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Ionic Basis of Resting and Action Potentials

Bertil Hille

10.1002/cphy.cp010104

Source: Supplement 1: Handbook of Physiology, The Nervous System, Cellular Biology of Neurons

Originally published: 1977

Published online: January 2011

Full Article on Wiley Online Library



Abstract

The sections in this article are:

1 Development of Membrane Theory
1.1 Before Intracellular Recording
1.2 First Intracellular Recordings from Squid Giant Axons
2 Direct Measurement of Ionic Currents in Axon Membranes
2.1 Voltage‐clamp Method
2.2 Electrochemical Separation of Ionic Currents
2.3 Pharmacological Separation of Ionic Currents
3 Hodgkin‐huxley Model
3.1 Quantitative Analysis of INa and Ik
3.2 Calculations with Hodgkin‐Huxley Model
4 Variety of Excitable Cells
4.1 Myelinated Nerve
4.2 Other Axons
4.3 Cell Bodies
4.4 Muscle
5 Ionic Channels
5.1 Sodium Channels
5.2 Potassium Channels
5.3 Calcium Channels
6 Equations of Ionic Hypothesis
6.1 Solving Hodgkin‐Huxley Model
6.2 Diffusion of Charged Particles in Electric Field
Figure 1. Figure 1.

Intracellularly recorded resting and action potentials from several nerve cells. A: single node of Ranvier of rat myelinated nerve fiber at 37°C. Brief stimulus applied at same node. (W. Nonner, M. Horáčkova, and R. Stämpfli, unpublished data.) B: same type of recording from frog myelinated fiber as in A, but at 22°C.

From Dodge 56.] C: cat lumbar spinal motoneuron at 37°C, excited antidromically by stimulation of motor axon. (W. E. Crill, unpublished data.) D: propagating action potential in squid giant axon at 16°C. Stimulus applied about 2 cm from recording site. [From Baker et al. 22
Figure 2. Figure 2.

Strength‐duration curve and refractory period in large myelinated fibers of cooled amphibian sciatic nerve. Threshold shock measured as the smallest amplitude shock to the nerve that makes a just‐detectable twitch in an attached whole muscle. A: threshold shock amplitude vs. shock duration for a single rectangular shock.

Data from Lucas 162.] B: threshold shock amplitude for a second shock vs. time after a first suprathreshold stimulus. For the first 3 ms the nerve cannot be reexcited [absolute refractory period (r.p.)]. For the next 7 ms only a supranormal stimulus will excite (relative refractory period). [Data from Adrian & Lucas 4
Figure 3. Figure 3.

Propagated action potential recorded intracellularly from 2 points in a squid giant axon. Recording micropipette electrodes A and B separated by 16 mm. Two traces below are the intracellular potentials recorded simultaneously from the microelectrodes showing a 0.75‐ms delay or propagation time between points A and B, corresponding to a condition velocity of 21.3 m/s. Temperature, 20°C; axon diameter, about 500 μm. STIM, stimulator

Adapted from del Castillo & Moore 53
Figure 4. Figure 4.

Membrane conductance increase during propagated action potential. Squid giant axon at about 6°C. Impedance is measured with the bridge circuit and a very high‐frequency alternating current applied to extracellular electrodes. Conductance increase shows as a widening of the white band of unresolved high‐frequency waves. Time course of action potential is given as a dotted line for comparsion.

From Cole & Curtis 41
Figure 5. Figure 5.

Potassium dependence of the resting potential in squid giant axon. Sum of external [K] and [Na] kept constant as [K]o is varied. Standard Woods Hole seawater has 13 mM K. Potentials (o) measured with axial micropipette electrode are plotted with the assumption that the resting potential in 13 mM K is −64 mV. Curves are theoretical assuming axoplasmic [Cl] is 90 mM, axoplasmic [Na] and [K] as in Table 3, and T = 20°C. Ek: Nernst potential for potassium. A: solution of the Goldman potential equation with Pk:PNa:PCl = 1.0:0.04:0.05. B: same as in A, but with Pk:PCl = 3.0:0.04:0.05

Data from Curtis & Cole 50
Figure 6. Figure 6.

Experiment showing that the action potential is smaller and rises more slowly in solutions containing less than the normal amount of sodium. Squid giant axon with axial micro‐pipette recording electrode. Bathing solutions: records 1 and 3 in seawater; record 2, part A in low‐sodium solution containing 1 part seawater to 2 parts isotonic dextrose; record 2, part B, same as above, but with a 1:1 mixture of seawater and dextrose. Recorded potentials are probably 10–15 mV too positive because of a junction potential between micropipette and axoplasm.

From Hodgkin & Katz 130
Figure 7. Figure 7.

Simplest form of the 3 common voltage‐clamp methods. In each case there is an electrode for voltage recording (E') connected to a high‐impedance follower (x1). The output of the follower is recorded at E and also compared with the voltage‐clamp command pulse by a feedback amplifier (FBA). The highly amplified difference of these signals sends a current through the current‐passing electrode (I') and across the membrane to a ground electrode, where it is recorded (I). Dashed arrows, path of current flow from current‐passing electrode to ground. In the 3 methods the membrane studied is bathed in appropriate saline. In the double‐gap method the central saline pool is separated from end pools by insulating gaps of air, sucrose, oil, or petroleum jelly, and the end pools contain isotonic KCl.
Figure 8. Figure 8.

Different character of voltage‐clamp currents with hyperpolarizing and depolarizing pulses. Outward current shown as an upward deflection. Top: squid axon hyperpolarized by 65 mV from rest to −130 mV at t = 0. Currents are small and inward. Bottom: axon depolarized from −65 mV to 0 mV at t = 0. Currents are biphasic and much larger than under hyperpolarization

Adapted from Hodgkin et al. 129
Figure 9. Figure 9.

Separation of ionic currents in squid giant axon by ionic substitution method. Voltage (E) is stepped from rest to −9 mV at t = 0. A: axon in seawater, showing inward and outward current. B: axon in low‐sodium seawater with 90% of the NaCl replaced by choline chloride, showing only outward current. C: algebraic difference between curves A and B, showing the transient inward component of current that requires external sodium.

From Hodgkin 119, adapted from Hodgkin & Huxley 123
Figure 10. Figure 10.

Ionic currents at large depolarizations showing reversal of early current around sodium equilibrium potential. Squid giant axon under voltage clamp depolarized from rest to the indicated voltages. In the first 0.5 ms the initial current is inward at 26 and 39 mV and outward at 65 and 78 mV. Reversal potential is near 52 mV. As elsewhere in this chapter, potential values are based on the assumption that the resting potential was −65 mV.

From Hodgkin 119, adapted from Hodgkin & Huxley 123
Figure 11. Figure 11.

Sodium ion currents at different voltages, showing that reversal potential falls as external sodium concentration is reduced. Node of Ranvier depolarized under voltage clamp at t = 0 to 7 different voltages spaced 15 mV apart and ranging from −15 to +75 mV. Capacity and leakage current already subtracted and potassium currents blocked by 6 mM TEA ion in all solutions. Sodium concentration (mM) is given under each family of curves. Tetramethylammonium bromide was substituted for NaCl to make the low‐sodium solutions. Labels on current traces are membrane potential in millivolts. The trace at 0 mV and the trace nearest to the reversal potential in each solution are labeled. Dotted line, zero‐current level

Unpublished data, described in Hille 105
Figure 12. Figure 12.

Reversal of the direction of late current by increasing external K+ concentration. Ionic currents, after subtracting leakage, of a node of Ranvier depolarized from rest to −30 mV at t = 0. In Ringer's solution with 120 mM NaCl there is a transient inward sodium current and a small outward late current. To permit better resolution of late current, sodium current has been reduced 8‐fold over normal by inclusion of 30 nM TTX in the medium. When NaCl of Ringer's is replaced by 120 mM KCl, inward sodium current disappears and late current becomes inward as expected for potassium flow with symmetrical potassium concentrations. At the moment the axon is repolarized, the electrical driving force on K+ is increased and a large tail of potassium current appears.
Figure 13. Figure 13.

Pharmacological separation of sodium and potassium currents. Ionic currents with capacity and leakage subtracted of frog myelinated nerve fiber under voltage clamp. Node depolarized at t = 0 to 9 or 10 voltage levels spaced at 15‐mV intervals from −60 to +75 mV. A: normal INa and Ik recorded in Ringer's solution. B: same node in Ringer's solution with 300 nM TTX. Only Ik remains. Temperature, 13°C.

Adapted from Hille 99.] C: normal INa, and Ik of a different node in Ringer's solution. D: same node in Ringer's solution with 6 mM TEA‐ion. Only INa remains. Temperature 11°C. [Adapted from Hille 100
Figure 14. Figure 14.

