§ B-07 Plasma Membrane Biophysics: Electrogenic Na⁺/K⁺-ATPase Pump & Resting Potential (Grade 10–11 · Membrane Biophysics)
Singer–Nicolson Fluid Mosaic Model, Active 3Na⁺/2K⁺ Transport & Nernst–Goldman Potential. “Per single ATP hydrolyzed, the Na⁺/K⁺-ATPase extrudes 3 Na⁺ ions out of the cell in exchange for 2 K⁺ ions pumped inward, establishing steep ionic gradients and maintaining the negative resting potential.”
Theory Summary & Scientific Mechanism
In the Singer–Nicolson fluid mosaic model, the plasma membrane is a 5 nm-thick amphipathic phospholipid bilayer whose hydrophobic core acts as an electrical capacitor (Cₘ ≈ 1.0 μF/cm²) impermeable to hydrated ions.
Steep transmembrane ion gradients ([K⁺]ᵢ ≈ 140 mM, [Na⁺]ᵢ ≈ 12 mM inside vs. [K⁺]ₒ ≈ 4.5 mM, [Na⁺]ₒ ≈ 145 mM outside) are maintained by the electrogenic Na⁺/K⁺-ATPase pump, which hydrolyzes 1 ATP per E₁ ≤ftrightarrow E₂ cycle to extrude 3 Na⁺ outward and import 2 K⁺ inward.
Because resting membrane permeability is dominated by open potassium leak channels (P_K ≫ P_Na), outward K⁺ diffusion leaves the cytosol electrically negative near the Nernst potential E_K = (RT)/(zF)ln ([K⁺]ₒ)/([K⁺]ᵢ) ≈ -90 mV, refined by the Goldman–Hodgkin–Katz equation to Vₘ ≈ -70 mV.
Everyday Analogy
The Na⁺/K⁺ pump acts like a revolving door that spends 1 ATP coin to eject 3 Na⁺ ions outside while letting only 2 K⁺ ions inside. Coupled with outward K⁺ diffusion through open leak channels, this keeps the cell interior negatively charged at -70 mV!
Interactive Question & Derivation
The sodium-potassium pump (Na⁺/K⁺-ATPase) transports ions uphill against their electrochemical gradients using ATP hydrolysis. What is its stoichiometry per 1 ATP molecule hydrolyzed, and why is the resting membrane potential (Vₘ ≈ -70 mV) close to the potassium Nernst potential E_K = (RT)/(F)ln ([K⁺]ₒ)/([K⁺]ᵢ)?
- A: The pump imports 2 Na⁺ and exports 3 K⁺ without consuming ATP
- B: Per ATP hydrolyzed, the pump exports 3 Na⁺ out of the cell and imports 2 K⁺ into the cytoplasm (electrogenic transport), while at rest membrane permeability to K⁺ through leak channels vastly exceeds Na⁺ permeability (P_K ≫ P_Na)
- C: At rest the membrane is impermeable to K⁺ and freely permeable to Na⁺
- undefined: The Nernst equilibrium potential does not depend on extracellular or intracellular ion concentrations
Study Hint: Per ATP hydrolyzed, the pump exports 3 Na⁺ and imports 2 K⁺, while resting permeability is dominated by K⁺ leak channels (P_K ≫ P_Na).
Proof & Explanation: Each conformational cycle of Na⁺/K⁺-ATPase hydrolyzes one ATP molecule to pump 3 Na⁺ ions out of the cell and 2 K⁺ ions into the cytosol. This maintains high intracellular potassium ([K⁺]ᵢ ≈ 140 mM vs. [K⁺]ₒ ≈ 4.5 mM) and high extracellular sodium ([Na⁺]ₒ ≈ 145 mM vs. [Na⁺]ᵢ ≈ 12 mM). Because open K⁺ leak channels dominate resting permeability (P_K ≫ P_Na), K⁺ diffuses outward down its concentration gradient, leaving net negative charge inside near E_K ≈ -90 mV (Vₘ ≈ -70 mV by the Goldman–Hodgkin–Katz equation).
Key Equations & 3D Simulation Parameters
3 Na⁺ᵢn + 2 K⁺ₒut + ATP longrightarrow 3 Na⁺ₒut + 2 K⁺ᵢn + ADP + Pᵢ
- Na⁺/K⁺-ATPase pump activity (ATP turnover rate): 0.4 … 2.5 rel. (default: 1.4 rel.)
- Extracellular potassium concentration [K⁺]ₒut (normal 4.5 mM): 2 … 15 mM (default: 4.5 mM)
- Intracellular sodium concentration [Na⁺]ᵢn: 5 … 30 mM (default: 12 mM)
- Relative permeability ratio P_Na / P_K in Goldman equation: 0.01 … 0.2 (default: 0.04)