A fit to nerve membrane rectification curves with a double-dipole-layer membrane model

Following Wei's suggestion that nerve stimulation and conduction properties are due to dipole layers at the two membrane surfaces (Wei, 1969), we have done steady-state electro-diffusion calculations in the constant field approximation for a simple double-dipole-layer model. We are thereby able to quantitatively fit the recent potassium iso-osmotic rectification curves of Gilbert and Ehrenstein for the squid giant axon membrane. For the squid axon membrane in a natural ion environment, only the outside dipole layer is present in the fit to the data.     

Ionic permeability of K, Na, and Cl in potassium-depolarized nerve. Dependency on pH, cooperative effects, and action of tetrodotoxin.

The passive ionic membrane conductances (gj) and permeabilities (Pj) of K, Na, and Cl of crayfish (Procambarus clarkii) medial giant axons were determined in the potassium-depolarized axon and compared with that of the resting axon. Passive ionic conductances and permeabilities were found to be potassium dependent with a major conductance transition occurring around an external K concentration of 12-15 mM (Vm = -60 to -65 mV). The results showed that K, Na, and Cl conductances increased by 6.2, 6.9, and 27-fold, respectively, when external K was elevated from 5.4 to 40 mM. Permeability measurements indicated that K changed minimally with K depolarization while Na and Cl underwent an order increase in permeability. In the resting axon (K0 = 5.4 mM, pH = 7.0) PK = 1.33 X 10(-5), PCl = 1.99 X 10(-6), PNa = 1.92 X 10(-8) while in elevated potassium (K0 = 40 mM, pH 7.0), PK = 1.9 X 10(-5), PCl = 1.2 X 10(-5), and PNa = 2.7 X 10(-7) cm/s. When membrane potential is reduced to 40 mV by changes in internal ions, the conductance changes are initially small. This suggests that resting channel conductances depend also on ion environments seen by each membrane surface in addition to membrane potential. In elevated potassium, K, Na, and Cl conductances and permeabilities were measured from pH 3.8 to 11 in 0.2 pH increments. Here a cooperative transition in membrane conductance or permeability occurs when pH is altered through the imidazole pK (approximately pH 6.3) region. This cooperative conductance transition involves changes in Na and Cl but not K permeabilities. A Hill coefficient n of near 4 was found for the cooperative conductance transition of both the Na and Cl ionic channel which could be interpreted as resulting from 4 protein molecules forming each of the Na and Cl ionic channels. Tetrodotoxin reduces the Hill coefficient n to near 2 for the Na channel but does not affect the Cl channel. In the resting or depolarized axon, crosslinking membrane amino groups with DIDS reduces Cl and Na permeability. Following potassium depolarization, buried amino groups appear to be uncovered. The data here suggest that potassium depolarization produces a membrane conformation change in these ionic permeability regulatory components. A model is proposed where membrane protein, which forms the membrane ionic channels, is oriented with an accessible amino terminal group on the axon exterior. In this model the ionizable groups on protein and phospholipid have varied associations with the different ionic channel access sites for K, Na, and Cl, and these groups exert considerable control over ion permeation through their surface potentials.     

Reversible electrical breakdown of squid giant axon membrane

Charge pulse relaxation experiments were performed on squid giant axon. In the low voltage range, the initial voltage across squid axon membrane was a linear function of the injected charge. For voltages of the order of 1 V this relationship between injected charge and voltage across the membrane changes abruptly. Because of a high conductance state caused by these large electric fields the voltage across the membrane cannot be made large enough to exceed a critical value, Vc, defined as the breakdown voltage, Vc has for squid axon membrane a value of 1.1 V at 12 degrees C. During breakdown the specific membrane conductance exceeds 1 S. cm-2. Electrical breakdown produced by charge pulses of few microseconds duration have no influence on the excitability of the squid axon membrane. The resealing process of the membrane is so fast that a depolarizing breakdown is followed by the falling phase of a normal action potential. Thus, membrane voltages close to Vc open the sodium channels in few microseconds, but do not produce a decrease of the time constant of potassium activation large enough to cause the opening of a significant percentage of channels in a time of about 10 mus. It is probable that the reversible electrical breakdown is mainly caused by mechanical instability produced by electrostriction of the membrane (electrochemical model), but the decrease in the Born energy for ion injection into the membrane, accompanying the decrease in membrane thickness, may play also an important role. Because of the high conductance of the membrane during breakdown it seems very likely that this results in pore formation.     

