For all the questions below, use the parameters µ = ω = χprot = χrna = 1 s
−1 and K1/2 = 0.33
mM.
1. (a) Implement the Forward Euler approach to integrating this system to determine the
concentration of both RNA and protein over time. Use a total time of 20 s and a
time step of 0.01 s, and an initial concentration of 0.5 mM for both RNA and protein.
Plot the concentrations as a function of time.
(b) Rerun the simulation from (a), but using an initial protein concentration of 0.2 mM
and an initial RNA concentration of 0 mM.
(c) Rerun the simulation from (a), but using an initial protein concentration of 0.5 mM
and an initial RNA concentration of 0 mM.
(d) Rerun the simulation from (a), but using an initial protein concentration of 0 mM
and an initial RNA concentration of 0.2 mM.
(e) Rerun the simulation from (a), but using an initial protein concentration of 0 mM
and an initial RNA concentration of 0.5 mM.
(f) Discuss your observations.