Current‐voltage relations in Myxicola showing that 1 μM TTX blocks INa but not Ik Myxicola giant axon under voltage clamp. Points are ionic currents during a voltage step from rest to the indicated voltage, measured on families of currents like those in Figs. 10 and 13. Ip, peak early current, consisting primarily of INa and leakage current. Iss, steady‐state current after about 25 ms, consisting of Ik and leakage current. ASW, artificial seawater. Temperature 1–3°C.

From Binstock & Goldman 30
Figure 15. Figure 15.

Electrical equivalent circuit for membrane of squid giant axon showing 4 pathways contributing to membrane current. Two ionic pathways have batteries given by the electromotive force of the appropriate ions and a time variant conductance g. Leakage pathway has a battery and a fixed conductance. Capacitance pathway is a simple capacitor. This circuit gives correct values for membrane current in an isolated patch of membrane and is exactly equivalent to the expressions for current in the Hodgkin‐Huxley analysis. Arrows point in the direction of positive outward current. I, current; E, electromotive force; C, capacitance.
Figure 16. Figure 16.

Time courses of sodium and potassium conductance changes during a depolarizing voltage step. Squid giant axon under voltage clamp. Conductances calculated from currents in Fig. 9 for a step depolarization to −9 mV. Dashed lines, effect of repolarizing the membrane at 0.63 ms when gNa is high or at 6.3 ms when gk is high.

From Hodgkin 119
Figure 17. Figure 17.

Time courses if gNa and gk at 5 potentials. Squid giant axon depolarized to indicated potentials at t = 0. (O) ionic conductances calculated from separated currents at 6.3°C using Eq. 27 and 13. Smooth curves, time courses of gNa and gk calculated from Hodgkin‐Huxley model.

From Hodgkin 119, adapted from Hodgkin & Huxley 124
Figure 18. Figure 18.

Relations among the parameters m, h, n and their products during a depolarization (left) and a repolarization (right). Purely hypothetical case with ratios τm: τh: τn = 1:5:4. Curves for n and m on left and h on right are 1 ‐ exp(‐t/τ), i.e., an exponential rise toward a value of 1.0. Curves for n and m on right and h on left are exp(‐t/τ), i.e., an exponential fall toward a value of 0. Other curves are the indicated powers and products of m, n, and h. Time from origin to repolarization (vertical line) is 4τh),. Unlike a real case, time constants during depolarization and repolarization are assumed to be the same.
Figure 19. Figure 19.

Analysis of sodium inactivation in myelinated nerve under voltage clamp. Left: membrane current elicited by depolarization to −15 mV after a 50‐ms prepulse to the 3 indicated voltages (Ep). Depolarizing prepulses reduce and hyperpolarizing ones increase the inward sodium current by altering the degree of sodium inactivation. Right: voltage dependence of the parameters hz and τh describing sodium inactivation from experiments like those of the left. Normal resting potential (ER) is at −75 mV.

From Dodge 55, copyright 1961 by the American Association for the Advancement of Science
Figure 20. Figure 20.

Time constants τm, τh, and τn and steady‐state values mx, hx, and nx from the Hodgkin‐Huxley model at 6.3°C. Calculated from Eq. 29–34 of the model using relations of Eqs. 20 and 21.

From Hille 103
Figure 21. Figure 21.

Time course of the propagated action potential calculated from the Hodgkin‐Huxley model. Stimulating current of 10 μA is applied for 0.2 ms at x = 0. Time course of action potential is shown at 4 positions in the axon, up to 3 cm from the stimulus. Compare with Fig. 3. Assumptions: axon diameter, 476 μm; resistivity of axoplasm, 35.4 Ω‐cm; resting potential, −65 mV

Adapted from Cooley & Dodge 49
Figure 22. Figure 22.

Comparison of propagated action potentials calculated from the Hodgkin‐Huxley model and measured on a real squid giant axon. Real fiber had a diameter of 476 μm, axoplasmic resistivity of 35.4 Ω‐cm, and conduction velocity of 21.2 m/s. The computed spike travels at 18.7 m/s with the same diameter and resistivity

Adapted from Hodgkin & Huxley 126
Figure 23. Figure 23.

Calculated time courses of the uniformly propagated action potential and underlying sodium and potassium conductance changes from the Hodgkin‐Huxley model. The voltage levels corresponding to the reversal potentials ENa and Ek are also shown. E1. is at −53 mV but is not shown. Assumed temperature 18.5°C. From same calculation as Fig. 22

Adapted from Hodgkin & Huxley 126
Figure 24. Figure 24.

Summary of the currents and membrane changes during the propagated action potential in the squid giant axon. All curves calculated from the Hodgkin‐Huxley equations at 18.5°C. A: membrane current and its ionic and capacitive components. B: membrane potential and the controlling parameters m, h, and n. C: total membrane conductance and its sodium and potassium components. D: ionic current and its sodium and potassium components

Adapted from Cooley & Dodge 48
Figure 25. Figure 25.

Different character of membrane current at the node of Ranvier and in the internode. Single myelinated fiber from a frog passes across 2 air gaps. Radial or membrane current during the propagated action potential is recorded as a voltage drop across the resistor R. Current is the lower noisy trace. Upper trace, rough sketch approximating time course of an action potential at 24°C. A: biphasic current from the node and neighboring internode. B: current from 1 mm of internode. 1–3, 3 pools of Ringer's solution.

Adapted from Tasaki 211
Figure 26. Figure 26.

Action potential and ionic currents in a repetitively firing neuron of Anisodoris at 5°C. A: comparison of experimentally recorded time course of firing and the time course predicted from the Connor‐Stevens 47 equations (arrows). Steady depolarizing current of 1.6 nA is turned on near the beginning of the trace. Repetitive firing at a frequency of 1.7 spikes/s is initiated. Reversal potentials El, EL, Ek, and EA of the 4 ionic current components are indicated on right. B: time courses of 3 of the ionic current components, considerably magnified to show better the subthreshold changes that control repetitive firing. Normalizing to the 14‐nF capacity of the cell indicates that 1 nA corresponds to a current density of only 0.07 μA/cm2

Adapted from Connor & Stevens 47


Figure 1.

Intracellularly recorded resting and action potentials from several nerve cells. A: single node of Ranvier of rat myelinated nerve fiber at 37°C. Brief stimulus applied at same node. (W. Nonner, M. Horáčkova, and R. Stämpfli, unpublished data.) B: same type of recording from frog myelinated fiber as in A, but at 22°C.

From Dodge 56.] C: cat lumbar spinal motoneuron at 37°C, excited antidromically by stimulation of motor axon. (W. E. Crill, unpublished data.) D: propagating action potential in squid giant axon at 16°C. Stimulus applied about 2 cm from recording site. [From Baker et al. 22


Figure 2.

Strength‐duration curve and refractory period in large myelinated fibers of cooled amphibian sciatic nerve. Threshold shock measured as the smallest amplitude shock to the nerve that makes a just‐detectable twitch in an attached whole muscle. A: threshold shock amplitude vs. shock duration for a single rectangular shock.

Data from Lucas 162.] B: threshold shock amplitude for a second shock vs. time after a first suprathreshold stimulus. For the first 3 ms the nerve cannot be reexcited [absolute refractory period (r.p.)]. For the next 7 ms only a supranormal stimulus will excite (relative refractory period). [Data from Adrian & Lucas 4


Figure 3.

Propagated action potential recorded intracellularly from 2 points in a squid giant axon. Recording micropipette electrodes A and B separated by 16 mm. Two traces below are the intracellular potentials recorded simultaneously from the microelectrodes showing a 0.75‐ms delay or propagation time between points A and B, corresponding to a condition velocity of 21.3 m/s. Temperature, 20°C; axon diameter, about 500 μm. STIM, stimulator

Adapted from del Castillo & Moore 53


Figure 4.

Membrane conductance increase during propagated action potential. Squid giant axon at about 6°C. Impedance is measured with the bridge circuit and a very high‐frequency alternating current applied to extracellular electrodes. Conductance increase shows as a widening of the white band of unresolved high‐frequency waves. Time course of action potential is given as a dotted line for comparsion.

From Cole & Curtis 41


Figure 5.

Potassium dependence of the resting potential in squid giant axon. Sum of external [K] and [Na] kept constant as [K]o is varied. Standard Woods Hole seawater has 13 mM K. Potentials (o) measured with axial micropipette electrode are plotted with the assumption that the resting potential in 13 mM K is −64 mV. Curves are theoretical assuming axoplasmic [Cl] is 90 mM, axoplasmic [Na] and [K] as in Table 3, and T = 20°C. Ek: Nernst potential for potassium. A: solution of the Goldman potential equation with Pk:PNa:PCl = 1.0:0.04:0.05. B: same as in A, but with Pk:PCl = 3.0:0.04:0.05

Data from Curtis & Cole 50


Figure 6.

