The Physics of Nerve Signals: How Electricity Travels Through Your Body at 120 Metres per Second

The Spark Inside You

Right now, as you read this sentence, roughly 86 billion neurons in your brain are firing electrical impulses. Your eyes are converting photons into voltage spikes. Your visual cortex is assembling those spikes into letters, words, meaning. Simultaneously, signals from your inner ear are keeping you balanced, your brainstem is regulating your breathing, and a continuous stream of electrical traffic is flowing between your spinal cord and every organ, muscle, and patch of skin in your body.

All of this runs on electricity. Not the kind that flows through copper wires — something stranger, slower, and in many ways more elegant. Nerve signals are self-regenerating voltage pulses that travel along biological cables, powered not by a battery or generator but by the chemical energy stored in ion concentration gradients across a membrane five nanometres thick.

The physics of how these signals work was cracked in the early 1950s by two Cambridge physiologists working on squid. The equations they wrote down remain the foundation of computational neuroscience seventy years later. And the story begins, as so many physics stories do, with a membrane and a voltage.

The Resting Potential: A Battery Made of Salt Water

A neuron at rest is not electrically neutral. The inside of the cell sits at about −70 millivolts relative to the outside — a small but crucial voltage difference called the resting membrane potential. This is the starting point for everything that follows.

The voltage arises from an unequal distribution of ions across the cell membrane. The extracellular fluid is rich in sodium ions (Na⁺, about 145 millimolar) and chloride (Cl⁻), while the intracellular fluid is rich in potassium ions (K⁺, about 140 millimolar) and negatively charged proteins. The membrane is selectively permeable: at rest, it’s about 50–100 times more permeable to K⁺ than to Na⁺, thanks to leak channels — potassium channels that are always open.

Potassium ions, driven by their concentration gradient, leak outward. But each K⁺ ion that leaves carries a positive charge with it, making the inside of the cell more negative. This growing electrical gradient (inside negative) opposes further outflow. Eventually, the electrical force pulling K⁺ back in exactly balances the concentration gradient pushing it out. The voltage at which this balance occurs is given by the Nernst equation:

E_K = (RT / zF) × ln([K⁺]_out / [K⁺]_in)

For potassium at body temperature: E_K ≈ −90 mV. The actual resting potential (−70 mV) is less negative than this because the membrane is slightly permeable to sodium, which leaks inward and pulls the voltage toward sodium’s equilibrium potential (+60 mV). The resting potential is a weighted average, described by the Goldman-Hodgkin-Katz equation, of the equilibrium potentials of all permeable ions, weighted by their relative permeabilities.

The sodium-potassium pump (Na⁺/K⁺-ATPase) maintains these gradients by continuously pumping 3 Na⁺ out and 2 K⁺ in per ATP molecule hydrolysed. This pump consumes roughly 20–40% of the brain’s total energy budget — a remarkable fraction, and it runs constantly. Your neurons are spending a significant share of their metabolic energy just to maintain the resting potential, ready to fire.

Think of it as a loaded spring. The ion gradients store potential energy. The resting potential is the cocked trigger.

The Action Potential: Firing the Spike

When a neuron receives sufficient excitatory input — from other neurons, from a sensory receptor, from an electrical stimulus — the membrane at the axon hillock (the junction between the cell body and the axon) depolarises. If the depolarisation reaches a critical value, typically about −55 mV (the threshold), an explosive sequence of events unfolds within a millisecond.

Phase 1: Depolarisation (Rising Phase)

At threshold, voltage-gated sodium channels open. These are remarkable molecular machines — protein complexes spanning the membrane that contain a voltage sensor (a positively charged helix that moves in response to electric field changes) and a gate that swings open when the sensor moves. When the membrane reaches −55 mV, enough sodium channels open to create a positive feedback loop:

Na⁺ rushes in → membrane depolarises further → more Na⁺ channels open → more Na⁺ rushes in

This is a classic regenerative process — an electrical avalanche. Within about 0.5 milliseconds, the membrane voltage swings from −55 mV to about +30 mV. The inside of the cell is now positive relative to the outside. The voltage has reversed.

