The N-Shaped Current-Potential Characteristic in Frog Skin: III. Ionic Dependence

A ramp voltage clamp measurement described previously is used to detect alterations in the frog skin current-potential (I-V) characteristic following removal or replacement of various ions in the solutions bathing the skin. The ionic requirements for the maintenance of a negative-slope I-V property are the following: Ca⁺⁺, Na⁺, and Cl^- must be in the outside solution; K⁺ and Cl^- must be in the inside solution. Removal of any one of these ions from its respective solution results in the decay and eventual disappearance of the negative slope.

The similarity between the I-V characteristic following Ca⁺⁺ removal with EDTA from the outside solution and the I-V relation in a refractory skin suggests that the loss (refractory state) and recovery of the negative slope is a consequence of unbinding and subsequent rebinding of Ca⁺⁺ to membrane sites. The role of the univalent ions is not clear—presumably some or all of these ions constitute the current through the skin; however, some of these ions may also be involved in maintaining a membrane condition necessary for the existence of a negative slope I-V relation. Further, excitation does not appear to be a direct consequence of the Na⁺ pump.

     

Negative conductance caused by entry of sodium and cesium ions into the potassium channels of squid axons

Internal Cs⁺, Na⁺, Li⁺, and, to a lesser degree, Rb⁺ interfere with outward current through the K pores in voltage clamped squid axons. Addition of 100 mM NaF to the perfusion medium cuts outward current for large depolarizations about in half, and causes negative conductance over a range of membrane voltages. For example, suddenly reducing membrane potential from +100 to +60 mv increases the magnitude of the outward current. Internal Cs⁺ and, to a small extent, Li⁺, also cause negative conductance. Na⁺ ions permeate at least 17 times less well through the K pores than K⁺, and Cs⁺ does not permeate measurably. The results strongly suggest that K pores have a wide and not very selective inner mouth, which accepts K⁺, Na⁺, Li⁺, Cs⁺, tetraethylammonium ion (TEA⁺), and other ions. The diameter of the mouth must be at least 8 A, which is the diameter of a TEA⁺ ion. K⁺ ions in the mouths probably have full hydration shells. The remainder of the pore is postulated to be 2.6–3.0 A in diameter, large enough for K⁺ and Rb⁺ but too small for Cs⁺ and TEA⁺. We postulate that Na⁺ ions do not enter the narrower part of the pore because they are too small to fit well in the coordination cages provided by the pore as replacements for the water molecules surrounding an ion.     

Graded and All-or-None Electrogenesis in Arthropod Muscle : I. The effects of alkali-earth cations on the neuromuscular system of Romalea microptera

Graded electrically excited responsiveness of Romalea muscle fibers is converted to all-or-none activity by Ba⁺⁺, Sr⁺⁺, or Ca⁺⁺, the two former being much the more effective in this action. The change occurs with as little as 7 to 10 per cent of Na⁺ substituted by Ba⁺⁺. The spikes now produced have overshoots and may be extremely prolonged, lasting many seconds. During the spike the membrane resistance is lower than in the resting fiber, but the resting resistance and time constant are considerably increased by the alkali-earth ions. The excitability is also increased, spikes arising neurogenically from spontaneous repetitive discharges in the axon as well as myogenically from spontaneous activity in the muscle fibers. Repetitive responses frequently occur on intracellular stimulation with a brief pulse. The data indicate that the alkali-earth ions exert a complex of effects on the different action components of electrically excitable membrane. They may be described in terms of the ionic theory as follows: The resting K⁺ conductance is diminished. The sodium inactivation process is also diminished, and sodium activation may be increased. Together these changes can act to convert graded responsiveness to the all-or-none variety. The alkali-earth ions can also to some degree carry inward positive charge during activity, since spikes are produced when Na⁺ is fully replaced with the divalent ions.     

The Permeability of the Sodium Channel to Metal Cations in Myelinated Nerve

The relative permeability of sodium channels to eight metal cations is studied in myelinated nerve fibers. Ionic currents under voltage-clamp conditions are measured in Na-free solutions containing the test ion. Measured reversal potentials and the Goldman equation are used to calculate the permeability sequence: Na⁺ ≈ Li⁺ > Tl⁺ > K⁺. The ratio P_K/P_Na is 1/12. The permeabilities to Rb⁺, Cs⁺, Ca⁺⁺, and Mg⁺⁺ are too small to measure. The permeability ratios agree with observations on the squid giant axon and show that the reversal potential E_Na differs significantly from the Nernst potential for Na⁺ in normal axons. Opening and closing rates for sodium channels are relatively insensitive to the ionic composition of the bathing medium, implying that gating is a structural property of the channel rather than a result of the movement or accumulation of particular ions around the channel. A previously proposed pore model of the channel accommodates the permeant metal cations in a partly hydrated form. The observed sequence of permeabilities follows the order expected for binding to a high field strength anion in Eisenman's theory of ion exchange equilibria.     

