The McGill Physiology Virtual Lab

RMP Laboratory

RMP >  Theory Nernst Equation
  The value of the equilibrium potential for any ion depends upon the concentration gradient for that ion across the membrane. If the concentrations on the two sides were equal, the force of the concentration gradient would be zero, and the equilibrium potential would also be zero. The larger the concentration gradient, the larger is the equilibrium potential. The equilibrium potential for any ion can be calculated using the so called Nernst equation.
   
In this experiment, we will test the hypothesis that the muscle membrane at rest is exclusively permeable to potassium. If this hypothesis is valid, then the resting membrane potential should be the same as the equilibrium potential for potassium.

Hypothesis: Em = Ek

Therefore it should be possible to predict the changes in resting membrane potential for various [K+]o using simply the Nernst equation which for potassium ions is :
R = gas constant (8.31 joule/degree Kelvin-mole)
T = absolute temperature (degrees Kelvin)
F = Faraday constant (9.65 x 10^4 coulomb/mole)
z = the valence of the ion, in this case 1
[K+]o = extracellular K concentration in mM
[K+]i = intracellular K concentration in mM
ln = logarithm with base e
At room temperature, this equation can be reduced to:

A graph of Ek vs log10[K+]o will be a straight line with a slope of 58. Note that for a 10-fold change in [K+]o, Ek will change by 58 mV. For a 100-fold change in [K+]o, Ek will change by 116 mV (58 + 58).   In the box below, you can enter sample [K+]o values and Ek will be calculated for you. For physiological conditions, we will assume that [K+]i = 139 mM. In the graph to the right, Ek is plotted, assuming that a [K+]i of 139mM remains the same as [K+]o changes. In the graph, note the general trend of the Ek: with increasing [K+]o, Ek is reduced, i.e. becomes less negative.

If Em=Ek, then the graph for Em should appear similar to that for Ek as given above. However as you will see after performing the lab, this is not the case. At physiological levels of [K+], the measured membrane potential is usually less negative than the potassium equilibrium potential (Ek), mainly because the Na+ permeability although small, is not zero at rest. Thus we will conclude that although Em is close to Ek, it is not exactly equal; especially at low [K+]o, due to the influence of Na+.

 

In the graph below, you can test the effect of changing the relative permeability to K and Na. To simplify, [Na+]o was assumed to be 140 mM, and [Na+]i was assumed to be 15 mM. [K+]i was assumed to be 139 mM. Note that the x-axis scale on the graph below is Log[K+]o; this is equivalent to plotting on an actual log scale as in the graphs above. Try the following combinations:

  • pk = 1 and pna = 0.025 (normal membrane permeabilities)

  • pk = 1 and pna =0 (the membrane is impermeable to Na)

  • pk = 0.5 and pna = 0.025 (the relative permeability to K has decreased)

The above graph for Em was determined using the Goldman Equation, which is similar in form to the Nernst Equation, but incorporates permeability to Na and Cl. (In fact, the inclusion of Cl does not appreciably affect the solution of the equation.)

Goldman Equation

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