The sodium influx is brief because the channels have a built-in timer: an inactivation gate (a protein domain that swings into the channel pore like a ball on a chain) blocks the channel within about 1 millisecond of opening. This is not the same as closing — the channel is inactivated, unable to reopen until the membrane repolarises.

Phase 2: Repolarisation (Falling Phase)

As sodium channels inactivate, voltage-gated potassium channels open. These channels are slower to respond (their gates take longer to open), which is why their opening coincides with the peak of the action potential. K⁺ ions flow outward, driven by both the concentration gradient and the now-positive interior. The membrane voltage plummets back toward −70 mV.

Phase 3: Undershoot (Hyperpolarisation)

The potassium channels are slow to close as well. They remain open briefly after the membrane has returned to −70 mV, driving the voltage to about −80 mV — more negative than the resting potential. This afterhyperpolarisation lasts a few milliseconds before the membrane settles back to −70 mV as the potassium channels finally close and the resting permeability balance is restored.

The entire event — from threshold to peak to recovery — takes about 1–2 milliseconds. During this time, and for a brief period afterward (the refractory period), the neuron cannot fire another action potential. This sets a maximum firing rate of about 500–1,000 spikes per second for the fastest neurons, though most neurons fire at much lower rates (1–100 Hz).

All-or-Nothing

The action potential is all-or-nothing: if threshold is reached, the full spike fires at standard amplitude (~100 mV swing) regardless of whether the stimulus was barely above threshold or overwhelmingly strong. A stronger stimulus doesn’t produce a bigger spike — it produces more spikes per second. Information in the nervous system is encoded in firing rate and timing patterns, not in spike amplitude. It’s a digital system, in that sense, built from analogue components.

The Hodgkin-Huxley Equations: Biology Becomes Physics

The quantitative understanding of the action potential is one of the great achievements of 20th-century biophysics. It came from Alan Hodgkin and Andrew Huxley, working at the Plymouth Marine Laboratory in the late 1940s and early 1950s on the giant axon of the squid — a nerve fibre up to 1 mm in diameter (visible to the naked eye) that the squid uses for its escape jet.

The giant axon was crucial because it was large enough to insert electrodes inside. Using the voltage clamp technique — a feedback circuit that holds the membrane voltage at a chosen value and measures the current flowing across the membrane — Hodgkin and Huxley could isolate and characterise the individual ionic currents.

They found two main currents: an early, transient inward current (Na⁺) and a delayed, sustained outward current (K⁺). By systematically clamping the membrane at different voltages and measuring the time course of each current, they constructed a mathematical model that describes the action potential quantitatively.

The Hodgkin-Huxley model treats the membrane as an electrical circuit:

The lipid bilayer is a capacitor (capacitance C_m ≈ 1 µF/cm², remarkably consistent across cell types — a consequence of the ~5 nm membrane thickness and the dielectric constant of lipids).

Each ion channel population is a variable conductance in series with a battery (the Nernst potential for that ion).

The total membrane current is:

I = C_m × dV/dt + ḡ_Na × m³h × (V − E_Na) + ḡ_K × n⁴ × (V − E_K) + ḡ_L × (V − E_L)

where:

• ḡ_Na, ḡ_K, ḡ_L are the maximum conductances for sodium, potassium, and leak channels
• m, h, n are gating variables (values between 0 and 1) describing the probability that channel gates are open
• E_Na ≈ +50 mV, E_K ≈ −77 mV, E_L ≈ −54 mV are the reversal potentials

The gating variables obey first-order kinetics:

dm/dt = α_m(V)(1 − m) − β_m(V)m

and similarly for h and n, where α and β are voltage-dependent rate constants that Hodgkin and Huxley determined empirically from their voltage-clamp data. The m³ factor (three activation gates for sodium) captures the sigmoidal turn-on of Na⁺ current; the h factor (one inactivation gate) captures the auto-inactivation; the n⁴ factor (four activation gates for potassium) captures the delayed K⁺ current.

