§ B-08 Action Potential Propagation: Hodgkin–Huxley Spike & Saltatory Conduction (Grade 10–11 · Neuron Action Potential)
Hodgkin–Huxley Model, Na⁺ Depolarization, K⁺ Repolarization, Myelin Sheath & Nodes of Ranvier. “Action potentials fire in an all-or-none fashion: crossing threshold triggers regenerative opening of voltage-gated Na⁺ channels, while myelination enables rapid saltatory conduction leaping from node to node of Ranvier.”
Theory Summary & Scientific Mechanism
An action potential is a regenerative, all-or-none electrical spike that propagates along an axon without attenuation, quantitatively described by the Hodgkin–Huxley equations (1952).
When a stimulus depolarizes the membrane from rest (-70 mV) past threshold (≈ -55 mV), voltage-gated Na⁺ channels rapidly open (m-gates), driving an inward Na⁺ current that reverses membrane polarity to +35 mV (overshoot). Within sim 1 ms, Na⁺ channels inactivate (h-gates close, creating the absolute refractory period) and delayed-rectifier K⁺ channels open (n-gates), driving K⁺ efflux to repolarize the membrane.
In unmyelinated axons, conduction is continuous and slow (v ∝ √(d)). In myelinated axons, insulating myelin sheaths lower membrane capacitance cₘ and increase transverse resistance rₘ, enlarging the electrotonic length constant λ = √(rₘ/rᵢ) so action potentials leap rapidly from node to node of Ranvier (saltatory conduction up to 100 m/s).
Everyday Analogy
An unmyelinated axon burns slowly like a continuous fuse, whereas a myelinated axon is wrapped in insulation with small gaps (nodes of Ranvier) so the electrical spike leaps kangaroo-style from node to node (saltatory conduction) ten times faster!
Interactive Question & Derivation
During a neuronal action potential, the membrane voltage swings from -70 mV to +35 mV and then repolarizes. Which ion fluxes drive the rapid depolarization and repolarization phases, and why does myelination with nodes of Ranvier increase conduction velocity tenfold?
- A: Depolarization is caused by Cl⁻ efflux, and myelin increases membrane capacitance
- B: Depolarization is driven by regenerative Na⁺ influx, repolarization by Na⁺ channel inactivation and K⁺ efflux; myelin reduces membrane capacitance and leak conductance so the impulse jumps saltatorily between nodes of Ranvier
- C: Action potential amplitude scales linearly with stimulus strength above threshold
- undefined: Nodes of Ranvier lack voltage-gated Na⁺ channels
Study Hint: Depolarization is driven by Na⁺ influx, repolarization by K⁺ efflux, and myelin enables rapid saltatory conduction between nodes of Ranvier.
Proof & Explanation: In the Hodgkin–Huxley model, a suprathreshold stimulus (Vₘ > -55 mV) triggers rapid opening of voltage-gated Na⁺ channels. Inward Na⁺ current drives Vₘ toward E_Na (+35 mV overshoot). Voltage-gated Na⁺ channels then inactivate (h-gate closes) while delayed-rectifier K⁺ channels open, allowing K⁺ efflux to repolarize and briefly hyperpolarize the membrane. Myelin wraps the internodal axon in a thick dielectric sheath that lowers capacitance cₘ and raises transverse resistance rₘ, increasing the electrotonic length constant λ = √(rₘ/rᵢ) so local circuit currents rapidly trigger the next node of Ranvier (saltatory conduction).
Key Equations & 3D Simulation Parameters
λ = √((rₘ)/(rᵢ)), v_cond ∝ (λ)/(τₘ) (myelin: cₘ ↓, rₘ ↑ ⇒ vₛalt ≫ vᵤnmyel)
- Depolarizing stimulus ratio Iₛtim / Iₜhreshold (≥1.0 fires spike): 0.4 … 2.5 Iₜh (default: 1.5 Iₜh)
- Axon fiber type (1=Unmyelinated continuous, 2=Myelinated saltatory): 1 … 2 (default: 2)
- Axon cylinder diameter dₐxon: 2 … 20 μm (default: 10 μm)
- Voltage-gated Na⁺ channel density at nodes of Ranvier: 0.6 … 1.8 rel. (default: 1.2 rel.)