Problem:

E. coli aspartate transcarbamoylase (ATCase) has a Hill coefficient of 1.7 and Vmax 4.5 ?M/min. The definition of Vmax is kcat*[Etot], where kcat is the rate constant for formation of product. The measured value of kcat for this reaction, which is determined in the absence of CTP, is 800 min-1. The dissociation constant for the allosteric effector CTP from ATCase is 1 mM. When CTP is bound to ATCase the K0.5 for aspartate is 20 mM; when CTP is not bound to ATCase the K0.5 for aspartate is 5 mM.

Required:

Question 1: Calculate what the concentration of total ATCase is under the conditions where Vmax was determined.

Question 2: Calculate how much ATCase is present with CTP bound and how much is present without CTP bound when the CTP concentration is 6 mM.

Question 3: Calculate how much ATCase is present with CTP bound and how much is present without CTP bound when the CTP concentration is 0.3 mM.

Question 4: Calculate the velocity of the ATCase reaction when aspartate is present at 4.2 mM and CTP is present at 6 mM.

Question 5: Calculate the velocity of the ATCase reaction when aspartate is present at 4.2 mM and CTP is present at 0.3 mM.

Show the pedigree and your calculation.