The enzyme urease catalyzes the hydrolysis of urea to ammonia plus carbon dioxid

Question

The enzyme urease catalyzes the hydrolysis of urea to ammonia plus carbon dioxide. At 21 degree C the uncatalyzed reaction has an activation energy of about 125 kJ/mol, whereas in the presence of urease the activation energy is lowered to about 46 kJ/mol. What is the rate enhancement of urea hydrolysis by urease? The catalytic efficiency of many enzymes depends on pH. Chymotrypsin shows a maximum value of k_cat/K_M at pH 8. Detailed analysis shows that k_cat increases rapidly between pH 6 and 7, then remains constant at higher pH. K_M increases rapidly between pH 8 and 10. Suggest explanations for these observations. Given the substrate below, design an active site that may accommodate be specific for this ligand. What are the primary differences between the lock-and-key model and the induced-fit model for enzyme catalysis? Using reaction coordinate diagrams, explain how (a) increasing temperature and (b) utilizing a catalyst/enzyme increase the rate of reaction. How do each of the discussed enzyme mechanisms (acid-base catalysis, covalent catalysis, etc.) lower the activation energy of the transition state? Other practice problems (you do not need to turn these in but are recommended for practice) Ch.11, odd questions Answers to odd questions from Voet and Voet, 5^th edition are available via link provided on Blackboard. Remember to practice drawing and naming the 20 standard amino acids!

Explanation / Answer

Answer 1)

Rate enhancement by enzyme = Kcat / Kuncat. .................. (1)

Kcat = Rate constant for catalyzed reaction

Kuncat = Rate constant for uncatalyzed reaction.

Rate constant (K) and Activation energy are related through Arhenus equation as,

k = Ae(-Ea/RT).

Let Ea1 be the activation energy for catalyzed reaction and Ea2 be that of for uncatalyzed reaction.

Kcat = Ae(-Ea1 / RT). and Kuncat = Ae(-Ea2/RT).

so,

Kcat / Kuncat = e(-Ea1 / RT)./e(-Ea2 / RT). = e[(Ea2 - Ea1) / RT] .............(2)

Comparing eq.(1) and (2) we get,

Rate Enhancment = e[(Ea2 - Ea1) / RT] .........(3)

We are given with the information,

Activation energy for Urase catalyzed reaction Ea1 = 46 kJ/mole = 46000 J/mole.

Activation energy for Uncatalyzed reaction = Ea2 = 125 kJ/mole = 125000 J/mole.

R = 8.314 J/K.mole.

T = 21 oC = 273 + 21 = 294 K

Using these values in above equation.(3)

Rate enhancement = e[(125000-46000) / 8.314x294] = e[79000/ 2444.316] = e[32.32] = 1.1 x 1014.

Rate enhancement = = 1.1 x 1014.

Being a ratio of same quantities, Rate enhancment is an unitless quantity.

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