Significant potassium ion accumulation at the external surface of Myxicola giant axons

Potassium accumulation associated with outward membrane potassium current was investigated experimentally in Myxicola giant axon. During prolonged voltage-clamp pulses to positive transmembrane potentials, the K+ equilibrium potential may approach zero mV, suggesting massive K+ accumulation outside the axonal membrane to concentrations many-fold higher than those in the bathing medium. The potassium accumulation can be satisfactorily described by a three-compartment model, consisting of the nerve fiber, a restricted physiological periaxonal space and the bulk solution. The average thickness, theta, of the periaxonal space is calculated as 177 +/- 59 A, i.e., comparable to that in the squid, while the permeability coefficient of the external barrier, PKs, was calculated to be (1.4 +/- 0.4) X 10(-4) cm/s. These conclusions are well supported by morphological study.     

Evidence for the utilization of extracellular [γ-32P]ATP for the phosphorylation of intracellular proteins in the squid giant axon

Proteins in the squid giant axon were labeled with ³²P by in vitro incubation of isolated axoplasm with radioactive [γ-³²P]adenosine triphosphate (ATP) and separated by polyacrylamide sodium dodecyl sulfate gel electrophoresis. The two major phosphorylated regions on the gel had molecular weights of 400 000 and 200 000. These two peaks appear to be neurofilament proteins of squid axoplasm. The same set of proteins was phosphorylated in the axoplasm regardless of whether the [γ-³²P]ATP was applied in situ intracellularly or extracelarly. These results suggest that ATP in the extracellular space is, by some ATP-translocation mechanism, utilized in the process of intracellular phosphorylation. Measurements of the apparent influx of ATP across the squid axon membrane yielded results consistent with the view that ATP in the extracellular fluid could be transported into the axoplasm.     

Action of External Divalent Ion Reduction on Sodium Movement in the Squid Giant Axon

Voltage clamp measurements of the sodium potential have been made on the resting squid giant axon to study the effect of variations in external divalent ion concentration upon net sodium flux. From these measurements the intracellular sodium concentration and the net sodium inflow were calculated using the Nernst relation and constant activity coefficients. While an axon bathed in artificial sea water shows a slow increase in internal sodium concentration, the rate of sodium accumulation is increased about two times by reducing external calcium and magnesium concentrations to 0.1 times their normal values. The mean inward net sodium flux increases from a mean control value of 97 pmole/cm² sec. to 186 pmole/cm² sec. in low divalent solution. Associated with these effects of external divalent ion reduction are a marked decrease in action potential amplitude, little or no change in resting potential, and a shift along the voltage axis of the curve relating peak sodium conductance to membrane potential similar to that obtained by Frankenhaeuser and Hodgkin (1957). These results implicate divalent ions in long term (minutes to hours) sodium permeability.     

Sodium channel gating currents. Origin of the rising phase

There has been some uncertainty in the past as to the origin of the rising phase of the gating current. We present evidence here that proves that the gating current does not have a rising phase and that the observed rising phase is due to an uncompensated series resistance in the Frankenhaeuser-Hodgkin (F-H) space. When a squid giant axon is bathed in a solution that is 10-20% hyperosmotic with respect to the internal solution, the rising phase of the gating current is eliminated. In parallel with this, a component of the capacity transient (time constant, 20 microseconds) is reduced so that the capacity transient now appears to be closer to a single fast (5-10 microseconds) component. These changes in the capacity transient and gating current occur without altering the amount of charge moved in either. This indicates that the charge is simply redistributed in time. The gating current without a rising phase can still be immobilized by inactivation. Supporting evidence is provided by measuring the accumulation and washout of K+ from the F-H space. It was found that K+ washes out 35% faster when the axon is bathed in hyperosmotic solution. It was estimated that the F-H space thickness (theta) increased 2.5 +/- 0.4-fold (mean +/- SEM) in hyperosmotic solution. Similarly, K+ accumulation in the F-H space was decreased, leading to an estimate of a 5 +/- 1.4-fold increase in theta in hyperosmotic solution. These results are consistent with the simple structural model presented.     

