Human Physiology Homework II
Imagine a neuron with no dendrites and 1m axon. The distance between nodes of Ranvier 1mm. Cell body diameter 20µm. Axon internal diameter 10µm.
Assume normal concentration of potassium and sodium:
[K+] inside=140mM; [K+]outside=4mM;
[Na+]inside=15mM; [Na+]outside=150mM;
1. Approximate membrane potential at equilibrium when K+ permeability is infinitely greater than Na+ permeability:
Approximate membrane potential at equilibrium when Na+ permeability is infinitely greater than K+ permeability:
Approximate membrane potential at equilibrium when Na+ permeability is equal to K+ permeability:
Approximate membrane potential at equilibrium when membrane permeability of K+ is 100 times that of Na+.
2. Imagine that you are the luckiest neurophysiologist on the Earth. You have succeeded in penetrating the neuron with 5 intracellular electrodes as indicated in the Figure above.
· Electrode 1 penetrated the cell body
· Electrode 2 penetrated axon hillock
· Electrode 3 penetrated the axon at the 1st internodal space under myelin sheath
· Electrode 4 penetrated the axon at the 1st node of Ranvier
· Electrode 5 penetrated nerve terminal
You are recording the electrical signal from all 5 electrodes simultaneously. The figure below shows the recording of an action potential obtained from electrode 2. Horizontal axis indicates time. On the same figure please reconstruct the recordings from electrodes 4 and 5. Please assume constant conduction velocity along the axon.
Again the figure below shows the recording of an action potential obtained from electrode 2. Copy the recordings from electrodes 4 and 5 from the figure above. Now approximate the voltage you will measure in electrode 3.
3. This is the record obtained from electrode 2.
Reconstruct corresponding Na+ and K+ permeability changes at the axon hillock
4. Draw distribution of charges across the axon membrane at rest:
5. Draw distribution of charges across the axon membrane when the action potential is initiated at the axon hillock. Indicate the major currents of ions (electrical current):
6. Draw distribution of charges across the axon membrane when the action potential arrives at the electrode 4. Indicate the major currents of ions (electrical current):
8. This is the record obtained from electrode 2.
Reconstruct record from electrode 3. Indicate corresponding Na+ and K+ permeability changes at the first internodal space (under the myelin), half way between the axon hillock and the next node of Ranvier.
9. You are fed up with the experiment and decided to drive the neuron to death. After 30 min of stimulating the cell at the frequency of 100 Action Potentials per second you find out that the neuron is alive and happy! Assume that only intracellular concentrations of K+, and Na+ were affected: new [K+]inside=80mM (reduced from [K+]i=140mM; [K+]outside=4mM;
new [Na+]inside=70mM (increased from [Na+]inside=15mM); [Na+] outside=150mM;
-Approximate the new membrane potential at equilibrium when K+ permeability is infinitely greater than Na+ permeability:
-Approximate the new membrane potential at equilibrium when Na+ permeability is infinitely greater than K+ permeability:
-Approximate the new membrane potential at equilibrium when Na+ permeability is equal to K+ permeability:
-Approximate the new membrane potential at equilibrium when membrane permeability of K+ is 100 times that of Na+:
10. This is the record obtained from electrode 2 before you overstimulated the neuron.
Draw the record from electrode 2 after you overstimulated the neuron.
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