The Membrane Potential

The membrane potential (Vm) is the difference in electrical voltage between the inside and outside of a cell, conventionally reported as inside minus outside. At rest, most animal cells sit at a resting membrane potential somewhere between −60 mV and −90 mV, with neurons typically near −70 mV, skeletal muscle near −90 mV, and many non-excitable cells (fibroblasts, glia) in a shallower −20 to −40 mV range. The negative sign means the cytoplasm carries a net negative charge relative to the extracellular fluid — but crucially, this "net negative charge" corresponds to an almost imperceptibly tiny excess of anions over cations right at the membrane surface, not a bulk imbalance of charge in the cytoplasm. Two ingredients are jointly necessary and neither alone is sufficient. First, concentration gradients: the Na⁺/K⁺-ATPase pump continuously exports 3 Na⁺ and imports 2 K⁺ per ATP hydrolyzed, so a typical mammalian cell maintains roughly 140 mM K⁺ inside versus 5 mM outside, and roughly 145 mM Na⁺ outside versus 12 mM inside. Chloride is typically higher outside (~110 mM) than inside (~10 mM in neurons, though this varies with the activity of chloride transporters). Second, selective permeability: the plasma membrane is studded with leak channels (particularly K⁺ leak/"two-pore domain" channels) that let K⁺ cross far more readily than Na⁺ crosses at rest — permeability ratios of roughly 1 (K⁺) : 0.04 (Na⁺) : 0.45 (Cl⁻) are typical estimates for resting squid axon, though exact ratios vary by cell type. Without gradients, permeability does nothing (there'd be nothing to diffuse down). Without permeability, gradients do nothing (ions are locked in place and no charge separation develops). The resting potential is what emerges when both are present simultaneously. It is essential to separate two distinct physical roles that are easy to conflate. The pump (the Na⁺/K⁺-ATPase) is a battery-charger: it uses ATP hydrolysis to move ions uphill, against their gradients, establishing and maintaining the concentration differences. The channels (leak channels, mainly for K⁺) are the actual voltage generators on a moment-to-moment basis: it is K⁺ diffusing down its gradient through open channels — not the pump directly — that produces the bulk of the resting voltage. If you poisoned the pump acutely (say, with ouabain) the resting potential would not instantly collapse; it would decay slowly over minutes to hours as the gradients the pump had built gradually ran down through leak pathways. This distinction between the gradient-builder and the voltage-generator is the crux of the entire chapter.

Step 1 — Build the gradients. The Na⁺/K⁺-ATPase, embedded in the plasma membrane, binds 3 intracellular Na⁺ ions and 1 ATP, phosphorylates itself, changes conformation, releases Na⁺ outside, binds 2 extracellular K⁺ ions, dephosphorylates, and releases K⁺ inside — a cycle repeated continuously. Because it moves 3 positive charges out for every 2 positive charges in, the pump is itself modestly electrogenic: every cycle removes one net positive charge from the cytoplasm. In most cells this direct electrogenic contribution is small (a few mV at most) compared to the diffusion potential described next, but it is not zero, and in some cells (renal epithelium, cardiac Purkinje fibers) it is physiologically significant.

Step 2 — Ions diffuse down their gradients through leak channels. At rest, the dominant conductance pathway is the K⁺ leak channel. Because [K⁺]inside ≫ [K⁺]outside, K⁺ ions diffuse out of the cell down their concentration gradient. Each K⁺ ion that leaves carries one positive charge outward, leaving one uncompensated negative charge behind (largely on impermeant intracellular anions — proteins, organic phosphates, sulfates — that cannot follow K⁺ out through the channel).

Step 3 — Charge separation creates an electric field that opposes further diffusion. As K⁺ efflux proceeds, the inside becomes progressively more negative and the outside more positive. This growing voltage exerts an electrical force pulling K⁺ back into the cell — opposing the chemical force pushing K⁺ out. Net efflux slows as the voltage builds, until the electrical pull exactly cancels the chemical push. At that point, K⁺ ions still cross the membrane in both directions continuously (there is no net flux, but flux in each direction continues), and the system is at electrochemical equilibrium for K⁺.

