Membrane transport: passive, facilitated, and active

Every membrane is a barrier that lets some molecules cross and stops others. The gap between “what a cell needs inside” and “what is outside” is filled by a spectrum of transport mechanisms — from unassisted lipid-bilayer diffusion, through selective channels, to ATP-powered pumps. This guide sorts membrane transport into three thermodynamically distinct classes, walks the mathematics of each, and works the numbers for the two most important pumps in physiology (Na⁺/K⁺-ATPase and the H⁺ gradient at ATP synthase).

Prerequisites: Bioenergetics: ΔG in a metabolic pathway and Electron transport chain. Both use the electrochemical gradient thinking that transport builds on.

Three transport classes, by thermodynamics

Transport is classified by whether it (a) requires an energy input and (b) requires a protein carrier:

1. Simple diffusion. Solutes cross the lipid bilayer directly. No protein, no ATP. Driven by concentration gradient alone. Works only for small non-polar molecules (O₂, CO₂, N₂, urea, water via aquaporins) and lipid-soluble drugs. ΔG = RT ln(C_in / C_out), so the direction is set purely by concentration.

2. Facilitated diffusion. A membrane protein (channel or carrier) provides a permeation path. No ATP required — still driven by the electrochemical gradient. Includes:

• Ion channels (voltage-gated Na⁺, K⁺, Ca²⁺; ligand-gated ACh receptor). Move ions fast (10⁶-10⁷ per second per channel) once open.
• Uniport carriers (glucose transporter GLUT1). Bind one substrate at a time, cycle through conformational states.
• Aquaporins. Water-specific pores that allow rapid osmotic water flow with proton exclusion.

3. Active transport. Uses energy to move a substrate against its electrochemical gradient. Two subclasses:

• Primary active — uses ATP or another chemical energy directly. Na⁺/K⁺-ATPase, Ca²⁺-ATPase, H⁺-ATPase, ABC transporters.
• Secondary active — couples the movement of one substrate down its gradient (usually Na⁺ or H⁺) to the movement of another against its gradient. Includes symport (both same direction) and antiport (opposite directions).

The Na⁺/glucose cotransporter (SGLT1) in the gut epithelium is the textbook secondary active transporter: 2 Na⁺ moving into the cell (down their gradient) pull 1 glucose molecule in with them, even against glucose’s concentration gradient. That is how the intestine can absorb glucose against a concentration gradient — an indirect ATP cost, since the Na⁺ gradient itself is maintained by the primary active Na⁺/K⁺-ATPase.

The electrochemical potential — the currency of transport

For any charged species i crossing a membrane, the driving force is the electrochemical potential difference:

$\Delta \mu_i = RT \ln \frac{C_{i,in}}{C_{i,out}} + z_i F \Delta \psi$

where z_i is charge and Δψ = V_in − V_out is the membrane potential (typical value −70 mV in a resting mammalian cell, matrix negative). Two components:

• Chemical gradient (RT ln term): drives ion from high to low concentration.
• Electrical gradient (zFΔψ term): drives cation from + side to − side, anion from − to +.

At equilibrium, Δμ_i = 0. Solving for Δψ at equilibrium gives the Nernst equation:

$\Delta \psi_{eq,i} = -\frac{RT}{z_i F} \ln \frac{C_{i,in}}{C_{i,out}} = -\frac{59}{z_i} \log_{10} \frac{C_{i,in}}{C_{i,out}} \text{ mV at 25 °C}$

For a mammalian cell with K⁺ at 140 mM inside and 4 mM outside: E_K = (−59/1) log(140/4) = −91 mV. If the membrane were selectively permeable to K⁺ only, its resting potential would be −91 mV. The measured resting potential is around −70 mV because Na⁺ leaks in slightly (E_Na = +60 mV) and pulls the membrane away from pure K⁺ equilibrium.

Worked example — energy cost of pumping Na⁺ out

The Na⁺/K⁺-ATPase — physiology’s canonical pump

Na⁺/K⁺-ATPase (also called the sodium pump) is the archetypal primary active transporter. Per catalytic cycle:

• 3 Na⁺ move out (against their gradient)
• 2 K⁺ move in (against their gradient)
• 1 ATP hydrolysed (energy source)
• Net: 1 positive charge exported per cycle (electrogenic; contributes to the resting potential)

The pump is inhibited by ouabain (a cardiac glycoside from Strophanthus plants) and digoxin (from foxglove) — both bind to the K⁺-binding site on the extracellular face. Cardiac glycosides are used therapeutically because Na⁺/K⁺-ATPase inhibition in heart muscle raises intracellular Na⁺, which reduces the driving force for the Na⁺/Ca²⁺ exchanger; Ca²⁺ accumulates in the cell, and contraction strengthens.

