t 0.00 ms Vm −65.0 mV

Gating variables

m (Na⁺ activation)h (Na⁺ inactivation)n (K⁺ activation)

Ionic currents

INa (inward < 0)IK (outward > 0)IL

Anatomy and conduction

Explore a myelinated motor neuron part by part, then race an action potential along a myelinated and an unmyelinated axon of the same diameter.

Synapse and summation

Fire excitatory and inhibitory synapses. Each release produces a small postsynaptic potential; they add up in time and space at the axon hillock, and the neuron fires only when the sum reaches threshold.

Key facts to remember

  • Resting potential −70 mV (−65 mV in this squid model). Set by high K⁺ permeability; the Na⁺/K⁺-ATPase (3 Na⁺ out : 2 K⁺ in) maintains the gradients.
  • Nernst at 37 °C: $E_X = 61.5/z \cdot \log_{10}([X]_o/[X]_i)$ mV. EK ≈ −90 mV, ENa ≈ +60 mV, ECl ≈ −64 mV.
  • Threshold ≈ −55 mV. The spike is all-or-none: stimulus strength is coded by firing frequency, never by spike height.
  • Phases: Na⁺ in (rise) → Na⁺ inactivation + K⁺ out (fall) → K⁺ still open (after-hyperpolarisation).
  • Absolute refractory period = Na⁺ channels inactivated, no stimulus works. Relative = a stronger stimulus works, giving a smaller spike. This sets the maximum firing rate and stops the impulse running backwards.
  • Myelin raises membrane resistance and lowers capacitance → saltatory conduction, node to node. Myelinated: v ≈ 6 × d (µm) m/s. Unmyelinated: v ∝ √d.
  • Fibres: Aα motor 80–120 m/s · Aβ touch 35–75 · Aδ sharp pain 5–35 · C dull pain/autonomic 0.5–2. Small, unmyelinated fibres are blocked first by local anaesthetic, so pain goes before touch and power.
  • Synapse: spike → voltage-gated Ca²⁺ in → vesicle fusion (SNARE) → transmitter across a 20–40 nm cleft → EPSP (glutamate/AMPA, Na⁺ in) or IPSP (GABAA, Cl⁻ in). One EPSP is only 0.5–5 mV, so many must summate.
  • Summation: temporal (one synapse, rapid repeats) and spatial (several synapses at once). Spikes start at the axon hillock / initial segment: highest density of voltage-gated Na⁺ channels.
  • Electrolytes: K⁺ sets the resting potential (hyperkalaemia depolarises, inactivates Na⁺ channels and risks cardiac arrest); Ca²⁺ sets the threshold (hypocalcaemia lowers it → tetany).
  • Channel blockers: lidocaine and tetrodotoxin block voltage-gated Na⁺ channels (no spike); tetraethylammonium blocks K⁺ channels (spike is prolonged).
Educational simulator, not a clinical tool. The cases, numbers and drug examples on this page are teaching examples used to explain physiology. For patient care, follow current national and hospital protocols and your clinical supervisor.

The resting membrane potential

A neuron keeps different ion concentrations on the two sides of its membrane. The Na⁺/K⁺-ATPase pumps 3 Na⁺ out and 2 K⁺ in for every ATP it hydrolyses, so the cytoplasm is rich in K⁺ and poor in Na⁺. At rest the membrane is far more permeable to K⁺ than to Na⁺ (through K⁺ leak channels), so K⁺ diffuses out until the growing inside-negative voltage balances the concentration gradient. Each ion has an equilibrium (Nernst) potential at which its electrical and chemical driving forces cancel:

Words used below: $V_m$ is the membrane potential (inside minus outside). Depolarise = make the inside less negative; hyperpolarise = make it more negative. In the equation, $R$ is the gas constant, $T$ the absolute temperature, $F$ the Faraday constant (charge per mole of ions), $z$ the ion's charge (+1 for K⁺) and $[X]$ its concentration.

$$E_X = \frac{RT}{zF}\ln\frac{[X]_\text{out}}{[X]_\text{in}}$$

For K⁺ (140 mM inside, 5 mM outside, 37 °C) this gives about −89 mV: the inside is negative because positive K⁺ leaks out. With several permeant ions (ions that can cross), the steady resting potential is a permeability-weighted compromise given by the Goldman–Hodgkin–Katz (GHK) voltage equation:

$$V_m = \frac{RT}{F}\ln\frac{P_K[K^+]_o + P_{Na}[Na^+]_o + P_{Cl}[Cl^-]_i}{P_K[K^+]_i + P_{Na}[Na^+]_i + P_{Cl}[Cl^-]_o}$$

Note the chloride terms are swapped (inside on top) because Cl⁻ carries a negative charge. At 37 °C, $RT/F = 26.7$ mV; at the 6.3 °C used for squid axon, $RT/F = 24.1$ mV.

