1. Plot the functions x1 and x as functions of voltage

2. Assume that you hold the membrane potential V at -120 mV until the system reaches equilibrium (i.e. until dx=dt = 0, where x = (V;m; h; n; a; b;M;H)T ) and that at time t = 0 you suddenly change and hold the value of the membrane potential at a value Vo. Plot the currents IL, INa, IK, IA, ICaT as well as the total current as functions of time for a number of dierent values Vo of you choice in the range -75 to +40 mV.

3. Write an algorithm for numerically approximating the solution to the above model.

4. Using the algorithm you developed in Question 2, illustrate the presence of post-inhibitory rebound (PIR) in the above model.

5. Using the algorithm you developed in Question 2 and assuming that ICaT is completely blocked (i.e. GCaT = 0), construct the gain function of the above model.

6. How does the gain function you constructed in Question 5 dier from the gain function of the original Hodgkin-Huxley model?