a)Solve the differential equations for [S], [ES], [P] using MATLAB.
Let k1 = 10,000 (M-s)-1, k-1 = 10 s-1, and k2 = 100 s-1. The initial enzyme concentration (Eo) is 0.5 mM and the initial substrate concentration is 2 mM.Note that you will solve for [S], [ES], and [P] using ODE45.Plot [S] vs. t and [P] vs. t

Hint: substitute [E]= [Eo] –[ES] in differential equation 1 and 2 solved in class to get to the equations that will be used in MATLAB

At time t=0, [P]=0, [S]= 2 mM, and [ES]=0

b) Use the code written above to calculate product at three different initial substrate concentrations.

[S]= 2, 1, 0.5 mM. Plot [P] vs. t graphs for all three concentrations on the same graph. Compare the [P] curve from each substrate concentration and comment on the trend.

c)Also plot the Michaelis-Menten relationship for rate of product formation as a function of substrate concentration using the k values above. Use initial substrate concentration=2*10^-3:0.001:1;

Plot three curves with three different k1 and k-1 conditions on the same graph.

k1= 10000, k-1= 1000
k1=10000, k-1=100
k1=10000, k-1=10
Discuss why change in k-1 changes the rate of product formation.

Sample Solution