Experiment showing that the action potential is smaller and rises more slowly in solutions containing less than the normal amount of sodium. Squid giant axon with axial micro‐pipette recording electrode. Bathing solutions: records 1 and 3 in seawater; record 2, part A in low‐sodium solution containing 1 part seawater to 2 parts isotonic dextrose; record 2, part B, same as above, but with a 1:1 mixture of seawater and dextrose. Recorded potentials are probably 10–15 mV too positive because of a junction potential between micropipette and axoplasm.

From Hodgkin & Katz 130


Figure 7.

Simplest form of the 3 common voltage‐clamp methods. In each case there is an electrode for voltage recording (E') connected to a high‐impedance follower (x1). The output of the follower is recorded at E and also compared with the voltage‐clamp command pulse by a feedback amplifier (FBA). The highly amplified difference of these signals sends a current through the current‐passing electrode (I') and across the membrane to a ground electrode, where it is recorded (I). Dashed arrows, path of current flow from current‐passing electrode to ground. In the 3 methods the membrane studied is bathed in appropriate saline. In the double‐gap method the central saline pool is separated from end pools by insulating gaps of air, sucrose, oil, or petroleum jelly, and the end pools contain isotonic KCl.



Figure 8.

Different character of voltage‐clamp currents with hyperpolarizing and depolarizing pulses. Outward current shown as an upward deflection. Top: squid axon hyperpolarized by 65 mV from rest to −130 mV at t = 0. Currents are small and inward. Bottom: axon depolarized from −65 mV to 0 mV at t = 0. Currents are biphasic and much larger than under hyperpolarization

Adapted from Hodgkin et al. 129


Figure 9.

Separation of ionic currents in squid giant axon by ionic substitution method. Voltage (E) is stepped from rest to −9 mV at t = 0. A: axon in seawater, showing inward and outward current. B: axon in low‐sodium seawater with 90% of the NaCl replaced by choline chloride, showing only outward current. C: algebraic difference between curves A and B, showing the transient inward component of current that requires external sodium.

From Hodgkin 119, adapted from Hodgkin & Huxley 123


Figure 10.

Ionic currents at large depolarizations showing reversal of early current around sodium equilibrium potential. Squid giant axon under voltage clamp depolarized from rest to the indicated voltages. In the first 0.5 ms the initial current is inward at 26 and 39 mV and outward at 65 and 78 mV. Reversal potential is near 52 mV. As elsewhere in this chapter, potential values are based on the assumption that the resting potential was −65 mV.

From Hodgkin 119, adapted from Hodgkin & Huxley 123


Figure 11.

Sodium ion currents at different voltages, showing that reversal potential falls as external sodium concentration is reduced. Node of Ranvier depolarized under voltage clamp at t = 0 to 7 different voltages spaced 15 mV apart and ranging from −15 to +75 mV. Capacity and leakage current already subtracted and potassium currents blocked by 6 mM TEA ion in all solutions. Sodium concentration (mM) is given under each family of curves. Tetramethylammonium bromide was substituted for NaCl to make the low‐sodium solutions. Labels on current traces are membrane potential in millivolts. The trace at 0 mV and the trace nearest to the reversal potential in each solution are labeled. Dotted line, zero‐current level

Unpublished data, described in Hille 105


Figure 12.

Reversal of the direction of late current by increasing external K+ concentration. Ionic currents, after subtracting leakage, of a node of Ranvier depolarized from rest to −30 mV at t = 0. In Ringer's solution with 120 mM NaCl there is a transient inward sodium current and a small outward late current. To permit better resolution of late current, sodium current has been reduced 8‐fold over normal by inclusion of 30 nM TTX in the medium. When NaCl of Ringer's is replaced by 120 mM KCl, inward sodium current disappears and late current becomes inward as expected for potassium flow with symmetrical potassium concentrations. At the moment the axon is repolarized, the electrical driving force on K+ is increased and a large tail of potassium current appears.



Figure 13.

Pharmacological separation of sodium and potassium currents. Ionic currents with capacity and leakage subtracted of frog myelinated nerve fiber under voltage clamp. Node depolarized at t = 0 to 9 or 10 voltage levels spaced at 15‐mV intervals from −60 to +75 mV. A: normal INa and Ik recorded in Ringer's solution. B: same node in Ringer's solution with 300 nM TTX. Only Ik remains. Temperature, 13°C.

Adapted from Hille 99.] C: normal INa, and Ik of a different node in Ringer's solution. D: same node in Ringer's solution with 6 mM TEA‐ion. Only INa remains. Temperature 11°C. [Adapted from Hille 100


Figure 14.

Current‐voltage relations in Myxicola showing that 1 μM TTX blocks INa but not Ik Myxicola giant axon under voltage clamp. Points are ionic currents during a voltage step from rest to the indicated voltage, measured on families of currents like those in Figs. 10 and 13. Ip, peak early current, consisting primarily of INa and leakage current. Iss, steady‐state current after about 25 ms, consisting of Ik and leakage current. ASW, artificial seawater. Temperature 1–3°C.

From Binstock & Goldman 30


Figure 15.

Electrical equivalent circuit for membrane of squid giant axon showing 4 pathways contributing to membrane current. Two ionic pathways have batteries given by the electromotive force of the appropriate ions and a time variant conductance g. Leakage pathway has a battery and a fixed conductance. Capacitance pathway is a simple capacitor. This circuit gives correct values for membrane current in an isolated patch of membrane and is exactly equivalent to the expressions for current in the Hodgkin‐Huxley analysis. Arrows point in the direction of positive outward current. I, current; E, electromotive force; C, capacitance.



Figure 16.

Time courses of sodium and potassium conductance changes during a depolarizing voltage step. Squid giant axon under voltage clamp. Conductances calculated from currents in Fig. 9 for a step depolarization to −9 mV. Dashed lines, effect of repolarizing the membrane at 0.63 ms when gNa is high or at 6.3 ms when gk is high.

From Hodgkin 119


Figure 17.

Time courses if gNa and gk at 5 potentials. Squid giant axon depolarized to indicated potentials at t = 0. (O) ionic conductances calculated from separated currents at 6.3°C using Eq. 27 and 13. Smooth curves, time courses of gNa and gk calculated from Hodgkin‐Huxley model.

From Hodgkin 119, adapted from Hodgkin & Huxley 124


Figure 18.

Relations among the parameters m, h, n and their products during a depolarization (left) and a repolarization (right). Purely hypothetical case with ratios τm: τh: τn = 1:5:4. Curves for n and m on left and h on right are 1 ‐ exp(‐t/τ), i.e., an exponential rise toward a value of 1.0. Curves for n and m on right and h on left are exp(‐t/τ), i.e., an exponential fall toward a value of 0. Other curves are the indicated powers and products of m, n, and h. Time from origin to repolarization (vertical line) is 4τh),. Unlike a real case, time constants during depolarization and repolarization are assumed to be the same.



Figure 19.

Analysis of sodium inactivation in myelinated nerve under voltage clamp. Left: membrane current elicited by depolarization to −15 mV after a 50‐ms prepulse to the 3 indicated voltages (Ep). Depolarizing prepulses reduce and hyperpolarizing ones increase the inward sodium current by altering the degree of sodium inactivation. Right: voltage dependence of the parameters hz and τh describing sodium inactivation from experiments like those of the left. Normal resting potential (ER) is at −75 mV.

From Dodge 55, copyright 1961 by the American Association for the Advancement of Science


Figure 20.

Time constants τm, τh, and τn and steady‐state values mx, hx, and nx from the Hodgkin‐Huxley model at 6.3°C. Calculated from Eq. 29–34 of the model using relations of Eqs. 20 and 21.

From Hille 103


Figure 21.

Time course of the propagated action potential calculated from the Hodgkin‐Huxley model. Stimulating current of 10 μA is applied for 0.2 ms at x = 0. Time course of action potential is shown at 4 positions in the axon, up to 3 cm from the stimulus. Compare with Fig. 3. Assumptions: axon diameter, 476 μm; resistivity of axoplasm, 35.4 Ω‐cm; resting potential, −65 mV

Adapted from Cooley & Dodge 49


Figure 22.

Comparison of propagated action potentials calculated from the Hodgkin‐Huxley model and measured on a real squid giant axon. Real fiber had a diameter of 476 μm, axoplasmic resistivity of 35.4 Ω‐cm, and conduction velocity of 21.2 m/s. The computed spike travels at 18.7 m/s with the same diameter and resistivity

Adapted from Hodgkin & Huxley 126


Figure 23.

Calculated time courses of the uniformly propagated action potential and underlying sodium and potassium conductance changes from the Hodgkin‐Huxley model. The voltage levels corresponding to the reversal potentials ENa and Ek are also shown. E1. is at −53 mV but is not shown. Assumed temperature 18.5°C. From same calculation as Fig. 22

Adapted from Hodgkin & Huxley 126


Figure 24.

Summary of the currents and membrane changes during the propagated action potential in the squid giant axon. All curves calculated from the Hodgkin‐Huxley equations at 18.5°C. A: membrane current and its ionic and capacitive components. B: membrane potential and the controlling parameters m, h, and n. C: total membrane conductance and its sodium and potassium components. D: ionic current and its sodium and potassium components

Adapted from Cooley & Dodge 48


Figure 25.