The Hodgkin–Huxley model

In 1952 Alan Hodgkin and Andrew Huxley used voltage-clamp recordings from the squid giant axon to describe the membrane as a capacitor in parallel with three conductances. In words: the voltage changes when net current flows onto the membrane, and each channel type pushes $V$ towards its own equilibrium potential with a strength set by how many of its channels are open (its conductance $g$). The membrane current balance is

$$C_m\frac{dV}{dt} = I_\text{stim} - \bar g_{Na}\,m^3h\,(V-E_{Na}) - \bar g_K\,n^4\,(V-E_K) - g_L\,(V-E_L)$$

The gates have intuitive roles: m is the fast Na⁺ activation gate (opens when depolarised), h the slower Na⁺ inactivation gate (closes when depolarised, which ends the Na⁺ influx) and n the slow K⁺ gate (opens to repolarise). You can watch all three in the Gating variables plot. Each gating variable $x \in \{m,h,n\}$ is the probability that one gate is in its permissive state and relaxes towards a voltage-dependent steady state:

$$\frac{dx}{dt} = \phi\,[\alpha_x(V)(1-x) - \beta_x(V)\,x],\qquad \phi = 3^{(T-6.3)/10}$$
$$\begin{aligned}\alpha_m &= \frac{0.1(V+40)}{1-e^{-(V+40)/10}}, & \beta_m &= 4e^{-(V+65)/18}\\ \alpha_h &= 0.07e^{-(V+65)/20}, & \beta_h &= \frac{1}{1+e^{-(V+35)/10}}\\ \alpha_n &= \frac{0.01(V+55)}{1-e^{-(V+55)/10}}, & \beta_n &= 0.125e^{-(V+65)/80}\end{aligned}$$

Rates are in ms⁻¹ with $V$ in mV. The simulator uses the standard squid parameters: $C_m = 1\ \mu\text{F/cm}^2$, $\bar g_{Na} = 120$, $\bar g_K = 36$, $g_L = 0.3$ mS/cm², $E_{Na} = +50$, $E_K = -77$, $E_L = -54.4$ mV, resting potential $-65$ mV. The equations are integrated with a fourth-order Runge–Kutta method at $\Delta t = 0.01$ ms.

Anatomy of an action potential

  1. Depolarisation to threshold. A stimulus raises $V$; a few Na⁺ channels open (m rises, fast).
  2. Rising phase. Na⁺ influx depolarises further, opening more Na⁺ channels: positive feedback. $V$ heads towards $E_{Na}$.
  3. Peak and repolarisation. Inactivation gates close (h falls, slower) and K⁺ channels open (n rises, slower still); K⁺ efflux drives $V$ back down.
  4. Undershoot. K⁺ channels close slowly, so $V$ briefly approaches $E_K$ (after-hyperpolarisation).
  5. Recovery. h recovers and n falls; the membrane can fire again.

All-or-none. Below threshold the response decays; above it the spike has nearly the same size whatever the stimulus. Stimulus strength is coded by firing frequency, not spike height.

Absolute refractory period. While most Na⁺ channels are inactivated (h small) no stimulus can trigger a second spike.

Relative refractory period. As h recovers and n is still high, a larger stimulus is needed and the spike is smaller.

Strength–duration. Short pulses need more current; the minimum current for a very long pulse is the rheobase (≈2.2 µA/cm² in this model).

Very few ions move during one spike. Charging $1\ \mu\text{F/cm}^2$ through 100 mV needs $Q = CV = 10^{-7}$ C/cm², about $6\times10^{3}$ Na⁺ per µm² of membrane, which barely changes the intracellular concentration. The pump restores gradients over many spikes.

Propagation: cable properties and myelin

Current entering at one point spreads passively along the axon and decays with the length constant $\lambda = \sqrt{r_m / r_i}$, where $r_m$ is the membrane resistance (how hard it is for current to leak out) and $r_i$ the internal resistance of the axoplasm; a larger $\lambda$ means the signal spreads further before fading. Where it depolarises the next patch above threshold, a new spike is generated: the action potential regenerates itself and travels without decrement. Refractoriness behind the spike keeps it moving forwards.

