Potassium Ion Current in the Squid Giant Axon: Dynamic Characteristic

Measurements of the potassium current in the squid axon membrane have been made, after changes of the membrane potential to the sodium potential of Hodgkin and Huxley (HH), from near the resting potential, from depolarizations of various durations and amplitudes, and from hyperpolarizations of up to 150 mv. The potassium currents I given by I = I_∞ {1 - exp [- (t + t₀)/τ]}²⁵, where t₀ is determined by the initial conditions, represent the new data and approximate the HH functions in the regions for which they are adequate. A corresponding modification for the sodium current does not appear necessary. The results support the HH assumptions of the independence of the potassium and sodium currents, the dependence of the potassium current upon a single parameter determined by the membrane potential, and the expression of this parameter by a first order differential equation, and, although the results drastically modify the analytical expressions, they very considerably extend the range of apparent validity of these assumptions. The delay in the potassium current after severe hyperpolarization is used to estimate a potassium ion mobility in the membrane as 10^-5 of its value in aqueous solutions.     

Ammonium Ion Currents in the Squid Giant Axon

Voltage-clamp studies on intact and internally perfused squid giant axons demonstrate that ammonium can substitute partially for either sodium or potassium. Ammonium carries the early transient current with 0.3 times the permeability of sodium and it carries the delayed current with 0.3 times the potassium permeability. The conductance changes observed in voltage clamp show approximately the same time course in ammonium solutions as in the normal physiological solutions. These ammonium ion permeabilities account for the known effects of ammonium on nerve excitability. Experiments with the drugs tetrodotoxin (TTX) and tetraethyl ammonium chloride (TEA) demonstrate that these molecules block the early and late components of the current selectively, even when both components are carried by the same ion, ammonium.     

An Analysis of the Surface Fixed-Charge Theory of the Squid Giant Axon Membrane

The observed shift in threshold potential, after perfusion of the squid giant axon with solutions of low ionic strength, can be predicted by assuming a fixed negative charge on the inside of the membrane. The constant field equation, together with the double-layer potential due to this charge, has been used to determine the change in resting potential during perfusion with solutions of low ionic strength. Neither the modified constant field equation nor Planck's diffusion equation can successfully predict the observed shift in resting potential. It is suggested that a positive charge distribution exists about the sodium channel on the outside of the membrane. The double-layer potential due to this positive charge, together with the independence principle, has been used to predict the relationship between sodium current and membrane potential when the ionic strength and sodium activity of the external solution are decreased. These predictions have been compared with the available experimental observations.     

The Squid Giant Axon: Mathematical Models

The voltage clamp results of Hodgkin and Huxley have been reanalyzed in terms of alternative mathematical models. The model used for the potassium conductance changes is similar to that of the HH model except that an empirical functional relationship replaces the fourth power Law used by HH and the twenty-fifth power law used by Cole and Moore. The model used for the sodium conductance changes involves the explicit use of one variable only rather than the two variables m and h of HH. The rise and fall of the sodium conductance during a depolarizing voltage clamp is obtained by specifying that this one variable satisfies a second order differential equation which results from the coupling of two first order equations. Not only can the adjustable parameters of these models be made to give good fit to the clamp conductance data but the models can also then be used to compute action potential curves. Theoretical interpretations can also be given to these mathematical models.     

Kinesin mRNA Is Present in the Squid Giant Axon

Abstract: Recently, we reported the construction of a cDNA library encoding a heterogeneous population of polyadenylated mRNAs present in the squid giant axon. The nucleic acid sequencing of several randomly selected clones led to the identification of cDNAs encoding β-actin and β-tubulin, two relatively abundant axonal mRNA species. To continue characterization of this unique mRNA population, the axonal cDNA library was screened with a cDNA probe encoding the carboxy terminus of the squid kinesin heavy chain. The sequencing of several positive clones unambiguously identified axonal kinesin cDNA clones. The axonal localization of kinesin mRNA was subsequently verified by in situ hybridization histochemistry. In addition, the presence of kinesin RNA sequences in the axoplasmic polyribosome fraction was demonstrated using PCR methodology. In contrast to these findings, mRNA encoding the squid sodium channel was not detected in axoplasmic RNA, although these sequences were relatively abundant in the giant fiber lobe. Taken together, these findings demonstrate that kinesin mRNA is a component of a select group of mRNAs present in the squid giant axon, and suggest that kinesin may be synthesized locally in this model invertebrate motor neuron.     

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.     