Bioelectric effects of ions microinjected into the giant axon of Loligo

1. A technique is described for recording the bioelectric activity of the squid giant axon during and following alteration of the internal axonal composition with respect to ions or other substances. 2. Experimental evidence indicates that the technique as described is capable of measuring changes in local bioelectric activity with an accuracy of 10 to 15 per cent or higher. 3. Alterations of the internal K⁺ or Cl^- concentrations do not cause the change in resting potential expected on the basis of a Donnan mechanism. 4. The general effect of microinjection of K⁺ Rb⁺, Na⁺, Li⁺, Ba⁺⁺, Ca⁺⁺, Mg⁺⁺, or Sr⁺⁺ is to cause decrease in spike amplitude, followed by propagation block. 5. The resting potential decreases when the amplitude of the spike becomes low and block is incipient. 6. The decrease in resting potential and spike amplitude may be confined to the immediate vicinity of the injection. 7. At block, the resting potential decreases up to 50 per cent, but injection of small quantities of divalent cations may cause much larger localized depolarization. 8. The blocking effectiveness of K⁺, Na⁺, and Ca⁺⁺ expressed as reciprocals of the relative amounts needed to cause block is approximately 1:5:100. Rb⁺ has the same low effectiveness as does K⁺. Li⁺ resembles Na⁺. Ba⁺⁺ and Mg⁺⁺ are approximately as effective as Ca⁺⁺. 9. Microinjection of Na⁺ may cause marked prolongation of the spike at the injection site as well as decrease in its amplitude. 10. The anions used (Cl^-, HCO₃^-, NO₃^-, SO₄^-, aspartate, and glutamate) do not seem to exert specific effects. 11. A tentative explanation is offered for the insensitivity of the resting potential to changes in the axonal ionic composition. 12. New data are presented on the range of variation, in a large sample, of the magnitude of the resting potential and spike amplitude.     

Muscle: A Three Phase System : The partition of divalent ions across the membrane

The partition of sulfate, Ca⁺⁺, and Mg⁺⁺ across the membrane of the sartorius muscle has been studied, and the effect of various concentrations of these ions in the Ringer solution on the cellular level of Na⁺, K⁺, and Cl^- has been determined. The level of the three divalent ions in toad plasma and muscle in vivo has been assayed. Muscle was found to contain an almost undetectable amount of inorganic sulfate. Increases in the external level of these ions brought about increases in intracellular content, calculated from the found extracellular space as determined with radioiodinated serum albumin or inulin. Less of the cell water is available to sulfate than to Cl^-, and the Mg⁺⁺ space is less than the Na⁺ space. An amount of muscle water similar to that found for Li⁺ and I^- appears to be available to these divalent ions. Sulfate efflux from the cell was extremely rapid, and it was not found possible to differentiate kinetically between intra- and extracellular material. These results are consistent with the theory of a three phase system, assuming the muscle to consist of an extracellular phase and two intracellular phases. Mg⁺⁺ and Ca⁺⁺ are adsorbed onto the ordered phase, and increments in cellular content found on raising the external level are assumed to occur in the free intracellular phase.     

A Single-File Model for Potassium Transport in Squid Giant Axon: Simulation of Potassium Currents at Normal Ionic Concentrations

A physical model for potassium transport in squid giant axon is proposed. The model is designed to explain the empirical data given by the Hodgkin-Huxley model and related experiments. It is assumed that K⁺ moves across the axon membrane by single-file diffusion through narrow pores. In the model a pore has three negatively charged sites that can be occupied alternatively by K⁺ or by a gating particle, GP⁺⁺, coming from the external surface. GP⁺⁺ is considered to be part of the membrane rather than a diffusible component of the surrounding solutions. A high activation barrier for GP⁺⁺ is supposed at the inner membrane border so that it cannot change over to the internal surface. Therefore potassium diffusion can be blocked by GP⁺⁺ penetrating into the pores. This mechanism controls the dynamic behaviour of the model. The time-dependent probabilities of the pore states are described by a system of differential equations. The rate constants in these equations depend on the ionic concentrations, the membrane voltage, and the electrostatic interaction between ions in a single pore. Detailed computational tests for normal composition of external and internal solutions show that the model agrees remarkably well with the stationary and dynamic behaviour of the Hodgkin-Huxley model. However, the hyperpolarization delay is not reproduced. A structural modification, concerning this delay and the way in which GP⁺⁺ is attached to the membrane, is proposed, and the qualitative behavior of the model at varied external and internal concentrations is discussed.     