These four coupled ordinary differential equations, plus the voltage equation, are the Hodgkin-Huxley equations. They reproduce the action potential waveform, the threshold behaviour, the refractory period, the conduction velocity, and the repetitive firing patterns of real neurons with remarkable accuracy.

Huxley solved the equations numerically by hand — using a Brunsviga mechanical calculator, cranking through thousands of arithmetic operations over weeks. The solutions, published in 1952, matched the experimental recordings almost exactly. It was a tour de force of mathematical biology, and it earned Hodgkin and Huxley the 1963 Nobel Prize in Physiology or Medicine.

I want to pause on what they actually achieved here. In 1952, they took a biological process — the nerve impulse — and reduced it to physics. A capacitor, some variable resistors, a few batteries. Differential equations. The action potential is not a mystery or a vital force — it’s a nonlinear dynamical system, describable and predictable by the same mathematics that governs electronic circuits. The boundary between biology and physics dissolved.

The Cable Equation: Propagation Along the Axon

A single action potential at one point on the axon would be useless. What the nervous system needs is propagation — the signal must travel from one end of the nerve to the other without losing amplitude.

The axon is a cable: a cylindrical conductor (the cytoplasm, filled with ion-rich solution) surrounded by a thin insulating membrane, immersed in another conductor (the extracellular fluid). The physics of signal propagation along such a cable was first worked out for undersea telegraph cables in the 19th century by Lord Kelvin, and the same mathematics applies to nerve fibres.

The cable equation describes how voltage changes spread passively along the axon:

τ_m × ∂V/∂t = λ² × ∂²V/∂x² − (V − V_rest)

where τ_m = R_m × C_m is the membrane time constant (how fast the membrane charges/discharges) and λ = √(r_m / r_i) is the length constant (the distance over which a voltage signal decays to 1/e ≈ 37% of its original value). Here r_m is the membrane resistance per unit length and r_i is the internal (axoplasmic) resistance per unit length.

For an unmyelinated axon, the length constant is typically 0.1–1 mm — meaning a passive voltage signal decays to 37% of its amplitude within a millimetre. This is terrible for long-distance signalling. A signal passively spreading from your toe would be immeasurably small before it reached your ankle.

This is exactly why action potentials exist. They solve the decay problem through active regeneration: at each point along the axon, local sodium channels detect the approaching depolarisation, fire a fresh action potential, and regenerate the signal at full amplitude. The signal propagates as a wave of sequential channel activations — like a line of dominoes, where each domino falling knocks over the next.

The conduction velocity of this wave depends on how quickly the depolarisation at one point can reach threshold at the next point, which depends on the cable properties:

v ∝ √(d / (R_i × C_m))

For unmyelinated fibres, conduction velocity scales as the square root of fibre diameter. To double the speed, you need to quadruple the diameter. The squid giant axon achieves ~25 m/s by brute force — growing the fibre to 0.5–1 mm in diameter. But this approach doesn’t scale. A human nervous system with millions of fast fibres can’t afford to make them all a millimetre across.

Evolution found a better solution.

Myelin: The Insulation Revolution

Myelin is a fatty sheath wrapped around nerve fibres by specialised glial cells — Schwann cells in the peripheral nervous system and oligodendrocytes in the central nervous system. A single Schwann cell wraps around one axon segment about 1–2 mm long, spiralling its membrane around the axon 20–200 times to create a thick, multi-layered insulating coat.

Between adjacent myelin segments are tiny gaps — the nodes of Ranvier — about 1 µm wide, where the axon membrane is bare and packed with voltage-gated sodium channels at extraordinary density (about 1,000–2,000 per µm², compared to roughly 100 per µm² in unmyelinated axon).

Myelin transforms the cable properties of the axon:

Membrane resistance at the myelinated segments increases by a factor of ~5,000 (fewer ions leak out through the thick insulation).

Membrane capacitance decreases by a factor of ~5,000 (the myelin sheath acts as a thicker dielectric — capacitance is inversely proportional to dielectric thickness, and 200 wraps of membrane are ~200× thicker than a single bilayer).

