REFMAC (CCP4: Supported Program)

User's manual for the program REFMAC, version 5.0.36

Input and output files - The .log file

All statistics and lots of useful information about the behaviour of the program are printed out to the standard output file called .log file.

The .log file contains information about:

input script
input and default parameters
geometric statistics
- geometric outliers
- overall geometric statistics
NCS operators
X-ray statistics
- X-ray statistics by resolution bin
- overall X-ray statistics
scale and sigmaA parameters
TLS parameters
rigid body parameters

Input and default parameters

Information on input and default parameters is always written to the .log file in a set order.

Input keywords (see also the input script).

If there is a comment line, the program prints out:

Comment line--- #
Comment line--- #####   Makecif parameters
Comment line--- #

This means there are 3 comment lines.

Keywords are written as Data line. For example:

Data line--- NONX NCHAIns 6 CHNID A B C D E F NSPANS 1 12 72 5

This means there is a command line describing NONX which is for non-crystallographic restraints parameters. If there is an error in the command line, the program prints out a warning message describing the nature of the error.

Reflection file information

If there is a reflection file (MTZ), the program prints out information about MTZ (this is done by CCP4 library routines).

Refinement and idealisation parameters

Input and default parameters describing those used for refinement or idealisation or other refinement modes used. For example:

****    Make restraint parameters *****

Dictionary files for restraints : /usr/o4/people/garib/refmac/ftncheck/linux/newdic/add_dict/dic/mon*cif
Parameters for new entry and VDW: /usr/o4/people/garib/refmac/ftncheck/linux/newdic/add_dict/dic/ener_lib.cif
    Cis peptides will be found and used automatically

Form factors

Form factors of the atoms in a psuedo CIF form:

loop_
     _atom_type_symbol
     _atom_type_scat_Cromer_Mann_a1
     _atom_type_scat_Cromer_Mann_b1
     _atom_type_scat_Cromer_Mann_a2
     _atom_type_scat_Cromer_Mann_b2
     _atom_type_scat_Cromer_Mann_a3
     _atom_type_scat_Cromer_Mann_b3
     _atom_type_scat_Cromer_Mann_a4
     _atom_type_scat_Cromer_Mann_b4
     _atom_type_scat_Cromer_Mann_c


  N     12.2126   0.0057   3.1322   9.8933   2.0125  28.9975   1.1663   0.5826 -11.5290
  C      2.3100  20.8439   1.0200  10.2075   1.5886   0.5687   0.8650  51.6512   0.2156
  O      3.0485  13.2771   2.2868   5.7011   1.5463   0.3239   0.8670  32.9089   0.2508
  S      6.2915   2.4386   3.0353  32.3337   1.9891   0.6785   1.5410  81.6937   1.1407

This information could be checked to see if the program has correctly interpreted all the scattering atom types present in the input coordinate file.

Statistics about geometry

The program prints out outliers of the geometric restraints, overall statistics about the geometry and NCS operators if there are any. For more information about geometry see geometric part of the Description of the program.

Outliers of the geometric restraints

Outliers will be printed out at every cycle if

MONItor MANY

has been specifed. If

MONItor MEDium

has been specified, they will be printed out only at the first and last cycles. If

MONItor FEW

has been specified, no outliers will be printed out.

By default if the value of restrained parameters deviates from the ideal by more than 10 sigma (for non-bonding interactions this is 3 sigma), these restraints are printed out. These parameters can be changed using the MONItor keyword. Sigmas of most restraints (apart from sigmas for non-bonded interactions and non-crystallographic symmetry) are taken from the dictionary file.

Bond length outliers:

If at least one bond length deviates from the ideal value by more than alpha*sigma (alpha is defined by MONItor DISTance alpha, default 10), then the following message is printed:

    ****               Bond distance outliers               ****

Bond distance deviations from the ideal > 3.000Sigma will be monitored

A  15 ARG C   . - A  15 ARG O   . mod.= 1.295 id.= 1.231 dev= -0.064 sig.= 0.020

This means that the distance between C of Arg15 of chain A and O of Arg15 of chain A is 1.295, the expected value is 1.231, the deviation from "ideal" value is 0.064, and the sigma for this bond distance restraint is 0.020.

Bond angle outliers:

If at least one bond angle deviates from the ideal by more than alpha*sigma (alpha is defined by MONItor ANGLE alpha, default 10), then the following message is printed out:

    ****                Bond angle outliers                 ****

Bond angle deviations from the ideal >10.000Sigma will be monitored

A  50 GLU O   B - A  51 LEU N     mod.= 100.81 id.= 123.00 dev= 22.193 sig.=  1.600

This means that the angle corresponding to the B conformation of main chain atom O of Glu50 of chain A and N of Leu51 of chain A is 100.81, the expected "ideal" value is 123, the deviation is 22.193 and the sigma is 1.6. Only the first and last atoms of the angle are printed. Middle atom is not printed.