Step 4 — Quantify with the Nernst equation. The voltage at which a single ion species reaches this equilibrium is its equilibrium potential, given by the Nernst equation:

where R is the gas constant, T is absolute temperature, z is the ion's charge, and F is Faraday's constant. At human body temperature (37 °C) with base-10 logarithms, RT/F ≈ 61.5 mV, so for a monovalent cation:

Plugging in typical mammalian neuron values:

Note that EK is deeply negative (K⁺ "wants" to leave, pulling Vm negative) while ENa is strongly positive (Na⁺ "wants" to enter, pulling Vm positive). These two ions pull Vm in opposite directions; which one wins depends entirely on relative permeability.

Step 5 — Combine multiple ions with the GHK equation. No real membrane is permeable to only one ion, so the actual resting potential is not exactly EK — it is a weighted average of all the equilibrium potentials, weighted by each ion's relative permeability (P). This is the Goldman-Hodgkin-Katz (GHK) voltage equation:

(Note chloride's inside/outside terms are flipped relative to the cations because of its negative charge.) Because resting PK is roughly 25-fold greater than PNa in many neurons, Vm sits close to but not exactly at EK — typically around −70 mV rather than −90 mV, dragged slightly positive by the small but nonzero Na⁺ permeability. This is the single most important quantitative fact in the chapter: the resting potential is not the equilibrium potential of any one ion — it is a permeability-weighted compromise, dominated by whichever ion the membrane leaks most.

Step 6 — Recognize the physical scale involved. A remarkable and often-missed feature: the number of ions that actually need to cross the membrane to build the resting potential is minute — far too small to measurably change bulk ionic concentrations. For a spherical cell of typical size, achieving a 70 mV potential requires the net movement of roughly 1 K⁺ ion per 100,000 to move across the membrane relative to the total number present. This is why the resting potential can be established and abolished (as in an action potential) essentially instantaneously without "running out" of gradient — the pump only needs to restore this vanishingly small imbalance, not re-establish the whole concentration gradient, after each electrical event.

Bernstein's membrane hypothesis (1902). Julius Bernstein first proposed that the resting potential arises because the cell membrane is selectively permeable to K⁺ and that Vm should approximately equal EK, calculated from the Nernst equation. His theory correctly predicted the order of magnitude and sign of the resting potential and predicted that raising extracellular K⁺ should depolarize cells — later broadly confirmed. But his model, built before ion channels were understood, assumed the membrane became transiently and uniformly permeable to all ions during excitation, and it could not explain a puzzling fact discovered decades later: the action potential overshoots zero, becoming briefly positive inside — something impossible if K⁺ permeability alone governed the membrane at all times.

Cole and Curtis (1939) and Hodgkin and Huxley's overshoot observation (1939). Using the giant axon of the squid Loligo — large enough (up to ~1 mm diameter) to insert an internal electrode directly into the cytoplasm — Kenneth Cole and Howard Curtis, and separately Alan Hodgkin and Andrew Huxley, made the first direct intracellular recordings of membrane potential. They found the resting potential was indeed negative (roughly −60 to −70 mV) as Bernstein predicted, but during an action potential, Vm swung not just to zero but to roughly +40 mV — a genuine overshoot. This flatly contradicted the simple Bernstein hypothesis of uniform, non-selective permeability increase.

Hodgkin and Katz (1949) — the decisive experiment. Alan Hodgkin and Bernard Katz reasoned that if the overshoot reflected a transient increase specifically in Na⁺ permeability (since ENa is positive, near where the overshoot peaks), then systematically varying external Na⁺ concentration should predictably shift the overshoot's amplitude, while leaving the resting potential comparatively unaffected. They bathed squid giant axons in seawater diluted with isotonic dextrose to lower external [Na⁺] to various fractions of normal, and measured both resting potential and action potential peak.