On the role of subthreshold dynamics in neuronal signaling

The role of subthreshold dynamics in neuronal signaling is examined using periodic pulse train stimulation of the Fitzhugh-Nagumo (FN) model of nerve membrane excitability and results from the squid giant axon as an experimental data base. For a broad range of stimulus conditions the first pulse in a pulse train elicited an action potential, whereas all subsequent pulses elicited subthreshold responses, both in the axon and in the FN model. These results are not well described by the Hodgkin and Huxley 1952 model. Various different patterns of subthreshold responses, including chaotic dynamics, can be observed in both systems-the FN model and the axon-depending upon stimulus conditions. For some conditions action potentials are occasionally interspersed among the subthreshold events with randomly occurring interspike intervals. The randomness is directly attributable to the underlying subthreshold chaos-deterministic chaos-rather than to a stochastic noise source. We conclude that this mechanism may contribute to multimodal interspike interval histograms which have been observed from individual neurons throughout the nervous system.     

A Computer Evaluation of Equations for Predicting the Potential across Biological Membranes

The Goldman, Henderson, and Planck junction potential equations can be used to describe the potential across the resting giant squid axon. These equations are used to calculate the relative Na, K, and Cl permeabilities of the squid axon using the experimental measurements of Hodgkin and Katz. The equations all provide excellent agreement with the observed data and yield similar permeability values.     

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.     

The flow properties of axoplasm in a defined chemical environment: influence of anions and calcium.

The flow properties of axoplasm have been studied in a defined chemical environment. Axoplasm extruded from squid giant axons was introduced into porous cellulose acetate tubes of diameter roughly equal to that of the original axon. Passage of axoplasm along the tube rapidly coated the tube walls with a layer of protein. By measuring the rate of low back and forth along the tube, the rheological properties of the axoplasm plug were investigated at a range of pressures and in a variety of media. Axoplasm behaves as a classical Bingham body the motion of which can be characterized by a yield stress (theta) and a plastic viscosity (eta p). In a potassium methanesulphonate medium containing 65 nM free Ca2+, theta averaged 109 +/- 46 dyn/cm2 and eta p1 146 +/- 83 P. These values were little affected by ATP, COLCHICINE, CYTOCHOLASIN B or by replacing K by Na but were sensitive to the anion composition of the medium. The effectiveness of different anions at reducing theta and eta p1 was in the order SCN greater than I greater then Br greater than Cl greater than methanesulphonate. Theta and eta p1 were also drastically reduced by increasing the ionized Ca. This effect required millimolar amounts of Ca, was unaffected by the presence of ATP and was irreversible. It could be blocked by the protease inhibitor TLCK. E.p.r. measurements showed that within the matrix of the axoplasm gel there is a watery space that is largely unaffected by anions or calcium.     

Current-Voltage Relations in the Lobster Giant Axon Membrane Under Voltage Clamp Conditions

The sucrose-gap method introduced by Stämpfli provides a means for the application of a voltage clamp to the lobster giant axon, which responds to a variety of different experimental procedures in ways quite similar to those reported for the squid axon and frog node. This is particularly true for the behavior of the peak initial current. However, the steady state current shows some differences. It has a variable slope conductance less than that of the peak initial current. The magnitude of the steady state slope conductance is related to the length of the repolarization phase of the action potential, which does not have an undershoot in the lobster. The steady state outward current is maintained for as long as 100 msec.; this is in contrast to a decline of about 50 per cent in the squid axon. Lowering the external calcium concentration produces shifts in the current-voltage relations qualitatively similar to those obtained from the squid axon. On the basis of the data available, there is no reason to doubt that the Hodgkin and Huxley analysis for the squid giant axon in sea water can be applied to the lobster giant axon.     