TRANSVERSE IMPEDANCE OF THE SQUID GIANT AXON DURING CURRENT FLOW

The change in the transverse impedance of the squid giant axon caused by direct current flow has been measured at frequencies from 1 kc. per second to 500 kc. per second. The impedance change is equivalent to an increase of membrane conductance at the cathode to a maximum value approximately the same as that obtained during activity and a decrease at the anode to a minimum not far from zero. There is no evidence of appreciable membrane capacity change in either case. It then follows that the membrane has the electrical characteristics of a rectifier. Interpreting the membrane conductance as a measure of ion permeability, this permeability is increased at the cathode and decreased at the anode.     

Grayanotoxin, veratrine, and tetrodotoxin-sensitive sodium pathways in the Schwann cell membrane of squid nerve fibers

The actions of grayanotoxin I, veratrine, and tetrodotoxin on the membrane potential of the Schwann cell were studied in the giant nerve fiber of the squid Sepioteuthis sepioidea. Schwann cells of intact nerve fibers and Schwann cells attached to axons cut lengthwise over several millimeters were utilized. The axon membrane potential in the intact nerve fibers was also monitored. The effects of grayanotoxin I and veratrine on the membrane potential of the Schwann cell were found to be similar to those they produce on the resting membrane potential of the giant axon. Thus, grayanotoxin I (1-30 muM) and veratrine (5-50 mug-jl-1), externally applied to the intact nerve fiber or to axon-free nerve fiber sheaths, produce a Schwann cell depolarization which can be reversed by decreasing the external sodium concentration or by external application of tetrodotoxin. The magnitude of these membrane potential changes is related to the concentrations of the drugs in the external medium. These results indicate the existence of sodium pathways in the electrically unexcitable Schwann cell membrane of S. sepioidea, which can be opened up by grayanotoxin I and veratrine, and afterwards are blocked by tetrodotoxin. The sodium pathways of the Schwann cell membrane appear to be different from those of the axolemma which show a voltage-dependent conductance.     

ELECTRIC IMPEDANCE OF THE SQUID GIANT AXON DURING ACTIVITY

Alternating current impedance measurements have been made over a wide frequency range on the giant axon from the stellar nerve of the squid, Loligo pealii, during the passage of a nerve impulse. The transverse impedance was measured between narrow electrodes on either side of the axon with a Wheatstone bridge having an amplifier and cathode ray oscillograph for detector. When the bridge was balanced, the resting axon gave a narrow line on the oscillograph screen as a sweep circuit moved the spot across. As an impulse passed between impedance electrodes after the axon had been stimulated at one end, the oscillograph line first broadened into a band, indicating a bridge unbalance, and then narrowed down to balance during recovery. From measurements made during the passage of the impulse and appropriate analysis, it was found that the membrane phase angle was unchanged, the membrane capacity decreased about 2 per cent, while the membrane conductance fell from a resting value of 1000 ohm cm.² to an average of 25 ohm cm.² The onset of the resistance change occurs somewhat after the start of the monophasic action potential, but coincides quite closely with the point of inflection on the rising phase, where the membrane current reverses in direction, corresponding to a decrease in the membrane electromotive force. This E.M.F. and the conductance are closely associated properties of the membrane, and their sudden changes constitute, or are due to, the activity which is responsible for the all-or-none law and the initiation and propagation of the nerve impulse. These results correspond to those previously found for Nitella and lead us to expect similar phenomena in other nerve fibers.     

