Concept

The action potential

T-051Home BU-205Threads regulation · systems

Statement

The all-or-nothing electrical impulse of a neuron.

Why it matters

fluid-mosaic-membrane established that the plasma membrane is a selectively permeable barrier studded with channel and pump proteins; the action potential is the single most important consequence of that architecture in excitable tissue. It is the mechanism by which a neuron converts a graded, decaying stimulus into a fixed-amplitude, non-decaying signal that can be sent reliably over distances of up to a metre, and it is the trigger that couples the nervous system to the rest of physiology — sliding-filament's excitation-contraction coupling begins with an action potential arriving at a motor neuron terminal, and hormonal-regulation provides the slower, non-electrical channel of control that complements it.

Because the underlying ion channels and pumps are common to essentially all animal cells, the same quantitative framework developed here — equilibrium potentials set by concentration gradients and voltage-dependent gating — recurs throughout this unit, from oxygen-dissociation-curve's cooperative binding to countercurrent-kidney's ion transport.

Hypotheses

The Na\(^+\)/K\(^+\)-ATPase and other transporters maintain steep, stable concentration gradients for Na\(^+\), K\(^+\) and Cl\(^-\) across the resting membrane.Without continuously maintained gradients (K\(^+\) concentrated inside the cell, Na\(^+\) concentrated outside), there would be no electrochemical driving force available to depolarise or repolarise the membrane at all; the pump's continuous, ATP-consuming activity is what makes the resting state a steady state rather than a true equilibrium. Ion channels are voltage-gated, and Na\(^+\) and K\(^+\) channels have different kinetics: Na\(^+\) channels activate and then inactivate quickly, while K\(^+\) channels activate more slowly and do not inactivate on the same timescale.This kinetic difference is exactly what produces a transient, self-terminating spike rather than either no response or a stable new resting state; without it, depolarisation would have no natural mechanism to reverse itself. The treatment here uses the Nernst equation for single-ion equilibrium potentials and only qualitatively invokes the Goldman-Hodgkin-Katz equation for the resting potential; a fully quantitative treatment weights each permeant ion's contribution by its membrane permeability, and those permeabilities themselves change through the course of the spike, which a fixed single-ion Nernst calculation alone cannot capture.

Proof

\[ E_{\text{ion}} = \frac{RT}{zF}\ln\frac{[\text{ion}]_{\text{out}}}{[\text{ion}]_{\text{in}}} \]

For any single permeant ion, the Nernst equation gives the membrane potential at which that ion's electrical and concentration gradients exactly balance, so there is no net electrochemical driving force on it; \(z\) is the ion's charge, \(R\) the gas constant, \(T\) absolute temperature and \(F\) the Faraday constant. A

\[ \text{At rest, membrane permeability to K}^+\text{ dominates, so } V_m \approx E_K \approx -70\ \text{to}\ -90\,\text{mV} \]

Because resting K\(^+\) permeability is much higher than resting Na\(^+\) permeability, the permeability-weighted (Goldman-Hodgkin-Katz) resting potential sits close to, though not exactly at, the K\(^+\) equilibrium potential found in Step 1, rather than at some simple average of all permeant ions' equilibrium potentials. B

\[ \text{Depolarisation to threshold (}\approx-55\,\text{mV) opens voltage-gated Na}^+\text{ channels}\ \Rightarrow\ g_{Na}\uparrow\ \Rightarrow\ V_m\to E_{Na}\,(\approx+60\,\text{mV}) \]

Once enough Na\(^+\) channels open to push \(V_m\) past threshold, the resulting depolarisation itself opens still more Na\(^+\) channels — positive feedback — driving \(V_m\) rapidly toward, but not all the way to, \(E_{Na}\) (Worked examples). This regenerative step is what makes the response an all-or-nothing spike rather than a graded reflection of stimulus size. A

\[ \text{Na}^+\text{ channels inactivate; delayed voltage-gated K}^+\text{ channels open}\ \Rightarrow\ g_K\uparrow\ \Rightarrow\ V_m\to E_K\ \text{(repolarisation, often with hyperpolarisation)} \]