Single sodium channels from the squid giant axon

Since the work of A. L. Hodgkin and A. F. Huxley (1952. J. Physiol. [Lond.].117:500-544) the squid giant axon has been considered the classical preparation for the study of voltage-dependent sodium and potassium channels. In this preparation much data have been gathered on macroscopic and gating currents but no single sodium channel data have been available. This paper reports patch clamp recording of single sodium channel events from the cut-open squid axon. It is shown that the single channel conductance in the absence of external divalent ions is approximately 14 pS, similar to sodium channels recorded from other preparations, and that their kinetic properties are consistent with previous results on gating and macroscopic currents obtained from the perfused squid axon preparation.     

Axonal excitability revisited

The original papers of Hodgkin and Huxley (J. Physiol. 116 (1952a) 449, J. Physiol. 116 (1952b) 473, J. Physiol. 116 (1952c) 497, J. Physiol. 117 (1952d) 500) have provided a benchmark in our understanding of cellular excitability. Not surprisingly, their model of the membrane action potential (AP) requires revisions even for the squid giant axon, the preparation for which it was originally formulated. The mechanisms they proposed for the voltage-gated potassium and sodium ion currents, IK, and INa, respectively, have been superceded by more recent formulations that more accurately describe voltage-clamp measurements of these components. Moreover, the current-voltage relation for IK has a non-linear dependence upon driving force that is well described by the Goldman-Hodgkin-Katz (GHK) relation, rather than the linear dependence on driving force found by Hodgkin and Huxley. Furthermore, accumulation of potassium ions in the extracellular space adjacent to the axolemma appears to be significant even during a single AP. This paper describes the influence of these various modifications in their model on the mathematically reconstructed AP. The GHK and K+ accumulation results alter the shape of the AP, whereas the modifications in IK and INa gating have surprisingly little effect. Perhaps the most significant change in their model concerns the amplitude of INa, which they appear to have overestimated by a factor of two. This modification together with the GHK and the K+ accumulation results largely remove the discrepancies between membrane excitability of the squid giant axon and the Hodgkin and Huxley (J. Physiol. 117 (1952d) 500) model previously described (Clay, J. Neurophysiol. 80 (1998) 903).     

The effect of monovalent cations upon 45Ca fluxes in frog sciatic nerve

Investigation of Ca fluxes in desheathed bundles of myelinated nerve of frog indicates an intracellular Ca concentration of 5 x 10(-4) mol . kg-1 (axoplasm) and an average transmembrane flux of 6 x 10(-8) mol. kg-1 . s-1 at an extracellular Ca concentration of 1 mM. Replacement of extracellular Na by isosmotic sucrose increases Ca influx threefold and decreases efflux by 50%. Similar, but significantly smaller, effects are observed when Tris or choline are substituted for Na. Li replaces Na without significant changes in Ca fluxes. The data demonstrate that Ca transmembrane fluxes in this preparation are sensitive to changes in the Na gradient. The observed flux changes, however, are too small to establish a Na-Ca exchange as the sole homeostatic mechanism for intracellular Ca. Moreover, as Li appears to serve as a good Na substitute and even Tris and choline interact with Ca flux, the exchange does not show the specificity described for squid axon.     

Potassium ion accumulation at the external surface of the nodal membrane in frog myelinated fibers.

Potassium accumulation associated with outward membrane potassium current was investigated experimentally in myelinated fibers and analyzed in terms of two models-three-compartment and diffusion in an unstirred layer. In the myelinated fibers, as in squid giant axons, the three-compartment model satisfactorily describes potassium accumulation. Within this framework the average space thickness, theta, in frog was 5,900 +/- 700 A, while the permeability coefficient of the external barrier, PK, was (1.5 +/- 0.1) X 10(-2) cm/s. The model of ionic diffusion in an unstirred aqueous layer adjacent to the axolemma, as an alternative explanation for ion accumulation, was also consistent with the experimental data, provided that D, the diffusion constant, was (1.8 +/- 0.2) X 10(-6) cm/s and l, the unstirred layer thickness, was 1.4 +/- 0.1 micron, i.e., similar to the depth of the nodal gap. An empirical equation relating the extent of potassium accumulation to the amplitude and duration of depolarization is given.     

Morphology and electrical properties of Schwann cells around the giant axon of the squids Loligo forbesi and Loligo vulgaris.