Torsion angle outliers:

If at least one torsion angle deviates from the "ideal" value by more than alpha*sigma (alpha is defined by MONItor TORSion alpha, default 10), then the following message is printed out:

    ****               Torsion angle outliers               ****

Torsion angle deviations from the ideal > 3.000Sigma will be monitored

A  11 ASN CA    - A  12 LEU CA    mod.=-167.65 id.= 180.00 per.= 1 dev=-12.352 sig.=  3.000

This means that the torsion angle with end atoms CA of Asn11 of chain A and CA of Leu12 of chain A is -167.65, the "ideal" value is expected to be 180.0, this torsion angle has periodicity 360/1 = 360, it deviates from the ideal by -12.352, and the sigma for this torsion angle is 3.0. Middle atoms of the torsion angle are not printed.

Chiral volume outliers:

If at least one chiral volume deviates from the "ideal" by more than alpha*sigma (alpha is defined using MONItor CHIRal alpha, default 10), then the following message is printed out:

    ****               Chiral volume outliers               ****

Chiral volume deviations from the ideal >10.000Sigma will be monitored

A  51 LEU CG    mod.=   2.79 id.=  -2.59 dev= -5.375 sig.=  0.200

This means that the chiral volume with centre at CG of Leu51 of chain A is 2.79, the expected value is -2.59, the deviation is -5.375, and the sigma for this chiral volume is 0.2. In this case CD1 and CD2 of LEU should be changed.

Planar group outliers:

If at least one atom in one planar group deviates from planarity more than alpha*sigma (alpha is defined by MONItor PLANe alpha, default 10), then the following message is printed out:

    ****      Large deviation of atoms from planarity       ****

Deviations from the planarity >10.000Sigma will be monitored
Atom: A  59 ASP C   B deviation=   0.31 sigma.=   0.02

The program first calculates the plane for the given set of atoms which are supposed to be in one plane and then calculates the deviation of each atom from this plane. Here C of Asp59 chain A deviates from the plane by 0.31Å, the sigma for this plane is 0.02

Non-bonding interaction outliers:

If at least one of the distances for non-bonding repulsions (vdw, hydrogen bond, metal-ion) deviates from the ideal by more than alpha*sigma (alpha is defined by MONItor VDWR alpha, default 3), the program prints out the following message:

    ****                    VDW outliers                    ****

VDW deviations from the ideal > 2.000Sigma will be monitored

A  26 CYS SG  A - A  75 ILE CD1 . mod.= 2.812 id.= 3.820 dev= -1.008 sig.= 0.300

This means the distance between SG of Cys26 of chain A, A conformer and CD1 of Ile75 of chain A is 2.812, the expected "ideal" value is 3.82, the deviation from the "ideal" value is -1.008, and the sigma for this interaction is 0.3.

B-value outliers:

If the difference between the B-values of bonded atoms or angle-related atoms is more than alpha*sigma (alpha is defined by MONItor BFACtors alpha, default is 10), the following message is printed out:

    ****                  B-value outliers                  ****

B-value differences > 10.00Sigma will be monitored
B   5 PHE N     - B   4 GLN C        ABS(DELTA)= 15.990   Sigma=  1.500

This means that the difference between B-values of the atoms N Phe5 of chain B and C of Gln4 chain B is 15.9, and the sigma for this B-value restraint is 1.5.

NCS outliers:

If, after transformation of positional or thermal parameters, the difference between NCS-related atoms deviates from 0.0 by more than alpha*sigma (alpha is defined by MONItor NCSR alpha, default is 10), the following message is printed out:

    ****               NCS restraint outliers               ****

Deviations from the average position > 3.000Sigma will be monitored

Positional: A  12 LEU N   . deviation = 0.544 sigma= 0.050
B-value   : B  50 ASN CA  . deviation =20.000 sigma= 1.500

This means that the position of atom N of Leu12 of chain A deviates from the average position by 0.544Å; the sigma for this NCS-related atoms is 0.05. The B-value of CA Asn50 of chain B deviates from the average B-value by 20.00; the sigma for this B-value is 1.5.

Sphericity outliers:

If at least one anisotropic U-value of one atom deviates from the sphere by more than alpha*sigma (alpha is defined by MONItor BSPHere alpha, default 10), the following message is printed out:

    ****                Sphericity outliers                 ****

U-values different from sphere >   2.00Sigma will be monitored
A  26 CYS SG  B U-value= 0.2014 0.2329 0.2399 0.0179 0.0227-0.0064 Delta= 0.051 Sigma=  0.025

This means the B conformer of atom SG of Cys26 of chain B deviates from sphericty by more than 2sigma, the U-value for this atom is U11 = 0.2014, U22= 0.2329, U33=0.2399, U12=0.0179, U13=0.0227 U14=-0.0064, the Delta of U-values is 0.051 and the sigma is 0.025. The isotropic equivalent of the U-value is calculated as U_iso = (U11+U22+U33)/3. In this case U_iso = 0.2247. The B-value equivalent of U_iso is 17.74.

