The generic system is A(X)è(K1)èB(Y)è(K1’)èC(Z)
1. Create the A compartment (containing substance X) in SL and PROVE that when you start with a certain amount of X (the IC of an integrator) you get the expected result of X leaving the compartment exponentially. Label all axes and show the model with the blocks identified with appropriate labels. Submit the identified and labeled screen shot.
Reminder: To create a text box by double-clicking, and move by dragging the edge of the box.
2. Write the differential time dependent equations for the entire system of AèBèC with substances X, Y, and Z respectively. Submit the equations done neatly and in large text.
3. Now create the SIMULINK model for the ENTIRE system in 2 (above). Be sure to label lines and blocks with the variables or parts of the equation that are associated with the line or block. Make k1=k1’ - this is your initial, stable state). Submit a labeled screen shot of a RUN.
4. RUN the model in #3 with all 3 outputs: X(t), Y(t), Z(t) on ONE scope set to autoscale and label axes and each curve with X, Y, Z (with color coding). Submit a screen shot.
5. Now change k1 and k1’ to show the effect on Y, the B component. Do two different combinations of k1 and k1’ that CLEARLY show the effects on Y(t), the B component. Show a screen shot of each run. In doing this do as follows:
A. For EACH combination above, describe what you expect to happen to ALL 3 variables. Does the simulation verify your expectation?
B. Assume that Y(t) is an enzyme that participates significantly in manufacturing epinephrine. For EACH of the two conditions in 6A, describe what you expect will happen to heart rate AND blood pressure compared to the normal state.
HINT: If your ‘k’ value appears more than once in your model, be sure that you change all of them.
6. “Make it – Take it” (MI-TI) is a ubiquitous, omnipresent process in physiology and biochemistry. In a BRIEF 2 sentence statement, how does the simulation in #5 and #6 above demonstrate the MI-TI principle?
7. Given that the k and k’ rate values are enzyme-like steps, how would you use a drug to increase the B value (Y) by:
A. Manipulating k
B. Manipulating k’