Na\(^+\) channel inactivation — a distinct process from closing, and one that requires repolarisation to reset — removes the depolarising conductance, while the slower K\(^+\) conductance now dominates and drives \(V_m\) back toward \(E_K\); inactivated Na\(^+\) channels cannot reopen until the membrane repolarises, the molecular basis of the absolute refractory period. A

\[ \text{Amplitude of a fired spike is independent of stimulus strength above threshold; intensity is instead encoded in firing frequency} \]

Because the rising phase is regenerative once threshold is crossed, every suprathreshold stimulus produces an identical, stereotyped spike, and sub-threshold stimuli produce no propagating spike at all. Along an axon, local depolarisation from an active patch of membrane brings the adjacent patch to threshold in turn, propagating the spike without decay — sped up considerably wherever the axon is myelinated. A

Result

\[ E_K\approx-90\,\text{mV},\quad E_{Na}\approx+60\,\text{mV},\quad V_{\text{rest}}\approx-70\,\text{mV},\quad V_{\text{threshold}}\approx-55\,\text{mV} \]

Reading. Sequential opening and closing of two distinct voltage-gated conductances — fast Na\(^+\), slower K\(^+\) — drives a stereotyped depolarisation-repolarisation cycle whenever threshold is crossed.

Scope. Applies to any excitable cell with the standard complement of voltage-gated Na\(^+\)/K\(^+\) channels (neurons, and via sliding-filament's excitation-contraction coupling, skeletal muscle fibres); the specific millivolt values vary with species, cell type and ion concentrations, and cardiac action potentials in particular also involve significant Ca\(^{2+}\) conductances not treated here.

Corollaries & converses

sliding-filament's excitation-contraction coupling begins with exactly this depolarisation propagating into a muscle fibre's T-tubules.
Myelination increases conduction velocity by restricting depolarisation to unmyelinated nodes of Ranvier (saltatory conduction), letting the regenerative Step 3 event skip electrically between nodes rather than regenerating continuously along the whole membrane.
Converse: graded potentials (e.g. postsynaptic potentials, the inputs that may or may not bring a neuron to threshold) do not obey the all-or-none property; they vary continuously with stimulus size and summate spatially and temporally, in direct contrast to Step 5.

Fails without

Drop Na\(^+\) channel inactivation (e.g. a channelopathy or toxin that holds the channel open): depolarisation fails to terminate on its own, the membrane cannot repolarise on schedule, and the refractory period disappears — the self-limiting, all-or-nothing spike degrades into a sustained depolarisation block rather than a discrete impulse.
Collapse the maintained ionic gradients (e.g. inhibiting the Na\(^+\)/K\(^+\)-ATPase with ouabain): the Nernst potentials for Na\(^+\) and K\(^+\) converge toward each other, the driving force for both the depolarising and repolarising phases falls, and the neuron becomes progressively unable to generate full-amplitude action potentials at all.

Common errors

Treating the action potential as an electrical signal that simply flows down the axon like current in a wire, rather than as a self-regenerating wave actively reconstructed at each point of membrane (Discussion).
Believing the amplitude of an action potential scales with the strength of the triggering stimulus; stimulus strength is encoded in firing frequency, not spike size (Step 5).
Confusing the resting membrane potential (a steady state maintained by pumps, dominated by but not identical to \(E_K\)) with the K\(^+\) equilibrium potential itself.
Assuming a stronger-than-threshold stimulus during the absolute refractory period can still trigger a new spike; inactivated Na\(^+\) channels cannot reopen regardless of stimulus size until the membrane has repolarised (Step 4).

Discussion

Alan Hodgkin and Andrew Huxley worked out the ionic basis of the action potential in the squid giant axon in the early 1950s, using the newly developed voltage-clamp technique to separate and directly measure the Na\(^+\) and K\(^+\) conductances described in Steps 3–4; the resulting mathematical model earned them the Nobel Prize in Physiology or Medicine in 1963, shared with John Eccles.