Different character of membrane current at the node of Ranvier and in the internode. Single myelinated fiber from a frog passes across 2 air gaps. Radial or membrane current during the propagated action potential is recorded as a voltage drop across the resistor R. Current is the lower noisy trace. Upper trace, rough sketch approximating time course of an action potential at 24°C. A: biphasic current from the node and neighboring internode. B: current from 1 mm of internode. 1–3, 3 pools of Ringer's solution.

Adapted from Tasaki 211


Figure 26.

Action potential and ionic currents in a repetitively firing neuron of Anisodoris at 5°C. A: comparison of experimentally recorded time course of firing and the time course predicted from the Connor‐Stevens 47 equations (arrows). Steady depolarizing current of 1.6 nA is turned on near the beginning of the trace. Repetitive firing at a frequency of 1.7 spikes/s is initiated. Reversal potentials El, EL, Ek, and EA of the 4 ionic current components are indicated on right. B: time courses of 3 of the ionic current components, considerably magnified to show better the subthreshold changes that control repetitive firing. Normalizing to the 14‐nF capacity of the cell indicates that 1 nA corresponds to a current density of only 0.07 μA/cm2

Adapted from Connor & Stevens 47
References
 1. Adelman, W. J., Jr. (Editor). Biophysics and Physiology of Excitable Membranes. New York: Van Nostrand Reinhold, 1971.
 2. Adelman, W. J., Jr., and Y. Palti. The effects of external potassium and long duration voltage conditioning on the amplitude of sodium currents in the giant axon of the squid, Loligo pealei. J. Gen. Physiol. 54: 589–606, 1969.
 3. Adelman, W. J., Jr., and J. P. Senft. Voltage clamp studies on the effect of internal cesium ion on sodium and potassium currents in the squid giant axon. J. Gen. Physiol. 50: 279–293, 1966.
 4. Adrian, E. D., and K. Lucas. On the summation of propagated disturbances in nerve and muscle. J. Physiol. London 44: 68–124, 1912.
 5. Adrian, R. H., W. K. Chandler, and A. L. Hodgkin. Voltage clamp experiments in striated muscle fibres. J. Physiol. London 208: 607–644, 1970.
 6. Agin, D. Hodgkin‐Huxley equations: logarithmic relation between membrane current and frequency of repetitive activity. Nature 201: 625–626, 1964.
 7. Agin, D. P. (Editor). Perspectives in Membrane Biophysics, a Tribute to Kenneth S. Cole. New York: Gordon and Breach, 1972.
 8. Almers, W., and S. R. Levinson. Tetrodotoxin binding to normal and depolarized frog muscle and the conductance of a single sodium channel. J. Physiol. London 247: 483–509, 1975.
 9. Anderson, N. C., Jr. Voltage‐clamp studies on uterine smooth muscle. J. Gen. Physiol. 54: 145–165, 1969.
 10. Armstrong, C. M. Time course of TEA+‐induced anomalous rectification in squid giant axons. J. Gen. Physiol. 50: 491–503, 1966.
 11. Armstrong, C. M. Inactivation of the potassium conductance and related phenomena caused by quaternary ammonium ion injection in squid axons. J. Gen. Physiol. 54: 553–575, 1969.
 12. Armstrong, C. M. Interaction of tetraethylammonium ion derivatives with the potassium channels of giant axons. J. Gen. Physiol. 58: 413–437, 1971.
 13. Armstrong, C. M. Channels and voltage dependent gates in nerve. In: Membranes — a Series of Advances. Artificial and Biological Membranes, edited by G. Eisenman. New York: Dekker, 1975, vol. 3, 325–358.
 14. Armstrong, C. M. Ionic pores, gates, and gating currents. Quart. Rev. Biophys. 7: 179–210, 1974.
 15. Armstrong, C. M., and F. Bezanilla. Currents related to movement of the gating particles of the sodium channels. Nature 242: 459–461, 1973.
 16. Armstrong, C. M., and F. Bezanilla. Charge movement associated with the opening and closing of the activation gates of the Na channels. J. Gen. Physiol. 63: 533–552, 1974.
 17. Armstrong, C. M., F. Bezanilla, and E. Rojas. Destruction of sodium conductance inactivation in squid axons perfused with pronase. J. Gen. Physiol. 62: 375–391, 1973.
 18. Armstrong, C. M., and L. Binstock. Anomalous rectification in the squid giant axon injected with tetraethylammonium chloride. J. Gen. Physiol. 48: 859–872, 1965.
 19. Armstrong, C. M., and B. Hille. The inner quaternary ammonium ion receptor in potassium channels of the node of Ranvier. J. Gen. Physiol. 59: 388–400, 1972.
 20. Arrhenius, S. Öber die Dissociation in Wasser geloUster Stoffe. Z. Physik. Chem. Leipzig 1: 631–648, 1887.
 21. Asano, T., and W. P. Hurlbut. Effects of potassium, sodium, and azide on the ionic movements that accompany activity in frog nerves. J. Gen. Physiol. 41: 1187–1203, 1958.
 22. Atwater, I., F. Bezanilla, and E. Rojas. Sodium influxes in internally perfused squid giant axons during voltage clamp. J. Physiol. London 201: 657–664, 1969.
 23. Baker, P. F. Transport and metabolism of calcium ions in nerve. Progr. Biophys. Mol. Biol. 24: 177–223, 1972.
 24. Baker, P. F., A. L. Hodgkin, and E. B. Ridgway. Depolarization and calcium entry in squid giant axons. J. Physiol. London 218: 709–755, 1971.
 25. Baker, P. F., A. L. Hodgkin, and T. I. Shaw. Replacement of the axoplasm of giant nerve fibres with artificial solutions. J. Physiol. London 164: 330–354, 1962.
 26. Baker, P. F., and J. S. Willis. On the number of sodium pumping sites in cell membranes. Biochim. Biophys. Acta 183: 646–649, 1969.
 27. Beeler, G. W., and H. Reuter. The relation between membrane potential, membrane currents and activation of contraction in ventricular myocardial fibres. J. Physiol. London 207: 211–229, 1970.
 28. Beeler, G. W., Jr., and H. Reuter. Membrane calcium current in ventricular myocardial fibres. J. Physiol. London 207: 191–209, 1970.
 29. Bennett, M. V. L. Comparative physiology: electric organs. Ann. Rev. Physiol. 32: 471–528, 1970.
 30. Bernstein, J. Untersuchungen zur Thermodynamik der bioelektrischen Strötne. Erster Theil. Pfluegers Arch. Ges. Physiol. 92: 521–562, 1902.
 31. Bernstein, J. Elektrobiologie. Braunschweig: Vieweg, 1912.
 32. Bezanilla, F., and C. M. Armstrong. Negative conductance caused by entry of sodium and cesium ions into the potassium channels of squid axons. J. Gen. Physiol. 60: 588–608, 1972.
 33. Bezanilla, F., E. Rojas, and R. E. Taylor. Time course of the sodium influx in squid giant axon during a single voltage clamp pulse. J. Physiol. London 207: 151–164, 1970.
 34. Binstock, L., and L. Goldman. Current‐ and voltage‐clamped studies on Myxicola giant axons. Effect of tetrodotoxin. J. Gen. Physiol. 54: 730–740, 1969.
 35. Blankenship, J. E. Action of tetrodotoxin on spinal motoneurons of the cat. J. Neurophysiol. 31: 186–194, 1968.
 36. Bunch, W. H., and G. Kallsen. Rate of intracellular diffusion as measured in barnacle muscle. Science 164: 1178–1179, 1969.
 37. Burg, D. Untersuchungen am Ranvierschen Schnürring einzelner Taubennervenfasern. Pfluegers Arch. Ges. Physiol. 317: 278–286, 1970.
 38. Burrows, T. M. O., I. A. Campbell, E. J. Howe, and J. Z. Young. Conduction velocity and diameter of nerve fibres of cephalopods. J. Physiol. London 179: 39P–40P, 1965.
 39. Chandler, W. K., A. L. Hodgkin, and H. Meves. The effect of changing the internal solution on sodium inactivation and related phenomena in giant axons. J. Physiol. London 180: 821–836, 1965.
 40. Chandler, W. K., and H. Meves. Voltage clamp experiments on internally perfused giant axons. J. Physiol. London 180: 788–820, 1965.
 41. Chandler, W. K., and H. Meves. Sodium and potassium currents in squid axons perfused with fluoride solutions. J. Physiol. London 211: 623–652, 1970.
 42. Cohen, L. B. Changes in neuron structure during action potential propagation and synaptic transmission. Physiol. Rev. 53: 373–418, 1973.
