Dear Sen
On Tue, Mar 05, 2019 at 11:05:26AM -0500, Yao, Sen wrote:
> Thank you Ian! The response is really informative.
>
> I am aware that electron density is a point sample. And multiply it by the
> voxel volume is an estimated average. I do have a normalization step in my
> calculation that should average this potential error out. It would be nice
> to sample it finely, but given that I am working with just the ccp4 files
> available, how they sampled it is what went directly in my calculations.
> Hope this clarifies your concerns.
>
> For the second issue, I've also notice that as well and did actually
> optimize the radii for each atom type based on the criteria that they need
> to include a significant number of electrons across the whole PDB
> structures. Voronoi polyhedra is probably another way to do it; as for my
> calculation, I think once the density is below 1.5 sigma (for 2mFo-DFc),
> there is not much information gain to keep extending the radii around an
> atom.
The term "1.5 sigma" says it all: this "sigma" a root-mean-square
deviation from the average density in the map, which is zero because
of the absence of the F000 term in the Fourier synthesis used to
compute that map. To get the pointwise density you want, you have to
add back that missing true mean density per voxel, i.e. on absolute
scale the total number of electrons in the unit cell divided by the
number of voxels in that unit cell.
> And for the first issue you mentioned, it is a very interesting point. I
> don't have anything to directly correct for that on an atom level. But I do
> aggregate atoms into chains (sum of all density together of all atoms on a
> chain and divide by the total number of voxels involved). Maybe that will
> account for potential atomic misplacement? But for the density being only
> part of the true density, I am not sure there is an easy way to account for
> that from ccp4 data only.
>
> Best,
> Sen
>
>
> On Mon, Mar 4, 2019 at 12:43 PM Ian Tickle <ianj...@gmail.com> wrote:
>
> >
> > Hi Sen
> >
> > If you multiply the electron density in a voxel by the voxel volume you
> > should get an estimate of the number of electrons contained in that voxel,
> > and then you can add up the numbers of electrons in all the voxels occupied
> > by an atom to get the total number of electrons in that atom, which is
> > basically the same as what you are saying.
> >
> > However note that the electron density is a point sample: it's not the
> > average density in the voxel, so the above calculation won't be quite
> > accurate, depending on the 'smoothness' of the density. This is like the
> > error in an integral by use of Simpson's rule. To be sure of accounting
> > for all the density you need to sample it finely, say not more that Dmin/4.
> >
> > There are two more issues here: first the atomic positions are never
> > error-free which reduces the contribution to the density by the factor D in
> > the expression 2mFo-DFc (or mFo for centric phases) for the map
> > coefficients. So if the errors were sufficiently large D would tend to
> > zero and you would get no density at all! The density that you see is
> > really only that part of the true density for which there is evidence in
> > the experimental data.
> >
> > Second, what exactly do you mean by "add all voxel densities around an
> > atom"? The electron density could easily extend 2 Ang. from an atomic
> > centre, depending on the atom's finite size (represented by the form
> > factor), its thermal motion (B factor) and series termination effects
> > (resolution). So if you don't go out far enough you will fail to account
> > for some fraction of the electron count. The problem is of course you
> > can't go so far as to overlap bonded atoms which will be well within 2 Ang.
> > distance. The standard method of dealing with this is to represent 'soft'
> > atoms (where the distance between atoms may be less than the sum of their
> > radii) as Voronoi polyhedra (like the packing of soap bubbles!). Is that
> > how you handled it?
> >
> > Cheers
> >
> > -- Ian
> >
> >
> > On Mon, 4 Mar 2019 at 15:47, Yao, Sen <yaosen1...@gmail.com> wrote:
> >
> >> Hi all,
> >>
> >> I have been using the electron density maps available on the PDBe website
> >> to run some analysis. And I run into this question that I hope that I can
> >> get some help from the community.
> >>
> >> In the ccp4 format, the electron density is represented as a 3-d array
> >> map, with each number corresponds to the density value of a voxel in real
> >> space. If I add all voxel densities around an atom together and divided it
> >> by the number of electrons of that atom, in theory it should give me a
> >> ratio with the unit Å-3 (angstrom to the power of -3), and this ratio
> >> should be inversely related to the voxel volume. (Correct me if I am wrong
> >> here.) However, after I got this ratio for each atom, aggregated it into
> >> chains and calculated a median, and then compared the chain median to the
> >> voxel volume over all PDB structures with electron density available, they
> >> show a slope of ~1/3 instead of expected 1 (see attached link). That is,
> >> almost all the values in the electron density maps are only about 1/3 of
> >> represented electrons.
> >>
> >>
> >> https://drive.google.com/file/d/1K_3uxZfUPuTdH1DtKJgKHLRUA5NHTVPB/view?usp=sharing
> >>
> >>
> >> So my question is, is there a conversion or scaling factor that PDBe uses
> >> to generate the ccp4 files? If so, is that information stored in the ccp4
> >> files or anywhere else? And if not, why do I observe this 1/3 ratio pretty
> >> consistently across the whole PDB?
> >>
> >> I would really appreciate any insights on this matter. Thank you!
> >>
> >> Sincerely,
> >> Sen
> >>
> >> --
> >>
> >> Sen Yao, PhD
> >> Center for Environmental and Systems Biochemistry
> >> Markey Cancer Center
> >> University of Kentucky, Lexington KY
> >>
> >>
> >> ------------------------------
> >>
> >> To unsubscribe from the CCP4BB list, click the following link:
> >> https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCP4BB&A=1
> >>
> >
>
> --
>
> Sen Yao, PhD
> Center for Environmental and Systems Biochemistry
> Markey Cancer Center
> University of Kentucky, Lexington KY
>
> ########################################################################
>
> To unsubscribe from the CCP4BB list, click the following link:
> https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCP4BB&A=1
########################################################################
To unsubscribe from the CCP4BB list, click the following link:
https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCP4BB&A=1
