# User:TheLarry/Notebook/Larrys Notebook/2009/09/02

Agent Based Modeling of Kinesin Motility Main project page
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## Nucleotide Concentration Dependence

I really want to add the force dependence into the rate constants. For that i'll need a better grasp of Evans annual review. So I'm probably gonna discuss that piece of dense work with koch sometime in the next week. So to kill time before that i am gonna add a concentration dependence into the simulation.

This concentration dependence I think will be changing the rate constants from 1/s to 1/Ms. Then multiplying that number by the molar concentration. This should only impact the rate constants where something is binding to the foot. Somethign being ATP, ADP, P_i.

After putting this in there should be a Michaelis-Menten relationship between velocity and concentration.

OK added. that was really simple. It only impacted states where ADP --> ADP-P (because it captured P) or Empty --> ATP or Empty --> ADP. And both of that for unbound and bound. So that was pretty simple.

Left on the docket:

2. tweaking all the rate constants in a more precise manner than what i have now
• reading through guydosh/block paper for rate constant tweaking

I'd like to do this in this order

OK rethinking this: multiplying it in probably no the right thing to do since that probably only looks like the linear portion of michaelis menten. i am not sure how to add this concentration dependence in though

Andy was right multiplying only works for a low concentration. at higher levels it goes as V = Vmax * [ ]/k*[ ]
where [ ] denotes concentration, V is reaction rate, Vmax is maximum reaction rate, and k is the saturation constant

This looks like what i'll need for concentration dependence. this is similar to what Block used in the beginning of Force Production by Single Kinesin Motors.

Right now i am reading "Generalized rate equation for single-substrate enzyme catalyzed reactions" by Kargi. it was published in "Biochemical and Biophysical Research Communications"

so i think my idea is i can use this equation and look up in literature what Vmax is since it's gotta be somewhere (and i'll tweak it a bit) but Vm/k seems to be the rate constant because at low concentration this turns into c* [ ] which is what i was thinking above. and c is Vm/k.

I haven't looked into this really hard yet but the Ma and Taylor paper "Interacting Head Mechanism of Microtubule-Kinesin" has a Vmax for ATP to be about 100 s^-1. ok that doesn't make any sense when most people are saying it is about 300 and not at the max. this is why i don't look at the older papers.

now i added the michaelis menten equation into the locations i used to have just a multiplier. i mentioned these spots above. so now i need to have a number for Vmax, saturation constant Ks, and concentration for ADP, ATP, P binding events. But this covers the concentration dependence. i am still holding out hope that i can find these values (possibly not P) in the literature somewhere.

Oooh i might have this wrong. Not the michaelis menten that seems right but what takes that. This is an enzymatic reaction so it isn't that the binding gets affected by it but the hydrolysis. So should only ATP -> ADP-P be Michaelis impacted?

OK now i fixed it. so the Michaelis only affects ATP --> ADP-P. So two times in the simulation for ATP bound and unbound.