Rigid bond outliers:

If at least for one pair of bonded atoms the rigid bond restraint deviates from 0 by more than alpha*sigma (alpha is defined by MONItor RBONd alpha, default 10), the following message is printed out

    ****                Rigid bond outliers                 ****

Rigid bond differences >   2.00Sigma will be monitored
A  12 LEU N     - A  11 ASN C      Delta  =  4.625 Sigma=  2.000

This means the rigid bond restraint between atoms N of Leu12 chain A and C of Leu12 of chain A deviate from 0 by 4.625, the sigma for the rigid bond restraint in terms of B values is 2.0.

Overall statistics about the geometry

An example:

-------------------------------------------------------------------------------
             Restraint type            N restraints   Rms Delta   Av(Sigma)
Bond distances: refined atoms               3167       0.017       0.022
Bond distances: others                      2000       0.006       0.020
Bond angles  : refined atoms                4217       1.560       2.007
Torsion angles, period  1. refined           377       4.740       3.000
Torsion angles, period  3. refined           703      20.175      15.000
Chiral centers: refined atoms                503       0.110       0.200
Planar groups: refined atoms                2186       0.006       0.020
VDW restraints: refined atoms               4658       0.397       0.431
VDW restraints: refined atoms                190       0.197       0.363
VDW restraints: refined atoms                106       0.285       0.300
VDW restraints: refined atoms                  9       0.227       0.300
M. chain bond B-values: refined atoms       1900       0.335       1.500
M. chain angle B-values: refined atoms      3076       0.617       2.000
S. chain Bond B-values: refined atoms       1267       1.307       3.000
S. chain angle B-values: refined atoms      1141       1.956       4.500
NCS: tight positional, group  1 chain A       26       0.081       0.050
NCS: medium positional, group  1 chain A     170       0.420       0.500
NCS: loose positional, group  1 chain A      171       1.031       5.000
NCS: tight thermal, group  1 chain A          26       0.068       0.500
NCS: medium thermal, group  1 chain A        170       0.626       2.000
NCS: loose thermal, group  1 chain A         171       2.339      10.000
-------------------------------------------------------------------------------

Where

N restraints

Number of restraints for this particular geometric value.

Rms Delta

Root mean square deviation of model values of geometric paramters from ideal ones. It is calculated as:

Rms Delta = sqrt(sum(Geom_ideal-Geom_model)²/N_restraints)

Geom_ideal: ideal value for the geometric parameter (bond distance, bond angle etc.), taken from the dictionary.
Geom_model: value of the geometric parameter calculated from the current model.
N_restraints: number of restraints for this particular geometric parameter, over which the summation runs.

Av(Sigma)

Average sigma for this restraint type. Each restraint has its own sigma value. Most of them are stored in the dictionary file.

refined atoms

Restraints corresponding to the atoms included in the geometric and X-ray gradient and second derivative calculations.

others

Restraints corresponding to the atoms included in the geometric calculation, gradients, and structure factor calculations but not included in the X-ray gradient and second derivative calculations. By default hydrogens are dealt with in this way.

Statistics about the following restraints are printed out: bond lengths, bond angles, torsion angles, chiral volumes, planar groups, non-bonding interactions, B-value, NCS, sphericity, rigid bond.

Details should be in the description of the program and theory behind the program. But they are not ready yet.

Bond lengths:

Root mean square deviation of covalent bond lengths from the "ideal" ones. For example:

Bond distances: refined atoms                  3167     0.017     0.022

The first number is the number of covalent bond lengths, the second is the root mean square deviation of the bond lengths from the dictionary values and the third is the average sigma for this restraint type. Bond lengths are calculated in Ås.

Bond angles:

Statistics about agreement of the bond angles calculated from the current refined model and corresponding ideal angles from the dictionary. For example:

Bond angles  : refined atoms                   4217     1.560     2.007

The first value is the number of restraints, the second is the root mean square deviation of the bond angles from dictionary values and the third is the average sigma. Bond angles are given in degrees (°).

Torsion angles:

Root mean square deviation of the model torsion angles from the "ideal" values. For example:

Torsion angles, period  1. refined              677     4.874     3.000
Torsion angles, period  3. refined              950    18.910    15.000

This means that there are 677 torsion angles with period 1, the root mean square deviation from the ideal value for them is 4.874 and the average sigma for these torsion angles is 3.0. There are 950 torsion angles with period 3 and the root mean square deviation from the ideal value for them is 18.91 and the average sigma for these torsion angles is 15.0.

The first line gives statistics for the torsion angles with period 1 and the second line for the torsion angles with period 3. The period of a torsion angle means: if the ideal value of a torsion angle is alpha then alpha + n*360/period values are also ideal values (here n is integer). For example if the ideal value of a torsion angle is 60° and the period is 3, then 60 + 1*360/3 = 60 + 120 = 180 and 60 - 1*360/3 = 60 - 120 = -60 are also ideal values. All other possibilities (for example 60 + 2*360/3 = 60 + 240 = 300 is equivalent to -60) are equivalent to one of these values.

Chiral volumes:

This gives statistics about chiral volumes. For example:

Chiral centres: refined atoms                   816     0.355     0.200

This means that there are 816 chiral volumes, the root mean square deviation of these chiral volumes from the dictionary values is 0.355 and the average sigma for them is 0.2.

