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Probabilities and Certainties
For the record I don't know what the title means.
Anyway, i think i figured out what's wrong with using the fundamental equation to figure out the probabilities for dissociation. This matrix gives the probability that if i start in an initial state that it will end in a final state after an infinite number of steps. But what i want is the probability to detach after x tries. So I should take the numbers i get from the fundamental equation and raise them to the power of times in the initial state.
I still can't find that error from yesterday, but it is rearing its head again. The Markov Method says that the probability of starting from the initial state and staying on the microtubule is .998 but the 1000 sim says it is .994. The same error that I got yesterday .086 for M.M. and .082 for ksim. (OK my abbreviation might not have been as cool as i thought but M.M. is markov method and ksim is the 1000 sims. See clever right. whatever. i probably won't use that again.)
Anyway i really want to see this mistake, but i don't think it is in the simulations because .994^177 is about 34% while .998^177 is 70%. And the simulation has the kinesin coming off at ~177 steps which wouldn't make sense if it were still probabilistically favorable to stay on the microtubule.
My problem may come from something called explosion. I don't know anything about this nor do i know if it's my problem, but it is woth looking into. The more i do this the more i wanna just give up on the markov and just adjust each side chain as i add them in 1 at a time.
Well i am gonna try to find this problem again in time, but i want to move on and add another side chain from the second state here. ADP/μ-Φ
Ok I added this side chain. It was pretty easy. Before this chain the <length> was 2827.7 and <t> 2.9. Now the <length> is 2711.8 and <t> is 2.79. This gives a velocity of 972. So I am still in good shape. This chain didn't do much to give the the kinesin a chance to escape from the microtubule. Maybe the next one will. I still have ~1,700 to drop from the <length> and corresponding <time>. The velocity is still good.
The markov predicted value for this chain is .997. Since this chain is now combined with the other side chain i don't know exactly how they combine, but the 1000 sims gave me a probability of .997 as well. Which could be just the other chain. i am not sure.
What i do to look at the probability from the 1000 sims is take a histogram of the number of times each state is entered. And i best fit that to P^n. And i am looking at that probability.
The interesting part is that i get a probability of .994 from the histogram of state 0 and a probability of .997 for state 1. I might be screwing something up since the histogram gives probability density and not probability and i am fitting it to P^n. So it could be that i have to integrate P^n. I am confusing myself, and i'll have to think about this more now.
OK i integrated the histogram and then fit it to (1-P^n). For state 0 it fit pretty perfectly with P=.994.
I am just spit balling right now. But it is possible i fixed the mistake some where. That it is a mistake for only a couple of states and state 1 not being one of those (since it was predicted well). that something more complicated is goings on. Well i'll keep up adding side chains and thinking of this. I am printing out the rate constants as i go to keep track of the progress.