If the membrane is selectively permeable to only one ion and we know the intracellular and extracellular concentrations of the ion then we should be able to predict the theoretical value of the membrane potential once equilibrium has been reached.
This theoretical value is known as the
The equilibrium potential for any ion can be conveniently calculated using the Nernst equation which was named after 
. The formulation of the equation requires a reasonable grasp of thermodynamics and electrochemistry (which we will leave to our friends in physical sciences), but suffice to say that the equilibrium potential for any ion (Eion) can be calculated using the
Where:
Eion = the equilibrium
potential for the ion (in mV)
R = Gas constant
T = Temperature (absolute)
z = ion valency (+1 for monovalent cations)
F = Faraday constant
[ion]in = intracellular ion concentration (in mM)
[ion]out=extracellular ion concentration (in mM)
However the above equation is very clumsy so we can try and simplify it a bit. Because the natural logarithm of a number is equal to 2.303 times the log10 we can rewrite the equation to give:
Again this equation is a little cumbersome but because R and F are constants and if we restrict ourselves to considering monovalent cations (i.e K+ and Na+) and body temperature (37oC) then we can rewrite the equation as:
This version of the Nernst equation is much more convenient to use providing we remember that it applies only to monovalent cations at 37oC.
The Nernst equation is important because it allows us to calculate the theoretical value of the membrane potential in a cell which is selectively permeable to one ion species providing we know the intracellular and extracellular ion concentrations. A few examples below should help illustrate this point:
Example 1.In this example the intracellular [K+] = 100 mM and the extracellular [K+] = 5 mM. Therefore the equilibrium potential for K+ under these circumstance can be calculated by substituting these values into the Nernst equation as follows: EK+ = -61 x Log10 (100/5) EK+ = -61 x Log10 (20) EK+ = -61 x 1.301 EK+ = -79.4 mV Consequently, given these intracellular/extracellular ion concentrations, if only K+ channels were open in this cell then the membrane potential would equal -79.4 mV. |
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Example 2.In this example the intracellular [Na+] = 15 mM and the extracellular [Na+] = 105 mM. Therefore the equilibrium potential for Na+under these circumstance can be calculated by substituting these values into the Nernst equation as follows: ENa+ = -61 x Log10 (15/105) ENa+ = -61 x Log10 (0.143) E Na+ = -61 x -0.845 E Na+ = +51.6 mV Consequently, given these intracellular/extracellular ion concentrations, if only Na+ channels were open in the cell then the membrane potential would equal +51.6 mV. |
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Example 3.In this example the intracellular [Cl-] = 35 mM and the extracellular [Cl-] = 165 mM. This example is a little different from the previous two because Cl- is a monovalent anion. Remember that in simplifying the Nernst equation we derived a formula which was applicable to monovalent cations. However from the derivation you should be able to see that all we have to do is change the sign on the standard formula and it will then apply to monovalent anions like Cl- Therefore the equilibrium potential for Cl- under these circumstance can be calculated by substituting these values into the slightly modified Nernst equation as follows ECl- = +61 x Log10 (35/165) ECl- = +61 x Log10 (0.212) ECl- = +61 x -0.673 ECl- = -41.1 mV Consequently, given these intracellular/extracellular ion concentrations, if only Cl- channels were open in this cell then the membrane potential would equal -41.1 mV. |
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Now have a go at doing a few of these types of calculations on your own. If you get the question wrong you can select the HELP option and it will take you through the calculation:
For the moment the physiological significance of equilibrium potentials may not be particularly obvious. However as we move through the nervous, muscular, cardiovascular and even reproductive systems we will come across cells whose functions are fundamentally controlled by changes in their membrane potential.
The critical thing for you to grasp at this stage is that if the membrane is selectively permeable to one ion species (i.e. only channels for this ion are open) then the membrane potential will be equal to the equilibrium potential for that ion (which in turn can be calculated from the Nernst equation). If you understand this concept you are well on your way to grasping one of the most complicated aspects of physiology and are once step closer to gaining total enlightenment!