Membrane Transport Calculator

Calculate membrane permeability coefficient, flux, and compare passive vs active transport.

Permeability coefficient P (cm/s) (cm/s)

Lipids: 10⁻³, ions: 10⁻¹⁰

Concentration gradient ΔC (mM) (mM)

Membrane area A (cm²) (cm²)

Transporter Vmax (nmol/s) (nmol/s)

Transporter Km (mM) (mM)

Please check your inputs and try again.

Why Lipid Solubility Governs Passive Permeability

To cross a bilayer by simple diffusion, a molecule must dissolve in the hydrophobic core. Permeability therefore tracks the oil–water partition coefficient, moderated by size — Overton's rule.

J = P × A × ΔC P ∝ K_partition × D / thickness

Species	P (cm/s)	Why
O₂, CO₂	~10⁻¹	Small, non-polar
Water	10⁻³	Small, polar — crosses despite polarity
Glucose	10⁻⁷	Large and polar
Na⁺	10⁻¹⁰	Charged — hydration shell must be shed

The nine-order gap between oxygen and sodium is the entire reason membranes can hold ion gradients while gases equilibrate freely. Charge is far more prohibitive than size: sodium is smaller than glucose yet a thousand times less permeant, because moving an ion into the hydrophobic core means stripping its hydration shell at enormous energetic cost.

Three Transport Modes

Mode	Saturable	Energy	Against gradient
Simple diffusion	No — linear in ΔC	None	No
Facilitated diffusion	Yes — Michaelis–Menten	None	No
Active transport	Yes	ATP or ion gradient	Yes

Saturation is the diagnostic test. Simple diffusion rises linearly with concentration difference without limit; anything carrier-mediated plateaus at V_max. Facilitated and active transport are distinguished by whether transport can proceed uphill.

Primary and Secondary Active Transport

The Na⁺/K⁺ ATPase consumes ATP directly and accounts for a substantial share of resting metabolic rate — roughly 20–30% in many tissues. Secondary active transport then spends the gradient it creates, moving glucose or amino acids uphill by coupling them to sodium flowing down.

This is why blocking the pump eventually stops intestinal glucose absorption too, despite glucose transport itself consuming no ATP. Aquaporins are the other refinement: water crosses bilayers slowly by simple diffusion, but tissues needing rapid water movement express channels that raise permeability roughly a hundredfold.

Worked Examples

Example 1: Water channel aquaporin: P=0.1cm/s, ΔC=1mM

vs lipid bilayer P=10⁻³

Result: Aquaporin: 100× faster water transport

Kidney collecting duct: ADH inserts aquaporins

Example 2: Na+ passive: P=1e-10, ΔC=145mM

Extremely low passive permeability

Result: Requires Na+/K+ ATPase active transport

Ion pumps maintain gradients against passive leak

Example 3: Why aquaporins exist

Water P through bilayer versus aquaporin

Result: Roughly a hundredfold difference

Water crosses lipid slowly despite its small size. Tissues needing rapid movement, such as kidney tubule, express channels to raise permeability.

Example 4: Sodium coupling in the gut

SGLT1 moving glucose uphill

Result: No ATP used directly

The transporter spends the sodium gradient rather than ATP. Blocking the Na⁺/K⁺ pump indirectly halts glucose absorption.

Common Mistakes

⚠️

Assuming size is the main barrier

Charge matters far more. Sodium is smaller than glucose but a thousandfold less permeant, because shedding its hydration shell is energetically prohibitive.

⚠️

Confusing facilitated diffusion with active transport

Both saturate, but only active transport moves solute against its gradient. Facilitated diffusion still runs downhill.

⚠️

Treating simple diffusion as saturable

It rises linearly with concentration difference without limit. Any observed plateau indicates a carrier or channel.

⚠️

Overlooking secondary active transport

Glucose uptake in the gut consumes no ATP directly but depends entirely on the sodium gradient the pump maintains.

Frequently Asked Questions

Lipid solubility rule?

Small nonpolar molecules (O2, CO2, steroids, ethanol): high P (10⁻³-10⁻¹ cm/s). Small polar (water): moderate with aquaporins. Ions (Na+, K+, Cl-): very low passive P (10⁻¹⁰), require channels/transporters. Large polar (glucose): very low, require GLUT transporters.

Active vs passive transport energetics?

Passive: down concentration/electrochemical gradient, no energy. Active (primary): ATP-driven (Na+/K+-ATPase, SERCA). Secondary active: use gradient built by primary ATPase (Na+-glucose symport: uses Na+ gradient to drive glucose uptake against its gradient).

Why are ions so impermeant?

Because entering the hydrophobic core requires shedding the hydration shell, which is energetically very costly. Charge is a greater barrier than size.

How do I distinguish simple from facilitated diffusion?

Simple diffusion is linear in concentration difference and never saturates. Facilitated diffusion follows Michaelis–Menten kinetics and plateaus at V_max.

What is secondary active transport?

Moving a solute uphill by coupling it to another ion flowing downhill. It uses no ATP directly but depends on gradients maintained by primary pumps.

Why do cells need aquaporins if water crosses membranes?

Simple diffusion of water is slow. Aquaporins raise permeability roughly a hundredfold, which tissues such as kidney tubule require.