Further Studies on the Roles of Sodium and Potassium in the Generation of the Electro-Olfactogram : Effects of mono-, di-, and trivalent cations

In the negative EOG-generating process a cation which can substitute for Na⁺ was sought among the monovalent ions, Li⁺, Rb⁺, Cs⁺, NH₄⁺, and TEA⁺, the divalent ions, Mg⁺⁺, Ca⁺⁺, Sr⁺⁺, Ba⁺⁺, Zn⁺⁺, Cd⁺⁺, Mn⁺⁺, Co⁺⁺, and Ni⁺⁺, and the trivalent ions, Al⁺⁺⁺ and Fe⁺⁺⁺. In Ringer solutions in which Na⁺ was replaced by one of these cations the negative EOG's decreased in amplitude and could not maintain the original amplitudes. In K⁺-Ringer solution in which Na⁺ was replaced by K⁺, the negative EOG's reversed their polarity. Recovery of these reversed potentials was examined in modified Ringer solutions in which Na⁺ was replaced by one of the above cations. Complete recovery was found only in the normal Ringer solution. Thus, it was clarified that Na⁺ plays an irreplaceable role in the generation of the negative EOG's. The sieve hypothesis which was valid for the positive EOG-generating membrane or IPSP was not found applicable in any form to the negative EOG-generating membrane. The reversal of the negative EOG's found in K⁺- , Rb⁺- , and Ba⁺⁺-Ringer solutions was attributed to the exit of the internal K⁺. It is, however, not known whether or not Cl^- permeability increases in these Na⁺-free solutions and contributes to the generation of the reversed EOG's.     

Graded and All-or-None Electrogenesis in Arthropod Muscle : II. The effects of alkali-earth and onium ions on lobster muscle fibers

Conversion of graded responsiveness of lobster muscle fibers to all-or-none activity by alkali-earth and tetraethylammonium (TEA) ions appears to be due to a combination of effects. The membrane is hyperpolarized, its resistance is increased, and its sensitivity to external K⁺ is diminished, all effects which indicate diminished K⁺ conductance. While the spikes are prolonged, the conductance is higher throughout the response than it is in the resting membrane. Repetitive activity becomes prominent. These effects indicate maintained high conductance for an ion which causes depolarization. This is normally Na⁺, since its presence in low concentrations potentiates the effects of Ba⁺⁺, but the alkali-earth ions and TEA can also carry inward charge. Ba⁺⁺, Sr⁺⁺, and TEA appear to be more effective than is Ca⁺⁺ in its normal role, which is probably to depress K⁺ conductance and Na inactivation. Thus, conversion of graded to all-or-none responsiveness appears to occur because of the relative increase of depolarizing inward ion flux and decrease of repolarizing outward flux.     

