Problem Statement: For an enzyme that follows the Michaelis-Menten kinetics in solution v=vm*s/(Km+s), derive the rate expression v when it is bound to a surface. Approximate your rate expression with the Michaelis-Menten expression of the form vmm=vmapp*sb/(Kmapp+sb), where vmapp is estimated as the maximum of your expression v, and Kmapp as the value of sb at which v=vmapp/2. Plot the full v and the approximated vmm to see how good the Michaelis-Menten approximation is. (See eqn 3.54 in Shuler and Kargi, but be cautioned that you may not reach the same expression given in eqn 3.54b.)
Solution:
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