Neuroscience Animations

John H. Krantz, Hanover College, krantzj@hanover.edu

Nernst Equations Illustration 1

Brief description and instructions (DRAFT):

Background:

The Nernst Equation [Ev = -58.0*Log([in]/[out]) for the human neuron] specifies the electrical potential (Ev) across a semipermeable membrane if there is only one ion with different concentrations on each side of the membrane. In this equation [] refers to concentrations. [in] therefore refers to the concentration of the ion inside the membrane. If the ion is negative, switch the [in] and [out] values.

The Goldman Equation (Ev = -58.0*Log((kP*[K+ In]+naP*[Na+ In]+clP*[Cl- Out])/ (kP*[K+ Out]+naP*[Na+ Out]+[clP*[Cl- In])), for the human axon) is similar but it p-predicts the equilibrium membrane voltage (Ev) when more than one ion is present, like in the human axon. P refers to the permeability so kP refers to the permeability or ease with which Potassium (K+) can cross the membrane. [] still refers to concentration so [K+ In] refers to the concentration of potassium inside the axon. The other two ions present are Sodium (Na+) and Cloride (Cl-). The Cloride is flipped in the equation because of its negative charges.

Using the illustration:

On the right side of the screen is a graph which plots the membrane voltages over time.

The left side of the screen are the controls. To show the Nerst value of any of the three ions (K+, Na+, Cl-) select the appropriate check box, e.g., Show K+. You can change the concentration values inside and outside the neuron using the sliders below each ion, e.g., [in] for the inside concentration. You can reset all of the concentration values to the values present at the resting potential using the Reset Concentrations. button in the middle of the left side of the screen. Notice, that each ion wants to drive the voltage to very different values if they were the only one present.

To work with the Goldman question, you can show it by pressing the Show Total Membrane Potential checkbox below all the sliders on the left. In addition to changing the concentrations you can also change the relative permeabilities of the different ions. You can resent them to the values for the resting potential by pressing the Reset Permeabilities button on the left. As you increase the permeability does the membrane potential move towards or away from the membrane potential predicted from the Nernst Equation for the ion alone? If you set the permabilities for two of the ions to 0 what does the Goldman Equation predict for the membrane potential? Compare it to the Nernst Equation value for that same ion.

In addition, there are a few other controls. You can show the resting potential on the graph by pressing the Show Resting Potential check box. You can also show the peak voltage of the depolarization phase by pressing the Show Depolarlization Voltage checkbox. Now the Goldman equation does not take into account the activity of the Sodium/Potassium pump. You can add that to the Golman Equation output by pressing the Add Na/K Pump check box.

Click here to open the applet. It will open a new window that will fill your screen.