The first successful dye-fills of Schwann cells around the split giant axon of Loligo show them to be spindle-shaped cells ca. 600 microns long and 20 microns wide lying parallel to the axonal axis. There are some 50,000 Schwann cells per cm2 of axonal membrane. Only a small part (ca. 6% of each Schwann cell membrane) is in contact with the periaxonal space, the remainder is overlain by adjacent Schwann cells, or applied to the basal lamina. The mean membrane potential of the Schwann cells in artificial seawater (ASW) varies from around -40 mV in fresh split-axon preparations to around -60 to -70 mV after 1-2 h; this hyperpolarization is not seen in preparations dissected and maintained in Ca2(+)-free ASW. Electrical- and dye-coupling (abolished by prior octanol treatment) is present between Schwann cells, but is weaker in cells with lower (less negative) membrane potentials. The implications for potassium homeostasis around the axon are briefly discussed.     

Effects of bath resistance on action potentials in the squid giant axon: myocardial implications.

This study presents a simplified version of the quasi-one-dimensional theory (Wu, J., E. A. Johnson, and J. M. Kootsey. 1996. A quasi-one-dimensional theory for anisotropic propagation of excitation in cardiac muscle. Biophys. J. 71:2427-2439) with two components of the extracellular current, along and perpendicular to the axis, and a simulation and its experimental confirmation for the giant axon of the squid. By extending the one-dimensional core conductor cable equations, this theory predicts, as confirmed by the experiment, that the shapes of the intracellular and the extracellular action potentials are related to the resistance of the bath. Such a result was previously only expected by the field theories. The correlation between the shapes of the intracellular and the extracellular potentials of the giant axon of the squid resembles that observed during the anisotropic propagation of excitation in cardiac muscle. Therefore, this study not only develops a quasi-one-dimensional theory for a squid axon, but also provides one possible factor contributing to the anisotropic propagation of action potentials in cardiac muscle.     

Diffusion coefficient of the cyclic GMP analog 8-(fluoresceinyl)thioguanosine 3'',5'' cyclic monophosphate in the salamander rod outer segment.

Cyclic GMP (cGMP) is the intracellular messenger mediating phototransduction in retinal rods, with its longitudinal diffusion in the rod outer segment (ROS) likely to be a factor in determining light sensitivity. From the kinetics of cGMP-activated currents in the truncated ROS of the salamander (Ambystoma tigrinum), the cGMP diffusion coefficient was previously estimated to be approximately 60 x 10(-8) cm2 s-1. On the other hand, fluorescence measurements in intact salamander ROS using 8-(fluoresceinyl)thioguanosine 3',5'-cyclic monophosphate (Fl-cGMP) led to a diffusion coefficient for this compound of 1 x 10(-8) cm2 s-1; after corrections for differences in size and in binding to cellular components between cGMP and Fl-cGMP, this gave an upper limit of 11 x 10(-8) cm2 s-1 for the cGMP diffusion coefficient. To properly compare the two sets of measurements, we have examined the diffusion of Fl-cGMP in the truncated ROS. From the kinetics of Fl-cGMP-activated currents, we have obtained a diffusion coefficient of 3 x 10(-8) cm2 s-1 for this analog; the cGMP diffusion coefficient measured from the same truncated ROSs was approximately 80 x 10(-8) cm2 s-1. Thus, a factor of 27 appears appropriate for correcting differences in size and intracellular binding between cGMP and Fl-cGMP. Application of this correction factor to the Fl-cGMP diffusion coefficient measurements by Olson and Pugh (1993) gives a cGMP diffusion coefficient of approximately 30 x 10(-8) cm2 s-1, in reasonable agreement with the value measured from the truncated ROS.     

Hindered diffusion in excised membrane patches from retinal rod outer segments.