Chiral volumes are defined with four atoms. The volume of a pyramid formed by these four atoms is calculated and compared with the "ideal" value from dictionary. Chiral volumes could be positive or negative. If two atoms have changed their positions, the chiral volume changes its sign. For example consider Val CB. Three other atoms involved are CA, CG1 and CG2. If CG1 and CG2 have swapped their positions, the chiral volume changes its sign.

Planar groups:

Statistics about the deviation of the atoms from the planes in planar groups like the rings of histidine residues. For example:

Planar groups: refined atoms                   4016     0.019     0.020

This means in total there are 4016 atoms in planar groups. The root mean square deviation of these atoms from the planes is 0.019 and the average sigma for the planar groups is 0.020.

Non-bonding interactions:

Four types of non-bonding interactions are considered:

The atoms can form a hydrogen bond. Acceptor-donor repulsion.
One of the atoms is acceptor and the other atom is hydrogen from donor.
One of the atoms is a metal and the other is an ion.
None of above. VDW repulsion.

If the interacting atoms are related through symmetry, they are considered separately. If the VDW repulsion is between atoms related by one torsion angle, they are considered separately. Sigma and "ideal" distance for them is different from other VDW pairs.

Statistics for above interactions; an example:

 
VDW repulsions: refined atoms                  2697     0.265     0.300
VDW; torsion: refined atoms                     488     0.154     0.500
HBOND: refined atoms                            451     0.160     0.500
VDW repulsions; symmetry: refined atoms         215     0.263     0.300
HBOND; symmetry: refined atoms                   50     0.266     0.500

Here the first number is the number of restraints for this repulsion type, the second is the root mean square deviation from the "ideal" value. The last number is the average sigma for this restraint type. Note that only repulsions are considered, i.e. if atoms are separated by more than the "ideal" distance they are not considered as interacting atoms.

B-values:

This statistic is about differences in B-values between atoms related by one covalent bond or bond angle. Side chains and main chains of the amino acids are considered separately. In other entries all bonds and angles are considered to be equivalent. The sigma and root mean square deviation of B-value differences from 0 are given in terms of B-values not U-values. Example of B-value restraint statistics:

M. chain bond B-values: refined atoms          3365     3.464     1.500
M. chain angle B-values: refined atoms         5393     4.960     2.000
S. chain Bond B-values: refined atoms          1900     3.839     3.000
S. chain angle B-values: refined atoms         1755     5.312     4.500

The first line states that there are 3365 pairs of atoms in main chain related by covalent bonds. The root mean square deviation from 0 of the B-value differences of these atoms is 3.465 and the average sigma for these pairs of atoms is 1.5. The second line is for main chain angle related atoms, the third line is for side chain bond related atoms and the fourth line is for side chain angle related atoms.

NCS:

The program prints out the agreement between NCS-related atoms. First transformation matrices for all chains are calculated and average positions for each atom after applying corresponding transformation matrices are calculated. Then the difference between transformed and average positions is calculated and used for statistics calculations.

NCS: tight positional, group  1 chain A          26     0.081     0.050
NCS: medium positional, group  1 chain A        170     0.420     0.500
NCS: loose positional, group  1 chain A         171     1.031     5.000
NCS: tight thermal, group  1 chain A             26     0.068     0.500
NCS: medium thermal, group  1 chain A           170     0.626     2.000
NCS: loose thermal, group  1 chain A            171     2.339    10.000

The first number is the number of atoms from this group (chain or part of chain), the second number is the root mean square deviation of transformed atoms from the average positions of NCS-related atoms and the third number is the sigma used for this restraint type.

REFMAC prints out statistics about tight, medium and loose NCS restraints. The difference between these restraint types is the weight used for restraints. Statistics about positional as well as thermal parameters are printed out. If NCS-related atoms have anisotropic thermal parameters then the transformation matrix corresponding to anisotropic U-values is calculated and used to compare NCS-related atomic U-values. All statistics about thermal parameters are given in B-value units.

Positional parameters are in Å and thermal parameters are in Å².

Sphericity:

The program prints out the root mean square deviation from a sphere, for anisotropic B-values. For each anisotropic atom their isotropic equivalent (B_iso=(B11+B22+B33)/3) and the deviation of the anisotropic B-value from the isotropic equivalent is calculated. Then the root mean square is calculated and printed out. For example:

Sphericity. Free atoms                          388     4.689     2.000
Sphericity. Bonded atoms                       5184     0.825     2.000

The program prints out statistics for free atoms (like water) and bonded atoms separately. For example the first line states that there are 388 free atoms, the root mean square deviation of these atoms' B-values from a sphere is 4.689 and the average sigma used for this restraint type is 2.0. Deviation of the anisotropic B-value from sphericity for bonded atoms is smaller than that for free atoms as expected. In general there are more restraints for bonded atoms (B-value restraints, rigid bond restraints and sphericity restraints) than for free atoms (only sphericity restraints).

