LGA

Document describes the format required to use the LGA facility


Citing LGA:
Zemla A., "LGA - a Method for Finding 3D Similarities in Protein Structures", Nucleic Acids Research, 2003, Vol. 31, No. 13, pp. 3370-3374. [PubMed]


LGA program is being developed for structure comparative analysis of two selected 3D protein structures or fragments of 3D protein structures. Structure comparative analysis can be made in two general modes:

As a basis for scoring function for LGA aligner serve two measures LCS and GDT. These two measures established by A. Zemla (see [1]-[3]) for detection of local and global structure similarities between two proteins were successfully verified during CASP process providing very good ranking of evaluated protein models. Comparing two protein structures LCS procedure is able to localize (along the sequence) the Longest Continuous Segments of residues that can fit under selected RMSD cutoff. Global Distance Test (GDT) algorithm is designed to complement analysis made with LCS searching for the largest (not necessary continuous) set of "equivalent" residues deviating by no more than a specified DISTANCE cutoff.


The data for LGA processing should contain two sets of 3D structures coordinates (molecule1 and molecule2) in the format of the PDB standard ATOM records. As a result of LGA processing user will get the rotated coordinates of the first structure (molecule1) , and (optionally) the coordinates of the second structure (target - molecule2, not changed).

For the purpose of structure similarity search and ordering of models (Molecule1: templates, PDB files), the target (Molecule2, frame of reference) should be fixed and then user may sort models (see SUMMARY line from the LGA output) by the number N of superimposed residues (under one selected DIST cutoff), or by GDT_TS (average from four fixed distance cutoffs), or LGA_S value (weighted results from the full set of distance cutoffs, see [1]).


Using LGA system you can choose several options:

   -1       standard RMSD
   -2       RMSD using ISP (Iterative Superposition Procedure)
   -3       LCS and GDT analysis
   -4       LGA structure alignment analysis

   -d:f.f   distance cutoff DIST (f.f Angstroms, 0.10 <= f.f <= 10.0) 
            (use with -2, -3, or -4 options)
            NOTE: lower value of DIST  => tighter superposition
                  larger value of DIST => superposition can be more relaxed

   -lw:n    2*n+1 (n>0) is the length of the residue window ("Lesk window"
            see [4]) on which the value of local RMSD is calculated 
            (can be used with -1, -2, -3, -4 options)

   -sda     facilitates the selection of residues for calculation: sequence
            dependent analysis (residue numbering, and chain ID should be the
	    same in both structures)
   -sia     facilitates the selection of residues for calculation: sequence
            independent analysis
            NOTE: you can use -sia option with -1, -2, or -3. In this
                  case the same number of the first residues from both
                  structures will be taken for LGA processing.

   -atom:CA    CA atoms will be used for calculations. NOTE (special character
               in the PARAMATER-OPTIONS line): use , instead of '
               (for example: H5,1 to select H5'1 atom)
   -ch1:A      chain A selected from molecule1
   -ch2:B      chain B selected from molecule2
   -ah:i       ATOM or HETATM records are used for calculations:
                 i=0 both
                 i=1 ATOM
                 i=2 HETATM

   -aa1:n1:n2  range of residues from the molecule1 used for calculations
                 -9999 < n1 < n2 < 9999
   -aa2:n1:n2  range of residues from the molecule2 used for calculations
                 -9999 < n1 < n2 < 9999
   -gap1:n1:n2 range of residues from the molecule1 removed from calculations
                 -9999 < n1 < n2 < 9999
   -gap2:n1:n2 range of residues from the molecule2 removed from calculations
                 -9999 < n1 < n2 < 9999

   -er1:s1:s2  exact range of residues from the molecule1 used for calculations
                 (s1 , s2 - strings: s1 = 13L_A < s2 = 45_B )
                 Up to 10 er1 parameters are allowed (WARNING: no overlaps)
   -er2:s1:s2  exact range of residues from the molecule2 used for calculations
                 (s1 , s2 - strings: s1 = 16 < s2 = 245A )
                 Up to 10 er2 parameters are allowed (WARNING: no overlaps)

