An analysis of conductance changes in squid axon

The membrane of the squid axon is considered on the basis of a pore model in which the distribution of the pore sizes strongly favors K⁺ transfer when there is no potential. Electrical asymmetry causes non-penetrating ions on the membrane capacitor to exert a mechanical force on both membrane surfaces and this force results in a deformation of the membrane pore system such that it assumes a distribution of sizes favoring the ions exerting mechanical force. The ions involved appear to be Ca⁺⁺ on the outside of the membrane and isethionate^-, (i^-) on the inside; as Ca⁺⁺ is equivalent in size to Na⁺, the charged membrane is potentially able to transfer Na⁺, when the ions deforming the membrane pore distribution are removed. A depolarization of the membrane leads to an opening of pores that will allow Na⁺ penetration and a release of the membrane from deformation. The pores revert to the zero-potential pore size distribution hence the Na permeability change is a transient. Calculation shows that the potassium conductance vs. displacement of membrane potential curve for the squid axon and the "inactivation" function, h, can be obtained directly from the assumed membrane distortion without the introduction of arbitrary parameters. The sodium conductance, because it is a transient, requires assumptions about the time constants with which ions unblock pores at the outside and the inside of the membrane.     

Slowing of sodium channel opening kinetics in squid axon by extracellular zinc

The interaction of Zn ion on Na channels was studied in squid giant axons. At a concentration of 30 mM Zn2+ slows opening kinetics of Na channels with almost no alteration of closing kinetics. The effects of Zn2+ can be expressed as a "shift" of the gating parameters along the voltage axis, i.e., the amount of additional depolarization required to overcome the Zn2+ effect. In these terms the mean shifts caused by 30 mM Zn2+ were +29.5 mV for Na channel opening (on) kinetics (t1/2 on), +2 mV for closing (off) kinetics (tau off), and +8.4 mV for the gNa-V curve. Zn2+ does not change the shape of the instantaneous I-V curve for inward current, but reduces it in amplitude by a factor of or approximately 0.67. Outward current is unaffected. Effects of Zn2+ on gating current (measured in the absence of TTX) closely parallel its actions on gNa. On gating current kinetics are shifted by +27.5 mV, off kinetics by +6 mV, and the Q-V distribution by +6.5 mV. Kinetic modeling shows that Zn2+ slows the forward rate constants in activation without affecting backward rate constants. More than one of the several steps in activation must be affected. The results are not compatible with the usual simple theory of uniform fixed surface charge. They suggest instead that Zn2+ is attracted by a negatively charged element of the gating apparatus that is present at the outer membrane surface at rest, and migrates inward on activation.     

Adaptation and accommodation in the squid axon

Current clamp data of the squid axon indicate that there is a qualitative change in the adaptive response as the magnitude of the current step is increased. Large stimulus currents have a strong inhibitory effect on spike generation and on active responses in general. Such currents always lead to only one action-potential and to the elimination of post-spike subthreshold oscillation. In view of a direct connection between stimulus current and potassium current I _K, the potassium channel of the Hodgkin-Huxley model is reinterpreted in a natural way such that the K⁺ conductance is directly dependent on I _K in addition to a voltage dependence. The I-_Kdependence seems to dominate whenever the stimulus current is greater than approximately 35 μA/cm². For current ramps, and large current steps, such a current formulation leads to good agreement with the data.     

Frequency domain analysis of asymmetry current in squid axon membrane.

The change in capacity of squid axon membrane during hyper- and depolarizations was investigated in the absence of ionic currents after the membrane was treated with pronase. In the presence of the inactivation process (h parameter), failure to observe the gating current in the frequency domain was attributed to the rapid attenuation of the possible capacity change during depolarizations, which is likely to be due to the sodium activation process. Elimination of the h process would therefore enable us to observe the gating current in the frequency domain as the change in the capacitance component of membrane admittance. However, even after the inactivation process was abolished by pronase, the capacity of the axon membrane remained constant when ionic currents were blocked by external tetrodotoxin and internal Cs+ ion. Actually capacity was observed to decrease slightly with depolarization, contrary to the prediction based on the magnitude of gating currents.     

