CAD in R32

(September 1999)

I am running CAD on a data set in the spacegroup R32 and am wondering why cad does what it does. Input reflections (4 -2 6) and (4 -1 -7) are transformed to (2 2 6) and (3 1 -7), respectively. How are these reflections equivalent? The matrix that seems to perform this transformation, is not a symmetry operator for R32. Nor is the transpose, which would presumably cater for real space. Can anyone tell me what asymmetric unit CCP4 uses for R32? And why?

CAD is correct, and those pairs of reflections are indeed equivalent.

Rember that if you generate a symmetry equivalent position in real space using this expression:

[Xj]     (Sj11 Sj12 Sj13 St1)[X1]
[Xj]  =  (Sj21 Sj22 Sj23 St2)[X1]
[Xj]     (Sj31 Sj32 Sj33 St3)[Z1]
         ( 0    0    0     1)[1 ]

                        (Sk11 Sk12 Sk13)
[Hk Kk Lk]=  [H1 K1 L1] (Sk21 Sk22 Sk23) 
                        (Sk31 Sk32 Sk33)

[X2]         ( 0 -1  0 0)[X1]
[Y2]      =  ( 1 -1  0 0)[X1]
[Z2]         ( 0  0  1 0)[Z1]
             ( 0  0  0 1)[1 ]

                        ( 0 -1  0)
[Hk Kk Lk]=  [H1 K1 L1] ( 1 -1  0)  = [ K1,-H1-K1,L1]
                        ( 0  0  1)

[h,k,l] [k,-h-k,l] [-h-k,h,l] [k,h,-l] [-h-k,k,-l] [h,-h-k,-l]
and the equivalent [-h,-k,-l] sets

Symmetry operator 5 gives (4,-2,6) equivalent to (-2,-2,-6) and negating all signs gives (2,2,6).
Symmetry operator 5 gives (4,-1,-7) equivalent to (-3,-1, 7) and negating all signs gives (3,1,-7).
(-h-k) is sometimes written as i, and people refer to the four-index Miller-Bravais symbols (h k (-h-k) l):
(4 -2 6) becomes (4 -2 -2 6); (4 -1 -7) becomes (4 -1 -3 -7).

Unexpected and artificial values

Temperature Factors and the Wilson Plot

(January 2000)

In a straigtforward REFMAC refinement of a structure with MAD phasing, with data good to 2.4Å, TRUNCATEd and UNIQUEified as should be, unexpected Bfactors ranging from 40 to 130 (average 65) appeared. The Wilson B value was 56.
I guess I have no real specific questions except to wonder if this is telling me something about the quality of either my data, my model, or my crystal. I have been unable to find a reference for the acceptable values for a Wilson B factor. Would anyone suspect that I ran TRUNCATE improperly? Any thoughts would be appreciated.

Thanks to the original enquirer for the summary:

The general consensus was that I have nothing to worry about. Several people pointed out that most temperature factors for protein structures are underestimated leading to the bias that "good" structures should have average temperature factors in the 20-30 range.
A couple of people asked about the solvent content of the crystal. As some of you guessed, this is high. I have a Vm of 4.0 yielding an approximate solvent content of 69 %. This explains some of the thermal motion. It was also suggested to check the native as well as the SeMet data. The Wilson B values are high for all data sets that I have, however the native is the lowest.
I was also advised to examine the Wilson plot to look for typical features of the dip around 5.5Å and the peak around 4Å. In this respect, my Wilson plot looks fine. One last suggestion was to compare the results to refinement with another program. I will give this a try.
A selection of a few comments I received:

As far as I can tell from your post your data seem to be alright. A B of 56 is quite high but your data extend to 2.4Å resolution only, so that is consistent. A model B being slightly higher than that is also ok, since your model is still incomplete. The only thing you need to watch is whether your model B keeps increasing from one round of REFMAC refinement to the next. If it does you should set the overall value back to the 56 before a new round.