   -aa      generates a list of all residues from the molecule1 and
              molecule2 (AAMOL* records)

   -o0      only summary results (no coordinates) are reported as an 
              output from the program
   -o1      summary results and the coordinates of molecule_1 (rotated) are reported 
              as a result of the analysis
   -o2      summary results, the coordinates of molecule_1 (rotated) and molecule_2 
              (target, not changed) both are reported as a result of the analysis

There is the default set of parameters: -4 -sia -o1 -d:5.0


If two structures from PDB have to be analyzed then please use the following notation:

   1cpi_A     for PDB entry: 1cpi, chain: 'A'
   1sip       for PDB entry: 1sip, chain: ' '
and specifying NMR MODEL:
   1bve_B_5   for PDB entry: 1bve, chain: 'B', model: 5 
   1awo___7   for PDB entry: 1awo, chain: ' ', model: 7


If your data (two structures) is already prepared as one file then please check if each one of the two 3D structures begins with MOLECULE and ends with END record:

MOLECULE name1
ATOM      1  N   ILE     2       1.002  23.117  39.181  1.00 82.49           N   
ATOM      2  CA  ILE     2       1.295  23.768  40.454  1.00 83.70           C   
  ---------
ATOM    400  CD1 LEU    54      14.696   9.978  30.085  1.00 56.40           C   
ATOM    401  CD2 LEU    54      12.844  11.030  31.407  1.00 31.93           C   
END
MOLECULE name2
ATOM    419  N   LEU A  57      13.121   3.012  34.495  1.00 40.04           N
ATOM    420  CA  LEU A  57      13.125   1.748  35.211  1.00 43.79           C
  ---------
ATOM    558  C   GLU A  74       7.298  12.565  26.328  1.00 43.72           C
ATOM    559  O   GLU A  74       6.545  13.347  26.910  1.00 49.34           O
END


Example of the output from the LGA program.
LGA-parameters used: -4 -sia -o2 -d:2.7


# Molecule1: number of CA atoms   13 ,  all atoms   98 , name name1
# Molecule2: number of CA atoms   18 ,  all atoms  141 , name name2

# PARAMETERS: -4 -sia -o2 -d:2.7

# Sequence Independent Analysis
# Structure alignment analysis

  --- residue-residue equivalences reported by LGA ---

#      Molecule1      Molecule2       DISTANCE
LGA    I       2      L    57_A           -
LGA    V       3      L    58_A           -
LGA    T       4      -     -             -
LGA    Q       5      -     -             -
LGA    L      46      Q    59_A          1.586
LGA    K      47      K    60_A          0.967
LGA    P      48      W    61_A          1.470
LGA    T      49      E    62_A          0.595
LGA    P      50      N    63_A          2.575
LGA    E      51      G    64_A          2.643
LGA    G      52      E    65_A          1.206
LGA    D      53      C    66_A           -
LGA    L      54      A    67_A          0.911
LGA    -       -      Q    68_A           -
LGA    -       -      K    69_A           -
LGA    -       -      K    70_A           -
LGA    -       -      I    71_A           -
LGA    -       -      I    72_A           -
LGA    -       -      A    73_A           -
LGA    -       -      E    74_A           -

In DISTANCE column the distances in Angstroms between 
corresponding residues are reported when final global 
superposition is applied ("-" is present when residues 
are not aligned under selected distance cutoff DIST).

#              N1   N2   DIST      N    RMSD   Seq_Id      LGA_S      LGA_Q
SUMMARY(LGA)   13   18    2.7      8    1.65    12.50     15.123      0.456
                |    |     |       |      |        |           |        |
  number of residues |     |       |      |        |           |        |  
  from mol1 (model)  |     |       |      |        |           |        |
                     |     |       |      |        |           |        |
  number of residues from  |       |      |        |           |        |
  mol2 (target)            |       |      |        |           |        |
                           |       |      |        |           |        |  
  selected distance cutoff DIST    |      |        |           |        |  
                                   |      |        |           |        |  
  N number of residues superimposed under |        |           |        | 
  distance cutoff DIST                    |        |           |        | 
                                          |        |           |        | 
  RMSD calculated on N residues superimposed under |           |        |
  distance cutoff DIST                             |           |        |
                                                   |           |        |
  Sequence Identity. Percent of identical residues from the    |        |
  total of N aligned under distance DIST                       |        |
                                                               |        | 
  LGA_S score (0.00 - 100.00) calculated with reference to the number   |
  of residues in target (mol2 name2 - here 18 residues)                 |
                                                                        |
  LGA_Q (quality) score calculated with use of the formula: Q=0.1*N/(0.1+RMSD)
  (Q below 2.0 indicates rather weak alignment)


