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K S COLE

Publications and source records attributed to K S COLE.

15 recordsLinked to original sources
PubMed1964

THEORETICAL POTASSIUM LOSS FROM SQUID AXONS AS A FUNCTION OF TEMPERATURE.

Theoretical net ionic movements have been calculated for the propagated impulse of the squid axon from the Hodgkin-Huxley equations. The computed potassium movements agree approximately with the experimental data of Shanes, but vary too much with temperature (Q(10) = 1/2.75 from computation, 1/1.91 from experiment). Theoretical corrections providing higher ionic conductances increasing with temperature (according to J. W. Moore's experiments) give a Q(10) of 1/2.24, but the incorporation of the higher values of the maximum conductances, as observed under improved environmental conditions, leads to potassium movements that are considerably higher than Shanes's values.

Animals↗
PubMed1962

Platinized silver chloride electrode.

A hybrid electrode made by platinizing silver-silver chloride has been found to combine the stable potential and low direct-current resistance properties of a silver-silver chloride electrode with the low high-frequency impedance characteristic of a platinized platinum electrode.

Electrodes↗
PubMed1962

Theoretical stability properties of a space-clamped axon.

A mathematical method for determining the stability properties of a uniform nerve membrane is developed. Two basically similar tests of stability are considered: examination of the real characteristic roots of the linearized equations and application of a modified Nyquist criterion to the linearized alternating current admittance. The method is applied to the Hodgkin-Huxley equations for the squid axon membrane at 6.3 degrees C to decide theoretically whether stable membrane behavior might be expected in a space clamp experiment. The equations are solved for step depolarizations similar to those used in voltage clamp experiments. Each solution can be represented by a trajectory in the phase space of the variables V, m, h, and n. The stability of motion of a phase point on a given trajectory, and hence the adequacy of the control of the membrane potential, is shown to be a function of the effective conductance in series with the membrane. (For a patch of membrane away from the point controlled by feedback, the effective conductance is the combined conductance of the axial current electrode, axoplasm, and an external layer of sea water, all in series.) In particular, there is a (uniquely determined) critical conductance, defined as the minimum effective series conductance consistent with stability, associated with each point on the trajectory. During a step depolarization the critical conductance goes through a maximum. The values of such maxima as a function of voltage are closely similar to the negative slopes of the peak inward current versus voltage curve. This empirical correlation may be helpfup in the prediction of stability in experimental situations.

Animals↗
PubMed1961

An analysis of the membrane potential along a clamped squid axon.

A partially depolarized squid axon membrane is assumed to have a quasi-steady state negative resistance, the membrane potential is clamped at one point, and a distribution of potential along the axon is obtained from the cable equation. Nominal experimental values of -2 ohm cm(2) for the membrane and 6 ohm cm(2) for the internal and external current electrodes and the axoplasm and sea water between them are used for illustration. The potential and current may be uniform for an axon and electrode length less than 1.2 mm. For a long axon the potential varies as the cosine of the distance within 0.8 mm of the control point. Beyond this the potential variation is exponential and the entire pattern is about 5 mm long. The average current density out to 0.3 mm from the control point is within 10 per cent of the potential clamp value. These distributions are stable for control amplifications of about unity and more.

Animals↗
PubMed1961

Non-linear current-potential relations in an axon membrane.

The membrane current density, I(m), in the squid giant axon has been calculated from the measured external current applied to the axon, I(o), by the equation See PDF for Equation where V(m) is the membrane potential under the current electrode and r(1) and r(2) are the external and internal longitudinal resistances. The original derivation of this equation included in one step an assumption of a linear relation between I(m) and V(m). It is shown that the same equation can be obtained without this restricting assumption.

Axons↗
PubMed1960

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(infinity) {1 - exp [- (t + t(0))/tau]}(25), where t(0) 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.

Animals↗
PubMed1960

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 cm(2) could lead to serious errors in interpretation.

Animals↗
PubMed1960

Resting and action potentials of the squid giant axon in vivo.

Blood oxygenation and circulation were maintained in Loligo pealii for several hours by a strong flow of sea water over both gills on the open, flat mantle. Potentials were measured with a 3 M KCl-filled glass microelectrode penetrating the giant axon membrane. An hour or more after the mantle was opened, the potentials were similar to those observed in excised axons and in preparations without circulation; spike height 100 mv.; undershoot 12 mv., decaying at 6 v./sec.; resting potential 63 mv. However, the earliest (20 minute) resting potentials were up to 70 mv. and 73 mv. Occasional initial action potential measurements (40 to 50 minute) showed a decay of the undershoot that was less than one-tenth the rate observed later. This suggests that in even better preparations there would be no decay, thereby increasing the resting potential and spike height by 12 mv. With the calculated liquid junction potential of 4 mv. the absolute resting potential in the "normal" axon in vivo is estimated to be about 77 mv., which is close to the Nernst potential for the potassium ratio between squid blood and axoplasm. The differences between such a normal axon and the usual isolated axon can be accounted for by a negligible leakage conductance in the normal axon.

Action Potentials↗
PubMed1960

Liquid junction and membrane potentials of the squid giant axon.

The potential differences across the squid giant axon membrane, as measured with a series of microcapillary electrodes filled with concentrations of KCl from 0.03 to 3.0 M or sea water, are consistent with a constant membrane potential and the liquid junction potentials calculated by the Henderson equation. The best value for the mobility of an organic univalent ion, such as isethionate, leads to a probably low, but not impossible, axoplasm specific resistance of 1.2 times sea water and to a liquid junction correction of 4 mv. for microelectrodes filled with 3 M KCl. The errors caused by the assumptions of proportional mixing, unity activity coefficients, and a negligible internal fixed charge cannot be estimated but the results suggest that the cumulative effect of them may not be serious.

Animals↗
PubMed1960

Ionic current measurements in the squid giant axon membrane.

The concepts, experiments, and interpretations of ionic current measurements after a step change of the squid axon membrane potential require the potential to be constant for the duration and the membrane area measured. An experimental approach to this ideal has been developed. Electrometer, operational, and control amplifiers produce the step potential between internal micropipette and external potential electrodes within 40 microseconds and a few millivolts. With an internal current electrode effective resistance of 2 ohm cm.(2), the membrane potential and current may be constant within a few millivolts and 10 per cent out to near the electrode ends. The maximum membrane current patterns of the best axons are several times larger but of the type described by Cole and analyzed by Hodgkin and Huxley when the change of potential is adequately controlled. The occasional obvious distortions are attributed to the marginal adequacy of potential control to be expected from the characteristics of the current electrodes and the axon. Improvements are expected only to increase stability and accuracy. No reason has been found either to question the qualitative characteristics of the early measurements or to so discredit the analyses made of them.

Animals↗