I believe that average B factors given for structures are more often too low than too high. If the data peters out at 3Å it is very difficult to get any sensible estimate of a Wilson plot gradient, but it is most likely that a true Av_B should be in the range 80-100, rather than 10 as is sometimes given!
REFMAC values should reflect the gradient of the Wilson plot, and they do seem to do so quite well in your case.

Seems fine to me, the low B factors (~20) were normal when people only worked on crystals that diffracted strongly on weak x-ray sources. Synchrotrons and mirror optics allow the measurement of weaker diffracting crystals (with higher B-factors).
I found that different crystals within one batch might yield quite different B-factors (45-75 avg). But they didn't really make any difference to the biological interpretation.

Anisotropic Scaling to get at 'true' Bfactors

(September 1999)

For a 2.3Å structure, using strict NCS and group Bfactors (2 per residue) in XPLOR, with anisotropic scaling, improves the Rfactors but the Bfactors start to behave strangely. They increase, and some main chain atoms have higher Bfactors than the side chain atoms in the same residue. This is found in the Protein Data Bank, too. Am I the only one worried about it?

The general consensus is that striving for low Bfactors is a thing of the past. High Bfactors can be very 'true' Bfactors. Relatively low side chain Bfactors would make sense if they are buried, but connected to an exposed piece of main chain which would then have higher Bfactors. The PDB is not a reliable source of information about Bfactors, since the scaling algorithms in XPLOR inevitably mean that most low resolution structures have totally unrealistic Bfactors. XPLOR scales Fobs rather than Fcalc, which, especially at lower resolution and at the beginning of a refinement procedure, could cause problems. It would be sensible to start refinement not with an average B of 20 (as output by many model building programs), but with an average B that represents the Wilson plot as closely as possible. Also, to apply Bfactor corrections sensibly before each round of refinement.
There may be valid reasons for adjusting the Bfactor of the Fobs, for making maps or Patterson or rotation function searches, sharpening the data to accentuate the high resolution details, but the final atomic Bfactors should be refined against an uncorrected dataset.
With regards to the use of NCS, most people now accept that relaxing it, with care, is good crystallographic practice, and could have a beneficial effect on Bfactors in refinement.

Artificial Bfactors for NMR Structures

(October 1999)

Can anyone tell me what program I can use to compute artificial temperature factors for a NMR structure based on rmsd of the average structure?

Have a look at:

Wilmanns & Nilges, Acta Cryst (1996) D52:973-982. Molecular Replacement with NMR Models Using Distance-Derived Pseudo B Factors. Script available from Jovine Luca.

and also at:

Molecular Replacement and NMR models - what gives? and the corresponding script through FTP.

What to Expect of Correlation Coefficients in AMoRe

(September 1999)

The correlation coefficient in AMoRe's FITFUN behaves unexpectedly in an otherwise fairly straightforward molecular replacement case. The starting cc in FITFUN is much lower than the one that came out of the rotation and translation steps, while there is also an unexpected Bfactor correction. Interestingly, this behaviour is not seen when using E instead of F.
Following a request to do so, more specific information was supplied: the data extends to 4Šonly, are very strong to 7Šand trail off quite steeply. Estimating the Bfactor from the Wilson plot is therefore not straightforward, but put at approximately 50Ų. The average Bfactor of the search model is 44Ų.

If you calculate the correlation between Fobs and Fcalc you will always get a positive outcome because they are correlated in the sense that both decrease with resolution. If you use E values you do not see this since E values do not decrease with resolution, as you noted. In your case the effects may have been more severe, perhaps due to too large B-values for the search model?

Predicting the Number of Reflections

(January 2000)

What is the easiest way to calculate the theoretical number of reflections in a particular resolution shell given that all cell dimensions are known?

Quick and dirty

Get volume of reciprocal lattice unit, and divide volume of spherical shell by this.

More precise

Run UNIQUE to generate a reflection list within the resolution range required and see how many sets are generated.

