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Constantly changing these rate constants
So i keep getting closer to the points i want--an expected time of ~1 second and an expected length of 800nm - 1μm--but the more i do the more i doubt myself. So i've been working all morning on this, but now i am thinking...
my core cycle has a k effective of 110 or so. Which is good means it can take about 110 steps in a second. So if i set all of those values then theoretically i am good. so then i can set all the off cycles to have happen once in ever 100 cycles. Now if it had this probability then it should have something like 100% chance of detaching if it hit a weird state. I can set these probabilities by looking at instantaneous rate/total rate constants for every state. Or i can set the weird states to be something like 1 in 50 steps and then set off cycles to have a 50% chance to unbind completely or get back on the core cycle. i might be able to set this by looking at the side "weird" cycle and find it's k effective to reattach or to detach through the Markov approximations. so the ratio of the k effectives for each one of those would be the probability of one to the other. so i can play with that until i get the 50% i want. i like this reasoning and it seems to be more accurate thinking than just fucking with numbers.
But i gotta go study for evans test on Tuesday so i'll come back to this after studying and some lunch. i am excited to see if it works. And koch if you are reading this i know it doesn't make much sense but i think i can explain it better in person. i just wanted to type it up before i forget since i gotta leave now. and i just came up with this plan.
So i have come back to the drawing board kind of like i said above. I changed everything that isn't on the cycle that Andy and I drew on the white board to zero and have everything that is on the white board to the value there. I am checking what i get from the agent based model simulation to the Markov approximation. And it is working pretty well. The part i have to remember is that the markov works when i distinguish head 1 from head 2. So the state in the markov keeps track of which head is in front or behind. I tried making it a cycle without that and it is way off, but with that it seems to work really well.
So now by making separate states for each head in front or not. The values from the whiteboard give me a k effective of 55.36 which means that in 1 second it will take 55 steps or about half as far as i want it to go. And this matches the simulation run 1000 times as well as the linear fit to the simulation. The linear fit is from the fact that it doesn't stop since this is the ideal cycle. So now i am back to having to figure out the basic cycle and then i can move to figuring out all the weird side cycles.
But i am happy that i understand how the Markov approximation and the simulation fit together a bit better.
So i am gonna call it a day. So i changed all the rate constants to either 0 or what i have on the board. The simulation will still stop when the kinesin unbinds but right now that won't happen since it can't enter a weird state. I am going to have to get the basic cycle to give me a reasonable number probably higher than 100 for k effective. and then I'll add the side cycles and watch as k effective drops but keep it from falling too far. my biggest question is how often does it enter a weird state. if it only enters once then the probability to go from weird state to unbound is 100% if it does it twice then it has a 50/50 shot to come off the core cycle and come back on as it does to detach. I can choose this by looking at the ratio of k effective for weird cycle to reenter core cycle compared to k effective of weird state to detach. i think that makes sense. it might be wrong i have to see when i actually get there. but right now i have to fix the core rate constants.