Unitary ROTATION matrix and the shift VECTOR superimpose MOLECULES  (1=>2)
  X_new =   0.727720 * X  +   0.667720 * Y  +   0.156762 * Z  + -87.991600
  Y_new =   0.113780 * X  +  -0.342916 * Y  +   0.932450 * Z  +  10.198357
  Z_new =   0.676371 * X  +  -0.660726 * Y  +  -0.325520 * Z  +  54.671837

Euler angles from the ROTATION matrix (XYZ convention, two solutions)
  Psi   =  -2.028563    1.113030  [ DEG:  -116.2281     63.7719 ]
  Theta =  -0.742825   -2.398768  [ DEG:   -42.5607   -137.4393 ]
  Phi   =   0.155095   -2.986497  [ DEG:     8.8863   -171.1137 ]

LGA-Parameters -4 -sia -o2 -d:2.7
REMARK  ----------------------------------------------------------
REMARK   Citing LGA:
REMARK   Zemla A., LGA - a Method for Finding 3D Similarities in
REMARK   Protein Structures, Nucleic Acids Research, 2003, V. 31,
REMARK   No. 13, pp. 3370-3374.
REMARK  ----------------------------------------------------------
REMARK     Superimposed MOLECULES (1=>2)
REMARK       1: name1                                         
REMARK       2: name2                                         
REMARK     Structure alignment analysis. DISTANCE 2.70
REMARK  ---------------------------------------------------------- 

MOLECULE name1 (rotated coordinates)
ATOM      1  N   ILE     2      27.152 -15.625  42.659  1.00 82.49           N
ATOM      2  CA  ILE     2      28.468 -15.120  43.039  1.00 83.70           C   
  ---------
ATOM    400  CD1 LEU    54       9.942  -3.565  43.787  1.00 56.40           C
ATOM    401  CD2 LEU    54      12.007  -4.798  43.080  1.00 31.93           C
END
MOLECULE name2 (unchanged coordinates)
ATOM    419  N   LEU A  57      13.121   3.012  34.495  1.00 40.04           N
ATOM    420  CA  LEU A  57      13.125   1.748  35.211  1.00 43.79           C
  ---------
ATOM    558  C   GLU A  74       7.298  12.565  26.328  1.00 43.72           C
ATOM    559  O   GLU A  74       6.545  13.347  26.910  1.00 49.34           O
END


Example of the output from the LGA program (LCS and GDT analysis).
LGA-parameters used: -3 -sda -o0 -d:4.0


# Sequence Dependent Analysis
# GDT and LCS analysis 

LCS - RMSD CUTOFF   5.00      length       segment         l_RMS    g_RMS
  LONGEST_CONTINUOUS_SEGMENT:   255         7 - 261         3.12     3.12
  LCS_AVERAGE:    100.00

LCS - RMSD CUTOFF   2.00      length       segment         l_RMS    g_RMS
  LONGEST_CONTINUOUS_SEGMENT:   117       145 - 261         1.99     3.47
  LCS_AVERAGE:     37.19

LCS - RMSD CUTOFF   1.00      length       segment         l_RMS    g_RMS
  LONGEST_CONTINUOUS_SEGMENT:    44       163 - 206         0.97     3.29
  LCS_AVERAGE:     12.60


