Electrochemical Potential in Biological Membranes

The existence of life depends on maintaining a state of disequilibrium across cell membranes, which is quantified by electrochemical potential gradients. The sodium-potassium pump (\(Na^+/K^+\)-ATPase), for example, uses the energy from ATP hydrolysis to actively transport \(Na^+\) ions out of the cell and \(K^+\) ions in. This action establishes steep concentration gradients (a chemical potential difference) and contributes to an electrical potential difference, as more positive charge is pumped out than in.

The cell membrane is studded with ion channels, which are proteins that allow specific ions to pass through. The resting membrane potential is primarily established by ‘leak’ channels that are more permeable to \(K^+\) than \(Na^+\). \(K^+\) ions flow out of the cell down their concentration gradient, leaving behind a net negative charge inside and thus creating an electrical potential that opposes further outflow. The equilibrium, described by the Goldman-Hodgkin-Katz equation, is reached when the electrical force pulling \(K^+\) in balances the chemical force pushing it out.

This stored energy in the electrochemical gradient is harnessed for vital functions. In neurons, a stimulus can open voltage-gated ion channels, allowing a rapid influx of \(Na^+\) that depolarizes the membrane and creates an action potential. In mitochondria, the electron transport chain pumps protons across the inner membrane, creating a powerful electrochemical gradient that drives ATP synthase to produce the cell’s primary energy currency, ATP.