Role of membrane curvature in mechanoelectrical transduction: Ion carriers nonactin and valinomycin sense changes in integral bending energy

We describe the phenomenon of mechanoelectrical transduction in macroscopic lipid bilayer membranes modified by two cation-selective ionophores, valinomycin and nonactin. We found that bulging these membranes, while maintaining the membrane tension constant, produced a marked supralinear increase in specific carrier-mediated conductance. Analyses of the mechanisms involved in mechanoelectrical transduction induced by the imposition of a hydrostatic pressure gradient or by an amphipathic compound chlorpromazine reveal similar changes in the charge carrier motility and carrier reaction rates at the interface(s). Furthermore, the relative change in membrane conductance was independent of membrane diameter, but was directly proportional to the square of membrane curvature, thus relating the observed phenomena to the bilayer bending energy. Extrapolated to biological membranes, these findings indicate that ion transport in cells can be influenced simply by changing shape of the membrane, without a change in membrane tension.     

Gating currents in the node of Ranvier: voltage and time dependence.

Like the axolemma of the giant nerve fibre of the squid, the nodal membrane of frog myelinated nerve fibres after blocking transmembrane ionic currents exhibits asymmetrical displacement currents during and after hyperpolarizing and depolarizing voltage clamp pulses of equal size. The steady-state distribution of charges as a function of membrane potential is consistent with Boltzmanns law (midpoint potential minus 33.7 mV; saturation value 17200 charges/mum-2). The time course of the asymmetry current and the voltage dependence of its time constant are consistent with the notion that due to a sudden change in membrane potential the charges undergo a first order transition between two configurations. Size and voltage dependence of the time constant are similar to those of the activation of the sodium conductance assuming m-2h kinetics. The results suggest that the presence of ten times more sodium channels (5000/mum-2) in the node of Ranvier than in the squid giant axon with similar sodium conductance per channel (2-3 pS).     

Increased effectiveness of a motorneuron after partial denervation of its target muscle in the cricket Teleogryllus oceanicus

Fibers of the metathoracic extensor tibia muscle of the cricket Teleogryllus oceanicus are innervated by a slow excitatory axon (slow fibers), a fast excitatory axon (fast fibers), or by both slow and fast axons (dual fibers). Sectioning metathoracic nerve 5 removes the fast axon input to the muscle but not that of the slow axon. Following such partial denervation, the mechanical responses initiated by the slow axon increase progressively for at least 30 days; twitch tensions reach 5–10 times those of control muscles and tetanic tensions 10–30 times control values. After sectioning nerve 5, resting membrane potentials decrease in those fibers which originally received fast axon input and the input resistance of all fiber types increases, including that of slow fibers which are not innervated through nerve 5. Excitatory junctional potentials (EJPs) initiated by the slow axon become larger following partial denervation, accounting in part for the larger contraction amplitudes. The increased input resistance is adequate to account for the larger EJPs in slow fibers but not for the proportionally greater increase in EJP amplitude in fibers which were formerly dually innervated. The change in EJP amplitude is abrupt in slow fibers and gradual in formerly dual fibers.     

Slow Changes of Potassium Permeability in the Squid Giant Axon

A slow potassium inactivation i.e. decrease of conductance when the inside of the membrane is made more positive with respect to the outside, has been observed for the squid axon. The conductance-potential curve is sigmoid shaped, and the ratio between maximum and minimum potassium conductance is at least 3. The time constant for the change of potassium conductance with potential is independent of the concentration of potassium in the external solution, but dependent upon potential and temperature. At 9 degrees C and at the normal sea water resting potential, the time constant is 11 sec. For lower temperature or more depolarizing potentials, the time constant is greater. The inactivation can be described by modifying the Hodgkin-Huxley equation for potassium current, using one additional parameter. The modified equation is similar in form to the Hodgkin-Huxley equation for sodium current, suggesting that the mechanism for the passive transport of potassium through the axon membrane is similar to that for sodium.     

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.     

Action of Certain Tropine Esters on Voltage-Clamped Lobster Axon

Tropine p-tolylacetate (TPTA) and its quaternary analogue, tropine p-tolylacetate methiodide (TPTA MeI) decrease the early transient (Na) and late (K) currents in the voltage-clamped lobster giant axon. These agents, which block the nerve action potential, reduce the maximum Na and K conductance increases associated with membrane depolarization. They also slow the rate at which the sodium conductance is increased and shift the (normalized) membrane conductance vs. voltage curves in the direction of depolarization along the voltage axis. All these effects are qualitatively similar to those resulting from the action of procaine on the voltage-clamped axon. One unusual effect of the tropine esters, noticeable particularly at large depolarization steps, is that they cause the late, K current to reach a peak and then fall off with increasing pulse duration. This effect has not been reported to occur as a result of procaine action. Tropine p-chlorophenyl acetate (TPClA), which differs from TPTA only by the substitution of a p-Cl for a p-CH₃ group on the benzene ring, had a negligible effect on axonal excitability.     