LCS_GDT    MOLECULE-1    MOLECULE-2    LENGTH_OF_THE
LCS_GDT     RESIDUE       RESIDUE         CONTINUOUS
LCS_GDT   NAME NUMBER   NAME NUMBER          SEGMENT     GLOBAL DISTANCE TEST - GDT_DATA_COLUMNS                             NUMBER OF THE RESIDUES:  255
LCS_GDT     S       7     S       7     37   96  255    27  121  185  206  216  224  226  230  234  237  239  241  242  243  246  248  249  251  252  253 
LCS_GDT     V       8     V       8     37   96  255    50  132  188  206  216  224  226  230  234  237  239  241  242  243  246  248  249  251  252  253 
LCS_GDT     K       9     K       9     37   96  255    36  126  188  206  216  224  226  230  234  237  239  241  242  243  246  248  249  251  252  253 
LCS_GDT     G      10     G      10     37   96  255    21  117  187  206  216  224  226  230  234  237  239  241  242  243  246  248  249  251  252  253 
LCS_GDT     L      11     L      11     37   96  255    50  132  188  206  216  224  226  230  234  237  239  241  242  243  246  248  249  251  252  253 
LCS_GDT     V      12     V      12     37   96  255    50  132  188  206  216  224  226  230  234  237  239  241  242  243  246  248  249  251  252  253 
...........................................................................
LCS_GDT     A     256     A     256     42  117  255    29  131  188  206  216  224  226  230  234  237  239  241  242  243  246  248  249  251  252  253 
LCS_GDT     I     257     I     257     42  117  255    20  126  188  206  216  224  226  230  234  237  239  241  242  243  246  248  249  251  252  253 
LCS_GDT     R     258     R     258     42  117  255     6   88  160  198  209  224  226  230  234  237  239  241  242  243  246  248  249  251  252  253 
LCS_GDT     M     259     M     259     14  117  255     3   17   53   90  176  204  217  228  234  237  239  241  242  243  246  248  249  251  252  253 
LCS_GDT     Q     260     Q     260      6  117  255     3    5   25   55  104  158  208  220  233  237  239  241  242  243  246  248  249  251  252  253 
LCS_GDT     P     261     P     261      6  117  255     4   13   25   36   96  125  179  207  222  234  238  241  242  243  246  248  249  251  252  253 
LCS_AVERAGE  LCS_A:  49.93  (  12.60   37.19  100.00 )

GLOBAL_DISTANCE_TEST (the largest set of residues that can fit under specified DISTANCE_CUTOFF)
GDT DIST_CUTOFF  0.50   1.00   1.50   2.00   2.50   3.00   3.50   4.00   4.50   5.00   5.50   6.00   6.50   7.00   7.50   8.00   8.50   9.00   9.50  10.00
GDT NUMBER_CA     50    132    188    206    216    224    226    230    234    237    239    241    242    243    246    248    249    251    252    253 
GDT PERCENT_CA  19.61  51.76  73.73  80.78  84.71  87.84  88.63  90.20  91.76  92.94  93.73  94.51  94.90  95.29  96.47  97.25  97.65  98.43  98.82  99.22
GDT RMS_LOCAL    0.36   0.68   0.89   1.01   1.14   1.27   1.32   1.49   1.58   1.68   1.74   1.89   1.92   2.00   2.25   2.39   2.47   2.67   2.72   2.86
GDT RMS_ALL_CA   3.25   3.24   3.23   3.23   3.24   3.25   3.26   3.30   3.24   3.25   3.26   3.22   3.22   3.21   3.16   3.16   3.16   3.14   3.14   3.13

#                N1   N2   DIST    N   RMSD   GDT_TS    LGA_S    LGA_Q 
SUMMARY(GDT)    261  255    4.0  230   1.49   80.000   81.425   14.460 

#      Molecule1      Molecule2       DISTANCE
LGA    S       7      S       7          2.026
LGA    V       8      V       8          1.301
LGA    K       9      K       9          1.719
LGA    G      10      G      10          2.103
LGA    L      11      L      11          1.277
LGA    V      12      V      12          1.302
LGA    A      13      A      13          1.558
LGA    V      14      V      14          1.387
...........................................................................

