Neuron Energy Budget: The ATP Cost of a Spike

Axon & Firing

Firing rate 20 Hz

Axon diameter 1.0 µm

Na⁺/K⁺ channel overlap 2.0×

Energy Readouts

ATP / spike

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ATP / second

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Signaling power

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Conduction speed

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Energy saved by myelin (same axon, same rate)

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How it works

Every action potential is paid for after the fact by the Na⁺/K⁺-ATPase pump, which restores the ionic gradients that ran downhill during the spike — 3 Na⁺ pumped out per ATP hydrolyzed. This is a simplified version of the classic energy budget model (Attwell & Laughlin, 2001, J Cereb Blood Flow Metab):

Q  = C_m · ΔV · A          (charge moved to depolarize area A)
Na⁺ = (Q / e) · k_overlap   (k ≈ 1 in theory, 2–4 in real axons —
                             Na⁺ and K⁺ channels open at overlapping
                             times, so more charge crosses than the
                             bare minimum needed)
ATP = Na⁺ / 3               (pump stoichiometry: 3 Na⁺ out per ATP)

C_m ≈ 1 µF/cm² (membrane capacitance) and ΔV ≈ 100 mV (spike amplitude) are fixed. The active membrane area A is where it gets interesting: an unmyelinated axon depolarizes along its whole length, but a myelinated one only depolarizes at the tiny, exposed nodes of Ranvier — the insulating sheath in between costs nothing to re-polarize. That is why myelination is not just faster (saltatory conduction) but dramatically cheaper per spike, which is exactly what the "energy saved by myelin" readout compares, holding diameter and rate fixed.

Firing rate — spikes per second; ATP/second scales linearly with it.
Axon diameter — larger axons expose more membrane per spike, so cost rises with diameter (linearly here); it also sets the (unmyelinated) conduction speed via v ∝ √d.
Channel overlap — how much Na⁺ and K⁺ currents overlap in time; real cortical axons run at roughly 2–4× the theoretical minimum, which is exactly this dial.
Myelination — restricts the active area to short nodes of Ranvier, cutting the ATP bill by roughly the ratio of node length to internode spacing.

This is a first-order teaching model, not a full Hodgkin–Huxley integration — it captures the real scaling relationships (and the real reason brains are myelinated) without simulating every channel.

Na⁺ influx (depolarizing) K⁺ efflux (repolarizing) ATP consumed by pump

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