User:TheLarry/Notebook/Larrys Notebook/2009/09/07/Force Dependence

Koch was able to send out an e-mail last night and this morning which was helpful. He said that well i shouldn't paraphrase when i can quote, "The loading rate stuff is more complicated than constant force stuff, so maybe you should focus on constant force (can't remember if it's in that paper) effects on lifetime." Yesterday I complained I don't know what to do when r = 0 and the force was constant. Apparently that is because i had the wrong equation. I don't think evans annual review does talk about a constant force so i gotta start digging. I didn't give it much through yesterday that force wasn't changing. Maybe this'll make it easier

ughh. that 1997 is an easier read but doesn't give me what i want. i am returning to Schnitzer Block of 2000. I am being strongly tempted just to use Bell's equation $$k=k_0e^{\tfrac{-Fd}{k_BT}}$$. if only i knew where Scnitzer and Block got their funky looking equations. i just don't trust what Block is doing in this paper is what I want. I feel like he is looking at an overall change in rate and not just of a single off rate. It looks like that is right. That he just uses Bell equation above and solves the differential equation over how many states there are and gets his weird equation. So it seems to be for the overall path not just a state. A paper from Block's lab gave me this insight. The title is "Force and Velocity Measured for Single Molecules of RNA Polymerase." They look at RNAP but there is a section pseudo-deriving the equations from Schnitzer. In this paper there is also a quick explanation of how rebinding might be affected by force. Again it is bell equation but with a different term in for d. a Δ-d where Δ is the difference between the states. (In case you are looking at the paper, my variables are a bit different since i wrote my bell equation above before finding this paper)

Say i wanted to use that equation above for how a rate constant changes under force. I am not happy with the rebinding idea. Now i might have it wrong since i wasn't concentrating so hard, but most people say that the rebind should be extremely small. I agree with this since with a force it should pull it in a direction, and the tilt of the energy landscape should make it less likely to move backward. (Unless the force is in that direction since pulling kinesin backwards will make it step backwards.) So what's wrong with saying in forward direction exp{-Fd) while other direction exp(+Fd). I don't know i am just spitballing, but that means if a force applied less likely to move backwards, but a backwards force will make it more likely. I don't really know. Would the d be the same? i doubt it since that is the distance forward in the rate reaction. So going backward should have a different d.

The more i think about it the more i like the idea. I mean exponential force should be extremely large thus making it less likely to happen. I found a paper by Bustamante where he is looking at free energy and force. I haven't read it since it is long, but after a quick skimming i found he says about the same thing as far as rebinding goes. (He has Gibbs Free Energy in there too, but outside of that it is the same idea.) "Mechanical Processes in Biochemistry." I was looking at page 9.

Ok right now i am gonna say this is my idea until Koch tells me differently. I am liking this though. It is simple and seems to make sense to me. This page is getting kind of long so i'll just say summarily here that after looking through not a lot of literature I think i'll go with bell's equation. $$k_\pm=k_{\pm,0}e^{\mp\tfrac{Fd_\pm}{k_BT}}$$. alright i am sure i'll try to find reasons why that is wrong later