Squid Axon Membrane Response to White Noise Stimulation

The current from a white noise generator was applied as a stimulus to a space-clamped squid axon in double sucrose gap. The membrane current and the voltage response of the membrane were then amplified, recorded on magnetic tape, and the stimulus was cross-correlated with the response. With subthreshold stimuli, a cross-correlation function resembling that obtained from a resonant parallel circuit is obtained. As the intensity of the input noise is increased, the cross-correlation function resembles that obtained from a less damped oscillatory circuit. When the noise intensity is further increased so that an appreciable frequency of action potentials is observed, an additional component appears in the experimental cross-correlogram. The subthreshold cross-correlogram is analyzed theoretically in terms of the linearized Hodgkin-Huxley equations. The subthreshold axon approximates a parallel resonant circuit. The circuit parameters are temperature dependent, with resonant frequency varying from approximately 100 Hz at 10°C to approximately 250 Hz at 20°C. The Q₁₀ of the resonant frequency is equal to 1.9. These values are in agreement with values found previously for subthreshold oscillations following a single action potential.     

Uptake of Protein by the Giant Axon of the Squid

THE uptake of macromolecules by neurones and glia may be relevant to an understanding of the relationships between these cells and to the concept of the glia-neurone unit¹. Protein uptake has been studied biochemically using suspensions of animal cells², but little morphological evidence has been gathered from neuronal systems^3–5. This problem can be investigated conveniently using the giant axon of the squid; biochemical analyses can be carried out on samples of axoplasm after incubation of intact axons with a labelled macromolecule. To do this we have used¹²⁵I-albumin as a model protein because of its commercial availability and the lack of reincorporation of free ¹²⁵I-tyrosine into protein².     

Organization of the Cortical Endoplasmic Reticulum in the Squid Giant Axon

The organization of the cortical endoplasmic reticulum in the squid giant axon was investigated by rapid freeze and freeze-substitution electron microscopy, thereby eliminating the effects of fixatives on this potentially labile structure. Juvenile squid, which have thinner Schwann sheaths, were used in order to achieve freezing deep enough to include the entire axonal cortex. The smooth endoplasmic reticulum is composed of subaxolemmal and deeper cisternae, tubules, tethers and vesicles. The subaxolemmal cisternae make junctional contacts with the axolemma which are characterized by filamentous-granular bridging structures approximately 3 nm in diameter. The subaxolemmal junctions with the axolemma resemble the coupling junctions between the sarcoplasmic reticulum and the T-tubules in muscle. Reconstruction of short series of sections showed that a number of the elements of the endoplasmic reticulum were continuous but numerous separate vesicles were present as well. The morphology of endoplasmic reticulum as described here suggests that it is a highly dynamic entity as well as a Ca²⁺ sequestering organelle.     

Subthreshold Behavior and Phenomenological Impedance of the Squid Giant Axon

The oscillatory behavior of the cephalopod giant axons in response to an applied current has been established by previous investigators. In the study reported here the relationship between the familiar "RC" electrotonic response and the oscillatory behavior is examined experimentally and shown to be dependent on the membrane potential. Computations based on the three-current system which was inferred from electrical measurements by Hodgkin and Huxley yield subthreshold responses in good agreement with experimental data. The point which is developed explicitly is that since the three currents, in general, have nonzero resting values and two currents, the "Na" system and the "K" system, are controlled by voltage-dependent time-variant conductances, the subthreshold behavior of the squid axon in the small-signal range can be looked upon as arising from phenomenological inductance or capacitance. The total phenomenological impedance as a function of membrane potential is derived by linearizing the empirically fitted equations which describe the time-variant conductances. At the resting potential the impedance consists of three structures in parallel, namely, two series RL elements and one series RC element. The true membrane capacitance acts in parallel with the phenomenological elements, to give a total impedance which is, in effect, a parallel R, L, C system with a "natural frequency" of oscillation. At relatively hyperpolarized levels the impedance "degenerates" to an RC system.     

Permeability of Squid Axon Membrane to Various Ions

The permeability of the squid axon membrane was determined by the use of radioisotopes of Na, K, Ca, Cs, and Br. Effluxes of these isotopes were measured mainly by the method of intracellular injection. Measurements of influxes were carried out under continuous intracellular perfusion with an isotonic solution of potassium sulfate. The Na permeability of the resting (excitable) axonal membrane was found to be roughly equal to the K permeability. The permeability to anion was far smaller than that to cations. It is emphasized that the axonal membrane has properties of a cation exchanger. The physicochemical nature of the "two stable states" of the excitable membrane is discussed on the basis of ion exchange isotherms.     

Anomalous Rectification in the Squid Giant Axon Injected with Tetraethylammonium Chloride

The injection of tetraethylammonium chloride into the giant axon of the squid prolongs the action potential and eliminates most of the late current under voltage-clamp. Experiments on fibers in an external medium of high potassium ion concentration demonstrate that injected tetraethylammonium chloride causes rectification of the instantaneous current-voltage curve for potassium by excluding outward current. This interference with the flow of outward potassium ion current underlies the prolongation of the action potential seen in tetraethylammonium-injected fibers.     

