[phenixbb] Estimation of ligand binding affinity by occupancy refinement

Edward A. Berry BerryE at upstate.edu
Fri Apr 27 14:23:54 PDT 2012

 > one, and yet Ki's routinely vary by many orders of magnitude.  Only by the
 > most fantastic stroke of luck would the range of Ki for your inhibitors fall
 > into the tiny range measurable by x-ray diffraction.

But by varying the ligand concentration over three orders of magnitude
(uM to mM) you could improve the chances a bit? But since the protein itself
is probably mM this would require protein and ligand concentration very
accurately to estimate free concentration. And if the Kd is much below
the protein concentration it will look like stoichiometric binding.
Kind of the opposite of the dialysis method, where Kd needs to be below
the protein concentration. So useful range would be from protein
concentration up to the solubility of the ligand (or where it interferes
with crystallization) which could be quite limited.

I would not be so pessimistic about estimating occupancy, at least if
the ligand is fairly large.
The B factor spreads the density out, but integrated electron density
over a largish area should be the same. For an individual atom the density
might get lost by spreading out under other atoms, but for a cluster of atoms
what is lost from one will mostly be gained by others, and in the end the
refinement program has to account total electron density in the area.

I remember one well-known crystallographer used a procedure of calibrating
occupancy by integrating the electron density of a single well-defined water
(perhaps in a difference map omitting the water).

I once did Pavel's test by setting occupancy of a segment of the protein
main chain to 0.5 or 2 and refining occupancy (as a single group).
It returned pretty well to 1. in both cases.

As already mentioned, if occupancy is partial you will need to
contour at a lower level to get coverage.

What about the difference maps? is there positive difference density
if you refine with occupancy fixed at 0.2? Is there negative difference
density if you allow it to refine to around 0.5?
If yes and no, I would tend to trust the refinement. But try
approaching the refined value from both sides as was suggested.

Dale Tronrud wrote:
>     Pavel's test of the robustness of the resulting occupancy with respect to
> its starting value provides only a lower bound for the uncertainty of that
> parameter.  The goal of refinement is to find the most probable value for the
> set of parameters.  If you imagine the probability distribution as a Gaussian,
> the ability to repeatedly determine the location of the peak of the distribution
> does not tell you much about its width.
>     Compounding the problem is the correlation between the occupancies and B
> factors of the atoms.  You can get very similar likelihoods when increasing
> both parameters, but if you hold one fixed and vary the other the likelihood
> changes very rapidly.
>     On the other hand, I strongly suggest that you calculate the difference
> in Ki or the difference in binding energy between a ligand that binds with
> 0.1 occupancy and one that binds with 0.9.  The entire range of occupancies
> distinguishable by x-ray crystallography cover only a small range of Ki.
> There is way less than one order of magnitude between the smallest occupancy
> indistinguishable from zero and the largest occupancy indistinguishable from
> one, and yet Ki's routinely vary by many orders of magnitude.  Only by the
> most fantastic stroke of luck would the range of Ki for your inhibitors fall
> into the tiny range measurable by x-ray diffraction.
> Dale Tronrud
> On 04/27/12 10:01, Pavel Afonine wrote:
>> Hi Zoran,
>>> I have a question about sensitivity of occupancy refinement in phenix.
>>> I have a series of datasets done at our home instrument of relatively
>>> modest resolutions from 2.8 to 3 A.
>> occupancies and B-factors are correlated, especial at resolutions around
>> 2.5A and lower; see for example:
>> Correlation between occupancy and temperature factors of solvent
>> molecules in crystal structures of
>> proteins.
>> T. Bhat, Acta Cryst. (1989). A45, 145-146.
>>> These are performed on crystals soaked in progressively higher ligand
>>> concentrations. We are trying to see to which of the several active
>>> sites the ligand binds first so we went from low to high ligand
>>> concentrations. We wanted to estimate the amount of ligand bound by
>>> refining the occupancies of the ligand. We expect one active site to
>>> bind more strongly than the other two active sites. This was indeed
>>> what we observed but when we refine the occupancies of the ligands in
>>> weaker binding sites starting at 0.2 occupancies they rise to 0.5-0.6
>>> although some atoms are totally out of density and some are in. B
>>> factors are reasonable, i.e. don't go wild.
>> "Totally out of density" is not a precise description. Which level you
>> use to draw the 2mFo-DFc map? Did you look at 0.5 sigma (that's what I
>> would use to look at weakly/partially occupied site)? What's the local
>> map CC? What are the mFo-DFc (both, full and ligand-omit) and 2mFo-DFc
>> map values at atomic centers of the ligand? phenix.model_vs_data used
>> with comprehensive=true flag will give you all these values.
>> Did you refine group occupancy of the ligand - that is one occupancy
>> factor per whole ligand?
>> What happens if you run say a few dozens refinements until full
>> convergence (say 10-20 macro-cycles) each refinement starting with
>> different initial value of ligand's occupancy and B-factor? Do all
>> refinements arrive at the same refined occupancy and B? If not, the
>> spread in refined values will give you the uncertainty.
>>> My question would be: how reliable is this estimation of ligand
>>> binding by occupancy refinement?
>> The test suggested above will give you an idea about the answer.
>> Pavel
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