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Problem Set 5 Revised

Problem Set 5 Revised - ChE 101 2012 Problem Set 5 1...

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ChE 101 2012 Problem Set 5 1. Computational problem of the week: It is oft quoted that “when you ASSUME, you make an ASS of U and ME”. In kinetics, we often make simplifying assumptions to make our modeling more tractable, but a good kineticist must always be wary of the validity of these approximations. In this problem, we will develop bounds on the conditions under which the equilibrium and steady state approximations are valid in the case of enzyme kinetics. Consider the following standard reaction sequence in the Michaelis-Menten model, E + S k f GGGGGGB FGGGGGG k b ES k cat GGGGGGGA E + P For starters, consider the following kinetic parameters, typical for in vitro studies of biological catalysts: k cat = 10 s - 1 k b = 10 3 s - 1 k f = 10 6 M - 1 s - 1 [ E ] 0 = 1 μ M [ S ] 0 = 1 mM (a) Plot the product concentration as a function of time under (i) the equilibrium assump- tion, (ii) PSSA, (iii) exact calculation. Why do all three approaches yield the same result? Compare the computational costs of the three approaches. (b) Now we will see how the validity of the two approximations depends on the value of k cat . Holding all other parameters fixed, plot the time required for 80% conversion of S over several orders of magnitude of k cat values, and compare the results from the three approaches. Determine constraints on k cat /k b for validity of the approximate treatments. (c) Repeat (b), but this time vary [ E ] 0 relative to [ S ] 0 . Up to what catalyst loading are the approximations valid, and how does this compare to typical concentrations in biochem- ical experiments? 2. Bisubstrate reactions with enzymes: In lecture, we developed the rate law for single substrate reactions involving enzyme catalysis. However, many enzymatic reactions of interest involve two or more reacting species, such as reactions of two substrates or a substrate and a cofactor. For example, consider the 2+4 cycloaddition of a diene with a dienophile, aka the Diels-Alder reaction: 1
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HN O O CO 2 - X + O N Y N O NH O O CO 2 H P Figure 1
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