 43. Cole, K. S. Dynamic electrical characteristics of the squid axon membrane. Arch. Sci. Physiol. 3: 253–258, 1949.
 44. Cole, K. S. Membranes, Ions and Impulses. A Chapter of Classical Biophysics. Berkeley: Univ. of California Press, 1968.
 45. Cole, K. S., and R. F. Baker. Transverse impedance of the squid giant axon during current flow. J. Gen. Physiol. 24: 535–549, 1941.
 46. Cole, K. S., and H. J. Curtis. Electric impedance of the squid giant axon during activity. J. Gen. Physiol. 22: 649–670, 1939.
 47. Cole, K. S., and J. W. Moore. Ionic current measurements in the squid giant axon membrane. J. Gen. Physiol. 44: 123–167, 1960.
 48. Colquhoun, D., R. Henderson, and J. M. Ritchie. The binding of labelled tetrodotoxin to non‐myelinated nerve fibres. J. Physiol. London 227: 95–126, 1972.
 49. Colquhoun, D., and J. M. Ritchie. The interaction at equilibrium between tetrodotoxin and mammalian non‐myelinated nerve fibres. J. Physiol. London 221: 533–553, 1972.
 50. Connor, J. A., and C. F. Stevens. Inward and delayed outward membrane currents in isolated neural somata under voltage clamp. J. Physiol. London 213: 1–19, 1971.
 51. Connor, J. A., and C. F. Stevens. Voltage clamp studies of a transient outward membrane current in gastropod neural somata. J. Physiol. London 213: 21–30, 1971.
 52. Connor, J. A., and C. F. Stevens. Prediction of repetitive firing behaviour from voltage clamp data on an isolated neurone soma. J. Physiol. London 213: 31–53, 1971.
 53. Cooley, J. W., and F. A. Dodge. Digital computer solutions for excitation and propagation of the nerve impulse. IBM Res. Rept. 1496, 1965.
 54. Cooley, J. W., and F. A. Dodge. Digital computer solutions for excitation and propagation of the nerve impulse. Biophys. J. 6: 583–599, 1966.
 55. Coppin, C. M. L., and J. J. B. Jack. Internodal length and conduction velocity of cat muscle afferent nerve fibres. J. Physiol. London 222: 91P–93P, 1971.
 56. Curtis, H. J., and K. S. Cole. Membrane resting and action potentials from the squid giant axon. J. Cell. Comp. Physiol. 19: 135–144, 1942.
 57. Deck, K. A., R. Kern, and W. Trautwein. Voltage clamp technique in mammalian cardiac fibres. Pfluegers Arch. Ges. Physiol. 280: 50–62, 1964.
 58. Deck, K. A., and W. Trautwein. Ionic currents in cardiac excitation. Pfluegers Arch. Ges. Physiol. 280: 63–80, 1964.
 59. Del Castillo, J., and J. W. Moore. On increasing the velocity of a nerve impulse. J. Physiol. London 148: 665–670, 1959.
 60. De Weer, P., and D. Geduldig. Electrogenic sodium pump in squid giant axon. Science 179: 1326–1328, 1973.
 61. Dodge, F. A. Ionic permeability changes underlying nerve excitation. In: Biophysics of Physiological and Pharmacological Actions. Washington, D.C.: Am. Assoc. Advan. Sci., 1961, p. 119.
 62. Dodge, F. A. A Study of Ionic Permeability Changes Underlying Excitation in Myelinated Nerve Fibers of the Frog (Ph.D. thesis). New York: The Rockefeller University, 1963. [University Microfilms, Inc., Ann Arbor, Mich. (No. 64–7333).]
 63. Dodge, F. A., and B. Frankenhaeuser. Membrane currents in isolated frog nerve fibre under voltage clamp conditions. J. Physiol. London 143: 76–90, 1958.
 64. Dodge, F. A., and B. Frankenhaeuser. Sodium currents in the myelinated nerve fibre of Xenopus laevis investigated with the voltage clamp technique. J. Physiol. London 148: 188–200, 1959.
 65. Ehrenstein, G., and D. L. Gilbert. Slow changes of potassium permeability in the squid giant axon. Biophys. J. 6: 553–566, 1966.
 66. Ehrenstein, G., and H. Lecar. The mechanism of signal transmission in nerve axons. Ann. Rev. Biophys. Bioeng. 1: 347–368, 1972.
 67. Einstein, A. On the movement of small particles suspended in a stationary liquid demanded by the molecular‐kinetic theory on heat. Ann. Physik Leipzig 17: 549–560, 1905. [Reprinted in: Einstein, A. Investigations on the Theory of the Brownian Movement. New York: Dover, 1956.]
 68. Eisenman, G. Cation selective glass electrodes and their mode of operation. Biophys. J. 2, Suppl. 2: 259–323, 1962.
 69. Erlanger, J., and E. A. Blair. Manifestation of segmentation in myelinated axons. Am. J. Physiol. 110: 287–311, 1934.
 70. Erlanger, J., and H. S. Gasser. Electrical Signs of Nervous Activity. Philadelphia: Univ. of Pennsylvania Press, 1937.
 71. Evans, M. H. Tetrodotoxin, saxitoxin, and related substances: their applications in neurobiology. Intern. Rev. Neurobiol. 15: 83–166, 1972.
 72. Eyring, H., D. Henderson, B. J. Stover, and E. M. Eyring. Statistical Mechanics and Dynamics. New York: Wiley, 1964.
 73. Eyring, H., R. Lumry, and J. W. Woodbury. Some applications of modern rate theory to physiological systems. Record Chem. Progr. Kresge‐Hooker Sci. Lib. 10: 100–114, 1949.
 74. Fatt, P., and B. L. Ginsborg. The ionic requirements for the production of action potentials in crustacean muscle fibres. J. Physiol. London 142: 516–543, 1958.
 75. Fatt, P., and B. Katz. The electrical properties of crustacean muscle fibres. J. Physiol. London 120: 171–204, 1953.
 76. FitzHugh, R. A kinetic model of the conductance changes in nerve membrane. J. Cell. Comp. Physiol. 66, Suppl. 2: 111–117, 1965.
 77. FitzHugh, R., and H. A. Antosiewicz. Automatic computation of nerve excitation—detailed corrections and additions. J. Soc. Ind. Appl. Math. 7: 447–458, 1959.
 78. Frankenhaeuser, B. A method for recording resting and action potentials in the isolated myelinated nerve fibre of the frog. J. Physiol. London 135: 550–559, 1957.
 79. Frankenhaeuser, B. Quantitative description of sodium currents in myelinated nerve fibres of Xenopus laevis. J. Physiol. London 151: 491–501, 1960.
 80. Frankenhaeuser, B. Sodium permeability in toad nerve and in squid nerve. J. Physiol. London 152: 159–166, 1960.
 81. Frankenhaeuser, B. A quantitative description of potassium currents in myelinated nerve fibres of Xenopus laevis. J. Physiol. London 169: 424–430, 1963.
 82. Frankenhaeuser, B. Computed action potential in nerve from Xenopus laevis. J. Physiol. London 180: 780–787, 1965.
 83. Frankenhaeuser, B., and A. L. Hodgkin. The after‐effects of impulses in the giant nerve fibres of Loligo. J. Physiol. London 131: 341–376, 1956.
 84. Frankenhaeuser, B., and A. L. Hodgkin. The action of calcium on the electrical properties of squid axons. J. Physiol. London 137: 218–244, 1957.
 85. Frankenhaeuser, B., and A. F. Huxley. The action potential in the myelinated nerve fibre of Xenopus laevis as computed on the basis of voltage clamp data. J. Physiol. London 171: 302–315, 1964.
 86. Frankenhaeuser, B., and L. E. Moore. The effect of temperature on the sodium and potassium permeability changes in myelinated nerve fibres of Xenopus laevis. J. Physiol. London 169: 431–437, 1963.
 87. Frazier, D. T., T. Narahashi, and M. Yamada. The site of action and active form of local anesthetics. II. Experiments with quaternary compounds. J. Pharmacol. Exptl. Therap. 171: 45–51, 1970.
 88. Gasser, H. S. Unmedullated fibers originating in dorsal root ganglia. J. Gen. Physiol. 33: 651–690, 1950.
 89. Geduldig, D., and R. Gruener. Voltage clamp of the Aplysia giant neurone: early sodium and calcium currents. J. Physiol. London 211: 217–244, 1970.
 90. Gerasimov, V. D., P. G. Kostyuk, and V. A. Maiskii. Effect of bivalent cations on the electrical characteristics of the membrane of giant neurones. Biofizika 10: 447–453, 1965.
 91. Gilbert, D. L., and G. Ehrenstein. Effect of divalent cations on potassium conductance of squid axons: determination of surface charge. Biophys. J. 9: 447–463, 1969.
 92. Goldman, D. E. Potential, impedance, and rectification in membranes. J. Gen. Physiol. 27: 37–60, 1943.
