The Nernst Potential

The Nernst equation calculates the equilibrium potential (also referred to as the Nernst potential) for an ion based on the charge on the ion (i.e., its valence) and the concentrations across the membrane. Temperature also influences the Nernst potential. A Nernst potential will develop across a membrane if two criteria are met: (i) a concentration gradient exists across the membrane, and (ii) if selective permeation pathways (i.e., selective ion channels) exist that allow transmembrane movement of ions. Finally, for seletive ion channels, where the selectivity filter strongly favors the permeation of one ion over other ions, the Nernst potential also predicts the reversal potential (V_rev) of the current-voltage (I-V) relationship.

• V_Eq. is the equilibrium potential (Nernst potential) for a give ion. It is common to use the ion symbol as a subscript to denote the equilibrium potential for that ion (e.g., V_K, V_Na, V_Cl, V_Ca, etc.). If only one ionic species is present in the system, and/or channels for only one ionic species are present, then V_Eq. will also be the membrane potential (V_m). Note that the unit of V_Eq. is the Volt. However, the equilibrium potential is typically reported in millivolts (mV). If two or more ions contribute to the membrane potential, use the Goldman-Hodgkin-Katz (GHK) equation to calculate the V_m.
• R is the universal gas constant (8.314 J.K^-1.mol^-1).
• T is the temperature in Kelvin (°K = °C + 273.15).
• z is the valence of the ionic species. For example, z is +1 for Na⁺, +1 for K⁺, +2 for Ca²⁺, -1 for Cl^-, etc. Note that z is unitless.
• F is the Faraday's constant (96485 C.mol^-1).
• [X]_out is the concentration of the ionic species X in the extracellular fluid. Note that the concentration unit must match that of [X]_in.
• [X]_in is the concentration of the ionic species X in the intracellular fluid. Note that the concentration unit must match that of [X]_out. Typically, but not always, the concentrations are noted in mM.

• Universal Gas Constant (R) = 8.314 J.K^-1.mol^-1
• Faraday's Constant (F) = 96485 C.mol^-1

Enter appropriate values in all cells except the one you wish to calculate. Therefore, at least four cells must have values, and no more than one cell may be blank. The value of the blank cell will be calculated based on the other values entered. Please note that the unit of temperature is the Kelvin. It is also important to note that although this worksheet allows you to select different concentration units, during the calculation, the numerator and denominator units are converted so that they match. This ensures that the fraction ([X]_o/[X]_i) will be unitless. Also note that based on the constants used (R = 3.814 J.K^-1.mol^-1 and F = 96485 C.mol^-1), the unit of V_Eq. will be in Volts. Keeping this fact in mind, this worksheet simplifies the calculation by allowing you to calculate directly to or from mV.

As mentioned above, the Nernst equation calculates the equilibrium potential for an ion based on the charge on the ion (i.e., its valence) and the concentrations across the membrane. If only one ionic species is present in the system and/or one type of ion channel is present, the Nernst potential also determines the resulting membrane potential (V_m). Of course, it must be assumed that the ion channels are open in order to allow transmembrane movement of the ionic species for which the channel is specific. If channels for two or more ions are present (and are open), both ions contribute to the membrane potential. In this case, V_m will not be at the equilibrium potential for either ion and, thus, no ion will be at equilibrium. To calculate the membrane potential when two or more ions play a role, use the Goldman-Hodgkin-Katz (GHK) equation.