[Lo.Lee.Ta.]

I have been looking at this enzyme kinetics stuff forever and was trying to come up with a summary for things... #=_=

Is this even right...? :/

                 |---------------|This segment I'm calling "Part 2"
           k1         k2
E + S    ES    E + P
           k-1
|---------------|This segment I'm calling "Part 1"

Part 1 and Part 2 are separate reactions, but together, they form the overall enzyme reaction.
Part 1 is dependent on the Km value, Part 2 is dependent on the Kcat value, and the entire enzyme reaction is dependent on the ratio of Kcat to Km (or Kcat/Km).

Part 1:
Since it is dependent on the Km value, and Km = (k-1  +  k2)/k1, which means
 (ES breakdown)/(ES formation), you have to ask, "Is the ES breakdown higher than the formation?"
If yes, then it means  Km, so ES tends to break down (slow).
If no,  Km, so ES tends to stay together (fast rxn).

Part 2:
Have to ask, "Is Kcat high or low?"
If high, fast product formation.
If low, slow product formation.


So for the entire enzyme-catalyzed reaction, it seems like there would only be these 4 possibilities:

1.  Kcat +  Km = slow for ES to form, but once it does, quickly generates product.


2.  Kcat +  Km = fast for ES to form and quickly generates product.


3.  Kcat +  Km = slow for ES to form, and once it does, slowly generates product.


4.  Kcat +  Km = fast for ES to form, but slowly generates product.
             


...Well, is any of this even right???
Please help me! D:
Thank you SO much!

[Irlanur]

I didn't look at it too closely, but I guess that looks fine. of course you can have all kind of intermediate cases, not only the ones you have. anyways, they help to understand.

[Babcock_Hall]

Most enzymes have more than three rate constants, and the definitions of the various kinetic constants is accordingly more complex.  Your way of thinking about these issues seems a little different to me than what I am used to.  Some kineticists focus on V_max and V/K as the fundamental kinetic constants, and they think of K_m as the ratio of these two.  You might find Dexter Northrop's article to be helpful:  http://biochemlab.org/wp-content/uploads/2011/06/Biochemistry-concepts-enzyme-kinetics-Northrup.pdf