$(20$ Points$)$ In this exercise, we will be using Euler integration to model enzyme kinetics. The MATLAB code BME$201\_$HW$3\_$Q$4\_2024.$m simulates the following system:

E $+$ S $$ ES $->$ E $+$ P

by modeling the concentrations for species E$,$ S$,$ ES$,$ and P$.$ Look over the code and make sure you understand what each line is doing.

Use the MATLAB file to simulate an enzymatic reaction for a range of substrate concentrations. Use the rate constants given in Problem $3$ and choose Etot $=0\mathrm{.}1\backslash$mu M$.$ Use the plots and the data cursor tool to approximate the rate dP$/$dt for substrate concentrations $[$S$]=0,0\mathrm{.}3,1,$ and $3\backslash$mu M$.$ Hint: remember the graphical interpretation of the derivative dP$/$dt$.$ Choose a value of dt and read out dP from the graph. Report the values of $[$S$]$ and dP$/$dt in a table like the one below, comparing them to the dP$/$dt values reported from the Michaelis$-$Mente equation.