Secondary active transport — the gradient economy

Once Na⁺/K⁺-ATPase has built the Na⁺ gradient, other transporters spend it. Examples:

• SGLT1 (Na⁺/glucose symport): 2 Na⁺ + 1 glucose in. Used in intestine and kidney for glucose absorption.
• NCX (Na⁺/Ca²⁺ antiport): 3 Na⁺ in / 1 Ca²⁺ out. Extrudes Ca²⁺ after a contraction.
• NHE (Na⁺/H⁺ antiport): 1 Na⁺ in / 1 H⁺ out. Regulates intracellular pH.
• NKCC (Na⁺/K⁺/2 Cl⁻ symport): bulk salt import in kidney and secretory epithelia; loop diuretics inhibit it.

Each of these depends on the Na⁺ gradient (built by Na⁺/K⁺-ATPase at 25% of the cell’s ATP budget). The energy is stored once and spent many times through the whole cascade of secondary transporters.

Water — passive but non-trivial

Water crosses the bilayer slowly on its own (~10⁻² cm/s permeability) but rapidly through aquaporins (10³ cm/s). Water movement is driven by osmotic pressure (from colligative properties):

$J_v = L_p (\Delta P - \sigma \Delta \pi)$

where L_p is the hydraulic conductivity, ΔP is hydrostatic pressure difference, σ is the reflection coefficient (1 for ideal semipermeable, 0 for freely permeable), and Δπ is osmotic pressure difference. In most cells ΔP is negligible; water follows osmotic gradients set by solute movements. This is why a kidney tubule concentrating urine works by pumping salt out (setting Δπ) and then letting water follow through aquaporins.

Worked example — Nernst potential of a Ca²⁺ gradient

The Goldman equation — real membranes

A real membrane is permeable to several ions with different permeabilities. The resting potential is set by the Goldman-Hodgkin-Katz equation:

$\Delta\psi_m = \frac{RT}{F} \ln \frac{P_K [K^+]_o + P_{Na} [Na^+]_o + P_{Cl} [Cl^-]_i}{P_K [K^+]_i + P_{Na} [Na^+]_i + P_{Cl} [Cl^-]_o}$

For a typical resting mammalian neuron, P_K : P_Na : P_Cl ≈ 1 : 0.04 : 0.45. Because P_K dominates, the resting potential is close to E_K (−90 mV), but the finite P_Na and P_Cl pull it toward the average, giving a measured value of −70 mV.

Action potentials happen when P_Na transiently spikes to 10× P_K, driving the membrane close to E_Na (+60 mV). Then P_K resurges and P_Na shuts, and the membrane returns to resting. The whole spike is a sequential re-weighting of the Goldman equation’s numerator, driven by voltage-gated Na⁺ and K⁺ channels.

Common pitfalls

Confusing electrical and chemical driving forces. For a cation moving from + side to − side, the electrical driving force is helping (positive to negative), but the chemical driving force might be opposing (if the concentration is higher on the − side). Always sum both terms with correct signs.

Assuming Nernst equilibrium applies to non-equilibrium systems. Real cells are held far from Nernst equilibrium by continuous pump activity. The resting potential is a steady state, not thermodynamic equilibrium, and the two are different if pumps are running.

Ignoring the 3:2 stoichiometry of Na⁺/K⁺-ATPase. The pump is electrogenic — it exports one net positive charge per cycle. In cells with high pump density (neurons, cardiac myocytes), the pump itself contributes ~10 mV to the resting potential.

Treating water as a passive follower without permeability. Aquaporins are essential; bilayer-only water flow is 100× too slow for kidney, plant vacuoles, or erythrocyte volume regulation.

Confusing symport with antiport. Symporters carry both substrates the same direction; antiporters carry them opposite directions. Getting this wrong reverses the predicted physiology.

Practice

Where this leads

Membrane transport is the substrate for almost all excitable-cell physiology and modern drug design:

• The action potential — Goldman equation applied to a millisecond timescale with fast Na⁺ and K⁺ conductance changes.
• Neurotransmission — ligand-gated ion channels (nicotinic ACh, GABA-A, glutamate receptors) do fast synaptic signalling.
• Diuretics and antihypertensives — most classes target specific membrane transporters (furosemide → NKCC2 in loop of Henle; hydrochlorothiazide → NCC in distal tubule).
• P-glycoprotein and drug resistance — ABC-family active transporters that pump chemotherapeutics out of cancer cells are one of the largest obstacles to modern oncology.

Every one of them starts by writing Δμ = RT ln(C_in/C_out) + zFΔψ and asking how it is spent or built.