$1.15$ points. Consider the signaling network motif shown in Figure $2($a$)$ from the paper by

Tyson, Chen, and Novak. Assume that case $2$ is utilized $($Rp activates the degradation of X$).$

Note one correction to the paper: in the first ODE, the last term should be negative.

a$)$ Using MATLAB, solve the three ODE model with input signal S $=2.$ Plot the levels of X$,$

Yp$,$ and Rp over time.

b$)$ Solve the model for two additional values for S$,$ one less than Scrit$1$ and one greater than

Scrit$2.$ For each case, plot the levels of X$,$ Yp$,$ and Rp over time, and report the value of S

that you selected. What is the long$-$term behavior of the system for these values of S$?$