The effect on the length constant is dramatic. Recall λ = √(r_m / r_i). Increasing r_m by 5,000× increases λ by ~70×. A signal that would decay to 37% in 0.5 mm now reaches 37% amplitude only after ~35 mm — comfortably enough to span several internodal segments.

The result is saltatory conduction (from Latin saltare, to jump). The action potential fires at one node of Ranvier. The resulting depolarisation spreads passively — quickly, because of the high resistance and low capacitance of the myelinated segment — to the next node, 1–2 mm away. The voltage arriving at the next node is still well above threshold (because the length constant is now much longer than the internodal distance). The next node fires its own action potential. The signal “jumps” from node to node.

The speed gain is enormous. A myelinated fibre 10 µm in diameter conducts at about 60 m/s. An unmyelinated fibre would need to be about 500 µm in diameter to match this speed — 2,500 times the cross-sectional area. A 20 µm myelinated fibre reaches 120 m/s. The human nervous system achieves cable-like speed using biological fibres thinner than a human hair.

Myelin also saves energy. Since ionic current only flows at the nodes (which constitute about 0.1% of the axon surface area), far fewer ions cross the membrane per action potential, and the sodium-potassium pump has far less work to do.

The importance of myelin is starkly demonstrated by demyelinating diseases like multiple sclerosis (MS). When the immune system attacks myelin sheaths in the central nervous system, signals slow, become unreliable, and eventually block entirely. The symptoms — weakness, numbness, impaired vision, loss of coordination — directly reflect the physics of signal propagation in a degraded cable.

The Synapse: Where Electricity Becomes Chemistry (and Back Again)

Action potentials propagate along individual neurons. But the nervous system is a network — 86 billion neurons connected by roughly 100 trillion synapses. At most synapses, the signal jumps from one neuron to the next not electrically but chemically.

When an action potential reaches the axon terminal (the end of the nerve fibre), it opens voltage-gated calcium channels. Ca²⁺ ions flow into the terminal and trigger the fusion of synaptic vesicles — tiny membrane-bound packets containing neurotransmitter molecules — with the presynaptic membrane. The neurotransmitter spills into the synaptic cleft (a gap of about 20 nm) and diffuses across to the postsynaptic membrane, where it binds to receptor proteins that are themselves ion channels.

If the neurotransmitter opens channels permeable to Na⁺ (an excitatory synapse), the postsynaptic membrane depolarises. If it opens channels permeable to Cl⁻ or K⁺ (an inhibitory synapse), the membrane hyperpolarises, moving further from threshold. The postsynaptic neuron integrates inputs from thousands of synapses — a continuous, analogue computation — and fires an action potential only if the net depolarisation at the axon hillock reaches threshold.

The synaptic delay — the time from presynaptic spike to postsynaptic response — is about 0.5–1 millisecond, dominated by the time needed for vesicle fusion and neurotransmitter diffusion across the cleft. This is slow compared to electrical propagation, and it’s the main bottleneck in neural processing. A signal traversing 10 synapses accumulates 5–10 ms of synaptic delay, regardless of how fast the action potentials travel along the axons between them.

A small minority of synapses are electrical synapses (gap junctions), where channels directly connect the cytoplasm of two neurons. These are faster (no chemical intermediary, no synaptic delay) but lack the gain control, plasticity, and computational flexibility of chemical synapses. They’re found where speed matters more than sophistication — in escape reflexes, cardiac muscle synchronisation, and some brainstem circuits.

Information Coding: Spikes as Data

The action potential is all-or-nothing — it can’t carry information in its amplitude. So how does the nervous system encode information?

Rate coding is the simplest scheme: a stronger stimulus produces a higher firing rate. Press harder on your skin, and the mechanoreceptor fires more spikes per second. The relationship between stimulus intensity and firing rate is approximately logarithmic (the Weber-Fechner law), which compresses a huge dynamic range into a manageable firing rate range.

Temporal coding uses the precise timing of individual spikes. In the auditory system, neurons phase-lock to sound waves — firing at a particular phase of each cycle — allowing the brain to detect timing differences between the two ears as small as 10 microseconds (used for sound localisation). This is about 100 times shorter than the duration of a single action potential, which seems paradoxical — but it works because the brain compares the timing of thousands of spikes across many neurons.

