In this assignment, you will use Matlab to simulate protein binding to the glass surface in a flow cell. Use the following parameters:

[BSA] is 0.1, 1, 10 M

Time is 0, 1, 3, 10, 30, 100 sec

K_D = k_off/k_on

k_on = 0.1, 1, 10 M^-1s^-1, k_off varies

Volume = 10 l

Surface monolayer of BSA is 6 pmol of BSA bound = 0.6 M bound

For these simulations, think of surface binding sites at 0.6 M in the flow cell ([sites]_total = 0.6 M in equation below). BSA is partitioned into free in solution and bound to surface, such that:

[BSA]_total = [BSA]_free + [BSA]_bound

where [BSA]_total is what you put into the flow cell at time zero. You have to maintain mass balance (BSA is either bound or free) at all times. Also, there are a finite number of binding sites on the surface, so:

[sites]_total = [sites]_bound + [sites]_free.

You need to maintain mass balance of sites as well. Note also that

[sites]_bound = [BSA]_bound

by definition.

The differential equation for bound BSA is:

d[BSA]_bound/dt = k_on*[BSA]_free*[sites]_free k_off*[BSA]_bound

Q.8 First, we will simulate BSA binding to the surface over time. Starting with a K_D of 0.1 M and k_on of 10 M^-1s^-1, plot [BSA]_bound vs time for [BSA]_total of 0.1, 1, and 10 M. On same plot, repeat for same K_D but k_on of 1 and 0.1 M^-1s^-1. Repeat for K_D of 1 and 10 M to generate three plots total with 9 traces for each plot. Include legend on plot and label axes and include a descriptive caption for your figure.

Q.9 Next we will plot the amount of BSA bound at specific times versus the total BSA in the system. From the kinetics plots you generated above, generate plots for the amount of protein bound to the surface versus [BSA]_total at times 1, 3 and 10 sec (like you used for the experiment). Generate three plots of [BSA]_bound vs [BSA]_total, one for each K_D of 0.1, 1 and 10 M. For each one, plot [BSA]_bound vs. [BSA]_total for three different k_on values and three different times, so 9 traces per plot and one plot for each of three K_D values.

Hint: The Mathlab ode23 function maybe helpful for this simulation assignment. For more information of the function ode23, you may refer to https://www.mathworks.com/help/matlab/ref/ode23.html