Ok so I have a BioChem test tomorrow on kinetcis and am a little confused about Km. In the book it says that for a two step enzyme reaction, Km=(K2+K-1)/K1 (the numbers are subscripts). Then when step 2 is rate limiting, Km=K-1/K1 and when step 1 is rate limiting Km=K2/K1.

This seems backwards to me. Can someone please explain? I can just memorize the equations, but it is better if I actually understand them. Thanks!

Km is the generalized MM constant...its always (K2 + K-1) / K1. for MM kinetics, the second reaction (ES -> E + product) is always rate limiting (hence where the vmax = k2[ES] comes from)...thats like the basis of the entire equation along with [ES] being constant. your book is dumb.

Km is the generalized MM constant...its always (K2 + K-1) / K1. for MM kinetics, the second reaction (ES -> product) is always rate limiting...thats like the basis of the entire equation along with [ES] being constant. your book is dumb.

It says "When K2 is rate limiting, K2<<K-1 and Km reduces to K-1/K1 which is defined as the dissociation constant, Kd."
It then says something similar about when K-1 or K1 is rate limiting...

well Km is an estimator of how tightly a subtrate binds. a high Km means bad binding, a low Km means good (since low Km implies low K-1). thats all. Km is pretty similar to Kd is what your book is saying since often times k2 << k-1.

I think the reason that you are confused is because K-1 and K2 from your post are actually lowercase, because they represent the rates of the first and second reaction. Thus if step two is rate-limiting, the rate constant k2<<k-1

I think the reason that you are confused is because K-1 and K2 from your post are actually lowercase, because they represent the rates of the first and second reaction. Thus if step two is rate-limiting, the rate constant k2<<k-1

If you look at my first post you will see that I stated the numbers are subscripts. I made the K's capitalized so that the numbers were a little more "subscript looking." lol That is not why I am confused. If step 2 is rate limiting, why should Km even depend on k1 or k-1? It should be based on k2...

If you look at my first post you will see that I stated the numbers are subscripts. I made the K's capitalized so that the numbers were a little more "subscript looking." lol That is not why I am confused. If step 2 is rate limiting, why should Km even depend on k1 or k-1? It should be based on k2...

you need to look at the derivation for the MM equation...its not that hard. you will see near the end that you end up with a constant term (k2 + k-1)/k1. they just lumped all that **** together and called it the MM constant.

it just so happens that the MM constant relates to substrate binding.

I'll make it simple. Rate limiting means slow right? Therefore if step two is rate limiting, this means k2 is small (because of a low rate of rxn). Since k2 is small, the upper part of the equation (k2 + k-1) simply goes to k-1 because it is so much bigger than k2. I hope that helps!

i see what you mean here:
"Then when step 2 is rate limiting, Km=K-1/K1 and when step 1 is rate limiting Km=K2/K1."

well, when step 2 is limiting, that means k2 is hella small, so the MM constant is pretty comprised of only k-1 / k1, right?

i dont know about step one being rate limiting. im not sure how they removed the k-1 because i think it should be high if the substrate doesnt want to bind (ie step 1).

This makes sense on a hand-waving level because if the second step is slow, it does not play a large role in the ability of the enzyme to bind or dissociate from the ligand.

here we go.
Km is (roughly) an inverse measure of the affinity or strength of binding between the enzyme and its substrate. The lower the Km, the greater the affinity (so the lower the concentration of substrate needed to achieve a given rate).

Km literally has no importance besides this estimation. all that matters is that different substrate/enzymes obviously have different Kms. as i said earlier, Km is not derived from something...its just those 3 constants lumped together.

i see what you mean here:
"Then when step 2 is rate limiting, Km=K-1/K1 and when step 1 is rate limiting Km=K2/K1."

well, when step 2 is limiting, that means k2 is hella small, so the MM constant is pretty comprised of only k-1 / k1, right?

i dont know about step one being rate limiting. im not sure how they removed the k-1 because i think it should be high if the substrate doesnt want to bind (ie step 1).

Hmmm...okay. Thanks! That helps for the first part...
Now the biggest thing that confuses me is yeah, when step 1 is rate limiting. Because the teacher was talking about how Km is NOT always an estimation of the enzyme-substrate affinity, and yadda yadda and used that equation as an example. Because in that equation Km=k-1/k1 well that equation is actually the equation for the disassociationconstant of an enzyme reaction, and in the case of a step 1 limited reaction, then Km=Kd. Which means that Km is NOT an indicator of substrate affinity...in that particular case.... Seriously? lmao Why couldn't he just leave that part out? I would be anything it will be on the test though so I need to understand it.