
                              EMBOSS: distmat
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                                Program distmat
                                       
Function

   Creates a distance matrix from multiple alignments
   
Description

   distmat calculates the evolutionary distances between every pair of
   sequences in a multiple alignment. The sequences need to be aligned
   before running this program. The quality of the alignment is of
   paramount importance in obtaining meaningful information from this
   analysis. This application calculates a distance matrix for the set of
   sequences in the alignment. The distances are expressed in terms of
   the number of substitutions per 100 bases or amino acids.
   
   As sequence diverge so does the probability of there being multiple
   substitutions at any one site in the alignment increase. The distance
   will then be an underestimate of the true evolutionary distance
   between the sequences. Therefore, there are a number of methods for
   correcting the observed substitution rate for the occurence of
   multiple substutions.
   
   For nucleotides, the "-position" flag allows the user to choose base
   positions to analyse in each codon, i.e. 123 (all bases), 12 (the
   first two bases), 1, 2, or 3 individual bases.
   
  Uncorrected distances
  
   This method does not make any corrections for multiple substitutions.
   Therefore, the score will be an underestimate of the distance between
   the sequences. This will not be less significant for highly similar
   sets of sequences.
   
S = m/(npos + gaps*gap_penalty)                                  (1)

m           - score of matches (1 for an exact match, a fraction for partial
              matches and 0 for no match)
npos        - number of positions included in m
gaps        - number of gaps in the sequences
gap_penalty - the score given to a gapped position

D = uncorrected distance = p-distance = 1-S          (2)

   The score of match includes all exact matches. For nucleotides, if the
   flag "-ambiguous" is used then partial matches are included in the
   score. For example, a match of M (A or C) with A will increment m by
   0.5 (0.5*1.0). Gaps are not included in the calculation unless a non
   zero value is given with "-gapweight". It should be noted that end
   gaps and internal gaps will be weighted by the same amount. So it is
   recommended that this be used with "-sbegin"and "-send" to specify the
   start and end of the region to calculate the distance from.
   
Multiple Substitution correction algorithms

  Jukes-Cantor
  
   This can be used for nucleotide and protein sequences.
   
distance = -b ln (1-D/b)

D - uncorrected distance
b - constant. b= 3/4 for nucleotides and 19/20 for proteins.

   Partial matches and gap positions can be taken into account in the
   calculation of D, by setting the "-ambiguous" and "-gapweight" flags
   (see "uncorrected distance" method).
   
   Reference:
   "Phylogenetic Inference", Swofford, Olsen, Waddell, and Hillis, in
   Molecular Systematics, 2nd ed., Sinauer Ass., Inc., 1996, Ch. 11.
   
  Tajima-Nei
  
   This method is only for nucleotide sequences. It uses the same
   equation as Jukes-Cantor, but the b-parameter is not constant. Also,
   only exact matches are considered in the calculation of the match
   score and gap positions are ignored.
   
A = 1, T = 2, C = 3, G = 4

b = 0.5(1.- Sum(i=A,G)(fraction[i]^2  + D^2/h)

h = Sum(i=A,C)Sum(k=T,G) (0.5 * pair_frequency[i,k]^2/(fraction[i]*fraction[k])
)

distance = -b ln(1.-D/b)

pair_frequency[i,k]   - frequency of the i and k base pair at sites in
                        the alignement of the pair of sequences.
fraction[i]           - average content of the base i in both sequences

   Reference:
   F. Tajima and M. Nei, Mol. Biol. Evol. 1984, 1, 269.
   
  Kimura Two-Parameter distance
  
   This method is only for nucleotide sequences. This uses the principle
   that transition substitutions (purine-purine and pyrimidine-purine)
   are more likely than transversion substitutions (purine-pyprimidine).
   Purine being the nucleic acid constituent of A and G, and pyrimidine
   being the nucleic acid derivative of the bases C, T and U. Gaps are
   ignored and abiguous symbols other than R (purine) and Y (pyrimidine)
   are ingnored.
   
P = transitions/npos
Q = transversions/npos

npos - number of positions scored

distance = -0.5 ln[ (1-2P-Q)*sqrt(1-2Q)]

   Reference:
   M. kimura, J. Mol. Evol. 1980, 16, 111.
   