Results:

• Lowering external Na⁺ had little effect on the resting potential — consistent with rest being governed mainly by K⁺, not Na⁺, as Bernstein/GHK theory predicts.
• Lowering external Na⁺ substantially reduced the overshoot amplitude, and the reduction closely tracked the value predicted by the Nernst equation for ENa at each new [Na⁺]o — an approximately 58 mV shift per tenfold change in [Na⁺]o at room temperature, the expected Nernstian slope for a monovalent ion.
• Conversely, raising external K⁺ produced a graded, quantitatively predictable depolarization of the resting potential, again tracking the Nernst prediction for EK.

This was the crucial test: it showed the membrane potential at any moment is not fixed but tracks the equilibrium potential of whichever ion the membrane is, at that instant, most permeable to — resting state dominated by K⁺, action potential peak dominated by Na⁺. This directly established the ionic selective-permeability hypothesis in its modern, quantitative form and led to the Hodgkin-Huxley model of the action potential (Nobel Prize in Physiology or Medicine, 1963, shared with John Eccles).

A complementary line of evidence: pump-poisoning experiments. If gradients (not just permeability) matter, blocking the Na⁺/K⁺-ATPase (with the cardiac glycoside ouabain, which binds the pump's extracellular K⁺-binding site and locks it) should — over time, as leak pathways dissipate the gradients — cause the resting potential to decay toward zero. This is exactly observed: ouabain-treated cells show intact resting potentials initially (proving the pump is not the instantaneous voltage source) followed by slow depolarization over tens of minutes to hours as [Na⁺]in rises and [K⁺]in falls, confirming the pump's separate role as gradient-maintainer rather than moment-to-moment voltage generator.

Example 1 — Calculating Vm with the GHK equation for an atypical cell. Consider a glial cell with unusually leaky chloride channels alongside standard K⁺ and Na⁺ permeabilities. Measured concentrations:

First compute each equilibrium potential using 61.5 mV × log₁₀(ratio) at 37 °C:

• EK = 61.5 × log₁₀(5/130) = 61.5 × (−1.415) ≈ −87.0 mV
• ENa = 61.5 × log₁₀(150/15) = 61.5 × (1.0) ≈ +61.5 mV
• ECl = −61.5 × log₁₀(120/5) = −61.5 × (1.380) ≈ −84.9 mV (note the sign flip for anions)

Now apply GHK, weighting by permeability (using the flipped Cl⁻ convention baked into the formula):

Numerator: 5 + 7.5 + 2 = 14.5 Denominator: 130 + 0.75 + 48 = 178.75 Vm = 61.5 × log₁₀(14.5/178.75) = 61.5 × log₁₀(0.0811) = 61.5 × (−1.091) ≈ −67.1 mV Notice Vm (−67.1 mV) sits between EK (−87.0 mV) and ECl (−84.9 mV) on one side and ENa (+61.5 mV) on the other, much closer to the two negative equilibrium potentials because K⁺ and Cl⁻ dominate the permeability-weighted sum. This illustrates the general rule: Vm is always bounded by the most extreme equilibrium potentials of the permeant ions, and pulled toward whichever ion has the largest P × concentration term.

