Problem Set 2, Problem 1

a.	Start the Nernst Potential Simulator, and load the file Problem2A.init (note that due to a recent renumbering of the problem set, this file name does not match the problem number!). Note that the model membrane is now permeable solely to potassium, and that both Selective Permeability and Electrostatics are active; thus, you will note that the channels in the membrane only allow potassium ions through, and the program changes the probability that ions may cross the membrane based on the membrane potential. The membrane potential is always initialized to $0\ \text{mV}$; you can imagine that there are impermeable charges not shown (such as charged proteins inside the cell) that provide the appropriate charge balance to make the membrane potential initially $0\ \text{mV}$. Before starting the simulation, please calculate the predicted potential across the membrane using the Nernst equation. Show your work. Note that the temperature in this simulation is $298\ \text{K}$ (which is warmer than we earlier assumed) and that actual concentrations in the simulator are rounded to the nearest whole number of ions. Thus, the value predicted by the simulation (the red line on the plot) may not exactly match your calculation.
b.	Now start the simulation briefly, immediately pause it, and click on a red ion on the left side (the intracellular side) so that you can readily track the movements of the ion. Then continue the simulation. Describe the behavior of the single ion, and of all the potassium ions. Also, explain the changes in the graph of membrane potential (black line), and contrast it to the predicted value (the red line). Predict what will happen over long periods of time. Run the simulation for 5,000 iterations to see if your prediction is correct. Explain the results. Take a screenshot of the simulation for your lab notebook, and be sure to include the Membrane Potential plot in the picture.
c.	Press the "Reset with Default Settings" button. Note that the zoom window shows channels selectively permeable to potassium, sodium or chloride ions (tinted red, blue, and green, respectively). Before running the simulation, use the Goldman-Hodgkin-Katz (GHK) equation to calculate the predicted membrane potential (the simulation provides you the concentrations of the key ions inside and outside of the cell, as well as their permeabilities, which you need to solve the equation). Show your work. Again, because of small differences in temperature and concentration, your calculation may differ slightly from the value predicted by the simulator.
d.	Briefly start the simulation, pause it, and select a potassium (red), sodium (blue) and chloride (green) ion to track. Describe the movements of the selected ions and the graph of the membrane potential relative to the predicted potential (red line). Predict what will happen over time. Run the simulation for about 5,000 iterations to see if your prediction is correct. Explain the results. Again, take a screenshot of the simulation for your lab notebook, and be sure to include the Membrane Potential plot in the picture.
e.	The simulation represents only a very small number of the very large numbers of ions that are actually present in real nerve cells. To see how this may affect the results, press the "Reset with Default Settings" button, and then, under the File menu, select Load Initial Conditions, and load the file Problem2B.init (note that due to a recent renumbering of the problem set, this file name does not match the problem number!). The initial conditions are the same, but the "world's" thickness has been greatly reduced. This would be similar to a dendritic spine surrounded by a limited extracellular space. Predict what may happen under these circumstances to the concentration gradients, and to the long term potential across the membrane. Now run the simulation for 5,000 iterations, and see what happens. Once more, take a screenshot of the simulation for your lab notebook, and be sure to include the Membrane Potential plot in the picture. After about 5,000 iterations have passed, pause the simulation, and calculate the new predicted potential from the measured concentrations (found in the table on the right) and the GHK equation. Explain the results, contrasting the mechanisms generating the resting potential with those that generate the Nernst potential for a single ion (parts a and b of this question). How is it that the results you obtained are not observed in most nerve cells?