THE UPTAKE OF INORGANIC ELECTROLYTES BY THE CRAYFISH

1. Reasons are given for believing that the uptake of Na⁺, Cl^-, and NaCl by the crayfish occurs through the gills. 2. A crayfish in fresh water, with a Cl concentration of about 0.2 mEq./l., can) by active Cl absorption, compensate entirely for Cl lost in the urine. 3. The carbonic anhydrase activity of the gills is markedly higher than that of other tissues of the crayfish, but the equivalent CO₂ output of the crayfish is far in excess of the equivalent Cl absorption per unit time and weight and thus fails to warrant the supposition that Cl absorption is of respiratory importance. 4. The carbonic anhydrase activity of the soft integument of the lobster, before and after molting, and of the hypodermis of the hard-cuticled animal is almost identical and of the same order as that of other tissues of the lobster. 5. The concentration of the electrolytes was about 7.5 mEq./l.; i.e., considerably lower than in the blood of the crayfish. Cl^- can be taken up independently of the complementary cation. Na₊ can be taken up independently of the complementary anion. K⁺ and SO₄ ⁼ are not taken up at all. In pure NaCl, the Na⁺ and Cl^- are absorbed evidently largely together. Ca⁺⁺ is absorbed only in newly molted animals and in animals preparing to molt but is not absorbed by hard-cuticled animals not preparing to molt. Ca⁺⁺ is taken up independently of Cl^- in pure CaCl₂. 6. Newly molted animals absorb Ca⁺⁺ at a rate exceeding that of the absorption of other absorbable ions (Na⁺ and Cl_-) in the same equivalent concentration. 7. A crayfish utilizes the Ca⁺⁺ in fresh water in the calcification of its cuticle. Since the animal does not swallow water, the Ca⁺⁺ must enter through the exterior. Reasons are given for believing that, unlike Na⁺ and Cl^-, Ca⁺⁺ is absorbed directly from the exterior by the integument and does not enter the body through the gills. 8. During molting, only about 4 per cent of the raw ash and 2.3 per cent of the organic material of the old cuticle is resorbed.     

Junctional membrane permeability

Summary Substitution of extracellular Na⁺ by Li⁺ causes depression of junctional membrane permeability inChironomus salivary gland cells; within 3 hr, permeability falls to so low a level that neither fluorescein nor the smaller inorganic ions any longer traverse the junctional membrane in detectable amounts (uncoupling). The effect is Li-specific: if choline⁺ is the Na⁺ substitute, coupling is unchanged. The Li-produced uncoupling is not reversed by restitution of Na⁺. Long-term exposure (>1 hr) of the cells to Ca, Mg-free medium leads also to uncoupling. This uncoupling is fully reversible by early restitution of Ca⁺⁺ or Mg⁺⁺. Coupling is maintained in the presence of either Ca⁺⁺ or Mg⁺⁺, so long as the total divalent concentration is about 12mm. The uncoupling in Ca, Mg-free medium ensues regardless of whether the main monovalent cation is Na, Li or choline.The uncouplings are accompanied by cell depolarization. Repolarization of the cells by inward current causes restoration of coupling; the junctional conductance rises again to its normal level. The effect was shown for Li-produced uncoupling, for uncoupling by prolonged absence of external Ca⁺⁺ and Mg⁺⁺, and for uncoupling produced by dinitrophenol. In all cases, the recoupling has the same features: (1) it develops rapidly upon application of the polarizing current; (2) it is cumulative; (3) it is transient, but outlasts the current; and (4) it appears not to depend on the particular ions carrying the current from the electrodes to the cell. The recoupling is due to repolarization of nonjunctional cell membrane; recoupling can be produced at zero net currernt through the junctional membrane. Recoupling takes place also as a result of chemically produced repolarization; restoration of theK gradients in uncoupled cells causes partial recoupling during the repolarization phase.An explanation of the results on coupling is proposed in terms of known mechanisms of regulation of Ca⁺⁺ flux in cells. The uncouplings are explained by actions raising the Ca⁺⁺ level in the cytoplasmic environment of the junctional membranes; the recoupling is explained by actions lowering this Ca⁺⁺ level.     

The action of certain polyvalent cations on the voltage-clamped lobster axon

Calcium appears to be an essential participant in axon excitation processes. Many other polyvalent metal ions have calcium-like actions on axons. We have used the voltage-clamped lobster giant axon to test the effect of several of these cations on the position of the peak initial (sodium) and steady-state (potassium) conductance vs. voltage curves on the voltage axis as well as on the rate parameters for excitation processes. Among the alkaline earth metals, Mg⁺² is a very poor substitute for Ca⁺², while Ba⁺² behaves like "high calcium" when substituted for Ca⁺² on a mole-for-mole basis. The transition metal ions, Ni⁺², Co⁺², and Cd⁺² also act like high calcium when substituted mole-for-mole. Among the trivalent ions, La⁺³ is a very effective Ca⁺² replacement. Al⁺³ and Fe⁺³ are extremely active and seem to have some similar effects. Al⁺³ is effective at concentrations as low as 10^-5 M. The data suggest that many of these ions may interact with the same cation-binding sites on the axon membrane, and that the relative effects on the membrane conductance and rate parameters depend on the relative binding constants of the ions. The total amount of Na⁺ transferred during a large depolarizing transient is nearly independent of the kind or amount of polyvalent ion applied.     