FOMs in MLPHARE for MAD

(September 1999)

Does anyone have a feel for whether MLPHARE will over estimate the FOM from its MAD analysis? Secondly, if you include the native and three wavelengths, given the sites are all the same XYZ and differ only slightly in AOCC and OCC, how do we judge the FOM?

It most definitely will if you refine the xyz and occupancy for all wavelengths at once. There is an implicit assumption in the algorithm that each "derivative" is independent, which is obviously not true when a "derivative" is taken as another wavelength, with all differences arising from the same atom sites. The more data sets at different wavelengths with the same sites, the fatter the FOMs get.

The best way to minimise this problem is to refine the coordinates and temperature factors against the largest set of dispersive differences for the centric reflections only (assuming you have such reflections). After that refinement fix the xyz and B for all wavelengths, and the ISOE and occupancies for that pair of dispersive differences. Then estimate the ISOE and occupancies for all other pairs of dispersive differences.

Only then with all XYZ, B, OCC and ISOEs fixed, start refining the anomalous occupancies for all wavelengths. There is a good deal of anecdotal evidence that many wavelengths actually gives worse maps than 2 or 3. This is probably not because the phases are worse, but because the FOMS are overestimated.

Be careful about including the native in the MAD phasing. I wouldn't put it in as the native, but as a derivative (with negative OCC and 0 AOCC). If you put it in as the native, the error estimates in the differences with all the other data sets may be bigger than your actual signal, unless the latter is truly gigantic. In that case the FOMS do reflect the quality of the phases (both would be kind of bad).

REFMAC for Partial Poly-Ala

(January 2000)

The problem we encountered is with a partial poly-Ala trace and poor MIR phases to 3Å. We employed example 9 in the REFMAC documentation, described as "very bad model, rms error 2Å". The resultant model is drastically distorted with some Ca-Ca distances over 6Å long. The question is which protocol should be followed with an initial Ca trace at 3Å?

Thanks to the original enquirer for the summary:

A straight answer to the question about the distortion, was found in the input to PROTIN: the start of the polypeptide chain needed to be dealt with slightly differently (NTERM 1 rather than NTERM 195).

The question also sparked a discussion about the use of all data in refinement, and the use of torsion angle refinement to decrease the number of parameters to refine. In this case, the data really only extended to 3Å, and careful testing of REFMAC and CNS produced very similar and equally interpretable maps.

Maximum-Likelihood refinement using experimental phases (as in REFMAC) can deal with poor/partial models correctly, if the phases have reliable FOMs. Including all data works best providing you are estimating errors from the Rfree set. Initially the weights assigned to the outer resolution bins are very small, but they still contribute significantly to the important overall scaling parameters. The amount of bias is often a function of the amount of missing data. By default REFMAC substitutes these reflections as Dfc instead of the 2mFo-dFc used for observed data, which usually gives better maps than omitting them altogether (that is tantamount to setting them to zero), but any such term will introduce bias. If you have many missing reflections you may have a problem.

Do not expect miracles, and keep an eye on the theory: ML is a minimisation CRITERION, and NOT a minimisation method. One can compare it with the least-square criterion. It works in the same way except that instead of fitting calculated magnitudes to the observed ones, it suggests to fit them to some MODIFIED VALUES, and these modifications are estimated through the model quality and completeness (see, for example, Maximal Likelihood refinement. It works, but why? in the October 1999 CCP4 Newsletter). If the model is incomplete, it is wrong to fit the FC only to experimental amplitudes (as is the case in the LS refinement) and ML attempts to introduce corrections.
These corrections are estimated in resolution shells. If your model does not fit at all your data at a given resolution shell, the ML puts the "corrected experimental magnitudes" in this shell near to zero. As the model improves, the weighting will increase. This is similar to the "good old scheme" of slowly increasing the resolution to include in the refinement, but less subjective.

Various

AMoRe and CCP4 Asymmetric Unit

(January 2000)

Is there a program to transfer AMoRe solutions into the CCP4 asymmetric unit (i.e. just redefining rotation and translation from the AMoRe output)?