Rigid bond:

For bonded atoms REFMAC calculates projections of the anisotropic B-values onto the bond for both atoms and then calculates the difference between these projections. The root mean square of these differences then printed out. For example:

Rigid bond restraints                          5265     3.054     2.000

This states that there are 5265 covalent bonds, the root mean square value of differences of the projections of anisotropic B-values onto the bond between them is 3.054, and the sigma used for these restraints is 2.0.

NCS operators

REFMAC calculates transformation matrices for all chains specified to be related by NCS. The first chain (or group) is taken as reference so it has identity matrix of rotation and 0 translation vector. For all other chains the transformation matrix to this chain is calculated. The program prints out (if MONItor MANY has been specified) the transformation matrices, translations as well as rotation angles in polar coordinate system. For example (only one chain is considered):

 Transformation from chain B to chain A

         -0.9988         0.2784E-01    -0.4056E-01
 R =      0.2855E-01     0.9994        -0.1693E-01
          0.4006E-01    -0.1807E-01    -0.9990
 T =       2.848         -25.48          76.07

       DET(R) =       1.000

 Phi =   89.50 Psi(or Omega) =  -90.81 Chi(or Kapppa) =   177.69

Where R is the transformation matrix, T is the translation vector, Phi and Psi show the position of a vector around which the rotation takes place and Chi(or Kappa) is the amount of rotation around this vector. This NCS rotation is nearly 180°, i.e. nearly a 2-fold axis. For a 3-fold axis Chi would be 120, for a four-fold it would be 90 etc.

To get the transformed position, first the rotation matrix and after that the translation is applied (x_new = R x_old + T, x_new is transformed position and x_old is original position.).

If NCS-related atoms have anisotropic B-values, the corresponding matrix for anisotropic B-values is calculated. See reference [3].

The determinant of the rotation matrices should be 1. If the transformation includes inversion, then the determinant is equal to -1.

Statistics about X-ray

For more information about X-ray contribution to refinement and statistics see X-ray part of the Description of the program.

If MONItor MANY is specified, the program will print overall X-ray statistics as well as a distribution of X-ray statistics over resolution. It is a good idea to check if the behaviour of statistics is as expected. If MONItor MEDIum is specified, the program will print the behaviour of statistics over resolution only in the first and last cycles. In all other cycles only the minimum of overall statistics, namely "overall R-factor", "overall free R-factor" and "overall figure of merit" will be printed out. If MONItor FEW is specified, the program will print out only a minimum of statistics about X-ray.

Distribution of X-ray statistics over resolution

The behaviour of the X-ray statistics over resolution is printed out so that they can be utilised using loggraph. For example:

****      Things for loggraph, R factor and others      ****

$TABLE: Rfactor analysis, F distribution v resln  :
$GRAPHS:<rfactor> v. resln :N:1,6,7,11,12:
:<fobs> and <fc> v. resln :N:1,4,5,9,10:
:% observed v. resln :N:1,3:
$$
M(4SSQ/LL) NR_used %_obs M(Fo_used) M(Fc_used) Rf_used WR_used
NR_free M(Fo_free) M(Fc_free) Rf_free   WR_free $$
$$
 0.008     369  89.38   901.7   828.2  0.21  0.25      18  1013.0   905.9  0.25  0.28
 0.020     635 100.00   537.3   532.3  0.27  0.29      29   576.0   617.2  0.30  0.36
 0.032     769  99.88   423.7   457.2  0.27  0.28      52   407.6   403.0  0.32  0.32
 0.044     906  99.90   562.7   563.9  0.19  0.21      49   514.0   523.8  0.24  0.26
 0.055    1053  99.64   604.7   572.5  0.19  0.21      45   539.9   499.8  0.23  0.25
 0.067    1096  99.74   544.1   501.4  0.18  0.19      65   496.5   443.8  0.22  0.23
 0.079    1223 100.00   476.1   440.5  0.18  0.19      68   438.4   390.2  0.23  0.24
 0.091    1312  99.78   366.6   347.5  0.19  0.18      66   359.7   357.0  0.26  0.25
 0.103    1376  99.93   308.8   300.1  0.19  0.17      72   316.9   293.6  0.25  0.24
 0.114    1432  99.21   249.4   257.0  0.21  0.19      81   253.0   261.6  0.27  0.24
 0.126    1534  99.69   217.4   225.6  0.21  0.18      77   227.1   234.7  0.31  0.28
 0.138    1570  99.76   195.0   197.0  0.21  0.19      98   181.5   180.8  0.35  0.30
 0.150    1696  99.83   179.9   187.0  0.22  0.18      90   176.1   182.4  0.22  0.19
 0.161    1691  99.61   162.2   166.9  0.22  0.18      91   171.9   171.3  0.25  0.22
 0.173    1775  99.26   152.1   152.4  0.21  0.18      91   148.8   144.5  0.31  0.25
 0.185    1819  98.35   144.5   138.3  0.22  0.18      84   133.0   131.9  0.30  0.25
 0.197    1858  97.70   131.8   126.8  0.23  0.19      98   129.2   125.1  0.33  0.30
 0.209    1895  97.19   135.5   121.1  0.22  0.19     109   137.1   116.6  0.30  0.27
 0.220    1942  99.71   118.1   102.0  0.25  0.23     101   127.1   110.7  0.28  0.27
 0.232    1939 100.00   139.4    92.3  0.36  0.35      96   129.5    85.2  0.38  0.38
$$

