LIFE SCIENCE · the cell-culture lab · the math of the living · kept by THE CULTURE

THE NERNST EQUATION ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP

Every living cell is a tiny battery. Pump more potassium inside than out, let it leak, and the charge imbalance builds a VOLTAGE across the membrane — the Nernst equation says exactly how much: about −90 millivolts for potassium. That voltage is the resting state a nerve fires FROM. Concentration on one side, electricity on the other, balanced. Slide the ion gradient.

◆ LIT▲ AMBER
◧ THE MEASURE · 2D
◍ THE CELL'S VOLTAGE · 3D · a battery made of ions
◆ THE FOURTH · 4D · a tesseract turns
◐ THE SHADOW · one dimension down
👶 THE TODDLER CORNER — one fat tap
out/in
E (mV)
ion
K⁺
resting

◆ LIT — exact / checkable

The Nernst equation gives the equilibrium potential where an ion’s diffusion (down its concentration gradient) exactly balances the electrical force: E = (RT/zF)·ln([out]/[in]). At body temperature RT/F ≈ 26.7 mV, so for potassium (z=+1, ~5 mM out / 140 mM in) Eₖ ≈ −89 mV — close to a neuron’s resting potential, which the cell holds by leaking mostly K⁺. Every action potential is a controlled departure from these Nernst voltages. A fail-loud self-check throws unless K⁺ at 5/140 gives about −90 mV. ◆ real electrophysiology, node-verified.

▲ AMBER — the figure

Nernst gives ONE ion’s equilibrium; the real resting potential (Goldman equation) weights several ions by permeability, so it sits near but not exactly at Eₖ. The concentration↔voltage balance is the exact content.

LIFE SCIENCE: life is chemistry that keeps its own books.  — THE CULTURE
David Lee Wise / ROOT0 / TriPod LLC  ·  the life-science lab, with AVAN