Noise measurements in squid axon membrane

Summary A small area (10^–4 to 10^–5 cm² patch) of the external surface of a squid (Loligo pealei) axon was isolated electrically by means of a pair of concentric glass pipettes and sucrose solution to achieve a low extraneous noise measurement of spontaneous fluctuations in membrane potential and current. The measured small-signal impedance function of the isolated patch in seawater was constant at low frequencies and declined monotonically at frequencies beyond 100 Hz. It is shown that the power-density spectrum (PDS) of voltage noise, which generally reflects the current-noise spectrum filtered by the membrane impedance function, is equivalent to the power spectrum of current-noise up to frequencies where the impedance decline is significant (Fishman, 1973a, Proc. Nat. Acad. Sci. USA 70:876). This result is in contrast to an impedance resonance measured under uniform constant-current (internal axial wire) conditions, for which the voltage-noise PDS reflects the impedance resonance. The overdamped resonance in the patch technique is a consequence of the relatively low resistance (1 M) pathways through the sucrose solution in the interstitial Schwann cell space which surround and shunt the high resistance (10–100 M) membrane patch. Current-noise measurements during patch voltage clamp extend observation of patch ionconductance fluctuations to 1 kHz. Various tests are presented to demonstrate the temporal and spatial adequacy of patch potential control during current-noise measurements.     

Kinetic analysis of the sodium gating current in the squid giant axon

A critical study has been made of the characteristics of the kinetic components of the sodium gating current in the squid giant axon, of which not less than five can be resolved. In addition to the principal fast component Ig2, there are two components of appreciable size that relax at an intermediate rate, Ig3 alpha and Ig 3 beta. Ig3 alpha has a fast rise, and is present over the whole range of negative test potentials. Ig3 beta is absent below -40 mV, exhibits a delayed onset and disappears on inactivation of the sodium system. There are also two smaller components, Ig1 and Ig4, with very fast and much slower relaxation time constants, respectively.     

A model for conductance changes in the squid giant axon. II. Channel kinetics

The kinetics of the sodium and potassium channels in voltage clamped squid giant axon following a relaxation of the membrane subunits are examined and compared with the Hodgkin-Huxley equations. Mechanisms are suggested for the turn-off of the sodium conductance and a set of kinetic states are proposed for the potassium channel which are consistent with the experimental observations. Determination of the rate constants for relaxation of the surface subunits which triggers the subsequent changes within the independent channels provide information on the equilibrium constant and free energy for this process. The free energy is observed to approach zero as the depolarizing voltage of the clamp approaches $\text{E}{}_{\mathrm{<mtext>Na</mtext>}}$, the voltage for zero sodium current in voltage clamped axons. Analysis of the final rate constants in the kinetic sequence for potassium indicates a symmetry of the channel when it is in its steady-state configuration during clamp in the absence of external gradients.     

Kinetic analysis of pancuronium interaction with sodium channels in squid axon membranes

The interaction of pancuronium with sodium channels was investigated in squid axons. Sodium current turns on normally but turns off more quickly than the control with pancuronium 0.1-1mM present internally; The sodium tail current associated with repolarization exhibits an initial hook and then decays more slowly than the control. Pancuronium induces inactivation after the sodium inactivation has been removed by internal perfusion of pronase. Such pancuronium-induced sodium inactivation follows a single exponential time course, suggesting first order kinetics which represents the interaction of the pancuronium molecule with the open sodium channel. The rate constant of association k with the binding site is independent of the membrane potential ranging from 0 to 80 mV, but increases with increasing internal concentration of pancuronium. However, the rate constant of dissociation l is independent of internal concentration of pancuronium but decreases with increasing the membrane potential. The voltage dependence of l is not affected by changine external sodium concentration, suggesting a current-independent conductance block, The steady-state block depends on the membrane potential, being more pronounced with increasing depolarization, and is accounted for in terms of the voltage dependence of l. A kinetic model, based on the experimental observations and the assumption on binding kinetics of pancuronium with the open sodium channel, successfully simulates many features of sodium current in the presence of pancuronium.     

Frequency entrainment of squid axon membrane

Summary Sinusoidally varying stimulating currents were applied to space-clamped squid giant axon membranes in a double sucrose gap apparatus. Stimulus parameters varied were peak-to-peak current amplitude, frequency, and DC offset bias. In response to these stimuli, the membranes produced action potentials in varying patterns, according to variation of input stimulus parameters. For some stimulus parameters the output patterns were stable and obviously periodic with the periods being simple multiples of the input period; for other stimulus parameters no obvious periodicity was manifest in the output. The experimental results were compared with simulations using a computer model which was modified in several ways from the Hodgkin-Huxley model to make it more representative of our preparation. The model takes into account K⁺ accumulation in the periaxonal space, features of Na⁺ inactivation which are anomalous to the Hodgkin-Huxley model, sucrose gap hyperpolarization current, and membrane current noise. Many aspects of the experiments are successfully simulated but some are not, possibly because some very slow process present in the preparation is not included in the model.     

Noise measurements in squid axon membrane.