Effects of Replacement of External Sodium Chloride with Sucrose on Membrane Currents of the Squid Giant Axon

It was observed that a reduction of the sodium chloride concentration in the external solution bathing a squid giant axon by replacement with sucrose resulted in marked decreases in the peak inward and steady-state outward currents through the axon membrane following a step decrease in membrane potential. These effects are quantitatively acounted for by the increase in series resistance resulting from the decreased conductivity of the sea water and the assumption that the sodium current obeys a relation of the form I = k₁C₁ - k₂C₂ where C₁, C₂ are internal and external ion activities and k₁, k₂ are independent of concentration. It is concluded that the potassium ion current is independent of the sodium concentration. That the inward current is carried by sodium ions has been confirmed. The electrical potential (or barrier height) profile in the membrane which drives sodium ions appears to be independent of sodium ion concentration or current. A specific effect of the sucrose on hyperpolarizing currents was observed and noted but not investigated in detail.     

Characterization of the Resting Axolemma in the Giant Axon of the Squid

Previous electron microscope studies have shown that the Schwann cell layer is traversed by long and tortuous slit-like channels ~60Å wide, which provide the major route of access to the axolemma surface. In the present work the restriction offered by the resting axolemma to the passage of six small non-electrolyte molecules has been determined. The radii of the probing molecules were estimated from constructed molecular models. The ability of the axolemma to discriminate between the solvent (water) and each probing molecule was expressed in terms of the reflection coefficient σ. σ was then used to calculate an effective pore size for the resting axolemma. The value of 4.25 Å found for the pore radius is in excellent agreement with the 1.5 to 8.5 Å limiting values previously calculated from our measurements of water fluxes. The presence of pores with 4.25 Å radius in the resting axolemma is compatible with restricted diffusion of Na. The present paper leads to the conclusion that the axolemma is the only continuous barrier across which the ionic gradient responsible for the normal functioning of the nerve can be maintained. The combined findings of electron microscopy, water permeability, and molecular restricted filtration indicate that in all probability the axolemma is the "excitable membrane" of the physiologists.     

Analysis of Certain Errors in Squid Axon Voltage Clamp Measurements

Localized membrane current and potential measurements were made on the squid giant axon in voltage clamp experiments. Spatial control of potential was impaired by the use of axial current supplying electrodes with surface resistance greater than 20 ohms for a centimeter length of axon. No region of membrane which was indeed subjected to a potential step showed more than one inward current peak. Other patterns were results of space clamp failure. Membrane current and potential patterns during space clamp failure were approximately reproduced in computations on a model containing two membrane patches obeying the equations of Hodgkin and Huxley. Non-uniformities in the axon or electrodes are not necessary for non-uniform electrical behavior. An extension of the core conductor model which includes the axial wire and external solution has been analyzed. The space constant of electrotonic spread is less than 0.5 mm with a usable electrode. Errors of about 5 per cent are introduced by ignoring the external solution. Resistance between the membrane and the control electrodes reduces the control and a few ohm cm² could lead to serious errors in interpretation.     

Equilibrium and Kinetic Properties of the Interaction between Tetrodotoxin and the Excitable Membrane of the Squid Giant Axon

Squid giant axons were treated with tetrodotoxin (TTX) in concentrations ranging from 1 nM to 25 nM and the resulting decrease in sodium current was followed in time using the voltage clamp technique. The removal of TTX from the bathing solution produced only partial recovery of the sodium current. This suggests that the over-all interaction is more complex than just a reversible reaction. By correcting for the partial irreversibility of the decrease in sodium current, a dissociation constant of 3.31 x 10^-9 M was calculated for the reaction between TTX and the reactive site of the membrane. The data obtained fit a dose-response curve modified to incorporate the correction for partial irreversibility when calculated for a one-to-one stoichiometry. The fit disagreed with that calculated for a reaction between two molecules of TTX with a single membrane-reactive site, but neither supported nor disproved the possibility of a complex formed by two reactive sites with one molecule of TTX. Values of the rate constants for the formation and dissociation of the TTX-membrane complex, k ₁ and k ₂, respectively, were obtained from the kinetic data. The values are: k ₁ = 0.202 x 10⁸ M ^-1, and k ₂ = 0.116 min^-1. The magnitude of the dissociation constant derived from these values is 5.74 x 10^-9 M, which has the same order of magnitude as that obtained from equilibrium measurements. Arrhenius plots of the rate constants gave values for the thermodynamic quantities of activation.     

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.