Any MR program is simply going to find a CRYSTALLOGRAPHIC solution, and not care about building a sensible model. The following procedure would take care of this:

1. Always shift the first molecule to have translations between -1/2 and 1/2.
   Assuming you apply the solution to the coordinate file OUTPUT from the TABFUN run, which has its centre of mass at (0,0,0), proceed with:

   pdbset xyzin tabfun_out.pdb xyzout soln1.pdb
   cell A B C alpha beta gamma (new cell)
   rota euler ALPHA BETA GAMMA
   shift frac Tx Ty Tz
   CHAIN A
   end

2. Then for further molecules you may well want a symmetry equivalent of the AMoRe solution to build up a tetramer or something.
   Easiest way:
   • Generate all molecules from the AMoRe solutions with different CHAIN IDs and make one coordinate file (all_solns.pdb).
   • Run:

     distang xyzin all_solns.pdb 
     SYMM whatever
     RADI CA 4
     dist VDW
     END

   • That will give you contacts between molecules, complete with symmetry codes: e.g. 2 -1 0 1.
     There are various choices, but once you see that maybe there are better contacts between molecule 1 and molecule 2 using symmetry 2 -1 0 1, you would generate a new version of molecule 2:

     pdbset xyzin soln2.pdb xyzout soln2a.pdb 
     SYMGEN -X-1, Y+1/2,-z+1  (symmetry 2 -1 0 1 in spacegroup P21)

   • Then rebuild the all_solns.pdb with the new soln2a.pdb and run distang again.

You are aiming to get a nice compact molecule with good contacts produced by symmetry X,Y,Z generated by particular symmetry operators. Can be messy but it saves a lot of time on the graphics later!

Distinguish Ca²⁺ from Mg

(December 1999)

I am having troubles in identifying two metal ions in a structure. I used Mg²⁺ in sample preparation and Ca²⁺ in crystallization. The coordination geometry, refinement statistics (both Rfactors and Bfactors) and maps do not resolve the ambiguity.
I would like to know about the experts' opions. The queston in my mind is whether the bonding distance with the coordinating oxygens is a discriminator (~2.3Å in my case)? Also how much the B-factor can tell? (in my case, Mg²⁺ ~12, Ca²⁺ ~29, average of the molecule ~37).

There are a few things you can do to distinguish between Mg²⁺ and Ca²⁺:

Crystallographically

Do you still have the raw data? If yes, even a little anomalous data will decide this question. Don't merge the Friedel pairs and calculate an anomalous difference Fourier (CCP4 FFT with DANO=D_nat PHI=PHIC, i.e. coefficients (F+ - F-)exp[i(phimodel - pi/2)]). You should see very clear peaks for Ca and none for Mg. This is because Ca has an f'' of 1.286 electrons at CuKa radiation, whereas magnesium has only an f''=0.177.
Everyone collects some anomalous data - but if you run SCALEPACK with ANOM NO, you can lose it. If you always set ANOM YES, you still get a merged <I> for all hkl and -h-k-l pairs but the output also preserves the anomalous differences where observed. This is the default for SCALA.

You should be including the low resolution data if you have it (i.e., 20 - 30Å) and this will allow an accurate bulk solvent correction (this is really just general advice).

Ca²⁺ has 8 more electrons than Mg²⁺ which should give you a much higher electron density (contour at, say, ~4 rmsd(rho): do you see the well ordered sulfurs and your metal, only?). But with this you can only identify Ca²⁺ if its occupancy is close to unity. If the occupancies are close to unity, a falsely placed Mg²⁺ instead of a real Ca²⁺ would have a very low B-factor and vice versa.
Another way of looking at this, is:
The change in B-factor is mopping up the difference. You should check the B-factor of the protein atoms that are the ligands. If the atoms have B-factors around 12, then the Mg²⁺ appears to be appropriate. If they are around 29, then the Ca²⁺ is likely the answer.
Yet another contributor was surprised that difference maps weren't good indicators at 2.2Å: "At 1.9Å we observed respective peaks or troughs in the Fo-Fc maps when too light or too heavy a cation was used in the model, even though the B-factors were soaking up alot of the error."

