Problem 3:        
Enzyme Kinetics Analysis II

A pathogenic fungus (Ustilago rutabagus) that causes
the plant disease rutabaga smut is related to the fungus that
causes corn smut (Ustilago maydis, the main component of
huitlacoche). You have found that this fungus is able to
metabolize a variety of unusual sugars. One of these is psicose, an
epimer of fructose rarely found in nature, except in some
agricultural products. (Psicose is being considered as an
alternative sweetener, as it tastes almost as sweet as sucrose, but
is not generally metabolized by humans.)

Once the fungus takes up psicose, it is immediately
phosphorylated, which is usually the case for carbohydrates. You
have isolated the enzyme catalyzing this reaction, which requires
ATP as the other substrate:

psicose + ATP ® psicose-6-P_i
+ ADP

The sequence of the gene encoding this enzyme (which you call
psicokinase) is not closely related to other kinases
catalyzing similar sugar phosphorylation reactions, so this may be
a new type of kinase. You wish to explore its mechanism in more
detail. You set up 25 tubes containing buffer (pH 7.4), ions (to
mimic the cytoplasm), and various combinations of psicose and ATP.
You initiate each reaction by adding the enzyme (final
concentration = 1 nM), stop the reaction after
2-10 minutes, and measure psicose-6-P_i by a
chromatographic technique. The calculated rates are tabulated
below:

With which of these mechanisms are most consistent with
these data?

a) “Ping-Pong” mechanism

b) ternary complex with ordered
pathway (which one binds first?)

c) ternary complex with random
pathway

Briefly justify your conclusion.

Determine the following parameters for
psicokinase:

K_m and/or K_d for
psicose

K_m and/or K_d for
ATP

k_cat of the enzyme