Resting Potential - Equilibrium Potentials

Equilibrium Potentials

For most animal cells potassium ions (K+) are the most important for the resting potential. Due to the active transport of potassium ions, the concentration of potassium is higher inside cells than outside. Most cells have potassium-selective ion channel proteins that remain open all the time. There will be net movement of positively-charged potassium ions through these potassium channels with a resulting accumulation of excess negative charge inside of the cell. The outward movement of positively-charged potassium ions is due to random molecular motion (diffusion) and continues until enough excess negative charge accumulates inside the cell to form a membrane potential which can balance the difference in concentration of potassium between inside and outside the cell. "Balance" means that the electrical force (potential) that results from the build-up of ionic charge, and which impedes outward diffusion, increases until it is equal in magnitude but opposite in direction to the tendency for outward diffusive movement of potassium. This balance point is an equilibrium potential as the net transmembrane flux (or current) of K+ is zero. The equilibrium potential for a given ion depends only upon the concentrations on either side of the membrane and the temperature. It can be calculated using the Nernst equation:

where

• E_eq,K+ is the equilibrium potential for potassium, measured in volts
• R is the universal gas constant, equal to 8.314 joules·K−1·mol−1
• T is the absolute temperature, measured in kelvins (= K = degrees Celsius + 273.15)
• z is the number of elementary charges of the ion in question involved in the reaction
• F is the Faraday constant, equal to 96,485 coulombs·mol−1 or J·V−1·mol−1
• _o is the extracellular concentration of potassium, measured in mol·m−3 or mmol·l−1
• _i is likewise the intracellular concentration of potassium

Potassium equilibrium potentials of around -80 millivolts (inside negative) are common. Differences are observed in different species, different tissues within the same animal, and the same tissues under different environmental conditions. Applying the Nernst Equation above, one may account for these differences by changes in relative K+ concentration or differences in temperature.

For common usage the Nernst equation is often given in a simplified form by assuming typical human body temperature (37 C), reducing the constants and switching to Log base 10. (The units used for concentration are unimportant as they will cancel out into a ratio). For Potassium at normal body temperature one may calculate the equilibrium potential in millivolts as:

Likewise the equilibrium potential for sodium (Na+) at normal human body temperature is calculated using the same simplified constant. You can calculate E assuming an outside concentration, _o, of 10mM and an inside concentration, _i, of 100mM. For chloride ions (Cl-) the sign of the constant must be reversed (-61.54 mV). If calculating the equilibrium potential for calcium (Ca2+) the 2+ charge halves the simplified constant to 30.77 mV. If working at room temperature, about 21 C, the calculated constants are approximately 58 mV for K+ and Na+, - 58 mV for Cl- and 29 mV for Ca2+. At physiological temperature, about 29.5 C, and physiological concentrations (which vary for each ion), the calculated potentials are approximately 67 mV for Na+, -90mV for K+, -86 mV for Cl- and 123 mV for Ca2+.