Proline racemase, a bacterial enzyme, catalyzes the interconversion of D and L-proline. The K_m values for D and L-proline are 2.3 mM and 3.8 mM respectively.  The maximal velocity is 8 x 10^-3 mol/mg per min for L-proline. Various compounds have been tested as inhibitors of the enzymes. Their structure and extent of inhibition are indicated below.
 

Inhibitor	Concentration [M]	Percent Inhibition*
Pipecolate	1.1 x 10-1	18
Pyrrole-2-carboxylate	5.7 x 10-2 3.6 x 10-4	98 50
2-Thiophenecarboxylate	5.7 x 10-2	73
2-Furoate	5.7 x 10-2	11
Tetrahydrofuroate	1.1 x 10-2	10

1. Write the reaction catalyzed by proline racemase. What is the equilibrium constant for this reaction? What would be a reasonable structure for the transition state?

2. Using graph paper draw a Lineweaver-Burk Plot (1/v vs. l/[S]) for the uninhibited enzyme. Label the axes appropriately. On the same sheet draw the plot expected when 3.6 x 10^-4M pyrrole-2-carboxylate is present as a competitive inhibitor.

3. Calculate the catalytic constant K_cat for proline racemase. The enzyme is composed of two identical subunits each with a molecular weight of 38,000 daltons.

4. Rank the five compounds listed above in order of their inhibitory action. Explain why the best inhibitor has a K_i approximately 160 times lower than the K_m values for proline.