Non-Linear Current-Potential Relations in an Axon Membrane

The membrane current density, Im, in the squid giant axon has been calculated from the measured external current applied to the axon, Io, by the equation See PDF for Equation where Vm is the membrane potential under the current electrode and r1 and r2 are the external and internal longitudinal resistances. The original derivation of this equation included in one step an assumption of a linear relation between Im and Vm. It is shown that the same equation can be obtained without this restricting assumption

ELECTRIC PHASE ANGLE OF CELL MEMBRANES

From the theory of an electric network containing any combination of resistances and a single variable impedance element having a constant phase angle independent of frequency, it is shown that the graph of the terminal series reactance against the resistance is an arc of a circle with the position of the center depending upon the phase angle of the variable element. If it be assumed that biological systems are equivalent to such a network, the hypotheses are supported at low and intermediate frequencies by data on red blood cells, muscle, nerve, and potato. For some tissues there is a marked divergence from the circle at high frequencies, which is not interpreted

ELECTRIC IMPEDANCE OF SUSPENSIONS OF SPHERES

A general expression has been derived for the electric impedance of a suspension of spheres each having a homogeneous non-reactive interior and a thin surface layer with both resistance and reactance. The applications and limitations of impedance measurements on such suspensions are discussed

ELECTRIC IMPEDANCE OF SUSPENSIONS OF ARBACIA EGGS

Apparatus has been designed and constructed for the measurement of the electric impedance of suspensions of Arbacia eggs in sea water to alternating currents of frequencies from one thousand to fifteen million cycles per second. This apparatus is simple, rugged, compact, accurate, and rapid. The data lead to the conclusions that the specific resistance of the interior of the egg is about 90 ohm cm. or 3.6 times that of sea water, and that the impedance of the surface of the egg is probably similar to that of a "polarization capacity". The characteristics of this surface impedance can best be determined by measurements of the capacity and resistance of suspensions of eggs. No specific change has been found in the interior resistance or the surface impedance which can be related either to membrane formation or to cell division

ELECTRIC IMPEDANCE OF ARBACIA EGGS

The alternating current resistance and capacity of suspensions of unfertilized and fertilized eggs of Arbacia punctulata have been measured at frequencies from 103 to 1.64 x 107 cycles per second. The unfertilized egg has a static plasma membrane capacity of 0.73 µf./cm.2 which is practically independent of frequency. The fertilized egg has a static membrane capacity of 3.1 µf./cm.2 at low frequencies which decreases to a value of 0.55 µf./cm.2 at high frequencies. The decrease follows closely the relaxation dispersion of the dielectric constant if the dissipation of such a system is ignored. It is considered more probable that the effect is due to a fertilization membrane of 3.1 µf./cm.2 capacity lifted 1.5 µ. from the plasma membrane, the interspace having the conductivity of sea water. The suspensions show a frequency-dependent capacity at low frequencies which may be attributable to surface conductance. The equivalent low frequency internal specific resistance of both the unfertilized and fertilized egg is about 186 ohm cm. or about 6 times that of sea water, while the high frequency data extrapolate to a value of about 4 times sea water. There is evidence at the highest frequencies that the current is penetrating the nucleus and other materials in the cytoplasm. If this effect were entirely due to the nucleus it would lead to a very approximate value of 0.1 µf./cm.2 for the capacity of the nuclear membrane. The measurements do not indicate any change in this effect on fertilization

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

MEMBRANE AND PROTOPLASM RESISTANCE IN THE SQUID GIANT AXON

The direct current longitudinal resistance of the squid giant axon was measured as a function of the electrode separation. Large sea water electrodes were used and the inter-electrode length was immersed in oil. The slope of the resistance vs. separation curve is large for a small electrode separation, but becomes smaller and finally constant as the separation is increased. An analysis of the resistance vs. length curves gives the following results. The nerve membrane has a resistance of about 1000 ohm cm.2 The protoplasm has a specific resistance of about 1.4 times that of sea water. The resistance of the connective tissue sheath outside the fiber corresponds to a layer of sea water about 20µ in thickness. The characteristic length for the axon is about 2.3 mm. in oil and 6.0 mm. in sea water

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

TRANSVERSE ELECTRIC IMPEDANCE OF THE SQUID GIANT AXON

The impedance of the excised giant axon from hindmost stellar nerve of Loligo pealii has been measured over the frequency range from 1 to 2500 kilocycles per second. The measurements have been made with the current flow perpendicular to the axis of the axon to permit a relatively simple analysis of the data. It has been found that the axon membrane has a polarization impedance with an average phase angle of 76° and an average capacity of 1.1µf./cm2 at 1 kilocycle. The direct current resistance of the membrane could not be measured, but was greater than 3 ohm cm.2 and the average internal specific resistance was four times that of sea water. There was no detectable change in the membrane impedance when the axon lost excitability, but some time later it decreased to zero