Where (all statistics are for resolution bins):

M(4SSQ/LL): Middle of resolution bins in 4 sin²(theta)/lambda²
NR_used: Number of reflections included in the refinement.
%_obs: Percentage observed reflections.
M(Fo_used): Average value of the observed reflections used in the refinement.
M(Fc_used): Average value of the amplitudes of the calculated structure factors.
Rf_used: R-factors corresponding to the reflections used in the refinement.
WR_used: Weighted (with weights 1/sigma_Fo) R-factor corresponding to the reflections included in the refinement.
NR_free: Number of reflections used for free R-factor calculation and likelihood parameters estimation.
M(Fo_free): Average value of the amplitudes of the observed "free" reflections.
M(Fc_free): Average value of the amplitudes of the calculated "free" reflections.
Rf_free: R-factor corresponding to the "free" reflections.
WR_free: Weighted R-factors corresponding to the "free" reflections.

Another example:

****            Fom and SigmaA vs resolution            ****

 $TABLE: Fom(<cos(DelPhi)>-acentric, centric, overall v resln:
 $GRAPHS:<Fom> v. resln :N:1,3,5,7,8:
 $$
 <4SSQ/LL> NREFa  FOMa  NREFc FOMc NREFall FOMall  SigmaA_Fc1 $$
 $$
  0.0084   313   0.808    56   0.727   369   0.796  0.884
  0.0202   568   0.810    67   0.758   635   0.805  0.884
  0.0319   704   0.809    65   0.744   769   0.803  0.885
  0.0437   838   0.812    68   0.788   906   0.811  0.885
  0.0555   985   0.809    68   0.792  1053   0.808  0.885
  0.0673  1029   0.808    67   0.771  1096   0.806  0.885
  0.0790  1158   0.811    65   0.769  1223   0.809  0.885
  0.0908  1243   0.800    69   0.659  1312   0.792  0.885
  0.1026  1310   0.809    66   0.722  1376   0.805  0.885
  0.1143  1368   0.801    64   0.735  1432   0.798  0.885
  0.1261  1468   0.799    66   0.596  1534   0.790  0.885
  0.1379  1501   0.793    69   0.678  1570   0.788  0.885
  0.1497  1628   0.796    68   0.685  1696   0.791  0.885
  0.1614  1625   0.793    66   0.624  1691   0.787  0.885
  0.1732  1719   0.787    56   0.640  1775   0.782  0.885
  0.1850  1756   0.792    63   0.694  1819   0.789  0.885
  0.1967  1802   0.783    56   0.607  1858   0.777  0.885
  0.2085  1840   0.795    55   0.679  1895   0.792  0.885
  0.2203  1883   0.776    59   0.629  1942   0.772  0.885
  0.2321  1884   0.830    55   0.800  1939   0.829  0.885
 $$

Where:

<4SSQ/LL>: Middle of resolution bins in 4 sin²(theta)/lambda²
NREFa: Number of acentric reflections
FOMa: Figure of merit of the phases for the acentric reflections
NREFc: Number of centric reflections
FOMc: Figure of merit of the phases for the centric reflections
NREFall: Number of all reflections
FOMall: Figure of merit of the phases for all reflections

Full overall X-ray statistics

An example:

Resolution limits                    =     19.920     2.050
Number of used reflections           =      27890
Percentage observed                  =    99.1694
Percentage of free reflections       =     5.0392
Overall R factor                     =     0.2142
Free R factor                        =     0.2722
Overall weighted R factor            =     0.2076
Free weighted R factor               =     0.2630
Overall correlation coefficient      =     0.9403
Free correlation coefficient         =     0.9030
Cruickshank's DPI for coordinate error=     0.2245
DPI based on free R facotr           =     0.2019
Overall figure of merit              =     0.7948
ML based su of positional parameters =     0.1576
ML based su of thermal parameters    =     5.7279

Where:

Resolution limits

Resolution limits used for refinement (in Å)

Number of used reflections

Number of all reflections used for the refinement

Percentage observed

Fraction of the observed reflections in %. If uniqueify has been run before using REFMAC, this value will be calculated correctly. Otherwise it will be 100.0%.

Percentage of free reflections

Percentage of reflections observed but not included in refinement and used for purpose of free R-factor calculation and estimation of the overall maximum likelihood parameters

Overall R-factor

Overall R-factor. It is calculated as:

R-factor = sum||F_o-|F_c||/sum|F_o|

where sum is over all reflections included in the refinement, |F_o| is observed amplitude of the structure factor, |F_c| is amplitude of the calculated structure factor.

Before calculating an "R-factor", the observed and calculated structure factors are scaled to each other. Scale values (isotropic and anisotropic) are applied to the calculated structure factors. If bulk solvent is used then this is also taken into account. See scaling part of Description of program for details of scaling.