 93. Goldman, L., and J. S. Albus. Computation of impulse conduction in myelinated fibers; theoretical basis of the velocity‐diameter relation. Biophys. J. 8: 596–607, 1968.
 94. Goldman, L., and C. L. Schauf. Inactivation of the sodium current in Myxicola giant axons. Evidence for coupling to the activation process. J. Gen. Physiol. 59: 659–675, 1972.
 95. Goldman, L., and C. L. Schauf. Quantitative description of sodium and potassium currents and computed action potentials in Myxicola giant axons. J. Gen. Physiol. 61: 361–384, 1973.
 96. Hagiwara, S. Ca++ dependent action potentials. In: Membranes — a Series of Advances. Artificial and Biological Membranes, edited by G. Eisenman. New York: Dekker, 1975, vol. 3, 359–382.
 97. Hagiwara, S., J. Fukuda, and D. C. Eaton. Membrane currents carried by Ca, Sr, and Ba in barnacle muscle fiber during voltage clamp. J. Gen. Physiol. 63: 564–578, 1974.
 98. Hagiwara, S., H. Hayashi, and K. Takahashi. Calcium and potassium currents of the membrane of a barnacle muscle fibre in relation to the calcium spike. J. Physiol. London 205: 115–129, 1969.
 99. Hagiwara, S., and K‐I. Naka. The initiation of spike potential in barnacle muscle fibers under low intracellular Ca++ J. Gen. Physiol. 48: 141–162, 1964.
 100. Hagiwara, S., and S. Nakajima. Differences in Na and Ca spikes as examined by application of tetrodotoxin, procaine, and manganese ions. J. Gen. Physiol. 49: 793–806, 1966.
 101. Hagiwara, S., and K. Takahashi. Surface density of calcium ions and calcium spikes in the barnacle muscle fiber membrane. J. Gen. Physiol. 50: 583–601, 1967.
 102. Hardy, W. L. Propagation speed in myelinated nerve: theoretical dependence on external Na+ and on temperature. Biophys. J. 13: 1071–1089, 1973.
 103. Heckmann, K. Single‐file diffusion. In: Passive Permeability of Cell Membranes. Biomembranes, edited by F. Kreuzer and J. K. S. Jansen. New York: Plenum Press, 1972, vol. 3, 127–153.
 104. Henderson, R., J. M. Ritchie, and G. R. Strichartz. The binding of labelled saxitoxin to the sodium channels in nerve membranes. J. Physiol. London 235: 783–804, 1973.
 105. Henderson, R., and J. H. Wang. Solubilization of a specific tetrodotoxin‐binding component from garfish olfactory nerve membrane. Biochemistry 11: 4565–4569, 1972.
 106. Hille, B. The common mode of action of three agents that decrease the transient change in sodium permeability in nerves. Nature 210: 1220–1222, 1966.
 107. Hille, B. The selective inhibition of delayed potassium currents in nerve by tetraethylammonium ion. J. Gen. Physiol. 50: 1287–1302, 1967.
 108. Hille, B. Pharmacological modifications of the sodium channels of frog nerve. J. Gen. Physiol. 51: 199–219, 1968.
 109. Hille, B. Charges and potentials at the nerve surface. Divalent ions and pH. J. Gen. Physiol. 51: 221–236, 1968.
 110. Hille, B. Ionic channels in nerve membranes. Progr. Biophys. Mol. Biol. 21: 1–32, 1970.
 111. Hille, B. Voltage clamp studies on myelinated nerve fibers. In: Biophysics and Physiology and Excitable Membranes, edited by W. J. Adelman, Jr. New York: Van Nostrand Reinhold, 1971.
 112. Hille, B. The permeability of the sodium channel to organic cations in myelinated nerve. J. Gen. Physiol. 58: 599–619, 1971.
 113. Hille, B. The permeability of the sodium channel to metal cations in myelinated nerve. J. Gen. Physiol. 59: 637–658, 1972.
 114. Hille, B. Potassium channels in myelinated nerve. Selective permeability to small cations. J. Gen. Physiol. 61: 669–686, 1973.
 115. Hille, B. Ionic selectivity of Na and K channels of nerve membranes. In: Membranes — a Series of Advances. Artificial and Biological Membranes, edited by G. Eisenman. New York: Dekker, 1975, vol. 3, 255–324.
 116. Hille, B., A. M. Woodhull, and B. I. Shapiro. Negative surface charge near sodium channels of nerve: divalent ions, monovalent ions, and pH. Phil. Trans. Roy. Soc. 270: 301–318, 1975.
 117. Hinke, J. A. M. The measurement of sodium and potassium activities in the squid axon by means of cation‐selective glass microelectrodes. J. Physiol. London 156: 314–335, 1961.
 118. Hinke, J. A. M. Solvent water for electrolytes in the muscle fiber of the giant barnacle. J. Gen. Physiol. 56: 521–541, 1970.
 119. Hinke, J. A. M., J. P. Caillé, and D. C. Gayton. Distribution and state of monovalent ions in skeletal muscle based on ion electrode, isotope, and diffusion analyses. Ann. NY Acad. Sci. 204: 274–296, 1973.
 120. Hirst, G. D. S., and I. Spence. Calcium action potentials in mammalian peripheral neurones. Nature New Biol. 243: 54–56, 1973.
 121. Hodgkin, A. L. Evidence for electrical transmission in nerve. Part I. J. Physiol. London 90: 183–210, 1937.
 122. Hodgkin, A. L. Evidence for electrical transmission in nerve. Part II. J. Physiol. London 90: 211–232, 1937.
 123. Hodgkin, A. L. The subthreshold potentials in a crustacean nerve fibre. Proc. Roy. Soc. London Ser. B 126: 87–121, 1938.
 124. Hodgkin, A. L. The local electrical changes associated with repetitive action in a non‐medullated axon. J. Physiol. London 107: 165–179, 1948.
 125. Hodgkin, A. L. The ionic basis of electrical activity in nerve and muscle. Biol. Rev. 26: 339–409, 1951.
 126. Hodgkin, A. L. A note on conduction velocity. J. Physiol. London 125: 221–224, 1954.
 127. Hodgkin, A. L. Ionic movements and electrical activity in giant nerve fibres. Proc. Roy. Soc. London Ser. B 148: 1–37, 1958.
 128. Hodgkin, A. L. The Conduction of the Nervous Impulse. Springfield, Ill.: Thomas, 1964.
 129. Hodgkin, A. L., and P. Horowicz. The influence of potassium and chloride ions on the membrane potential of single muscle fibres. J. Physiol. London 148: 127–160, 1959.
 130. Hodgkin, A. L., and P. Horowicz. The effect of sudden changes in ionic concentrations on the membrane potential of single muscle fibres. J. Physiol. London 153: 370–385, 1960.
 131. Hodgkin, A. L., and A. F. Huxley. Action potentials recorded from inside a nerve fibre. Nature 144: 710–711, 1939.
 132. Hodgkin, A. L., and A. F. Huxley. Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. J. Physiol. London 116: 449–472, 1952.
 133. Hodgkin, A. L., and A. F. Huxley. The components of membrane conductance in the giant axon of Loligo. J. Physiol. London 116: 473–496, 1952.
 134. Hodgkin, A. L., and A. F. Huxley. The dual effect of membrane potential on sodium conductance in the giant axon of Loligo. J. Physiol. London 116: 497–506, 1952.
 135. Hodgkin, A. L., and A. F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. London 117: 500–544, 1952.
 136. Hodgkin, A. L., and A. F. Huxley. Movement of radioactive potassium and membrane current in a giant axon. J. Physiol. London 121: 403–414, 1953.
 137. Hodgkin, A. L., A. F. Huxley, and B. Katz. Ionic currents underlying activity in the giant axon of the squid. Arch. Sci. Physiol. 3: 129–150, 1949.
 138. Hodgkin, A. L., A. F. Huxley, and B. Katz. Measurement of current‐voltage relations in the membrane of the giant axon of Loligo. J. Physiol. London 116: 424–448, 1952.
 139. Hodgkin, A. L., and B. Katz. The effect of sodium ions on the electrical activity of the giant axon of the squid. J. Physiol. London 108: 37–77, 1949.
 140. Hodgkin, A. L., and R. D. Keynes. The mobility and diffusion coefficient of potassium in giant axons from Sepia. J. Physiol. London 119: 513–528, 1953.
 141. Hodgkin, A. L., and R. D. Keynes. The potassium permeability of a giant nerve fibre. J. Physiol. London 128: 61–88, 1955.
 142. Hodgkin, A. L., and R. D. Keynes. Movements of labelled calcium in squid giant axons. J. Physiol. London 138: 253–281, 1957.
 143. Hodgkin, A. L., and W. A. H. Rushton. The electrical constants of a crustacean nerve fibre. Proc. Roy. Soc. London Ser. B 133: 444–479, 1946.
