User:Steven J. Koch/Notebook/Kochlab/2010/08/19/Larry's rate constant work
Steve Koch 23:21, 19 August 2010 (EDT): Over the past month, Larry has done some kick-ass work on trying to model some of the unknown rate constants for kinesin in his discrete-state model. We have learned a whole lot in the process, but it's still confusing, so I'm going to try to summarize for my own (and maybe others') benefit here. His latest notebook entry is here: User:TheLarry/Notebook/Larrys Notebook/2010/08/19
There are two new things we're modeling now, compared with our earlier thinking, and also one that we were (I think) modeling previously: Unless I have a lot of time, this probably won't make enough sense, but maybe it will help when we describe this later. Everything we do is in one or zero dimensions.
- Neck linker docking on the bound head shifts the equilibrium position of the unbound head by 4.5 nm relative to un-docked.
- The unbound head diffuses in a potential well created by the worm-like chain properties of the undocked amino acids between the two heads.
- Binding to the binding site is modeled as a cusp in the potential, leading straight down to a very low value.
- Larry found a solution to this in the Hanggi paper, using Kramers reaction rate theory and a deep-well approximation. This deep-well approximation is probably good for most cases, but in the case of docked-bound / undocked-unbound, the well isn't all that deep.
- Larry used this model to predict binding rates for all the various conditions. Some rates are pretty high, some extremely low. Qualitatively, it makes sense, but the actual quantitative value could be off for these reasons:
- We don't account for need for head to be oriented correctly for binding. This could slow the rate down maybe up to a factor of 10?
- We don't exactly know the neck linker properties in all the states. Or at least we need to find a solid reference, probably the 2010 Miyazono paper is our best bet, especially the supplementary info.
- Our model is 1-D
- What we want is to produce reasonable values without having to make them up completely. I think we are already to that point, but tomorrow, Larry is going to try varying the neck-linker a bit and see how things change.
There are certain combinations of docking in two-head bound states that would lead to exceptionally high strain. We puzzled on how to deal with these "forbidden" states (see Guydosh and Block 2009). We decided that docking just wouldn't happen in these states. Thus, if both bound heads have ATP bound, they would both want to be docked. Back head docking is fine because it relieves strain. Front head docking would be high strain. So, instead, it is not docked, and the rate constants behave as if there were no inorganic phosphate (i.e., as if it were ADP). We reasoned this way because it's the inorganic phosphate binding to the switch that promotes docking. This reasoning could be flawed, but we feel it's better than guessing, since these rate constants aren't published. Larry will spell out which of the rate constants were dealt with in this fashion.
- When both heads are bound, there is strain that depends on the docking states. Larry has estimated these forces. The off rates are then modulated according to basic Kramers' theory (simple Arrhenius), with a distance of __ nm (from the literature), relative to the rate when only one head is bound.