AMBER Archive (2007)

Subject: Re: AMBER: Potential of mean force, how to calculate rate of dissociation?

From: David Mobley (dmobley_at_gmail.com)
Date: Fri May 04 2007 - 12:39:34 CDT

Thomas,

> I haven't much experience with US and WHAM analysis, but the way I always
> thought about
> it was that the PMF is a very nice thing because it gives you not only a
> free energy difference between two endstates (the binding constant) but
> also the maximum of the free energy curve between them and thus the
> activation free energy for the process. From that you could easily
> calculate the back and forth rates and even look at the conformations at
> the maximum that pose the critical chokepoint for dissociation.

> Someone please correct me if I'm wrong,

That, of course, depends on having picked the "right" reaction
coordinate for calculating the PMF along (if there is any single
"right" reaction coordinate). In practice this is probably essentially
impossible for biomolecules, since (a) association and dissociation
probably involved coupled motions of protein and ligand, and forcing
calculation along that reaction path would be very difficult, and (b)
there may be many different microscropic paths relevant for
association/dissociation, just as there can be many different paths
relevant for protein folding; the observed rate for
association/dissociation, like a protein folding rate, reflects some
kind of an average over microscopic paths.

Of course, from a PMF, you can calculate a reaction rate based on the
barrier heights, as you suggest. I just think the above considerations
mean that it shouldn't necessarily be expected to be meaningful.

Just one example: Suppose I calculate the PMF for removing a ligand
from a protein, along some particular vector V away from the protein,
and I've carefully picked this vector so the ligand encounters few
steric obstructions along the way. And then I do a second calculation
where I pull it along another vector, W, that is based on just a quick
inspection of the crystal structure to give me a rough idea of a
reasonable direction.If I converge the calculations, the two should
give me the same binding free energy, but will have different barrier
heights along the way, and hence give different rates.

David

> Kind Regards,
>
> Thomas
>
> Dr. Thomas Steinbrecher
> The Scripps Research Institute
> 10550 N. Torrey Pines Rd.
> San Diego CA 92037, USA
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