 144. Horáčkova, M., W. Nonner, and R. Stämpfli. Action potentials and voltage clamp currents of single rat Ranvier nodes. Proc. Intern. Union Physiol. Sci. 7: 198, 1968.
 145. Horowicz, P., P. W. Gage, and R. S. Eisenberg. The role of the electrochemical gradient in determining potassium fluxes in frog striated muscle. J. Gen. Physiol. 51: 193S–203S, 1968.
 146. Howarth, J. V., R. D. Keynes, and J. M. Ritchie. The origin of the initial heat associated with a single impulse in mammalian non‐myelinated nerve fibres. J. Physiol. London 194: 745–793, 1968.
 147. Hoyt, R. C., and W. J. Adelman, Jr. Sodium inactivation. Experimental test of two models. Biophys. J. 10: 610–617, 1970.
 148. Hursh, J. B. Conduction velocity and diameter of nerve fibers. Am. J. Physiol. 127: 131–139, 1939.
 149. Hursh, J. B. The properties of growing nerve fibers. Am. J. Physiol. 127: 140–153, 1939.
 150. Hutchinson, N. A., Z. J. Koles, and R. S. Smith. Conduction velocity in myelinated nerve fibers of Xenopus laevis. J. Physiol. London 208: 279–289, 1970.
 151. Huxley, A. F. Ion movements during nerve activity. Ann. NY Acad. Sci. 81: 221–246, 1959.
 152. Huxley, A. F., and R. Stämpfli. Evidence for saltatory conduction in peripheral myelinated nerve fibres. J. Physiol. London 108: 315–339, 1949.
 153. Huxley, A. F., and R. Stämpfli. Direct determination of membrane resting potential and action potential in single myelinated nerve fibres. J. Physiol. London 112: 476–495, 1951.
 154. Huxley, A. F., and R. Stämpfli. Effect of potassium and sodium on resting and action potentials of single myelinated nerve fibres. J. Physiol. London 112: 496–508, 1951.
 155. Julian, F. J., J. W. Moore, and D. E. Goldman. Current‐voltage relations in the lobster giant axon membrane under voltage clamp conditions. J. Gen. Physiol. 45: 1217–1238, 1962.
 156. Kato, G. On the excitation, conduction, and narcotisation of single nerve fibres. Cold Spring Harbor Symp. Quant. Biol. 4: 209–213, 1936.
 157. Katz, B. Experimental evidence for a non‐conducted response of nerve to subthreshold stimulation. Proc. Roy. Soc. London Ser. B 124: 244–276, 1937.
 158. Katz, B. The Release of Neural Transmitter Substances. Springfield, Ill.: Thomas, 1969.
 159. Keynes, R. D. The ionic movements during nervous activity. J. Physiol. London 114: 119–150, 1951.
 160. Keynes, R. D., and P. R. Lewis. The sodium and potassium content of cephalopod nerve fibres. J. Physiol. London 114: 151–182, 1951.
 161. Keynes, R. D., and J. M. Ritchie. The movements of labelled ions in mammalian non‐myelinated nerve fibres. J. Physiol. London 179: 333–367, 1965.
 162. Keynes, R. D., and E. Rojas. Characteristics of the sodium gating current in the squid giant axon. J. Physiol. London 233: 28P, 1973.
 163. Keynes, R. D., and E. Rojas. Kinetics and steady state properties of the charged system controlling sodium conductance in the squid giant axon. J. Physiol. London 239: 393–434, 1974.
 164. Keynes, R. D., E. Rojas, R. E. Taylor, and J. Vergara. Calcium and potassium systems of a giant barnacle muscle fibre under membrane potential control. J. Physiol. London 229: 409–455, 1973.
 165. Khodorov, B. I. The Problem of Excitability. Electrical Excitability and Ionic Permeability of the Nerve Membrane. New York: Plenum Press, 1974.
 166. Kohlhardt, M., B. Bauer, H. Krause, and A. Fleckenstein. Differentiation of the transmembrane Na and Ca channels in mammalian cardiac fibers by the use of specific inhibitors. Pfluegers Arch. Ges. Physiol. 335: 309–322, 1972.
 167. Koketsu, K., and S. Nishi. Effects of tetrodotoxin on the action potential in Na‐free media. Life Sci., Part 2, 5: 2341–2346, 1966.
 168. Koketsu, K., and S. Nishi. Calcium and action potentials of bullfrog sympathetic ganglion cells. J. Gen. Physiol. 53: 608–623, 1969.
 169. Koles, Z. J., and M. Rasminsky. A computer simulation of conduction in demyelinated nerve fibres. J. Physiol. London 227: 351–364, 1972.
 170. Koppenhöffer, E. Die Wirkung von Tetraäthylammoni‐umchlorid auf die Membranströme Ranvierscher Schnürringe von Xenopus laevis. Pfluegers Arch. Ges. Physiol. 293: 34–55, 1967.
 171. Koppenhöfer, E., and H. Schmidt. Die Wirkung von Skorpiongift auf die Ionenströme des Ranvierschen Schnürrings. I. Die permeabilitäten PNa und Pk. Pfluegers Arch. Ges. Physiol. 303: 133–149, 1968.
 172. Koppenhöfer, E., and H. Schmidt. Die Wirkung von Skorpiongift auf die Ionenströme des Ranvierschen Schnürrings. II. Unvollständige Natrium‐Inaktivierung. Pfluegers Arch. Ges. Physiol. 303: 150–161, 1968.
 173. Kushmerick, M. J., and R. J. Podolsky. Ionic mobility in muscle cells. Science 166: 1297–1298, 1969.
 174. Lillie, R. S. Factors affecting transmission and recovery in the passive iron nerve model. J. Gen. Physiol. 7: 473–507, 1925.
 175. Ling, G. N. A Physical Theory of the Living State. Waltham, Mass.: Blaisdell, 1962.
 176. Lucas, K. The analysis of complex excitable tissues by their response to electric currents of short duration. J. Physiol. London 35: 310–331, 1906.
 177. Lüttgau, V. H‐C. Sprunghafte Schwankungen unter‐schwelliger Potentiale an markhaltigen Nervenfasern. Z. Naturforsch. 13B: 692–693, 1958.
 178. Marmont, G. Studies on the axon membrane. I. A new method. J. Cellular Comp. Physiol. 34: 351–382, 1949.
 179. Martinez, D., A. A. Silvidi, and R. M. Stokes. Nuclear magnetic resonance studies of sodium ions in isolated frog muscle and liver. Biophys. J. 9: 1256–1260, 1969.
 180. Mauro, A., F. Conti, F. Dodge, and R. Schor. Subthreshold behavior and phenomenological impedance of the squid giant axon. J. Gen. Physiol. 55: 497–523, 1970.
 181. Meves, H. The ionic requirements for the production of action potentials in Helix pomatia neurones. Pfluegers Arch. Ges. Physiol. 304: 215–241, 1968.
 182. Meves, H., and W. Vogel. Calcium inward currents in internally perfused giant axons. J. Physiol. London 235: 225–265, 1973.
 183. Moore, J. W., and T. Narahashi. Tetrodotoxin's highly selective blockage of an ionic channel. Federation Proc. 26: 1655–1663, 1967.
 184. Moore, J. W., T. Narahashi, and T. I. Shaw. An upper limit to the number of sodium channels in nerve membrane? J. Physiol. London 188: 99–105, 1967.
 185. Moreton, R. B. An investigation of the electrogenic sodium pump in snail neurones, using the constant‐field theory. J. Exptl. Biol. 51: 181–201, 1969.
 186. Morton, S. D., and G. F. Lee. Calcium carbonate equilibria in the oceans. Ion pair formation. J. Chem. Educ. 45: 513–515, 1968.
 187. Mozhayeva, G. N., and A. P. Naumov. Effect of surface charge on the steady‐state potassium conductance of nodal membrane. Nature 228: 164–165, 1970.
 188. Murayama, K., N. J. Abbott, T. Narahashi, and B. I. Shapiro. Effects of allethrin and condylactis toxin on the kinetics of sodium conductance of crayfish axon membranes. Comp. Gen. Pharmacol. 3: 391–400, 1972.
 189. Nakajima, S. Analysis of K inactivation and TEA action in the supramedullary cells of puffer. J. Gen. Physiol. 49: 629–640, 1966.
 190. Narahashi, T., D. T. Frazier, and M. Yamada. The site of action and active form of local anesthetics. I. Theory and pH experiments with tertiary compounds. J. Pharmacol. Exptl. Therap. 171: 32–44, 1970.
 191. Narahashi, T., and H. G. Haas. Interaction of DDT with the components of lobster nerve membrane conductance. J. Gen. Physiol. 51: 177–198, 1968.
 192. Narahashi, T., J. W. Moore, and W. R. Scott. Tetrodotoxin blockage of sodium conductance increase in lobster giant axons. J. Gen. Physiol. 47: 965–974, 1964.
 193. Narahashi, T., J. W. Moore, and B. I. Shapiro. Condylactis toxin: interaction with nerve membrane ionic conductances. Science 163: 680–681, 1969.