The Hodgkin-Huxley model's real achievement was showing that a small number of voltage- and time-dependent conductance variables, fitted to voltage-clamp data, reproduce the full shape, threshold and refractory behaviour of the action potential quantitatively — a template later extended to describe far more complex excitable-cell behaviour, including cardiac pacemaker cells and the Ca\(^{2+}\)-dependent spikes of some neurons and muscle types.

Common misconception: that the action potential involves large numbers of ions crossing the membrane, substantially changing intracellular Na\(^+\) and K\(^+\) concentrations. The number of ions that cross during a single spike is a tiny fraction of the total intracellular pool; the Na\(^+\)/K\(^+\)-ATPase's job is simply to restore that small deficit over time, and concentration changes only become significant under sustained, very high-frequency firing.

Worked examples

\[ [\text{K}^+]_{\text{out}}=5\,\text{mM},\ [\text{K}^+]_{\text{in}}=140\,\text{mM},\ T=310\,\text{K} \]

Using the Nernst equation in base-10 form, \(E_{\text{ion}}=\dfrac{61.5\,\text{mV}}{z}\log_{10}\dfrac{[\text{ion}]_{\text{out}}}{[\text{ion}]_{\text{in}}}\) at body temperature (\(2.303RT/F\approx61.5\,\text{mV}\) at \(310\,\text{K}\)): \(E_K=61.5\log_{10}(5/140)=61.5\times(-1.45)\approx-89\,\text{mV}\), matching the standard textbook value. A

\[ [\text{Na}^+]_{\text{out}}=145\,\text{mM},\ [\text{Na}^+]_{\text{in}}=15\,\text{mM} \]

\(E_{Na}=61.5\log_{10}(145/15)=61.5\times0.985\approx+61\,\text{mV}\). The large gap between \(E_K\approx-89\,\text{mV}\) and \(E_{Na}\approx+61\,\text{mV}\) is exactly the swing the membrane traverses over the course of a single spike, driven entirely by which conductance dominates at each phase (Steps 2–4). A

\[ E_K\approx-89\,\text{mV},\quad E_{Na}\approx+61\,\text{mV} \]

Reading. Two ions with oppositely directed electrochemical gradients set the two extremes that the membrane potential is pulled toward, depending on which channel type is open.

Scope. The same calculation, repeated for any permeant ion given its inside/outside concentrations, gives that ion's individual equilibrium potential; Ca\(^{2+}\) and Cl\(^-\) equilibrium potentials are computed identically and matter in other excitable-cell contexts.

Further example. A squid giant axon has a resting membrane potential of \(V_m = -65\,\text{mV}\). The equilibrium potential for sodium is \(E_{Na} = +61\,\text{mV}\). If the membrane resistance to sodium is \(R_{Na} = 20\,\text{M}\Omega\), calculate the inward sodium current \(I_{Na}\) flowing at rest. Assume the membrane is at rest and only sodium conductance is considered for this specific current component.

\[ I_{Na} = \dfrac{V_m - E_{Na}}{R_{Na}} \]

Ohm's law for ionic currents states that the current is proportional to the driving force (\(V_m - E_{Na}\)) and inversely proportional to the resistance. The driving force is the difference between the actual membrane potential and the equilibrium potential for that ion. A

\[ V_m - E_{Na} = -65\,\text{mV} - (+61\,\text{mV}) = -126\,\text{mV} \]

The driving force is negative, indicating that the electrochemical gradient favors the movement of positive charge (Na\(^+\)) into the cell. The magnitude of the driving force is \(126\,\text{mV}\). A

\[ I_{Na} = \dfrac{-126\,\text{mV}}{20\,\text{M}\Omega} \]

Substituting the values into the Ohm's law equation. Units: \(1\,\text{mV}/1\,\text{M}\Omega = 10^{-3}\,\text{V}/10^{6}\,\Omega = 10^{-9}\,\text{A} = 1\,\text{nA}\). A

\[ I_{Na} = -6.3\,\text{nA} \]

The negative sign indicates that the current is inward (positive charge entering the cell), which is consistent with the driving force calculated in Step 2. A

\[ I_{Na} = -6.3\,\text{nA} \]

Reading. Even at rest, there is a small inward leak of sodium ions due to the large electrochemical driving force. This inward current is balanced by the outward potassium current to maintain the resting potential.

