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Ionic Basis of Resting and Action Potentials

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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 (W. Nonner, M. Horáčkova, and R. Stämpfli, unpublished data.)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 .] 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 (W. E. Crill, unpublished data.)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.
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 .] 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
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
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
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 , 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
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
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.
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 , adapted from Hodgkin & Huxley
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 , adapted from Hodgkin & Huxley
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
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 .] 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
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. and . 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
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. 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
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. and 13. Smooth curves, time courses of gNa and gk calculated from Hodgkin‐Huxley model.

From Hodgkin , adapted from Hodgkin & Huxley
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 , 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. of the model using relations of Eqs. and .

From Hille
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. . Assumptions: axon diameter, 476 μm; resistivity of axoplasm, 35.4 Ω‐cm; resting potential, −65 mV

Adapted from Cooley & Dodge
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
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.

Adapted from Hodgkin & Huxley
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
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
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 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


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 .] 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.


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 .] 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


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


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


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 , 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


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


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.


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 , adapted from Hodgkin & Huxley


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 , adapted from Hodgkin & Huxley


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


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 .] 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


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. and . 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


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. 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


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. and 13. Smooth curves, time courses of gNa and gk calculated from Hodgkin‐Huxley model.

From Hodgkin , adapted from Hodgkin & Huxley


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 , 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. of the model using relations of Eqs. and .

From Hille


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. . Assumptions: axon diameter, 476 μm; resistivity of axoplasm, 35.4 Ω‐cm; resting potential, −65 mV

Adapted from Cooley & Dodge


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


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.

Adapted from Hodgkin & Huxley


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


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


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 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
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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