Chemistry Cleland Diagram & Binding Order from Lineweaver Burke Plots

[The Head]

Homework Statement

(b) Draw a Cleland diagram for the mechanism of the reaction shown above that is consistent with the following data. Briefly justify your reasoning.

(d) In light of the data in parts (b) and (c), can you conclude that ATP binds first to the enzyme? Briefly explain your reasoning.

(e) Kinetic data give the following KM values for the three substrates:
ATP KM = 1.8 mM Cys KM = 0.1 mM GlcN KM = 0.2 mM
At steady-state inside the cell, the enzyme is entirely saturated with ATP. How would you rationalize this fact in light of the above KM data?

Relevant Equations

N/A

I am mostly focused on parts (b) and (d), which I typed out. For (b), I can tell the first pair of graphs is a sequential reaction (when Cysteine is saturated), but it appears ping-pong for the others because the slopes are roughly parallel. I know sequential has to reactants binding (so I guess that would be ATP and GlcN), and I suppose that a reaction occurs there and then maybe Cysteine binds to react with an intermediate?

But then again, if Cysteine is saturated, I don't know if that makes sense, because Cysteine should be able to bind.

Also, how do we know ATP binds first (part d)? Part (e) also confuses me, because ATP has the highest K_m, so the lowest binding affinity, but ATP is saturating the enzyme. It seems like there would be less binding for that.

 

[TeethWhitener]

I want to help, but I’m not sure how to handle 3 substrates at a time off the top of my head. I think there are some wrinkles that don’t appear in the two substrate case. There’s this:
https://books.google.com/books?id=-...I#v=onepage&q=trisubstrate mechanisms&f=false
Best of luck.