Example 2 — Clinical reasoning: hyperkalemia and cardiac risk. A patient in renal failure has a serum (extracellular) K⁺ of 7.5 mM instead of the normal ~4.5 mM, while intracellular K⁺ remains near 140 mM (intracellular concentration changes little acutely because most body K⁺ is intracellular and cellular buffering is fast). Estimate the new EK and reason about the clinical consequence. Normal: EK = 61.5 × log₁₀(4.5/140) ≈ 61.5 × (−1.493) ≈ −91.8 mV Hyperkalemic: EK = 61.5 × log₁₀(7.5/140) ≈ 61.5 × (−1.271) ≈ −78.2 mV Raising extracellular K⁺ makes EK less negative — it shifts by about +13.6 mV. Because resting Vm tracks EK closely (K⁺ dominates resting permeability), the cardiac myocyte resting potential depolarizes toward this new, less-negative EK. This is dangerous: cardiac voltage-gated Na⁺ channels are partially or fully inactivated at depolarized resting potentials, slowing or blocking the rapid upstroke of the cardiac action potential, which manifests on an ECG as widened QRS complexes and, if severe, can precipitate life-threatening arrhythmias (ventricular fibrillation, asystole). This is precisely why hyperkalemia is a medical emergency and why it is treated acutely with intravenous calcium (to stabilize cardiac membrane excitability) and insulin/glucose (to drive K⁺ back into cells and lower [K⁺]outside, restoring EK toward normal) — a direct clinical application of Nernst-equation reasoning.

Alan Lloyd Hodgkin trained as a physiologist at Cambridge and, together with Andrew Huxley, spent the years before and after World War II working on the squid giant axon — chosen specifically for its enormous diameter, which finally made it possible to thread a fine internal electrode down the axon's length and record transmembrane voltage directly, rather than only from the surface. Bernard Katz, a refugee from Nazi Germany who had trained under A.V. Hill, joined Hodgkin at University College London in the late 1940s. Their 1949 collaboration on sodium-dependence of the action potential — building directly on the surprising overshoot Hodgkin and Huxley had already measured in 1939, work interrupted for a decade by the war — supplied the decisive experimental proof that selective, dynamically changing ionic permeability, not a fixed "resting" permeability to all ions, underlies both the resting potential and its dramatic reversal during excitation. This work fed directly into the 1952 Hodgkin-Huxley equations describing the action potential quantitatively, a landmark achievement in quantitative biology that still underlies computational neuroscience today.

Cardiology relies daily on membrane-potential physics: antiarrhythmic drugs (class I agents like lidocaine, class III agents like amiodarone) work by modulating Na⁺ or K⁺ channel behavior, deliberately shifting how quickly and to what voltage cardiac cells depolarize and repolarize. Emergency treatment of hyperkalemia (see Worked Example 2) is textbook Nernst-equation medicine applied at the bedside.

Local and general anesthesia exploits voltage-gated Na⁺ channel blockade (lidocaine, procaine) to prevent the depolarizing Na⁺ influx needed to reach action potential threshold, silencing pain-fiber signaling without altering the resting potential itself.

Neurological and neuromuscular disease often traces to ion-channel dysfunction that perturbs resting or threshold potentials — the "channelopathies," including certain epilepsies (Na⁺ or K⁺ channel mutations), periodic paralyses, and myotonias, are diagnosed and understood through exactly this Nernst/GHK framework.

Diabetes and insulin secretion: pancreatic β-cells couple glucose metabolism to membrane depolarization via ATP-sensitive K⁺ channels — rising intracellular ATP closes these channels, reducing K⁺ efflux, depolarizing the cell, and triggering voltage-gated Ca²⁺ entry and insulin release. Sulfonylurea diabetes drugs (glibenclamide, glipizide) directly target these K⁺ channels, artificially closing them to stimulate insulin secretion — a direct pharmacological manipulation of resting-potential physiology.

Agricultural and pest-control biotechnology exploits insect-specific voltage-gated ion channel differences: pyrethroid insecticides target insect Na⁺ channels preferentially, disrupting resting and action potentials in pest nervous systems with far lower mammalian toxicity.

Bioelectronics and diagnostics — patch-clamp electrophysiology, EEG, ECG, and emerging optogenetic and voltage-sensitive-dye imaging technologies all fundamentally read out, manipulate, or depend on exactly the ionic mechanisms described here, linking basic membrane biophysics to cutting-edge neuroscience and cardiac diagnostics.

Ask the tutor: How does the resting membrane potential set up and interact with the driving forces used in secondary active transport?