what would the code be in Matlab?

Exercise 2 - An autoregulatory gene. We also discussed in class a model for a simple autoregulatory gene; that is, a gene that encodes a protein whose function (or part of whose function is to activate the transcription of itself. Recall that the system of differential equations for this is: d[Xmna] dt [Xprot)? K12+[Xprot] 2 X " - dt != w[Xmna] Xprot[Xprot] 1. Using = w = Xprot = Xena = 1 s- and K1/2 = 0.33 MM, use the Forward Euler approach 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. 2. Repeat (1), changing only the initial concentrations; run the simulation 4 times, first setting the initial protein concentration to 0.2 mM and 0.5 mm, with the initial RNA concentration set to 0.0 mm, and then setting the starting RNA concentration of 0.2 mM or 0.5 mm, while the initial protein concentration is zero. Briefly dicuss your observations. 3. In (1) and (2), the focus was on observing how the concentrations of protein and RNA varied (independently) with time; we will know consider how to look at the phase plane of this system. Re-run your simulation using all combinations of starting concentrations of both RNA and protein, ranging from 0.0 to 1.4 mM in intervals of 0.2 mm. This is a LOT of data, as you will have a total of 64 starting concentrations. So, instead of displaying this data as 64 different plots versus time, plot ALL the simulations on one plot of [Xrna) vs (Xprot). 4. Write a paragraph (or more) summarizing your observations, and how this may relate to the biology of the system. Hint: For part (3), you will want to use multiple "for loops. At the outer level, you should make a loop over the starting concentrations, something like: for (rnal = 0:0.2:1.4) for (proto = 0:0.2:1.4) Fill in this section with your simulation code. end end You will also need to make use of the "hold on" command. This makes new plots appear on the same graph without overwriting the previous figure. Exercise 2 - An autoregulatory gene. We also discussed in class a model for a simple autoregulatory gene; that is, a gene that encodes a protein whose function (or part of whose function is to activate the transcription of itself. Recall that the system of differential equations for this is: d[Xmna] dt [Xprot)? K12+[Xprot] 2 X " - dt != w[Xmna] Xprot[Xprot] 1. Using = w = Xprot = Xena = 1 s- and K1/2 = 0.33 MM, use the Forward Euler approach 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. 2. Repeat (1), changing only the initial concentrations; run the simulation 4 times, first setting the initial protein concentration to 0.2 mM and 0.5 mm, with the initial RNA concentration set to 0.0 mm, and then setting the starting RNA concentration of 0.2 mM or 0.5 mm, while the initial protein concentration is zero. Briefly dicuss your observations. 3. In (1) and (2), the focus was on observing how the concentrations of protein and RNA varied (independently) with time; we will know consider how to look at the phase plane of this system. Re-run your simulation using all combinations of starting concentrations of both RNA and protein, ranging from 0.0 to 1.4 mM in intervals of 0.2 mm. This is a LOT of data, as you will have a total of 64 starting concentrations. So, instead of displaying this data as 64 different plots versus time, plot ALL the simulations on one plot of [Xrna) vs (Xprot). 4. Write a paragraph (or more) summarizing your observations, and how this may relate to the biology of the system. Hint: For part (3), you will want to use multiple "for loops. At the outer level, you should make a loop over the starting concentrations, something like: for (rnal = 0:0.2:1.4) for (proto = 0:0.2:1.4) Fill in this section with your simulation code. end end You will also need to make use of the "hold on" command. This makes new plots appear on the same graph without overwriting the previous figure