Scope. This calculation applies to any ionic current where the driving force and resistance are known. It highlights the concept of driving force, which is central to understanding how changes in membrane potential or ion concentrations affect neuronal excitability.

Problems

Given \([\text{Cl}^-]_{\text{out}}=110\,\text{mM}\), \([\text{Cl}^-]_{\text{in}}=10\,\text{mM}\) (\(z=-1\)), \(T=37^{\circ}\text{C}\), find \(E_{Cl}\).
Solution
\(E_{Cl}=\dfrac{61.5}{-1}\log_{10}(110/10)=-61.5\times\log_{10}(11)=-61.5\times1.04\approx-64\,\text{mV}\), close to the standard textbook value of about \(-65\,\text{mV}\); the negative \(z\) inverts the sign relative to a cation with the same concentration ratio.
Explain why, during the absolute refractory period immediately after a spike, no stimulus, however strong, can trigger a second action potential.
Solution
Immediately after a spike, the voltage-gated Na\(^+\) channels responsible for the regenerative rising phase (Step 3) are in their inactivated state, not simply closed; inactivated channels cannot reopen regardless of how strong a depolarising stimulus is applied, and can only return to their resting, closable state once the membrane has sufficiently repolarised (Step 4). With no available Na\(^+\) conductance to recruit, no regenerative depolarisation, and hence no new spike, can occur.
A student claims that increasing extracellular K\(^+\) concentration makes neurons harder to excite because it "adds more positive charge outside." Evaluate this claim using Steps 1–2.
Solution
Raising \([\text{K}^+]_{\text{out}}\) reduces the outward K\(^+\) concentration gradient, making \(E_K\) less negative (closer to \(0\,\text{mV}\)), which depolarises the resting potential (Step 2) toward threshold and makes the cell more excitable, not less — the opposite of the student's reasoning. This is exactly why abnormally elevated serum K\(^+\) (hyperkalaemia) is clinically dangerous for excitable tissue.
A neuron has a resting membrane potential of \(V_m = -70\,\text{mV}\). The equilibrium potential for potassium is \(E_K = -90\,\text{mV}\). If the membrane resistance to potassium is \(R_K = 10\,\text{M}\Omega\), calculate the outward potassium current \(I_K\) at rest.
Solution
Using Ohm's law for ionic currents: \[ I_K = \dfrac{V_m - E_K}{R_K} \] Substitute the given values: \[ I_K = \dfrac{-70\,\text{mV} - (-90\,\text{mV})}{10\,\text{M}\Omega} \] \[ I_K = \dfrac{20\,\text{mV}}{10\,\text{M}\Omega} \] \[ I_K = 2.0\,\text{nA} \] The positive sign indicates an outward current (positive charge leaving the cell), which is consistent with the driving force favoring K\(^+\) efflux.
Explain why the action potential is described as "all-or-none" in the context of a single axon segment, and how this differs from the summation of postsynaptic potentials in a dendrite.
Solution
The action potential is "all-or-none" because the voltage-gated sodium channels have a threshold for activation. If the membrane potential is depolarized to this threshold, the positive feedback loop of Na\(^+\) influx is triggered, leading to a full-amplitude spike. If the depolarization does not reach threshold, no spike occurs. The amplitude of the spike is determined by the electrochemical gradients and channel properties, not by the strength of the stimulus (above threshold). In contrast, postsynaptic potentials (EPSPs and IPSPs) are graded potentials; their amplitude is proportional to the strength of the synaptic input. These graded potentials can summate (temporally or spatially) in the dendrites and soma to either reach or fail to reach the threshold for triggering an action potential.