Ions and Membranes
Every living cell is enclosed by a lipid bilayer that is selectively permeable to ions. Potassium, sodium, calcium, and chloride ions are maintained at vastly different concentrations inside and outside the cell by ATP-powered pumps. This concentration gradient is a form of stored energy — a biological battery. The Nernst equation quantifies the voltage that balances a single ion's concentration gradient, while the Goldman equation integrates contributions from all permeable ions.
The Nernst Potential
For potassium with typical mammalian concentrations (140 mM inside, 5 mM outside), the Nernst potential is approximately -89 mV. This means that at -89 mV, K+ ions are in electrochemical equilibrium — no net flow occurs. For sodium (12 mM inside, 145 mM outside), the Nernst potential is about +67 mV. The cell's actual resting potential lies between these extremes, weighted by relative permeabilities.
Goldman Equation and Resting Potential
The Goldman-Hodgkin-Katz voltage equation accounts for multiple ion species simultaneously. At rest, K+ permeability dominates, pulling the membrane potential toward -90 mV. During excitation, Na+ permeability surges, driving the potential toward +60 mV. This simulation lets you adjust permeability ratios and concentrations to see how the resting potential shifts in real time.
Clinical Relevance
Disruptions in ionic balance cause serious pathology. Hyperkalemia (high extracellular K+) depolarizes cardiac cells and can trigger fatal arrhythmias. Channelopathies — genetic defects in ion channels — underlie epilepsy, long QT syndrome, and cystic fibrosis. Understanding membrane transport physics is fundamental to pharmacology, cardiology, and neuroscience.