# [phenixbb] scaling in Fo-Fo maps

Pavel Afonine pafonine at lbl.gov
Thu Feb 4 08:51:18 PST 2016

```Hi Xun,

> I have a question on how the scaling is done when generating Fo-Fo
> maps in Phenix.

I read you are asking about scaling in Isomorphous Difference Map
(Phenix GUI -> Maps) or its command line equivalent
phenix.fobs_minus_fobs_map.

When implementing Fo-Fo map calculation in Phenix I could not find
literature that would sufficiently describe the protocol so I could use
it to write code (which is very typical for crystallographic protocols
and algorithms, unfortunately!). So I had to "re-invent the wheel"
myself from scratch. Below is the protocol I came up with.

Looking at the code in /cctbx_project/mmtbx/maps/fobs_minus_fobs_map.py:

You input two sets of Fobs: Fo1 and Fo2 and PDB file with a model that
serves as a source of phases. It's your responsibility to prepare this
model appropriately.

Then common sets are obtained: Fo1, Fo2 = Fo1.common_sets(Fo2) . This is
because Fo1 and Fo2 arrays may have different not necessarily matching
Miller indices hkl.

The following is then done:

Fmodel1 = ktotal1 * (Fcalc + Fbulk1)
and
Fmodel2 = ktotal1 * (Fcalc + Fbulk2)
are obtained from fitting to Fo1 and Fo2, correspondingly.

Then normalized Fobs are obtained (on "absolute" scale): Fo1n =
Fo1/ktotal1 and Fo2n = Fo2/ktotal2

Then they are scaled to each other using one scalar scale factor:

k = SUM(Fo1n*Fo2n) / SUM(Fo2n**2)

Instead (optionally), they can be scaled to each other using
"multiscale" protocol, very similar to what used to be in CNS, if you
know what I mean.

Finally, the synthesis is computed as {Fo1n - k*Fo2n, phases from one of
Fmodel above}. I can't see in the code which one of the two Fmodels I
choose, I think it's arbitrary.

> But I also want to compare the peaks in the three maps, so I want to
> make sure the maps are generated using the same scaling.

See other email posted to phenixbb from Sacha Urzhumtsev. This is the
way to do it! It is implemented in Phenix GUI: Maps->Map Comparison.
More intuitively, the procedure is described in Section "2.9. Note about
the comparison of maps" here:

FEM: feature-enhanced map. P.V. Afonine, N.W. Moriarty, M. Mustyakimov,
O.V. Sobolev, T.C. Terwilliger, D. Turk, A. Urzhumtsev, and P.D. Adams.
Acta Cryst. D71, 646-666 (2015).