Excised inside-out membrane patches are useful for studying the cGMP-activated ion channels that generate the electrical response to light in retinal rod cells. We show that strong ionic current across a patch changes the driving force on the current by altering the ionic concentration near the surface membrane, an effect somewhat like that first described by Frankenhaeuser and Hodgkin (1956) in squid axons. The dominant concentration change occurs in the solution adjacent to the cytoplasmic (inner) surface of the membrane, where diffusion is impaired by intracellular material that adheres to the patch during excision. The magnitude and time course of the ionic changes are consistent with the expected volume of this material and with an effective diffusion coefficient about an order of magnitude less than that in free solution. Methods are described for correcting current transients observed in voltage clamp experiments, so that channel gating kinetics can be obtained without contamination by changes in driving force. We suggest that restricted diffusion may occur in patches excised from other types of cells and influence rapid kinetic measurements.     

The rate of action of tetrodotoxin on sodium conductance in the squid giant axon.

When tetrodotoxin is applied to or washed away from the squid giant axon, the rates at which the sodium conductatnce is blocked and unblocked are an order of magnitude smaller than those reported for the isolated node of Ranvier. This slowing is to be expected if in squid the tetrodotoxin binding sites act as a saturable sink in series with the barrier to free diffusion imposed by the presence of the Schwann cell. A comparison has been made between the rates observed experimentally and those calculated for a computer model of the system, in order to estimate the apparent density in the membrane of both specific and non-specific tetrodotoxin binding sites. The figure thus obtained for the number of sodium channels in the squid giant axon, several hundred per square micrometre, agrees well with those derived from other lines of argument.     

The standard Hodgkin-Huxley model and squid axons in reduced external Ca++ fail to accommodate to slowly rising currents.

Accommodation may be defined as an increase in the threshold of an excitable membrane when the membrane is subjected to a sustained subthreshold depolarizing stimulus. Some excitable membranes show accommodation in response to currents which rise linearly at a very slow rate. In this report we point out a theoretical and an experimental counterexample, i.e., a nerve model and an axon which do not accommodate. The nerve model is the standard Hodgkin-Huxley axon, which Hodgkin and Huxley expected not to be excited by a very slowly rising current. This expectation is often quoted as fact, in spite of contrary calculations which we confirm. We have found that squid axons in seawater with reduced divalent cation concentration also do not accommodate to slowly rising currents.     

Transport methods for probing the barrier domain of lipid bilayer membranes.

Two experimental techniques have been utilized to explore the barrier properties of lecithin/decane bilayer membranes with the aim of determining the contributions of various domains within the bilayer to the overall barrier. The thickness of lecithin/decane bilayers was systematically varied by modulating the chemical potential of decane in the annulus surrounding the bilayer using different mole fractions of squalene in decane. The dependence of permeability of a model permeant (acetamide) on the thickness of the solvent-filled region of the bilayer was assessed in these bilayers to determine the contribution of this region to the overall barrier. The flux of acetamide was found to vary linearly with bilayer area with Pm = (2.9 +/- 0.3) x 10(-4) cm s-1, after correcting for diffusion through unstirred water layers. The ratio between the overall membrane permeability coefficient and that calculated for diffusion through the hydrocarbon core in membranes having maximum thickness was 0.24, suggesting that the solvent domain contributes only slightly to the overall barrier properties. Consistent with these results, the permeability of acetamide was found to be independent of bilayer thickness. The relative contributions of the bilayer interface and ordered hydrocarbon regions to the transport barrier may be evaluated qualitatively by exploring the effective chemical nature of the barrier microenvironment. This may be probed by comparing functional group contributions to transport with those obtained for partitioning between water and various model bulk solvents ranging in polarity or hydrogen-bonding potential. A novel approach is described for obtaining group contributions to transport using ionizable permeants and pH adjustment. Using this approach, bilayer permeability coefficients of p-toluic acid and p-hydroxymethyl benzoic acid were determined to be 1.1 +/- 0.2 cm s-1 and (1.6 +/- 0.4) x 10(-3) cm s-1, respectively. From these values, the -OH group contribution to bilayer transport [delta(delta G0-OH)] was found to be 3.9 kcal/mol. This result suggests that the barrier region of the bilayer does not resemble the hydrogen-bonding environment found in octanol, but is somewhat less selective (more polar) than a hydrocarbon solvent.