Voltage-Dependent Conductance Induced in Thin Lipid Membranes by Monazomycin

When present in micromolar amounts on one side of phospholipid bilayer membranes, monazomycin (a positively charged, polyene-like antibiotic) induces dramatic voltage-dependent conductance effects. Voltage clamp records are very similar in shape to those obtained from the potassium conductance system of the squid axon. The steady-state conductance is proportional to the 5th power of the monazomycin concentration and increases exponentially with positive voltage (monazomycin side positive); there is an e-fold change in conductance per 4–6 mv. The major current-carrying ions are univalent cations. For a lipid having no net charge, steady-state conductance increases linearly with KCl (or NaCl) concentration and is unaffected by Ca⁺⁺ or Mg⁺⁺. The current-voltage characteristic which is normally monotonic in symmetrical salt solutions is converted by a salt gradient to one with a negative slope-conductance region, although the conductance-voltage characteristic is unaffected. A membrane treated with both monazomycin and the polyene antibiotic nystatin (which alone creates anion-selective channels) displays bistability in the presence of a salt gradient. Thus monazomycin and nystatin channels can exist in parallel. We believe that many monazomycin monomers (within the membrane) cooperate to form a multimolecular conductance channel; the voltage control of conductance arises from the electric field driving monazomycin molecules at the membrane surface into the membrane and thus affecting the number of channels that are formed.     

Interaction of Tetraethylammonium Ion Derivatives with the Potassium Channels of Giant Axons

A number of compounds related to TEA⁺ (tetraethylammoniumion) were injected into squid axons and their effects on g_K (the potassium conductance) were determined. In most of these ions a quaternary nitrogen is surrounded by three ethyl groups and a fourth group that is very hydrophobic. Several of the ions cause inactivation of g_K, a type of ionic gating that is not normally seen in squid axon; i.e., after depolarization g_K increases and then spontaneously decreases to a small fraction of its peak value even though the depolarization is maintained. Observations on the mechanism of this gating show that (a) QA (quaternary ammonium) ions only enter K⁺ channels that have open activation gates (the normal permeability gates). (b) The activation gates of QA-occluded channels do not close readily. (c) Hyperpolarization helps to clear QA ions from the channels. (d) Raising the external K⁺ concentration also helps to clear QA ions from the channels. Observations (c) and (d) strongly suggest that K⁺ ions traverse the membrane by way of pores, and they cannot be explained by the usual type of carrier model. The data suggest that a K⁺ pore has two distinct parts: a wide inner mouth that can accept a hydrated K⁺ ion or a TEA⁺-like ion, and a narrower portion that can accept a dehydrated or partially dehydrated K⁺ ion, but not TEA⁺.     

The Ionic Permeability Changes during Acetylcholine-Induced Responses of Aplysia Ganglion Cells

ACh-induced depolarization (D response) in D cells markedly decreases as the external Na⁺ is reduced. However, when Na⁺ is completely replaced with Mg⁺⁺, the D response remains unchanged. When Na⁺ is replaced with Tris(hydroxymethyl)aminomethane, the D response completely disappears, except for a slight decrease in membrane resistance. ACh-induced hyperpolarization (H response) in H cells is markedly depressed as the external Cl^- is reduced. Frequently, the reversal of the H response; i.e., depolarization, is observed during perfusion with Cl^--free media. In cells which show both D and H responses superimposed, it was possible to separate these responses from each other by perfusing the cells with either Na⁺-free or Cl^--free Ringer's solution. High [K⁺]₀ often caused a marked hyperpolarization in either D or H cells. This is due to the primary effect of high [K⁺]₀ on the presynaptic inhibitory fibers. The removal of this inhibitory afferent interference by applying Nembutal readily disclosed the predicted K⁺ depolarization. In perfusates containing normal [Na⁺]₀, the effects of Ca⁺⁺ and Mg⁺⁺ on the activities of postsynaptic membrane were minimal, supporting the current theory that the effects of these ions on the synaptic transmission are mainly presynaptic. The possible mechanism of the hyperpolarization produced by simultaneous perfusion with both high [K⁺]₀ and ACh in certain H cells is explained quantitatively under the assumption that ACh induces exclusively an increase in Cl^- permeability of the H membrane.     