After setting an option: -lw:3
the LGA records will look like below:

#      Molecule1      Molecule2       DISTANCE    RMSD(lw:3)
LGA    S       7      S       7          2.026        -
LGA    V       8      V       8          1.301        -
LGA    K       9      K       9          1.719        -
LGA    G      10      G      10          2.103       0.586
LGA    L      11      L      11          1.277       0.596
LGA    V      12      V      12          1.302       0.652
LGA    A      13      A      13          1.558       0.487
LGA    V      14      V      14          1.387       0.412

where in the last column for each residue a RMSD value is 
calculated on 3+1+3=7 residues window. This information can be 
very helpful to detect local similarity of structures when such 
a similarity is difficult to capture from global superposition.

-------------------------------------------------------------------------------

Running program with an option: -aa
the following list will be generated:

AAMOL1    I       2      1
AAMOL1    V       3      2
AAMOL1    T       4      3
AAMOL1    Q       5      4
AAMOL1    L      46      5
AAMOL1    K      47      6
AAMOL1    P      48      7
AAMOL1    T      49      8
AAMOL1    P      50      9
AAMOL1    E      51     10
AAMOL1    G      52     11
AAMOL1    D      53     12
AAMOL1    L      54     13

AAMOL2    L      57      1
AAMOL2    L      58      2
AAMOL2    Q      59      3
AAMOL2    K      60      4
AAMOL2    W      61      5
AAMOL2    E      62      6
AAMOL2    N      63      7
AAMOL2    G      64      8
AAMOL2    E      65      9
AAMOL2    C      66     10
AAMOL2    A      67     11
AAMOL2    Q      68     12
AAMOL2    K      69     13
AAMOL2    K      70     14
AAMOL2    I      71     15
AAMOL2    I      72     16
AAMOL2    A      73     17
AAMOL2    E      74     18

If you attach to the end of your "mol1.mol2" file a list above
(AAMOL* records), then the only residues from that list will be
used for calculations.

...........................................................................

To select for calculations the exact set of residues user may also use
the following options: -er1:s1:s2 , -er2:s1:s2
For example we would like to perform LCS and GDT analysis ("-3" option)
to compare two structures (Molecule1 and Molecule2) in selected regions.
Using the set of parameters below:
  -3 -sia -o1 -d:5.0 -er1:10:23 -er2:45_B:50_B -er2:56_B:63_B
the following residue correspondence will be established:
Molecule1   Molecule2
   10        45_B
   11        46_B
   12        47_B
   13        48_B
   14        49_B
   15        50_B
   16        56_B
   17        57_B
   18        58_B
   19        59_B
   20        60_B
   21        61_B
   22        62_B
   23        63_B
and only these residue-pairs will be used for "-3" calculations.

Remember:
The options -1, -2, -3 work on already established residue-residue
correspondence. The residue-residue correspondence will not be changed
during calculations.
If user needs to find structure alignment (automatically establish the
residue-residue correspondence), then option "-4" has to be used.

...........................................................................


                            LCS and GDT description

Longest Continuous Segments under specified CA RMSD cutoff (LCS).
  The algorithm identifies all the longest continuous segments of residues 
  in the model deviating from the target by not more than specified 
  CA RMSD cutoff using many different superpositions.
  Each residue in a prediction is assigned to the longest of such segments
  provided if is a part of that segment (see LCS_GDT records). 
  For different values of the CA RMSD cutoff (1.0 A, 2.0 A, and 5.0 A) the 
  absolutely longest continuous segment in the model is reported as well. 

Global Distance Test (GDT). The algorithm identifies in the model 
  the sets of residues deviating from the target by not more than 
  specified CA DISTANCE cutoff using many different superpositions.
  Each residue from the model is assigned to the largest set of the residues 
  (not necessary continuous) deviating from the target by no more than a 
  specified distance cutoff (see LCS_GDT records: GDT_DATA_COLUMNS).
  For different values of DISTANCE cutoff (0.5 A, 1.0 A, 1.5 A, ... 10.0 A)  
  the several measures are reported:
    NUMBER_CA   - the number of CA's from the "largest set" that can fit 
                    under specified distance cutoff
    PERCENT_CA  - percent of CA's from the "largest set" comparing to the 
                    total number of CA's in target (see GDT_Pn below)
    RMS_LOCAL   - RMSD (root mean square deviation) calculated on the 
                    "largest set" of CA's
    RMS_ALL_CA  - RMSD calculated on all CA after superposition of the 
                    prediction structure to the target structure based on 
                    the "largest set" of CA's

