Reversal potential

Equilibrium potential

The equilibrium potential for an ion is the membrane potential at which there is no net movement of the ion. The flow of any inorganic ion, such as Na⁺ or K⁺, through an ion channel (since membranes are normally impermeable to ions) is driven by the electrochemical gradient for that ion. This gradient consists of two parts, the difference in the concentration of that ion across the membrane, and the voltage gradient. When these two influences balance each other, the electrochemical gradient for the ion is zero and there is no net flow of the ion through the channel; this also translates to no current across the membrane so long as only one ionic species is involved. The voltage gradient at which this equilibrium is reached is the equilibrium potential for the ion and it can be calculated from the Nernst equation.

Mathematical models and the driving force

We can consider as an example a positively charged ion, such as K⁺, and a negatively charged membrane, as it is commonly the case in most organisms. The membrane voltage opposes the flow of the potassium ions out of the cell and the ions can leave the interior of the cell only if they have sufficient thermal energy to overcome the energy barrier produced by the negative membrane voltage. However, this biasing effect can be overcome by an opposing concentration gradient if the interior concentration is high enough which favours the potassium ions leaving the cell.

An important concept related to the equilibrium potential is the driving force. Driving force is simply defined as the difference between the actual membrane potential and an ion's equilibrium potential ${\displaystyle V_{\mathrm{m}}-E_{\mathrm{i}}}$where ${\displaystyle E_{\mathrm{i}}}$refers to the equilibrium potential for a specific ion. Relatedly, the membrane current per unit area due to the type ${\displaystyle i}$ ion channel is given by the following equation:

${\displaystyle i_{\mathrm{i}}=g_{\mathrm{i}}\left(V_{\mathrm{m}}-E_{\mathrm{i}}\right)}$

where ${\displaystyle V_{\mathrm{m}}-E_{\mathrm{i}}}$ is the driving force and ${\displaystyle g_{\mathrm{i}}}$ is the specific conductance, or conductance per unit area. Note that the ionic current will be zero if the membrane is impermeable to that ion in question or if the membrane voltage is exactly equal to the equilibrium potential of that ion.