  • Unmyelinated axons: conduction velocity rises roughly with the square root of diameter, $v \propto \sqrt{d}$ (about 1 m/s for 1 µm; ≈20 m/s for the 500 µm squid giant axon).
  • Myelinated axons: myelin (Schwann cells in the PNS, oligodendrocytes in the CNS) raises membrane resistance and lowers capacitance, so current jumps from one node of Ranvier to the next (saltatory conduction). Velocity rises roughly linearly, $v \approx 6\ \text{m s}^{-1}\,\mu\text{m}^{-1} \times d$ (Hursh factor), and internodes are about $100\times d$ long.
FibreDiameter (µm)MyelinVelocity (m/s)Example
Aα13–20Yes80–120Motor neurons, muscle spindles
Aβ6–12Yes35–75Touch, pressure
Aδ1–5Thin5–35Sharp pain, cold
C0.2–1.5No0.5–2Dull pain, warmth, autonomic

Synaptic transmission and integration

At a chemical synapse the arriving spike opens voltage-gated Ca²⁺ channels; Ca²⁺ triggers SNARE-mediated fusion of vesicles and neurotransmitter diffuses across the 20–40 nm cleft to ligand-gated receptors. Glutamate opening AMPA receptors lets Na⁺ in and produces an EPSP; GABA opening GABAA receptors lets Cl⁻ in and produces an IPSP (hyperpolarising or shunting). A single EPSP is typically 0.5–5 mV, so a neuron sitting 15 mV below threshold needs many to fire.

  • Temporal summation: repeated inputs from one synapse arrive before the previous PSP has decayed (membrane time constant $\tau_m = r_m c_m$, typically 5–20 ms).
  • Spatial summation: inputs from different synapses arrive at about the same time. Proximal synapses contribute more because dendritic signals decay with distance.

Spikes are initiated at the axon hillock / initial segment, which has the highest density of voltage-gated Na⁺ channels and therefore the lowest threshold.

Model notes. The HH lab is the original deterministic squid-axon model (a space-clamped patch, no dendrites). TEA is modelled as blocking the voltage-gated delayed rectifier only; the small K⁺ conductance open at rest is kept, so the resting potential stays at −65 mV (in the bare HH equations a large cut in ḡK makes the patch fire spontaneously). The conduction race uses empirical velocity rules rather than solving the cable equation, and the synapse panel uses alpha-function PSPs with a stylised spike at threshold. These simplifications keep the essential behaviour while running in real time.

Nernst and Goldman calculator

Enter ion concentrations (mM), temperature and relative permeabilities. The chart shows each equilibrium potential and the GHK resting potential on a common voltage scale.

EK
—
ENa
—
ECl
—
GHK Vm
—

1. Equilibrium potentials in a mammalian neuron

At 37 °C, $T = 310.15$ K, so $RT/F = \dfrac{8.314 \times 310.15}{96\,485} = 0.02673$ V $= 26.73$ mV.

K⁺: $[K^+]_o = 5$ mM, $[K^+]_i = 140$ mM. $E_K = 26.73 \ln(5/140) = 26.73 \times (-3.332) = -89.1$ mV.

Na⁺: $[Na^+]_o = 145$, $[Na^+]_i = 15$ mM. $E_{Na} = 26.73 \ln(145/15) = 26.73 \times 2.269 = +60.6$ mV.

Cl⁻ ($z=-1$): $[Cl^-]_o = 110$, $[Cl^-]_i = 10$ mM. $E_{Cl} = -26.73 \ln(110/10) = -64.1$ mV.

Load the Mammalian neuron preset in the Nernst & Goldman tab to check these values.

2. Goldman resting potential

With $P_K : P_{Na} : P_{Cl} = 1 : 0.04 : 0.45$:

Numerator $= 1(5) + 0.04(145) + 0.45(10) = 5 + 5.8 + 4.5 = 15.3$

Denominator $= 1(140) + 0.04(15) + 0.45(110) = 140 + 0.6 + 49.5 = 190.1$

$V_m = 26.73 \ln(15.3/190.1) = 26.73 \times (-2.520) \approx -67.3$ mV. It lies close to $E_K$ because K⁺ dominates the resting permeability, but is pulled slightly positive by the Na⁺ leak.

3. Reading the HH simulation

A 1 ms, 10 µA/cm² pulse at 6.3 °C (default settings) produces a spike that peaks at about $+39$ mV from a rest of $-65$ mV, an amplitude of about 104 mV, close to the ≈100 mV recorded in squid axon.

Threshold depends on pulse duration. The Find threshold button bisects the amplitude: about 6.9 µA/cm² for 1 ms, 3.9 for 2 ms and 2.4 for 5 ms, approaching the rheobase of ≈2.2 µA/cm².

Total charge at threshold for 1 ms: $Q = I\,t = 6.9 \times 10^{-6} \times 10^{-3} = 6.9$ nC/cm², enough to depolarise $1\ \mu\text{F/cm}^2$ by $\Delta V = Q/C \approx 6.9$ mV before Na⁺ feedback takes over.

4. Ions per action potential

$\Delta Q = C\,\Delta V = (1\times10^{-6}\ \text{F/cm}^2)(0.1\ \text{V}) = 1\times10^{-7}$ C/cm².

Number of monovalent ions $= \Delta Q/e = 10^{-7}/1.602\times10^{-19} = 6.2\times10^{11}$ per cm² $= 6.2\times10^{3}$ per µm².

