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Combining Rate Constants
I am tired of skimming through papers to find rate constants. So after talking with Andy (i don't remember who exactly came up with the question) we realized that we don't know how to combine rate constants. Say the journal says it takes 300 1/s to hydrolyze ATP. Well what does that mean? Is that just for ATP --> ADP+Pi or is that for ATP-->ADP? It depends on the author what he considered. Well let's say it was ATP-->ADP. well that skipped over like four steps ATP-->ADP-P-->ADP+P->ADP. So what does that 300 mean for each substep.
I looked in the literature and it seems to get insanely complicated. But complicated usually means wrong or some author is trying to be impressive by being complicated. But I did keep coming upon Markhov Chain--that i gotta research later. But I am thinking it has a lot to do with the energy landscape. Where there are a couple of dips of equilibrium. But i still don't know what to do with that.
So I took to labview. And wrote a quick sim of an easy chemical reaction A ↔ B ↔ C → D. Where there is a rate constant between all that and when it reaches D i call it quits. So I ran it with 1 as the rate constant between all of the steps. I ran that 1000 times. That gave me a histogram that looked like an exponential decay. Like it should: e^(-k t). Since i am on the kick i took -ln of the histogram that gave me a straight line, and the slope of that line should be my k total. I want to upload a picture of it but the upload isn't working right now. Any ways, the slope of it was .19. Then i did it with all rate constants being 2 which gave a slope of .37. Then I did 3 which had a slope of .51. Then I did all forward rate constants 3 while all back 1. That gave a total k of 1.25. So I don't know how to figure out total rate constant.
But I am still on this kick of -ln of shit like Evans did which was so bad ass. So I said that if the reaction goes to B it increases 1 in height. Then from B to C it increases 3 and from B to C it increases 5. If it goes back it subtracts the appropriate height. Anyway, i ran that 10000 times, and took a histogram of that and then took -ln of that, and it showed what looks like a crappy energy landscape. Now again I don't know what to do with this, but it is what i expect.
So how does some one possibly like me combine rate constants? And how do i figure it out? I am sure Koch knows and I am sure Evans knows. So worse comes to worse I'll ask them tomorrow in class or koch before class. But geez what does a guy gotta do to figure this out. This is important for analyzing the rate constants we get from the literature when Andy and I are done finding them. Just a couple extra constraints.
I guess I can systematically increase 1 rate constant and watch how the slope increases or decreases. And do that for all of them and try to find a relationship. Is that what smart people do? Yes I think that is what smart people do. They take partial derivatives of each variable then integrate back up so they get rid of the constraint or some shit like that. hmmmm...
Oh I am a moron. It is a Michaelis Menten relation. Damn I actually thought of that earlier. So if i increase 1 rate constant, the graph of slope versus rate constant value is a michaelis menten relation. And slope again is the total k.This was a forward rate constant. Let's see what happens when i raise a reverse.
For the reverse the graph comes out to look like an exponential decay. Which says as the reverse rate constant increases the total rate constant decreases. but only to a certain point. Then it levels out. OK i am getting hungry. I'll have to think about this some more tomorrow.