Free R factor

As "Overall R-factor" described above, except the summation is over the reflections not included in the refinement.

Overall weighted R-factor

Overall weighted R-factor. It is calculated as:

weighted R factor = sum w ||F_o-|F_c||/sum w |F_o|

where w is 1/sigma_Fo, sigma_Fo is the uncertainty of the observed amplitudes of the structure factor.

Free weighted R factor

As "Overall weighted R-factor" except the summation is over the reflections not included in the refinement.

Overall correlation coefficient

Correlation between observed and calculated structure factor amplitudes. It is calculated as:

Correl =
(sum(|F_o||F_c|)-<|F_o|><|F_c|>)/((sum(|F_o|²)-<|F_o|>²)(sum(|F_c|²)-<|F_c|>²))^1/2

where <|F_o|>=sum(|F_o|)/N_used, <|F_c|>=sum(|F_c|)/N_used, summation is over the reflections included in the refinement, N_used is number of reflections included in the summation.

Free correlation coefficient

Same as "Overall correlation coefficient" except summation is over the reflections not included in the refinement.

Cruickshank's DPI for coordinate error

It is calculated using R-factor, number of the reflections, number of parameters and number of observables. Completeness of the data is also taken into account:

DPI = sqrt(N_atom/(N_refl-N_param)) R_factor D_max compl^-1/3

where N_atom is the number of the atoms included in the refinement, N_refl is the number of reflections included in the refinement, R_factor is the overall R-factor, D_max is the maximum resolution of reflections included in the refinement, compl is the completeness of the observed data.

DPI based on free R-factor

It gives some idea about precision of the positional parameters. It is calculated using the free R-factor:

DPI = sqrt(N_atom/N_free) R_free D_max compl^-1/3

where N_atom is the number of atoms included in the refinement, N_free is the number of reflections included in the free R-factor calculation, R_free is the free R-factor, D_max is the maximum resolution in Å, compl is the completeness of the reflection data.

Overall figure of merit

Overall figure of merit of the phases. It is calculated as:

ML based su of positional parameters

Overall standard uncertainties of the positional parameters based on the likelihood function

ML based su of the thermal parameters

Overall standard uncertainties of the thermal parameters (B-values) based on the likelihood function.

Scale and sigmaA parameters

REFMAC prints out the scale and sigmaA parameters at every cycle. However, if anisotropic scale is used it is estimated at the first cycle only. For example:

-----------------------------------------------------------------------------
Overall               : scale =   0.604, B  =  -0.050
Babinet's bulk solvent: scale =   0.299, B  = 200.000
Partial structure    1: scale =   0.727, B  =  13.532
Overall anisotropic scale factors
   B11 =  0.98 B22 = -0.91 B33 =  0.21 B12 =  0.00 B13 =  0.31 B23 =  0.00
Overall sigmaA parameters  : sigmaA0 =   0.930, B_sigmaA  =   2.136
Babinet's scale for sigmaA : scale =    -0.191, B  =        150.000
SigmaA fo partial structure   1: scale =   0.304, B  =  56.473
-----------------------------------------------------------------------------

Scale factors are estimated using the following equation:

sum(|F_o|-Sc_ovexp(-s^TB_ans)(1-Sc_bexp(-B_b|S|²))|F_cexp(-B_ov|S|²)+F_sSc_sexp(-B_s|S|²)|)²

where

`Sc_ov`	overall scale factor.
`B_an`	overall anisotropic B tensor. It is calculated so that it obeys crystal symmetry and in orthogonal system its trace is 0 (B11+B22+B33=0).
`Sc_b` and `B_b`	scale and B-values for bulk solvent, based on Babinet's principle.
`B_ov`	overall B-value applied to the structure factors calculated from the coordinates.
`Sc_s` and `B_s`	scale and B-values applied to the structure factors calculated from Fourier transformation of the solvent region.
`\|F_o\|`	observed amplitude of the structure factor.
`F_c`	structure factor (complex) calculated from the coordinates.
`F_s`	structure factor (complex) calculated from the solvent region
`s`	vector `(h a, k b, l c)`; `a, b, c` are reciprocal space cell dimensions, `(h,k,l)` are the Miller indices of a reflection.
`\|S\|`	length of reciprocal space vector or sin(theta)/lambda).

The summation in the above equation is over all reflections included in the refinement.

SigmaA parameters are estimated using the likelihood function. Reflections not included in the refinement are used for SigmaA estimations. This part should be completed or refer to description, theory whatever

Information about TLS parameters

If one of the following keywords has been specified:

#
# Refine TLS parameters before individual atomic refinement
#
REFI TLSCcycle ncycle

#
#   Refine TLS parameters
#
TLSCcycle ncycle

then REFMAC prints out the TLS parameters at each TLS refinement cycle. If TLSIN does not contain information about origin, T, L or S parameters then they are initialised to 0. For details of TLS parameters see, description whatever.

