There are several programs for integrating electron density, but please
let me assure you that it is almost always the wrong thing to do.
A much better strategy is occupancy refinement. Throw in dummy atoms,
turn off non-bonded interactions to them, and refine their occupancy
until it a) stops changing (may be more than one round), and b) there
are no Fo-Fc differences left in the region of interest. Then all you
do is add up the occupancies, multiply by the relevant atomic number
(usually 8), and voila! you get the best-fit number of electrons in your
blob. You may want to try re-running with random starting points to get
an idea of the error bars.
What is wrong with integrating density? Well, for one, it is hard to
know where to set the boundaries. Integrated density can be VERY
sensitive to the choice of radius, making your arbitrary decision of
which radius to use a source of error. Too small and you miss stuff. Too
big and you add unnecessary noise. Also, neighboring atoms have tails,
and if you don't subtract them properly, that is another source of
error. Also, because of the missing F000 term, there is an offset, which
adds a term proportional to the integration volume. For example, an
integral resulting in zero "electrons" does NOT mean you have vacuum. It
just means that the area you integrated has the same average density as
the entire map. This may not be the number you want.
The beauty of occupancy refinement is that it automatically handles all
these problems. The "vacuum level" and F000 are known quantities in the
calculated map. The B factors given to the dummy atoms als o allow the
borders of your integration region to be "soft": down-weighting the
contribution of map noise far from your region of interest. And,
finally, by including atoms in the green density, neighboring atoms
won't be sucked into it.
Think of it as fitting a smooth curve to noisy data and the number of
electrons is just a parameter in that fit, rather than trying to
integrate the noisy data itself. This is not an analogy. Refinement
programs are really just very sophisticated curve-fitting programs. And
if you have a forest of overlapping peaks and you are trying to
de-convolute the area/volume of one peak, it is best to include that
peak in the fit, rather than leave it out. Shoulder peaks especially
tend to get "eaten" by large neighboring peaks.
How do you turn off non-bonds? Well, there is documentation for refmac:
http://www.ysbl.york.ac.uk/refmac/data/refmac_keywords.html
and phenix:
https://phenix-online.org/documentation/reference/refinement.html
All that said, to answer the original question:
One very easy thing to do within the CCP4 suite is to use "mapmask" to
make a mask corresponding to your "sphere", or other region of
interest. Perhaps place a water at the center of your peak, and either
use the "border" feature of mapmask, or use "sfall" to compute a
calculated map and convert that to a mask using "threshold" in mapmask.
This mask should have values of 0 or 1 at every voxel. (or, if you feel
like being clever, something between 0 and 1 to reflect how much you
want to weight a given voxel). You can check it in coot. If you then
multiply this mask by your mFo-DFc map the result will have a non-zero
average value. This will be printed out in the log file. Multiply this
average value by the volume of the unit cell and you have your
integrated number of electrons. Yes, its that simple.
One issue you may have is map parameter compatibility (grid spacing,
axis order, xyz limits, etc.). You get around these by using the same
grid in all your fft or sfall runs, and then use mapmask to make the
axis and limits match before you multiply the map and mask. The only
other issue here might be the average value being a very small number
and rounded off by the default print precision. You can fix this by
multiplying the map by a large constant (again, using mapmask), then the
printed value will have lots of digits.
This may seem complicated, but the use of masks can be a very valuable
skill to develop. In fact, one way to simplify, stabilize and
accelerate the occupancy refinement described above is to use a mask to
isolate the region of interest. That is, take the mFo-DFc map, zero out
everything far away from your peak, and convert the result to structure
factors. You can then call these structure factors "Fobs" (alongside the
original sigma(Fobs)) in a new refinement. The Rwork/Rfree then becomes
a local statistic, indicative of the % error in your refined total
occupancy. One caveat is that if every atom in the new refinement is
having its occupancy refined you will lose the absolute scale. To fix
this, you need to add back at least one well-ordered atom into "Fobs",
and also include it in the model. For example, take a well-ordered
helix, extract those atoms, calculate a map using "sfall", and add it to
the masked-off difference map before doing the "new Fobs" structure
factor calculation. Include these same atoms in the new refinement. They
won't move, but they will keep the scale stable. Oh, and don't forget to
turn off the bulk solvent correction! The bulk solvent has already been
subtracted in the mFo-DFc map.
Hope this all makes sense and feel free to ask follow-up questions,
-James Holton
MAD Scientist
On 8/10/2022 9:59 AM, Neno Vuksanovic wrote:
Dear All,
I would like to quantify electron density inside of positive Fo-Fc
blobs in active sites of multiple protomers in the map and compare
them. I am aware that I can interpolate maps and obtain density values
at coordinate points using either MapMan, Chimera or Coot, but I would
like to know if there is a tool that would let me designate a sphere
of a certain volume and calculate total electron density inside it?
Best Regards,
Neno
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