For a 500 µm squid axon, a 1 µm length has volume $\pi (250)^2 \approx 1.96\times10^5$ µm³ containing roughly $50\ \text{mM}\times N_A \approx 5.9\times10^{9}$ Na⁺, but the membrane area is only $\pi d \approx 1571$ µm², so one spike adds about $10^{7}$ Na⁺: a 0.2 % change.

5. Conduction time

A sensory Aβ fibre (myelinated, $d = 10$ µm) conducts at $v \approx 6 \times 10 = 60$ m/s. Over 1 m from toe to spinal cord: $t = 1/60 = 16.7$ ms.

An unmyelinated C fibre ($d = 1$ µm, $v \approx 1$ m/s) needs about 1 s. This is why you feel the sharp first pain of stubbing a toe before the slow, dull second pain.

To match 60 m/s without myelin, $\sqrt{d} = 60$ so $d \approx 3600$ µm = 3.6 mm: an axon thicker than a pencil lead. Myelin saves enormous space and energy.

Guided challenges

Work through these in the labs above. Each one is checked automatically and lights up when you achieve it.

    Strength–duration curve

    Compute the threshold current for pulse durations from 0.1 to 20 ms with the current drug and temperature settings. Compare the curve with the Lapicque relation $I_\text{th} = I_\text{rh}(1 + t_\text{ch}/t)$, where $t_\text{ch}$ is the chronaxie (duration at twice rheobase).

    Open investigations

    1. Raise the temperature from 6.3 °C to 20 °C. What happens to spike width and peak? Above about 28–30 °C the threshold soars and the spike shrinks until the squid model effectively stops firing (heat block); explain why in terms of the relative speeds of m, h and n.
    2. Increase extracellular K⁺. Why does a modest rise make the cell more excitable, while a large rise (×4) abolishes firing? Relate this to h at rest (depolarisation block, as in severe hyperkalaemia).
    3. With TTX at 50 %, find the new threshold. Local anaesthetics such as lidocaine block the same channel from the inside.
    4. In the step protocol, measure firing frequency against current (an f–I curve). The HH neuron jumps from 0 to about 50 Hz near 6.2 µA/cm² (a type II excitability).

    Clinical cases at the membrane

    Eight conditions and agents met in clinical practice, each explained in the simulators above. Press Set up the simulation to load the settings, run it, then answer the check questions. Every case names the physiology that explains the sign at the bedside.

    Teaching cases only. Drug and electrolyte figures are illustrative examples for understanding mechanism; management follows current MoH/hospital protocols and your supervisor.

    OSCE station: explain the action potential to an examiner

    A common physiology viva station. You have six minutes at the simulator: the examiner asks you to explain one action potential from rest to recovery, using the trace and the channel diagram. Start the timer, talk out loud (or write your answer), then tick each point you actually said. Mark yourself honestly: the pass mark is 70 % (13 of 18).

    6:00

    Examiner's instruction: "Using this recording, take me through an action potential in a peripheral nerve. Tell me what each phase is, which ion moves and through which channel, and finish with the refractory periods and why they matter clinically."

      Your mark
      0/ 18
      Pass mark (70 %)
      13/ 18
      Verdict
      —
      Model answer the examiner is listening for

      "At rest the membrane sits at about −70 mV because it is mainly permeable to K⁺, which leaks out down its gradient; the Na⁺/K⁺-ATPase keeps K⁺ high inside and Na⁺ high outside. A stimulus depolarises the membrane. If it reaches threshold, about −55 mV, voltage-gated Na⁺ channels open: Na⁺ floods in, depolarising further and opening more Na⁺ channels, so the rising phase is a positive feedback that drives the inside towards ENa, peaking near +30 to +40 mV. It never reaches ENa because two things happen: the Na⁺ channel inactivation gate closes, and slower voltage-gated K⁺ channels open. K⁺ now flows out, repolarising the membrane. Because the K⁺ channels close slowly, the potential undershoots towards EK: the after-hyperpolarisation. While Na⁺ channels are inactivated the fibre is absolutely refractory, so no stimulus can fire it; as the inactivation gates recover it is relatively refractory and a stronger stimulus gives a smaller spike. Clinically, refractoriness limits the maximum firing frequency and forces the impulse to travel one way only, away from the stimulus. The spike is all-or-none, so the nervous system codes stimulus intensity as firing frequency, not spike size."

      If the examiner asks for one clinical link, the strongest are: lidocaine blocks these Na⁺ channels, so no spike is generated past the block; hyperkalaemia depolarises the resting potential until Na⁺ channels sit inactivated, which is why it stops the heart; and demyelination slows or blocks conduction, as in Guillain–Barré syndrome.

      Exam-style MCQ bank

      Thirty-two single-best-answer questions in the style of clinical qualifying exams, mixing recall, application and calculation. Each answer carries an explanation; your best score is saved on this device.