The program prints out information about TLS parameters into the .log file in the following form:

TLS group    1: From REFMAC
 T tensor ( 1) =    0.072   0.171   0.105  -0.064   0.034  -0.030
 L tensor ( 1) =    4.809   8.514   2.917   4.601  -1.762  -1.277
 S tensor ( 1) =   -0.751   0.397  -0.344   0.006   0.263   0.683  -0.012  -0.038
...
TLS group    6: chain F
 T tensor ( 6) =    0.160   0.295   0.304   0.034  -0.119   0.071
 L tensor ( 6) =    9.227   8.425  11.079   3.739   3.652   3.743
 S tensor ( 6) =   -0.167   0.090  -0.829  -0.203  -0.566   0.744   0.676   0.432

where numbers for the T-tensor correspond to T₁₁, T₂₂, T₃₃, T₁₂, T₁₃, T₂₃. Note that the T-tensor is symmetric. The same is true for the L-tensor. The S-tensor is printed out as S₂₂-S₁₁, S₁₁-S₃₃, S₁₂, S₁₃, S₂₃, S₂₁, S₃₁, S₃₂. The number inside the brackets show the domain (TLS group) number.

The unit for T is Å², for L it is degree², and for S it is Å*degree.

Note that by inspecting the L-tensor, one can make inference about the degree of order of specific domains. In the above example, the L parameter for domain 6 (rigid group 6) has a larger value than for domain 1. Electron density before and after TLS refinement shows that domain 6 is less ordered.

Information about the rigid body refinement

If either

#
#  Do rigid body refinement
#
MODE RIGId_body

#
#  Do rigid body refinement
#
REFInement TYPE RIGId_body

has been specified, then REFMAC prints out information about the progress of the rigid body refinement. In the case of rigid body refinement refmac prints out information about X-ray statistics, scale parameters and the parameters of the rigid body (or bodies).

#
#  Print out full refinement statistics. In case of the rigid body refinement
#  print out full x-ray statistics and parameters of the rigid bodies
#  at every cycle.
#
MONItor MANY

then the program prints out rigid body statistics at every cycle. If either:

#
#  Print out minimum information. In case of rigid body refinement
#  print out only minimum x-ray statistics (scale parameters, R factor,
#  free R factor, figure of merit) at every cycle and parameters of the
#  rigid body only in the last cycle.
#
MONItor FEW

#
#  Print out medium number statistics. In case of the rigid body
#  it means that print out rigid body parameters only at the last cycle,
#  full x-ray statistics at the first and last cycles. In all other cycles
#  only minimum information about x-ray (scale parameters, R factor, free R
#  factor and fom)
#
MONItor MEDIum

has been specified, then REFMAC prints out rigid body statistics only at the last cycle of refinement, i.e. only total rotation and translation.

After giving information about the input script in the "Input and default parameters" section, the program prints out information about rigid body groups. For example:

Refinement type                        : Rigid Body


    ****                 Domain Definition                  ****

  Group:   1:    No. of pieces:   1
 Chain:  A Span:    1  600 ** All atoms **

  Group:   2:    No. of pieces:   1
 Chain:  B Span:    1  600 ** All atoms **

This means that the program will perform rigid body refinement. The number of rigid body groups is 2. The first group contains residues from 1 to 600 of chain A, the second group contains residues from 1 to 600 of chain B. All atoms in all residues will be used for refinement and structure factor calculations.

At the end the program prints out a message about rigid body movement. For example:

----------------------------------------------------------
  Rigid body parameters will be applied to coordinates
  as following

 Xnew = Rot*Xold - Rot*Tg + Tg +deltaTg
Where
 Xnew and Xold are new and old coordinates of atoms in
              this domain
 Rot           is rotation matrix derived from Euler angles
 Tg            is centre of mass of this domain
 deltaTg       is shift of centre of mass
----------------------------------------------------------
Domain     1
Centre of mass:     62.077    15.442    64.907
 Euler angles and deltaTg:        -0.22     0.57    -0.08    -0.05    -0.09    -0.09

 Matrix and deltaTg
        1.000     0.005     0.010
       -0.005     1.000     0.000
       -0.010     0.000     1.000
       -0.045    -0.093    -0.087

   Polar angles: PHI, PSI(or Omega), CHI(or Kappa), deltaTg:    117.27    89.93     0.64
   -0.05    -0.09    -0.09

Domain     2
Centre of mass:     89.665    19.770     4.975
 Euler angles and deltaTg:        -0.21    -0.50    -0.06     0.15     0.11    -0.14

 Matrix and deltaTg
        1.000     0.005    -0.009
       -0.005     1.000     0.000
        0.009     0.000     1.000
        0.152     0.113    -0.144

   Polar angles: PHI, PSI(or Omega), CHI(or Kappa), deltaTg:    118.88   -90.07     0.57
    0.15     0.11    -0.14

Important numbers to look at are deltaTg, i.e. the domain's centre of mass's shift, and CHI (or Kappa), which gives the amount of rotation. For example:

Shift of the first domain in Å is ( -0.045,-0.093,-0.087)
and rotation is 0.64°.

Output coordinates correspond to the new rotated and shifted atoms.