    GDT_TS = (GDT_P1 + GDT_P2 + GDT_P4 + GDT_P8)/4.0
      where GDT_Pn is an estimation of the percent of residues that can
      fit under distance cutoff <= n.0 Angstroms


  The GDT procedure is the following. Each three-residue segment and each
continuous segment found by LCS is used as a starting point to give an
initial equivalencies (model-target CA pairs) for a superposition.
The list of equivalencies is iteratively extended to produce the largest
set of residues that can fit under considered distance cutoff.
For collecting data about largest sets of residues the 
Iterative Superposition Procedure (ISP) is used.
The goal of the ISP method is to exclude from the calculations atoms
that are more than some threshold (cutoff) distance between the
model and the target structure after the transform is applied.
Starting from the initial set of atoms (C-alphas) the algorithm is the
following:
  a) obtain the transform
  b) apply the transform
  c) identify all atom pairs for which distance is larger than the
     threshold
  d) re-obtain the transform, excluding those atoms
  e) repeat b) - d) until the set of atoms used in calculations
     is the same for two cycles running


  Results of the analysis given by LCS algorithm show rather local features of
the model, while the residues considered in GDT come from the whole model
structure (they do not have to maintain the continuity along the sequence).
From this point of view GDT can detect the kind of GLOBAL level of structure
similarity.

    REFERENCES

[1] A. Zemla: "LGA - a Method for Finding 3D Similarities in Protein Structures", 
    Nucleic Acids Research, 2003, Vol. 31, No. 13, pp. 3370-3374.

[2] A. Zemla, C. Venclovas, A. Reinhardt, K. Fidelis, T. J. Hubbard: "Numerical 
    criteria for the evaluation of ab initio predictions of protein structure", 
    PROTEINS: Structure, Function, and Genetics, Suppl.1, 1997, pp. 140-150. 

[3] A. Zemla, C. Venclovas, J. Moult, K. Fidelis: "Processing and Analysis 
    of CASP3 Protein Structure Predictions", PROTEINS: Structure, Function, 
    and Genetics, Suppl.3, 1999, pp. 22-29. 

[4] Arthur M. Lesk: "CASP2: Report on ab initio predictions", 
    PROTEINS: Structure, Function, and Genetics, Suppl.1, 1997, pp. 151-166. 

[5] A. Zemla, C. Venclovas, J. Moult, K. Fidelis: "Processing and evaluation of 
    predictions in CASP4", PROTEINS: Structure, Function, and Genetics,
    Volume 45, Issue S5, 2001, pp. 13-21.

[6] S. Cristobal, A. Zemla, D. Fischer, L. Rychlewski, A. Elofsson: "A study 
    of quality measures for protein threading models", BMC Bioinformatics 
    2001 2: 5 (1 August 2001).

-------------------------------------------------------------------------------

Changes, improvements, development:

-------------------------------------------------------------------------------

### Date: 15 Oct 1999

First version of the LGA program was tested.

### Date: 21 Mar 2000

An extensive analysis of the structure comparison results from PROSUP and LGA programs
used to evaluate CASP3 models was performed. Evaluation results were compared with Alexey
Murzin's "Fold recognition" CASP3 assessment.

### Date: 10 May 2000

An analysis of the LGA performance and other structure comparison programs was
performed. Collaborative work with: S. Cristobal, D. Fischer, L. Rychlewski,
and A. Elofsson.

### Date: 29 Aug 2000

The results of the comparison of different measures used for the analysis of the
quality of protein structure predictions were prepared for the manuscript [6]:
   S. Cristobal, A. Zemla, D. Fischer, L. Rychlewski, A. Elofsson: "A study
   of quality measures for protein threading models", BMC Bioinformatics
   2001 2: 5, 2001.