 194. Neher, E. Two fast transient current components during voltage clamp in snail neurons. J. Gen. Physiol. 58: 36–53, 1971.
 195. Nernst, W. Zur Kinetik der in Lösung befindlichen Körper: Theorie der Diffusion. Z. Physik. Chem. Leipzig 2: 613–637, 1888.
 196. Nernst, W. Die elektromotorische Wirksamkeit der Ionen. Z. Physik. Chem. Leipzig 4: 129–181, 1889.
 197. Noble, D. Applications of Hodgkin‐Huxley equations to excitable tissues. Physiol. Rev. 46: 1–50, 1966.
 198. Noble, D., and R. B. Stein. The threshold conditions for initiation of action potentials by excitable cells. J. Physiol. London 187: 129–162, 1966.
 199. Noble, D., and R. W. Tsien. The kinetics and rectifier properties of the slow potassium current in cardiac Purkinje fibres. J. Physiol. London 195: 185–214, 1968.
 200. Noble, D., and R. W. Tsien. Outward membrane currents activated in the plateau range of potentials in cardiac Purkinje fibres. J. Physiol. London 200: 205–231, 1969.
 201. Nonner, W. A new voltage clamp method for Ranvier nodes. Pfluegers Arch. Ges. Physiol. 309: 176–192, 1969.
 202. Nonner, W., and R. Stämpfli. A new voltage clamp method. In: Laboratory Techniques in Membrane Biophysics, edited by H. Passow and R. Stämpfli. Berlin: Springer Verlag, 1969.
 203. Paintal, A. S. Effects of temperature on conduction in single vagal and saphenous myelinated nerve fibres of the cat. J. Physiol. London 180: 20–49, 1965.
 204. Paintal, A. S. The influence of diameter of medullated nerve fibers of cats on the rising and falling phases of the spike and its recovery. J. Physiol. London 184: 791–811, 1966.
 205. Pearson, K. G., R. B. Stein, and S. K. Malhotra. Properties of action potentials from insect motor nerve fibres. J. Exptl. Biol. 53: 299–316, 1970.
 206. Pichon, Y., and J. Boistel. Current‐voltage relations in the isolated giant axon of the cockroach under voltage‐clamp conditions. J. Exptl. Biol. 47: 343–355, 1967.
 207. Planck, M. Ueber die Erregung von Elektricität und Wärme in Elektrolyten. Ann. Physik Chem. 39: 161–186, 1890.
 208. Planck, M. Ueber die Potentialdifferenz zwischen zwei verdünnten Lösungen binärer Elektrolyte. Ann. Physik Chem. 40: 561–576, 1890.
 209. Pooler, J. Photodynamic alteration of sodium currents in lobster axons. J. Gen. Physiol. 60: 367–387, 1972.
 210. Pumphrey, R. J., and J. Z. Young. The rates of conduction of nerve fibres of various diameters in cephalopods. J. Exptl. Biol. 15: 453–466, 1938.
 211. Rang, H. P., and J. M. Ritchie. On the electrogenic sodium pump in mammalian non‐myelinated nerve fibres and its activation by various external cations. J. Physiol. London 196: 183–211, 1968.
 212. Rasminsky, M., and T. A. Sears. Internodal conduction in undissected demyelinated nerve fibres. J. Physiol. London 227: 323–350, 1972.
 213. Reuter, H. Divalent cations as charge carriers in excitable membranes. Progr. Biophys. Mol. Biol. 26: 1–43, 1973.
 214. Ritchie, J. M. Electrogenic ion pumping in nervous tissue. In: Current Topics in Bioenergetics, edited by D. R. Sanadi. New York: Academic, 1971.
 215. Ritchie, J. M. Energetic aspects of nerve conduction: the relationships between heat production, electrical activity and metabolism. Progr. Biophys. Mol. Biol. 26: 147–187, 1973.
 216. Ritchie, J. M., and P. Greengard. On the mode of action of local anesthetics. Ann. Rev. Pharmacol. 6: 405–430, 1966.
 217. Robertson, J. D. The molecular structure and contact relationship of cell membranes. Progr. Biophys. Biophys. Chem. 10: 344–418, 1960.
 218. Robinson, R. A., and R. H. Stokes. Electrolyte Solutions. London: Butterworths, 1965.
 219. Rushton, W. A. H. A theory of the effects of fibre size in medullated nerve. J. Physiol. London 115: 101–122, 1951.
 220. Schwarz, J. R., and W. Vogel. Potassium inactivation in single myelinated nerve fibres of Xenopus laevis. Pfluegers Arch. Ges. Physiol. 330: 61–73, 1971.
 221. Schauf, C. L. Temperature dependence of the ionic current kinetics of Myxicola giant axons. J. Physiol. London 235: 197–205, 1973.
 222. Seeman, P. The membrane actions of anesthetics and tranquilizers. Pharmacol Rev. 24: 583–656, 1972.
 223. Shapiro, B. I., and F. K. Lenherr. Hodgkin‐Huxley axon: increased modulation and linearity of response to constant current stimulus. Biophys. J. 12: 1145–1158, 1972.
 224. Stämpfli, R., and B. Hille. Amphibian peripheral nerves In: Handbook of Frog Neurobiology, edited by R. Llinas and W. Precht. Heidelberg: Springer Verlag. In press.
 225. Stein, R. B. The frequency of nerve action potentials generated by applied currents. Proc. Roy. Soc. London Ser. B 167: 64–86, 1967.
 226. Stevens, C. F. Inferences about membrane properties from electrical noise measurements. Biophys. J. 12: 1028–1047, 1972.
 227. Strichartz, G. R. The inhibition of sodium currents in myelinated nerve by quaternary derivatives of lidocaine. J. Gen. Physiol. 62: 37–57, 1973.
 228. Takata, M., J. W. Moore, C. Y. Kao, and F. A. Fuhrman. Blockage of sodium conductance increase in lobster giant axon by tarichatoxin (tetrodotoxin). J. Gen. Physiol. 49: 977–988, 1966.
 229. Tasaki, I. Nervous Transmission. Springfield, Ill.: Thomas, 1953.
 230. Tasaki, I. Conduction of the nerve impulse. In: Handbook of Physiology. Neurophysiology, edited by H. W. Magoun. Washington, D.C.: Am. Physiol. Soc, 1959, sect. 1, vol. I, p. 75–121.
 231. Tasaki, I. Nerve Excitation. A Macromolecular Approach. Springfield, Ill.: Thomas, 1968.
 232. Tasaki, I., and M. Fujita. Action currents of single nerve fibers as modified by temperature changes. J. Neurophysiol. 11: 311–315, 1948.
 233. Tasaki, I., and K. Mizuguchi. The changes in the electric impedance during activity and the effect of alkaloids and polarization upon the bioelectric processes in the myelinated nerve fibre. Biochim. Biophys. Acta 3: 484–493, 1949.
 234. Tasaki, I., and T. Takeuchi. Der am Ranvierschen Knoten entstehende Aktionsstrom und seine Bedeutung für die Erregungsleitung. Pfluegers Arch. Ges. Physiol. 244: 696–711, 1941.
 235. Tasaki, I., and T. Takeuchi. Weitere Studien über den Aktionsstrom der markhaltigen Nervenfaser und über die elektrosaltatorische Ubertragung des Nervenimpulses. Pfluegers Arch. Ges. Physiol. 245: 764–782, 1942.
 236. Thomas, R. C. Electrogenic sodium pump in nerve and muscle cells. Physiol. Rev. 52: 563–594, 1972.
 237. Tomita, T., and E. B. Wright. A study of the crustacean axon repetitive response. I. The effect of membrane potential and resistance. J. Cell. Comp. Physiol. 65: 195–210, 1965.
 238. Ulbricht, W. The effect of veratridine on excitable membranes of nerve and muscle. Ergeb. Physiol. Biol. Chem. Exptl. Pharmakol. 61: 18–71, 1969.
 239. Ulbricht, W. Rate of veratridine action on the nodal membrane. I. Fast phase determined during sustained depolarization in the voltage clamp. Pfluegers Arch. Ges. Physiol. 336: 187–199, 1972.
 240. Ussing, H. H. The distinction by means of tracers between active transport and diffusion. The transfer of iodide across the isolated frog skin. Acta Physiol. Scand. 19: 43–56, 1949.
 241. Woodbury, J. W. Eyring rate theory model of the current‐voltage relationships of ion channels in excitable membranes. In: Chemical Dynamics: Papers in Honor of Henry Eyring, edited by J. O. Hirschfelder. New York: Wiley, 1971, p. 601–617.

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Article Title: Ionic Basis of Resting and Action Potentials
 

How to Cite

Bertil Hille. Ionic Basis of Resting and Action Potentials. Compr Physiol 2011, Supplement 1: Handbook of Physiology, The Nervous System, Cellular Biology of Neurons: 99-136. First published in print 1977. doi: 10.1002/cphy.cp010104