Ca++ fluxes in resealed synaptic plasma membrane vesicles

The effect of the monovalent cations Na⁺, Li⁺, and K⁺ on Ca⁺⁺ fluxes has been determined in resealed synaptic plasma membrane vesicle preparations from rat brain. Freshly isolated synaptic membranes, as well as synaptic membranes which were frozen (?80°C), rapidly thawed, and passively loaded with K₂/succinate and ⁴⁵CaCl₂, rapidly released approximately 60% of the intravesicular Ca⁺⁺ when exposed to NaCl or to the Ca⁺⁺ ionophore A 23187. Incubation of these vesicles with LiCl caused a lesser release of Ca⁺⁺. The EC₅₀ for Na⁺ activation of Ca⁺⁺ efflux from the vesicles was approximately 6.6mM. exposure of the Ca⁺⁺-loaded vesicles to 150 mM KCl produced a very rapid (?1 sec) loss of Ca⁺⁺ from the vesicles, but the Na⁺-induced efflux could still be detected above this K⁺ - sensitive effect. Vesicles pre-loaded with NaCl (150 mM) exhibited rapid ⁴⁵Ca uptake with an estimated EC₅₀ for Ca⁺⁺ of 7–10 μM. This Ca⁺⁺ uptake was blocked by dissipation of the Na⁺ gradient. These observations are suggestive of the preservation in these purified frozen synaptic membrane preparations of the basic properties of the Na⁺Ca⁺⁺ exchange process and of a K⁺ - sensitive Ca⁺⁺ flux across the membranes.     

Block of N-type Calcium Channels in Chick Sensory Neurons by External Sodium

L-type Ca²⁺ channels select for Ca²⁺ over sodium Na⁺ by an affinity-based mechanism. The prevailing model of Ca²⁺ channel permeation describes a multi-ion pore that requires pore occupancy by at least two Ca²⁺ ions to generate a Ca²⁺ current. At [Ca²⁺] < 1 μM, Ca²⁺ channels conduct Na⁺. Due to the high affinity of the intrapore binding sites for Ca²⁺ relative to Na⁺, addition of μM concentrations of Ca²⁺ block Na⁺ conductance through the channel. There is little information, however, about the potential for interaction between Na⁺ and Ca²⁺ for the second binding site in a Ca²⁺ channel already occupied by one Ca²⁺. The two simplest possibilities, (a) that Na⁺ and Ca²⁺ compete for the second binding site or (b) that full time occupancy by one Ca²⁺ excludes Na⁺ from the pore altogether, would imply considerably different mechanisms of channel permeation. We are studying permeation mechanisms in N-type Ca²⁺ channels. Similar to L-type Ca²⁺ channels, N-type channels conduct Na⁺ well in the absence of external Ca²⁺. Addition of 10 μM Ca²⁺ inhibited Na⁺ conductance by 95%, and addition of 1 mM Mg²⁺ inhibited Na⁺ conductance by 80%. At divalent ion concentrations of 2 mM, 120 mM Na⁺ blocked both Ca²⁺ and Ba²⁺ currents. With 2 mM Ba²⁺, the IC₅₀ for block of Ba²⁺ currents by Na⁺ was 119 mM. External Li⁺ also blocked Ba²⁺ currents in a concentration-dependent manner, with an IC₅₀ of 97 mM. Na⁺ block of Ba²⁺ currents was dependent on [Ba²⁺]; increasing [Ba²⁺] progressively reduced block with an IC₅₀ of 2 mM. External Na⁺ had no effect on voltage-dependent activation or inactivation of the channel. These data suggest that at physiological concentrations, Na⁺ and Ca²⁺ compete for occupancy in a pore already occupied by a single Ca²⁺. Occupancy of the pore by Na⁺ reduced Ca²⁺ channel conductance, such that in physiological solutions, Ca²⁺ channel currents are between 50 and 70% of maximal.     

