[phenixbb] Estimation of ligand binding affinity by occupancy refinement

Dale Tronrud det102 at uoxray.uoregon.edu
Fri Apr 27 11:49:28 PDT 2012

   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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