A small area (10(-4) to 10(-5) cm2 patch) of the external surface of a squid (Loligo pealei) axon was "isolated" electrically by means of a pair of concentric glass pipettes and sucrose solution to achieve a low extraneous noise measurement of spontaneous fluctuations in membrane potential and current. The measured "small-signal" impedance function of the isolated patch in seawater was constant at low frequencies and declined monotonically at frequencies beyond 100Hz. It is shown that the power-density spectrum (PDS) of voltage noise, which generally reflects the current-noise spectrum filtered by the membrane impedance function, is equivalent to the power spectrum of current-noise up to frequencies where the impedance decline is significant (Fishman, 1973a, Proc. Nat. Acad. Sci. USA 70:876). This result is in contrast to an impedance resonance measured under uniform constant-current (internal axial wire) conditions, for which the voltage-noise PDS reflects the impedance resonance. The overdamped resonance in the patch technique is a consequence of the relatively low resistance (1 Momega) pathways through the sucrose solution in the interstitial Schwann cell space which surround and shunt the high resistance (10-100 Momega) membrane patch. Current-noise measurements during patch voltage clamp extend observation of patch ion-conductance fluctuations to 1 kHz. Various tests are presented to demonstrate the temporal and spatial adequacey of patch potential control during current-noise measurements.     

Calcium currents in squid giant axon.

Voltage-clamp experiments were carried out on intracellularly perfused squid giant axons in a Na-free solution of 100 mM CaCl2+sucrose. The internal solution was 25 mM CsF+sucrose or 100 mM RbF+50mM tetraethylammonium chloride+sucrose. Depolarizing voltage clamp steps produced small inward currents; at large depolarizations the inward current reversed into an outward current. Tetrodotoxin completely blocked the inward current and part of the outward current. No inward current was seen with 100 mM MgCl2+sucrose as internal solution. It is concluded that the inward current is carried by Ca ions moving through the sodium channel. The reversal potential of the tetrodotoxin-sensitive current was +54mV with 25 mM CsF+sucrose inside and +10 mV with 100 mM RbF+50 mM tetraethylammonium chloride+sucrose inside. From the reversal potentials measured with varying external and internal solutions the relative permeabilities of the sodium channel for Ca, Cs and Na were calculated by means of the constant field equations. The results of the voltage-clamp experiments are compared with measurements of the Ca entry in intact axons.     

Delayed kinetics of squid axon potassium channels do not always superpose after time translation.

The activation of potassium ion conductance in squid axons by voltage-clamp depolarization is delayed when the depolarizing step is preceded by a conditioning hyperpolarization of the axonal membrane. Moreover, the control conductance kinetics superpose with the delayed kinetics when they are translated along the time axis by an amount equal to the delay. We have found that the degree of superposition with internally perfused axons depends upon voltage-clamp protocol. The kinetics superpose almost exactly for modest test depolarizations, whereas they clearly fail to superpose completely for more positive levels of membrane depolarization. We have modeled these results by incorporating a time dependence into the rate constant of activation of potassium channel gates in the Hodgkin and Huxley model of potassium ionic conductance.     

Gating kinetics of batrachotoxin-modified Na+ channels in the squid giant axon. Voltage and temperature effects.

The gating kinetics of batrachotoxin-modified Na+ channels were studied in outside-out patches of axolemma from the squid giant axon by means of the cut-open axon technique. Single channel kinetics were characterized at different membrane voltages and temperatures. The probability of channel opening (Po) as a function of voltage was well described by a Boltzmann distribution with an equivalent number of gating particles of 3.58. The voltage at which the channel was open 50% of the time was a function of [Na+] and temperature. A decrease in the internal [Na+] induced a shift to the right of the Po vs. V curve, suggesting the presence of an integral negative fixed charge near the activation gate. An increase in temperature decreased Po, indicating a stabilization of the closed configuration of the channel and also a decrease in entropy upon channel opening. Probability density analysis of dwell times in the closed and open states of the channel at 0 degrees C revealed the presence of three closed and three open states. The slowest open kinetic component constituted only a small fraction of the total number of transitions and became negligible at voltages greater than -65 mV. Adjacent interval analysis showed that there is no correlation in the duration of successive open and closed events. Consistent with this analysis, maximum likelihood estimation of the rate constants for nine different single-channel models produced a preferred model (model 1) having a linear sequence of closed states and two open states emerging from the last closed state. The effect of temperature on the rate constants of model 1 was studied. An increase in temperature increased all rate constants; the shift in Po would be the result of an increase in the closing rates predominant over the change in the opening rates. The temperature study also provided the basis for building an energy diagram for the transitions between channel states.     

