
DM for ncs averaging (CCP4: General)NAMEdm_ncs_averaging  dm for ncs averagingAVERAGING REQUIREMENTSIn order to perform an averaging calculation you need the following information:
MAKING AVERAGING MATRICESThe most likely place to find your averaging operators is from running a selfrotation and translation function, typically in AMORE. This will give the operator you need in Euler angles, which may be used in DM.You must get the matrices the right way round. For example, if you calculate a matrix which maps an A chain onto a B chain, then the averaging mask must cover the volume occupied by the A chain. Alternatively you can make your averaging matrices if you can build some corresponding fragments of structure in symmetry related molecules. Heavy atom coordinates can also be used in the determination of averaging matrices, especially if the rotation function has been solved. In this case you will need to run a program such as LSQKAB. MAKING AVERAGING MATRICES USING LSQKABYou can use the program LSQKAB from the CCP4 library to calculate the matrices relating one set of atoms to another. See the documentation of that program to find out more about writing the command script. Here is an example script which will find the matrix to map 125 residues from chain B onto chain A. You could also match e.g. chain A in one pdb file to another chain A in a different file.lsqkab REFRCD chmi.pdb \ WORKCD chmi.pdb \ LSQOP junk.pdb \ << 'ENDlsqkab' OUTPUT XYZ FIT WRESIDU MAIN 2 TO 126 WCHAIN B MATCH RRESIDU 2 TO 126 RCHAIN A END 'ENDlsqkab'The output of this run included the following information: SUM DISPLACEMENTS**2 = 78.070 SQRT(SUM DISPLACEMENTS**2)= 0.395 AVERAGE DISPLACEMENT = 0.236 MAXIMUM DISPLACEMENT = 5.001 ROTATION MATRIX: 0.43671 0.05443 0.89796 0.62780 0.69647 0.34754 0.64432 0.71551 0.26998 TRANSLATION VECTOR IN AS 43.63491 38.05914 62.72586 ......... CROWTHER ALPHA BETA GAMMA 158.84190105.66331 132.00317 SPHERICAL POLARS OMEGA PHI CHI 113.28130 103.41944 120.33858 DIRECTION COSINES OF ROTATION AXIS 0.21318 0.89350 0.39524The small average displacement is a good indication that a correct match has been found. The symmetry operators may then be input to DM, either as matrices using the ROTA MATRIX and TRANS cards, or as angles and translations. Alternatively, the matrix may be transposed and input in O/RAVE format. Thus in this case, the 'AVER' card in the DM command file was as follows (note that a second run of LSQKAB was used to determine the third symmetry, between chains A and C): AVER REF ROTA POLAR 0.0 0.0 0.0 TRANS 0.0 0.0 0.0 AVER REF ROTA MATRIX 0.43671 0.05443 0.89796 0.62780 0.69647 0.34754  0.64432 0.71551 0.26998 TRANS 43.635 38.059 62.726 AVER REF ROTA MATRIX 0.42948 0.62559 0.65130 0.06496 0.69793 0.71322  0.90074 0.34862 0.25911 TRANS 82.989 15.401 8.928or AVER REF ROTA POLAR 0.0 0.0 0.0 TRANS 0.0 0.0 0.0 AVER REF ROTA EULER 158.84190 105.66331 132.00317 TRANS 43.635 38.059 62.726 AVER REF ROTA EULER 47.59828 105.01736 21.15850 TRANS 82.989 15.401 8.928or AVER REF ROTA POLAR 0.0 0.0 0.0 TRANS 0.0 0.0 0.0 AVER REF ROTA POLAR 113.28130 103.41944 120.33858 TRANS 43.635 38.059 62.726 AVER REF ROTA POLAR 66.58067 76.78019 119.69176 TRANS 82.989 15.401 8.928or AVER REF OMAT 1.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 AVER REF OMAT 0.437 0.628 0.644 0.054 0.696 0.716 0.898 0.348 0.270 43.635 38.059 62.726 AVER REF OMAT 0.429 0.065 0.901 0.626 0.698 0.349 0.651 0.713 0.259 82.989 15.401 8.928 Making Averaging MasksThe easiest way to make an averaging mask is to let DM generate one by its built in localcorrelationmasking code. However even this requires some thought. The program must pick a correlation cutoff to isolate the correct masked volume, so it needs to know how much of the map will agree with a rotated copy of itself. This is avieved with the 'NCSMASK NMER <nmer>' card.You need to specify how many monomers will map onto matching density under the noncrystallographic symmtery transfomations. In the simplest case  purely improper ncs  the answer is 1. In the case of purely proper ncs (e.g. 3fold rotation, or 222 ncs), then it is the number of monomers in the crystallographic asymmetric unit (3 and 4 in these cases). More complex cases occur when ncs operators are related to crystallographic operators, usually to build up larger multimers. For example, in Insulin there is a 2fold ncs axis perpendicular to the crystallographic 3fold and intersecting it, with the result that the entire hexamer obeys the noncrystallographic symmetry, so <nmer>=6. If fact this case is further compilcated because neighbouring cells up and down the caxis are related onto each other, so the CLIM card must also be used. Given the complexity of the task, it is often better to make your own mask. The localcorrelation map can also be generated by MAPROT and used in conjuction with graphics programs, MAPROT, and NCSMASK, to generate an averaging mask. Making a mask from coordinatesThe other common method for generating an averaging mask is from corrdinates or bones. Coordinates are available when the model has been partly built, or when there is a molecular replacement solution.Bones are generally generated and then pruned in 'O'. The output bones file can be turned into a pseudopdb file using the utility BONDES2PDB. In either case, the .pdb file can be converted directly into an averaging mask using the NCSMASK program. AUTHORDr. Kevin Cowtan, Protein Structure Group, University of York, England 