Appendix B: Real space distributions in BUSTER

Content

• Introduction
• Model Based distributions
  • Binary masks
    • Table 1. (Radii and PDB models used in the generation of the binary masks.)
      • FRGRAD
      • BLKRAD
      • MSKRAD
    • PDBNUP.dat
  • Blurring of the binary masks
    • Bulk solvent distribution
    • Random atoms prior distribution
    • Table 2. (Binary masks and blurring factors used in the generation of the continuous distributions.)
• Guidelines for choosing the various mask radii
  • FRGRAD
  • BLKRAD and MSKRAD
    • Missing globular part (compact domain)
    • Missing around surface (loops, waters)
• Map Based distributions
• References

Introduction

1. based on an atomic model, computing binary envelopes that are then blurred;
2. based on an electron density and its local rmsd, computing a Fermi-Dirac envelope.

Both procedures are detailed in the paper quoted below.

Model Based distributions

1. Binary masks

   The binary envelopes are obtained by masking with a specified radius around the atomic model in the appropriate PDB file. First, the logical union of solid spheres of a given radius centred on each atom in that file is taken, to generate a binary mask around the molecular object. This binary mask is then symmetry expanded to the whole cell.

   The tracing of the binary envelopes is done via calls to the CCP4 program ncsmask. The symmetry expansion is done internally in BUSTER. All binary masks are written to disk as CCP4 formatted maps (and are removed once the blurring has taken place).

   Table 1. Radii and PDB models used in the generation of the binary masks.

   PDB Model	Masking radius parameter name (default radius)	Binary mask	Symmetry expanded mask
   PDBFRG.dat	FRGRAD (2 Å)	frgmsk	xpnfrgmsk
   BABSLV	BLKRAD (2 Å)	babslvmsk	xpnbabslvmsk
   PDBNUP.dat	MSKRAD (4 Å)	nupmsk	xpnnupmsk

   Note: if no PDBNUP.dat file is specified, the prior mask will just be the complement of the fragment mask (uniform prior).

2. Blurring of the binary masks

   The generation of the continuous distributions from the symmetry-expanded binary masks listed above proceeds as follows:

   • Bulk solvent distribution

     The xpnbabslv binary mask is blurred by a temperature factor ( BLKBLR) and normalised so that its integral over the unit-cell be equal to unity, to create a normalised distribution in the cell called babslv. This distribution is the Babinet opposite of the bulk solvent distribution.

     The contribution of the solvent is then calculated by Fourier analysing the babslv mask and applying Babinet's theorem (taking into account the given mean electron density and temperature factor for the solvent region).

   • Random atoms prior distribution
     • A new binary mask priormsk is first formed according to the logical expression

       priormsk = xpnnupmsk BUT NOT xpnfrgmsk
       		  

       reflecting the fact that the missing atoms will be found in the whole-molecule mask but will be excluded by the fragment itself.

     • The priormsk missing-atom mask is then blurred by application of a blurring factor (MSKBLR). It is then normalised to unity over the cell. This yields the "prior prejudice" for the probability distribution of the randomly-distributed missing atoms in the cell. This distribution is held in a file called prior;

   Table 2. Binary masks and blurring factors used in the generation of the continuous distributions.

   Symmetry expanded binary mask	Blurring factor parameter name (default value)	Distribution
   xpnbabslvmsk	BLKBLR (50)	babslv
   priormsk = xpnnupmsk BUT NOT xpnfrgmsk	MSKBLR (150)	prior

Guidelines for choosing the various mask radii

1. FRGRAD

   The fragment mask radius FRGRAD should be chosen so as to produce the correct mean electron density within that binary mask, e.g. about 0.42-0.425 eÅ^-3 for a protein. You can check the value of the density within the binary mask for the fragment in the file rhofrg.html, present in the shell.01 directory.

   If FRGRAD is chosen incorrectly, the exclusion of random atoms and solvent will be either insufficient or excessive, and this will imbalance the refinement and/or completion, resulting in artefacts near the fragment boundary. The default value of 2.0 Å seems adequate for proteins (we thank Dirk Kostrewa for communicating the results of his careful estimation of this optimal radius). We are not aware of equivalent results for nucleic acids.

2. BLKRAD and MSKRAD

   The flexibility in the choice of separate radii BLKRAD and MSKRAD for the other two masks is intended to address two main classes of situations:

   1. If the missing structure is essentially globular, i.e. if completion is expected to bring up detail within a compact domain rather than mostly on the surface, then use BLKRAD = FRGRAD and MSKRAD = FRGRAD, i.e. set all radii to 2.0 Å. This may result in the location and boundary details of the missing region (as specified in the *.pdbnup file and usually of a rather tentative nature) being taken rather too literally. However, these details get attenuated by blurring, and this is not such a serious problem since one is interested mostly in volume detail.

   2. If the missing structure is mostly near the surface of the whole molecule (e.g. surface loops, side chains to improve upon a poly-Ala model), and may even surround it (e.g. missing bound solvent molecules), then it is preferable to take MSKRAD > FRGRAD, e.g. MSKRAD = 3 or 4 Å. In this way, the prior will give the desired room for the missing structure to appear where it is expected.

      If we then choose BLKRAD = FRGRAD, the mean electron density in the whole molecule will have the correct value. The fact that the region on the surface of the whole molecule will receive overlapping contributions from missing atoms and from solvent should not be of too much concern, especially after 10 Å resolution.

Map Based distributions

References

• Roversi, P., Blanc, E., Vonrhein, C., Evans, G. and Bricogne, G. (2000). Modelling prior distributions of atoms for macromolecular refinement and completion. Acta Cryst., D56, 1313-1323