Injury-induced vesiculation and membrane redistribution in squid giant axon

Injury of isolated squid giant axons in sea water by cutting or stretching initiates the following unreported processes: (i) vesiculation in the subaxolemmal region extending along the axon several mm from the site of injury, followed by (ii) vesicular fusions that result in the formation of large vesicles (20-50 micron diameter), 'axosomes', and finally (iii) axosomal migration to and accumulation at the injury site. Some axosomes emerge from a cut end, attaining sizes up to 250 microns in diameter. Axosomes did not form after axonal injury unless divalent cations (Ca2+ or Mg2+) were present (10mM) in the external solution. The requirement for Ca2+ and the action of other ions are similar to that for cut-end cytoskeletal constriction in transected squid axons (Gallant, P.E. (1988) J. Neurosci. 8, 1479-1484) and for electrical sealing in transected axons of the cockroach (Yawo, H. and Kuno, M. (1985) J. Neurosci. 5, 1626-1632). Axosomes probably consist of membrane from different sources (e.g., axolemma, organelles and Schwann cells); however, localization of axosomal formation to the inner region of the axolemma and the formation dependence on divalent cations suggest principal involvement of cisternae of endoplasmic reticulum. Patch clamp of excised patches from axosomes liberated spontaneously from cut ends of transected axons showed a 12-pS K+ channel and gave indications of other channel types. Injury-induced vesiculation and membrane redistribution seem to be fundamental processes in the short-term (minutes to hours) that precede axonal degeneration or repair and regeneration. Axosomal formation provides a membrane preparation for the study of ion channels and other membrane processes from inaccessible organelles.     

Potassium-ion conduction noise in squid axon membrane.

Spectral analysis (1-1000 Hz) of spontaneous fluctuations of potential and current in small areas of squid (Loligo pealei) axon shows two forms of noise: f-1 noise occurs in both excitable and inexcitable axons with an intensity which depends upon the driving force for potassium ions. The other noise has a spectral form corresponding to a relaxation process, i.e. its asymptotic behavior at low frequencies is constant, and at high frequencies it declines with a slope of -2. This latter noise occurs only in excitable axons and was identified in spectra by (1) its disappearance after reduction of K+ current by internal perfusion with solutions containing tetraethylammonium (TEA+), Cs+ or reduced [Ki+] and (2) its insensitivity to block of Na+ conduction and active transport. The transition frequency of relaxation spectra are also voltage and temperature dependent and relate to the kinetics of K+-conduction in the Hodgkin-Huxley formulation. These data strongly suggest that the relaxation noise component arises from the kinetic properties of K+ channels. The f-1 noise is attributed to restricted diffusion in conducting K+ channels and/or leakage pathways. In addition, an induced K+ conduction noise associated with the binding of TEA+ and triethyldecylammonium ion to membrane sites is described. Measurement of the induced noise may provide an alternative means of characterizing the kinetics of interaction of these molecules with the membrane and also suggests that these and other pharmacological agents may not be useful in identifying noise components related to the sodium conduction mechanism which, in these experiments, appears to be much lower in intensity than either the normal K conduction or induced noise components.     

Extrinsic charge movement in the squid axon membrane

The absorption of the lipophilic anions dipycrilamine (DPA^-) and tetraphenylborate (TPhB^-) by the lipid matrix of the squid axon membrane, and the kinetics of their translocation, were studied by the charge pulse relaxation technique. The axons were treated with tetrodotoxin (TTX) and 4-aminopyridine to block the ionic currents responsible for nerve excitation. At high enough concentrations of absorbed ions ( 10^-12 mol/cm²) the membrane voltage relaxation following a brief current pulse consisted mainly of two exponential components, whose time constants and relative amplitudes were used for estimating the translocation rate constant, K, and the density of absorbed ions, N. These measurements were performed at different hydrostatic pressures in the range 1–100 MPa ( 1,000 atm), and at different temperatures in the range 5° C–20° C. Both K and N were found to be little affected by pressure. The pressure dependence of K indicated that the translocation of lipophilic ions across the nerve membrane involves activation volumes of the order of 5 cm³/mol. In all experiments the passive membrane resistance was little affected by pressures up to 80 MPa. However, above 100 MPa it fell dramatically to low values, presumably because of phase separation phenomena between the membrane components. The temperature dependence of K, both for DPa^- and TPhB^-, implied an activation energy for ion translocation of the order of 60 kJ/mol, close to that measured in artificial lipid bilayers.It is concluded that the lipid bilayer structure of the nerve membrane is not modified by pressures below 80 MPa and that the intramembrane movements of relatively small charged groups cannot account for the large activation volumes involved in the gating of ionic channels.