$(30$ pts$)$ On Canvas you will find Matlab code BME$201\_$HW$2\_2024.$m$.$ This code carries out Euler integration to solve for LR$($t$)$ based on the free parameters kon, koff and Rtot. The input is a

step increase in $L.$ Go through the code and make sure you understand what every step is doing. It may seem complicated at first, but most of the lines are comments to help you understand what's happening. Do you see how each line relates to your steps in Problem $3?$ Start with $k_{on}=1M^{-1}{s}^{-1},$koff$=1s^{-1}$ and $R_{\text{t}\text{o}\text{t}}=1M.$

a$)$ The final $LR$ is governed by the fractional occupancy equation. First, get the analytical solution to steady$-$state $[$LR$]$ across the following $[$L$]$ concentrations: $0\mathrm{.}3,1,3,10,$ and $30M.$ Note that fractional occupancy solves for LR$/$Rtot$.$ Now, run simulations for each concentration and using the Data Cursor tool, find the steadystate $[$LR$].$ Plot the theoretical and the computed solutions of $LR$ versus $L$ on separate figures. Do they agree?