The pH Dependency of Relative Ion Permeabilities in the Crayfish Giant Axon

The dependence of the membrane potential on potassium, chloride, and sodium ions, was determined at the pH's of 6.0, 7.5, and 9.0 for the resting and depolarized crayfish ventral nerve cord giant axon. In normal saline (external potassium = 5.4 mM), the dependence of the membrane potential on the external potassium ions decreased with lowered pH while that for chloride increased. In contrast, in the potassium depolarized axon (external potassium = 25 mM), the dependence of the membrane potential on external potassium was minimum around pH 7.5 and increased in either more acidic or basic pH. In addition, the dependence of the membrane potential on external chloride in the depolarized axon was maximum at pH 7.5 and decreased in either more acidic or basic pH. The sodium dependency of the membrane potential was small and relatively unaffected by pH or depolarization. The data are interpreted as indicating a reversible surface membrane protein-phospholipid conformation change which occurs in the transition from the resting to the depolarized axon.     

The Creation of Proton Hopping from a Drug?Receptor Encounter

We extend recent modeling studies of proton hopping, used to describe the functioning of membrane channels and axon nerve conduction, to offer an explanation of the initiation of the nerve impulse at an effector? ligand encounter. This encounter is proposed to create a hydronium ion in the vicinity of the effector and ligand, which leads to a continuous flow of protons, called proton hopping, through water adjacent to this encounter. This proton hopping is proposed to be the message carried from the encounter to the axon of a particular nerve system associated with that particular effector? ligand system.     

Competitive Action of Calcium and Procaine on Lobster Axon : A study of the mechanism of action of certain local anesthetics

Voltage clamp studies with the squid giant axon have shown that changes in the external calcium concentration (Frankenhaeuser and Hodgkin, 1957) shift the sodium and potassium conductance versus membrane potential curves along the potential axis. Taylor (1959) found that procaine acts primarily by reducing the sodium and, to a lesser extent, the potassium conductances. Both procaine and increased calcium also delay the turning on of the sodium conductance mechanism. Calcium and procaine have similar effects on lobster giant axon. In addition, we have observed that the magnitude of the response to procaine is influenced by the external calcium concentration. Increasing external calcium tends to reduce the effectiveness of procaine in decreasing sodium conductance. Conversely, procaine is more effective in reducing the membrane conductance if external calcium is decreased. The amplitude of the nerve action potential reflects these conductance changes in that, for example, reductions in amplitude resulting from the addition of procaine to the medium are partially restored by increasing external calcium, as was first noted by Aceves and Machne (1963). These phenomena suggest that calcium and procaine compete with one another with respect to their actions on the membrane conductance mechanism. The fact that procaine and its analogues compete with calcium for binding to phospholipids in vitro (Feinstein, 1964) suggests that the concept of competitive binding to phospholipids may provide a useful model for interpreting these data.     

Isomorphism on a physical system of the Hodgkin-Huxley equations for sodium conductance: toxin allosteric effects and gating currents

An isomorphism on a physical system of the Hodgkin-Huxley equations for sodium ion conductance in the nerve membrane is derived. The physical system consists of 8 states. It shows that the voltage dependence of the sodium conductance arises from a change in ionization of the molecule that provides the ion-selective conductance channels. It associates reversibly with singly charged (H+?) and doubly charged (Ca++?) ions. The inactivation process is the result of the associating of an ionized particle by half of the states. The effect of toxins and narcotics in blocking or inactivating sodium conductance can be understood as an enzyme or allosteric change of the standard free energy difference of the molecule that provides the sodium channels. The effect of changing pH and Ca++ substrate concentration on the sodium conductance is predicted. The gating charge current is predicted. The time constant predicted is in agreement with experiment.     