If you still have crystals, soak one with Mn²⁺ instead of Mg²⁺: Mn²⁺ is a very good substitute for Mg²⁺ but has 13 more electrons. If you calculate an (Fo(Mn²⁺)-Fo(unknown)) electron density map, you should see a clear signal if unknown=Mg²⁺ and a weak signal (if any) if unknown=Ca²⁺

Metal-Ligand Geometry

Looking at bond distances only, is rather risky; the refinement programs often have "hidden" restraints which can distort your geometry. For instance most programs apply a VDW repulsion unless you specifically request that it be turned off. However, if you have been careful, some or all of the following should help:

Mg²⁺ should be always octahedrally coordinated and an average Mg²⁺ to O distance of 2.1Å,
and
Ca²⁺ has preferably seven or eight ligand atoms with an average Ca²⁺ to O distance of 2.4Å.
These statements were challenged by another contributor:
It is dangerous to say "always" in any scientific discussion. We have refined a 1.25Å structure containing a Ca²⁺ coordinated by six ligands and a Mg²⁺ coordinated by five ligands, consistent with our ICP Atomic Emission Spectroscopy measurements. A search of the database at http://metallo.scripps.edu/current/raw.html turned up 43, 54 and 269 respective matches for Mg²⁺ coordinated respectively by 4, 5 or 6 ligands, while 102, 160, 369, 445 and 114 respective matches were made for Ca²⁺ coordinated by 4, 5, 6, 7 or 8 ligands. Clearly, there is considerable variability in metal ion coordination geometries.

Both metals are "hard" metals which like "hard" ligands, that is oxygen, only (nitrogen is a very rare exception, sulfur shouldn't appear). There are two excellent reviews about metals in proteins: Glusker, J. P. (1991) Advances in Protein Chemistry, Vol. 42, 1-75, and Harding, M. M. (1999 ) Acta Crystallographica, Vol. D55, 1432-1443.

You have observed an octahedral ligand sphere (indicative for Mg²⁺) with an average metal-to-ligand distance of 2.3Å (indicative for Ca²⁺). However, be cautious! Your metal-ligand distances are the result after refinement usually with geometrical restraints, in this case van der Waals radii. In X-PLOR and CNS, the van der Waals radii of Mg²⁺ and Ca²⁺ are by far too large resulting in too large metal-to-ligand distances (which could be an explanation for 2.3Å for Mg²⁺-to-oxygen distance)! I use sigma of 0.8552 for Mg²⁺ which gives an energy minimum for Mg²⁺-to-O at 2.08Å, and 1.4254 for Ca²⁺ which gives an energy minimum for Ca²⁺-to-O at 2.4Å (look at the formula for the energy minimum, insert the value for oxygen and solve for the "best" value for the metal). So, please, before you judge refined metal-to-ligand distances, check the "ideal" geometry parameter of the refinement program of your choice!

Predicted Rfree-R Difference

(October 1999)

Can someone post the reference to the paper dealing with the predicted Rfree-R difference as a function of data resolution again?

Tickle, I.J., Laskowski, R.A. & Moss, D.S. (1998) Acta Cryst D54, 547-557.

Packing Density

(January 2000)

Can anybody tell me how to calculate the packing density of residues in protein? Is there any standard programme for that?

See Applications for Volume and Packing Calculations (Yale). This will be very helpful, because so many related programmes are availabe in this site. Furthermore, try CCP4's AREAIMOL (please use your local version of the CCP4 Program Documentation to view this), and Columbia's GRASP.

f' and f''

(October 1999)

I am looking for a tool for calculating f-prime and f-doubleprime from X-ray fluorescence spectra for MAD-datasets. Does anyone know a good one?

• CCP4's CROSSEC (please use your local version of the CCP4 Program Documentation to view this)
• CHOOCH
• Crystallographic Computing Services - Scattering factors
• Anomalous Scattering Coefficients



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