Analysis of potassium conductance in squid giant axons

Assuming a model of facilitated ionic transport across axonal membranes proposed by McIlroy (1975) and extended by McIlroy and Hahn (1978), it is shown that if the selectivity coefficient, π_K, of the potassium conducting system ?59 the permeabilityP _Ks, of the periaxonal barrier of the squid giant axon for K⁺ ions?(1.2±0.44)×10^?4 cm sec^?1 and the thickness of the periaxonal space ?477±168 Å. Using a value (10^?4 cm sec^?1) ofP _Ks in the foregoing range the experimental curves for the steady state membrane ionic conductance versus measured membrane potential difference (p.d.), ?, of Gilbert and Ehrenstein (1969) are corrected for the effect of accumulation of K⁺ in the periaxonal space. This correction is most marked for the axon immersed in a natural ionic environment, whose conductance curve is shifted ?70mV along the voltage axis in the hyperpolarization direction. By assuming that the physico-chemical connection between a depolarization of the axonal membrane and the consequent membrane conductance changes is a Wien dissociative effect of the membrane's electric field on a weak electrolyte situated in the axolemma, the position of the peaks of the corrected conductance versus ? curves can be identified with zero membrane electric field and hence with zero p.d.across the axolemma. A set of values for the double-layer p.d.s at the axonal membrane interfaces with the external electrolytes in the vicinity of the K⁺ conducting pores can therefore be deduced for the various external electrolytes employed by Gilbert and Ehrenstein. A model of these double-layer p.d.s in which the membrane interfaces are assumed to possess fixed monovalent negatively charged sites, at least in the neighbourhood of the K⁺ conducting pores, is constructed. It is shown that, using the previously deduced values for the doublelayer p.d.s, such a model has a consistent, physically realistic solution for the distance between the fixed charged sites and for the dissociation constants of these sites in their interaction with the ions of the extramembrane electrolytes.     

A minimum mechanism for Na+−Ca++ exchange: Net and unidirectional Ca++ fluxes as functions of ion composition and membrane potential

Summary Both simultaneous and consecutive mechanisms for Na⁺–Ca⁺⁺ exchange are formulated and the associated systems of steady-state equations are solved numerically, and the net and unidirectional Ca⁺⁺ fluxes computed for a variety of ionic and electrical boundary conditions. A simultaneous mechanism is shown to be consistent with a broad range of experimental data from the squid giant axon, cardiac muscle and isolated sarcolemmal vesicles. In this mechanism, random binding of three Na⁺ ions and one Ca⁺⁺ on apposing sides of a membrane are required before a conformational change can occur, translocating the binding sites to the opposite sides of the membranes. A similar (return) translocation step is also permitted if all the sites are empty. None of the other states of binding can undergo such translocating conformational changes. The resulting reaction scheme has 22 reaction steps involving 16 ion-binding intermediates. The voltage dependence of the equilibrium constant for the overall reaction, required by the 31 Na⁺Ca⁺⁺ stoichiometry was obtained by multiplying and dividing, respectively, the forward and reverse rate constants of one of the translocational steps by exp(–FV/2RT). With reasonable values for the membrane density of the enzyme (120 sites m²) and an upper limit for the rate constants of both translocational steps of 10⁵·sec^–1, satisfactory behavior was obtainable with identical binding constants for Ca⁺⁺ on the two sides of the membrane (10⁶ m ^–1), similar symmetry also being assumed for the Na⁺ binding constant (12 to 60m ^–1). Introduction of order into the ion-binding process eliminates behavior that is consistent with experimental findings.     

Appearance and maturation of voltage-dependent conductances in solitary spiking cells during retinal regeneration in the adult newt

Summary Electrical membrane properties of solitary spiking cells during newt (Cynops pyrrhogaster) retinal regeneration were studied with whole-cell patch-clamp methods in comparison with those in the normal retina.The membrane currents of normal spiking cells consisted of 5 components: inward Na⁺ and Ca⁺⁺ currents and 3 outward K⁺ currents of tetraethylammonium (TEA)-sensitive, 4-aminopyridine (4-AP)-sensitive, and Ca⁺⁺-activated varieties. The resting potential was about -40mV. The activation voltage for Na⁺ and Ca⁺⁺ currents was about -30 and -17 mV, respectively. The maximum Na⁺ and Ca⁺⁺ currents were about 1057 and 179 pA, respectively.In regenerating retinae after 19–20 days of surgery, solitary cells with depigmented cytoplasm showed slowrising action potentials of long duration. The ionic dependence of this activity displayed two voltage-dependent components: slow inward Na⁺ and TEA-sensitive outward K⁺ currents. The maximum inward current (about 156 pA) was much smaller than that of the control. There was no indication of an inward Ca⁺⁺ current.During subsequent regeneration, the inward Ca⁺⁺ current appeared in most spiking cells, and the magnitude of the inward Na⁺, Ca⁺⁺, and outward K⁺ currents all increased. By 30 days of regeneration, the electrical activities of spiking cells became identical to those in the normal retina. No significant difference in the resting potential and the activation voltage for Na⁺ and Ca⁺⁺ currents was found during the regenerating period examined.