The representation of membrane admittance.

An integral representation for the membrane admittance in terms of its known current response to a voltage step function is presented. It is demonstrated that the frequency-dependent terms in the contribution to the membrane admittance by the ion-selective conductance of the nerve membrane are proportional to the static conductances. The additional information contained in the real and imaginary parts of the membrane admittance should allow the parameters of the ion conductance to be determined. Eventually, these measurements should also give information about the electric dipole displacement currents of the conductance systems themselves, and about the metabolically supported active ion transport currents that maintain the ion concentration gradients.     

Alpha-adrenergic vascular responsiveness to sympathetic nerve activity is intact after head-down bed rest in humans

Space-flight and its ground-based simulation model, 6 degrees head-down bed rest (HDBR), cause cardiovascular deconditioning in humans. Because sympathetic vasoconstriction plays a very important role in circulation, we examined whether HDBR impairs alpha-adrenergic vascular responsiveness to sympathetic nerve activity. We subjected eight healthy volunteers to 14 days of HDBR and before and after HDBR measured calf muscle sympathetic nerve activity (MSNA; microneurography) and calf blood flow (venous occlusion plethysmography) during sympathoexcitatory stimulation (rhythmic handgrip exercise). HDBR did not change the increase in total MSNA (P = 0.97) or the decrease in calf vascular conductance (P = 0.32) during exercise, but it did augment the increase in calf vascular resistance (P = 0.0011). HDBR augmented the transduction gain from total MSNA into calf vascular resistance, assessed as the least squares linear regression slope of vascular resistance on total MSNA (0.05 +/- 0.02 before HDBR, 0.20 +/- 0.06 U.min-1.burst-1 after HDBR, P = 0.0075), but did not change the transduction gain into calf vascular conductance (P = 0.41). Our data indicate that alpha-adrenergic vascular responsiveness to sympathetic nerve activity is preserved in the supine position after HDBR in humans.     

Light scattering spectroscopy of the squid axon membrane

Light scattering studies on the giant squid axon were done using the technique of optical mixing spectroscopy. This experimental approach is based on the use of laser light to detect the fluctuations of membrane macromolecules which are associated with conductance fluctuations. The light scattering spectra were similar to the Lorentzian-like behavior of conductance fluctuations, possibly reflecting an underlying conformational change in the specific membrane sites responsible for the potassium ion conductance. The amplitude of the spectra measured, increased when the membrane was depolarized and decreased on hyperpolarization. The spectra were fit to the sum of two terms, a (1/fcomponent and a simple Lorentzian term. Spectra from deteriorating axons did not show sensitivity to membrane potential changes. It is shown theoretically that fluctuations due to the voltage-dependent variable, n, of the Hodgkin-Huxley formalism are identical to the voltage fluctuations. The derived power spectrum is that of a second order system, capable of showing resonance peaking only if the voltage dependence of the potassium rate constants is included in the analysis. The lack of resonance peaking in the observed light scattering spectra, indicates that the data are best described by a damped second order system.     

Propagation of action potentials in squid giant axons. Repetitive firing at regions of membrane inhomogeneities

Effects of reduction in potassium conductance on impulse conduction were studied in squid giant axons. Internal perfusion of axons with tetraethylammonium (TEA) ions reduces G K and causes the duration of action potential to be increased up to 300 ms. This prolongation of action potentials does not change their conduction velocity. The shape of these propagating action potentials is similar to membrane action potentials in TEA. Axons with regions of differing membrane potassium conductances are obtained by perfusing the axon trunk and one of its two main branches with TEA after the second branch has been filled with normal perfusing solution. Although the latter is initially free of TEA, this ion diffuses in slowly. Up until a large amount of TEA has diffused into the second branch, action potentials in the two branches have very different durations. During this period, membrane regions with prolonged action potentials are a source of depolarizing current for the other, and repetitive activity may be initiated at transitional regions. After a single stimulus in either axon region, interactions between action potentials of different durations usually led to rebound, or a short burst, of action potentials. Complex interactions between two axon regions whose action potentials have different durations resembles electric activity recorded during some cardiac arrhythmias.