site model. However, by adding additional sites to yield a 3-barrier 4-site model either of the type 3B4S" where the extra site in each channel half is external to the mouth of the channel or of the type 3B4S' where the extra site is internal to the mouth of the channel, we obtain good agreement. Additionally, using the flux ratio data of Procopio and Andersen (19) to discriminate between 3B4S and 3B4S" models, we find the 3B4S" model to be the only satisfactory one.
A theory, recently developed by Sandblom, Eisenman and Neher (1977) for the conductance of single gramicidin A cha-nelspred icts three limiting behaviors of the relation between conductance and salt concentration. These are: (i) a saturating behavior resembling a simple adsorption isotherm at medium and high concentrations, (ii) a decrease in conductance at the highest obtainable concentrations and (iii) deviations from the isotherm at very low concentrations. Features i and ii have been described before. Experimental evidence for point iii is given here. The new feature points towards interactions among ions in the channel at ionic concentrations as low as 1--10 mM. Particular emphasis is given to the behavior at very low salt concentrations and the experimental problems encountered in this situation. In addition, mutual blocking effects among monovalent ions in symmetrical salt mixtures are characterized and found to be in satisfactory agreement with theoretical expectations, based upon the single salt conductance data presented here and zero-current potentials in salt mixtures to be described in a subsequent paper.
As a prototype for binding and interaction in biological Na and K channels, the single channel conductances for Li, Na, K, Rb, Cs, H, and Tl and the membrane potentials for Tl-K mixtures are characterized for gramicidin A over wider concentration rangers than previously and analyzed using an "equilibrium domain" model that assumes a central rate-determining barrier. Peculiarities in the conductance-concentration relationship for TlF, TlNO3, and TlAc suggest that anions bind to Tl-loaded channels, and the theory is extended to allow for this. For concreteness, the selectivity of cation permeation is characterized in terms of individual binding and rate constants of this model, with the conclusions that the strongest site binds Cs greater than Rb greater than K greater than Na greater than Li, while the next strongest binds Na greater than K greater than Li greater than Rb greater than Cs. However, because Schagina, Grinfeldt, and Lev's recent finding of single filing (personal communication) indicates that the channel sites in gramicidin cannot be at equilibrium with the solution, and work in progress with Hägglund and Enos (Biophys. J. 21:26a. [Abstr.]) indicates that the simplest model adequate to account for the observed concentration-dependences of flux-ratio, conductance, I--V characteristic, and permeability has three barriers and four sites, some implications of additional rate-determining barriers at the mouth of the channel are discussed. The results are summarized using phenomenological "experimental" parameters that provide a model-independent way to represent that data concisely and which can be interpreted physically in terms of any desired model.
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.
The manner in which molecular structure of the carrier and the lipid composition of the membrane modulate the membrane selectivity among monovalent cations has been investigated for nonactin, trinactin, and tetranactin, which differ only in their degrees of methylation, and for membranes made of two lipids, phosphatidyl ethanolamine and glyceryl dioleate, in which "equilibrium" and "kinetic" aspects of permeation, respectively, are emphasized. Bilayer permeability ratios for Li, Na, K, Rb, Cs, Tl,and NH4 have been characterized and resolved into "equilibrium" and "kinetic" components using a model for carrier-mediated membrane transport which includes both a trapezoid energy barrier for translocation of the complex across the membrane interior and a potential-dependence of the loading and unloading of ions at the membrane-solution interfaces. The bilayer permeability properties due to tetranactin have been characterized in each of these lipids and found not only to be regular but to be systematically related to those of the less methylated homologues, trinactin and nonactin. This analysis has led to the following conclusions: (1) The change in lipid composition alters the relative contributions of "kinetic" vs. "equilibrium" components to the observed carrier-mediated selectivity. (2) Increased methylation of the carrier increases the contribution of the "kinetic" component to the selectivity relative to that of the "equilibrium" component and additionally alters the "equilibrium component sufficiently that an inversion of Cs--Na selectivity occurs between trinactin and tetranactin. (3) For all ions and carriers examined, the "reaction plane" for ion-carrier complexation and the width for the "diffusion barrier can be represented by the same two parameters, independent of the ion or carrier, so that in all cases the complexation reaction senses 10% of the applied potential and the plateau of the "diffusion barrier" extends across 70% of the membrane interior.
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