### Date: 20 Mar 2001

Thanks to the suggestion from Daniel Barsky (barsky@llnl.gov) an option to
perform calculation on selected CA atoms was included (AAMOL1 and AAMOL2 records).

### Date: 06 Sep 2001

"Lesk window" option was included to the program. RMSD value calculated 
on length=2*n+1 residue window (-lw:n).

### Date: 15 Jul 2002

Thanks to the suggestion from Dat H. Nguyen (nguyend@gps01.llnl.gov) an option to
perform calculations on chosen atoms (NOT only CA) was included.

  -atom:CB    CB atoms will be used for calculations. NOTE (special character
              in the PARAMATER-OPTIONS line): use , instead of '
              (for example: H5,1 to select H5'1 atom)

  -ah:i       ATOM or HETATM records are used for calculations:
                i=0 both (default)
                i=1 ATOM
                i=2 HETATM

### Date: 05 Jan 2003

Thanks to the discussions with Michael Levitt (michael.levitt@stanford.edu) the
accuracy of LGA (GDT_TS) calculations was improved, and the problem with erroneous 
calculations on "singular structures" (compressed coordinates, very small distances
between atoms) was reduced. 

### Date: 02 Mar 2003

Thanks to the discussions with Nick Grishin (grishin@chop.swmed.edu)
LGA_S scoring function was improved.

### Date: 11 Oct 2003

Thanks to the suggestion from Bernhard Rupp (br@llnl.gov) the calculation of Euler
angles has been included:

The convention used (XYZ):
    psi is about x-axis
    theta is about y-axis
    phi is about z-axis

and the translation formulas are the following:

    theta=-asin(r[1][3]);
    psi=atan2(r[2][3],r[3][3]);
    phi=atan2(r[1][2],r[1][1]);

    c1 = cos(theta);  s1 = sin(theta);
    c2 = cos(psi);    s2 = sin(psi);
    c3 = cos(phi);    s3 = sin(phi);

    r[1][1] = c1   *    c3;
    r[2][1] = s1 * s2 * c3 - c2 * s3;
    r[3][1] = s1 * c2 * c3 + s2 * s3;
    r[1][2] = c1   *    s3;
    r[2][2] = s1 * s2 * s3 + c2 * c3;
    r[3][2] = s1 * c2 * s3 - s2 * c3;
    r[1][3] = -s1;
    r[2][3] = c1 * s2;
    r[3][3] = c1 * c2;

LGA reports ROTATION matrix, VECTOR and Euler angles in the following format:

Unitary ROTATION matrix and the shift VECTOR superimpose MOLECULES (1=>2)
  X_new =  -0.051329 * X  +  -0.215884 * Y  +  -0.975069 * Z  +  6.470616
  Y_new =   0.713412 * X  +  -0.691165 * Y  +   0.115472 * Z  + -6.793733
  Z_new =  -0.698862 * X  +  -0.689699 * Y  +   0.189491 * Z  + 65.934860 

Euler angles from the ROTATION matrix (XYZ convention, two solutions):
  Psi   =  -1.302667    1.838925  [ DEG:   -74.6373    105.3627 ]
  Theta =   0.773806    2.367787  [ DEG:    44.3358    135.6642 ]
  Phi   =   1.642622   -1.498971  [ DEG:    94.1153    -85.8847 ]

### Date: 21 Dec 2003

Alignment verification module has been improved.

### Date: 11 Jan 2004

New options: -er1:s1:s2 and -er2:s1:s2 have been included. This allows to select
for calculations the exact ranges of residues from molecule1 and molecule2.
Example: -er1:10_A:16_A -er1:B:B -er2:8_A:20_A -er2:7S_B:7_C
  where: -er1:10_A:16_A selects in molecule1 the residues 10-16 (chain A)
         -er1:B:B selects in molecule1 all residues from chain B
         -er2:8_A:20_A selects in molecule2 the residues 8-20 (chain A)
         -er2:7S_B:7_C selects in molecule2 the residues 7S_B (residue 7 insertion S
                       from chain B) up to 7_C (residue 7 from chain C)