Hey Pavel,
Thank you for your thoughtful comments and excellent references.
I also just realized I made a mistake in an earlier message. When you
"integrate" a map using its average value you want to multiply by the
volume of the asymmetric unit, not the volume of the unit cell. If you
multiply by the cell volume you are integrating over the symmetry mates
as well. You probably just want to know the number of electrons in one
blob (one ASU).
One quick response to Pavel's first comment below too.
On 8/22/2022 9:48 PM, Pavel Afonine wrote:
Hi James,
- Where exactly inside the blob of density do you place these
dummy atoms?
Where? At the peaks.
Peaks? This means you need to have atomic resolution data and also
blobs representing ordered atoms, so you actually have peaks!
Not so! Unless the map is completely featureless there is always a
highest point. That is where you put the first atom. Once placed, you
subtract (or otherwise remove) the density of that atom from the map. In
this new, modified, map somewhere else is now the new highest point.
This is where you put atom #2. Etc. With each iteration you transfer
density from the map into a model. I've tried to adopt a strategy that
keeps the total number of electrons (model + map) fixed, but that
creates some interesting problems. The trick is that as you remove
positive density you don't want to introduce negative density. And by
"negative" I mean dipping below the vacuum level. This vacuum level may
seem arbitrary at first, but in the calculated map it is a very real
thing that cannot be neglected. No amount of adjustment in xyz,
occupancy or B factor can generate a negative peak in the calculated
map. In a way, this positivity constraint is another reason why
occupancy refinement is a good way to integrate density.
Truth be told, although my "divot" approach seems to work fairly well,
I'm still not entirely happy with it. The general problem of finding a
minimally complex constellation of atoms that explain a given blob I
don't think is solved. But I imagine this would make for a good AI project?
Cheers,
-James Holton
MAD Scientist
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