Population coding distributes information across many neurons. No single photoreceptor in your retina tells you the colour of an object; colour perception emerges from the relative activity of three cone types, each sensitive to a different wavelength range — the same trichromatic principle used in colour displays.

Spike patterns — bursts, pauses, synchronised oscillations — carry additional information. Neurons in the hippocampus fire in sequences that encode spatial position (place cells) and form temporal sequences during memory consolidation. The interplay of excitatory and inhibitory neurons generates oscillations at characteristic frequencies (theta waves at 4–8 Hz, gamma waves at 30–100 Hz) that may coordinate information flow between brain regions.

The bandwidth of a single nerve fibre — treating spikes as binary events at rates up to ~500 Hz — is roughly 500 bits per second. This is astonishingly low by electronic standards (a USB cable carries billions of bits per second). The brain compensates with massive parallelism: 86 billion neurons, each with thousands of synapses, operating simultaneously.

Propagation Speed Across the Animal Kingdom

Evolution has found multiple solutions to the problem of nerve conduction speed, each reflecting different physical constraints:

The squid giant axon (up to 1 mm diameter, unmyelinated) conducts at ~25 m/s. The squid achieves speed through brute diameter — increasing d increases the length constant and reduces internal resistance. But it can only afford one or a few giant axons per mantle, used exclusively for the escape jet response.

Vertebrate myelinated fibres achieve 120 m/s with diameters of only 20 µm — the myelin solution described above. This allows millions of fast fibres to be packed into a spinal cord.

Insect nervous systems use a compromise: relatively thick axons (up to 50 µm) without myelin, achieving speeds of 2–4 m/s. Insects can get away with this because their bodies are small — a signal crossing the entire length of a fly needs only ~1 ms even at modest speed.

Electric fish (electric eels, torpedo rays) have evolved nerve-muscle interfaces that can discharge synchronised action potentials across thousands of cells, generating voltages up to 860 V (in Electrophorus electricus). The physics is the same — sodium channels, action potentials, cable theory — but deployed as a weapon.

The general scaling rule for unmyelinated fibres (v ∝ √d) and for myelinated fibres (v ∝ d) — where myelinated speed scales linearly with diameter rather than as the square root — reflects the different physics of saltatory versus continuous conduction. The linear scaling of myelinated fibres is more favourable: doubling the diameter doubles the speed, rather than increasing it by only 41%.

From Squid to Silicon: What Neurons Teach Engineers

The Hodgkin-Huxley model wasn’t just a triumph of biology — it was a contribution to nonlinear dynamics. The equations exhibit threshold behaviour, oscillation, excitability, and bifurcation — features that appear in electronic oscillators, laser physics, and chemical reactions.

Neuromorphic engineering — building electronic circuits that mimic neural computation — draws directly on the physics of nerve signals. Memristors (resistors with memory) can emulate the voltage-dependent conductances of ion channels. Spiking neural networks process information using discrete pulses rather than continuous values, promising dramatic improvements in energy efficiency for certain types of computation.

The brain processes information using about 20 watts of power — roughly what a dim light bulb consumes. A modern GPU performing comparable pattern-recognition tasks uses hundreds of watts. The neuron’s secret is not speed (it’s millions of times slower than a transistor) but architecture: massively parallel, event-driven (spikes are sent only when something happens), and extremely energy-efficient per operation.

The action potential is not the most efficient possible signalling mechanism — a physicist designing a nervous system from scratch might choose differently. But it’s the mechanism that evolution arrived at, starting from a cell membrane, some proteins, and a few ions. It works. Five hundred million years of animal nervous systems, from worms to whales, run on the same basic physics: a sodium spike, a potassium reset, and a cable that carries the message from here to there.

Every thought you’ve ever had was a pattern of these spikes. Every sensation, every memory, every decision — voltage pulses racing along biological wires at a hundred metres per second, encoded in timing and frequency, decoded at a hundred trillion synapses.

The physics is simple. What emerges from it is not.