  Tamura
  
   This method is only for nucleotide sequences. This method uses
   transition and transversion rates and takes into account the deviation
   of GC content from the expected value of 50 %. Gap and ambiguous
   positions are ignored.
   
P = transitions/npos
Q = transversions/npos

npos - number of positions scored

GC1 = GC fraction in sequence 1
GC2 = GC fraction in sequence 2
C = GC1 + GC2 - 2*GC1*GC2

distance = -C ln(1-P/C-Q) - 0.5(1-C) ln(1-2Q)

   Reference:
   K. Tamura, Mol. Biol. Evol. 1992, 9, 678.
   
  Jin-Nei Gamma distance
  
   This method applies to nucleotides only. This again uses transition
   and transversion rates. As with the Kimura two parameter method, gaps
   and ambiguous symbols other than R and Y are not oncluded in the
   score. The shape parameter, i.e. "a", is the square of the inverse of
   the coefficient of variation of the average substitution,
   
L = average substituition = transition_rate + 2 * transversion_rate
a = (average L)^2/(variance of L)

P = transitions/npos
Q = transversions/npos

npos - number of positions scored

distance = 0.5 * a ((1-2P-Q)^(-1/a) + 0.5 (1-2Q)^(-1/a) -3/2)

   It is suggested [Jin et al.], in general, that the distance be
   calculated with an a-value of 1. However, the user can specify their
   own value, using the "-parametera" option, or calculate for each pair
   of sequence, using "-calculatea".
   
   Reference:
   L. Jin and M. Nei, Mol. Biol. Evol. 1990, 7, 82.
   
  Kimura Protein distance
  
   This method is used for proteins only. Gaps are ignored and only exact
   matches and ambiguity codes contribute to the match score.
   
S = m/npos

m  - exact match
npos - number of positions scored

D = 1-S
distance = -ln(1 - D - 0.2D^2)

   Reference:
   M. Kimura, The Neutral Theory of Molecular Evolution, Camb. Uni.
   Press, Camb., 1983.
   
Usage

   Here is a sample session with distmat:
   
% distmat pax.align
Creates a distance matrix from multiple alignments
Multiple substitution correction methods for proteins
         0 : Uncorrected
         1 : Jukes-Cantor
         2 : Kimura Protein
Method to use [0]: 2
Output file [outfile.distmat]:

Command line arguments

   Mandatory qualifiers (* if not always prompted):
  [-msf]               seqset     File containing a sequence alignment.
*  -nucmethod          menu       Multiple substitution correction methods for
                                  nucleotides.
*  -protmethod         menu       Multiple substitution correction methods for
                                  proteins.
  [-outf]              outfile    Enter a name for the distance matrix

   Optional qualifiers (* if not always prompted):
*  -ambiguous          bool       Option to use the abiguous codes in the
                                  calculation of the Jukes-Cantor method or if
                                  the sequences are proteins.
*  -gapweight          float      Option to weight gaps in the uncorrected
                                  (nucleotide) and Jukes-Cantor distance
                                  methods.
*  -position           integer    Choose base positions to analyse in each
                                  codon i.e. 123 (all bases), 12 (the first
                                  two bases), 1, 2, or 3 individual bases.
*  -calculatea         bool       This will force the calculation of the
                                  a-parameter in the Jin-Nei Gamma distance
                                  calculation, otherwise the default is 1.0
                                  (see -parametera option).
*  -parametera         float      User defined a parameter to be use in the
                                  Jin-Nei Gamma distance calculation. The
                                  suggested value to be used is 1.0 [Jin et
                                  al.] and this is the default.

   Advanced qualifiers: (none)
   General qualifiers:
  -help                bool       report command line options. More
                                  information on associated and general
                                  qualifiers can be found with -help -verbose
   

   Mandatory qualifiers Allowed values Default
   [-msf]
   (Parameter 1) File containing a sequence alignment. Readable sequences
   Required
   -nucmethod Multiple substitution correction methods for nucleotides.
   0 (Uncorrected)
   1 (Jukes-Cantor)
   2 (Kimura)
   3 (Tamura)
   4 (Tajima-Nei)
   5 (Jin-Nei Gamma)
   0
   -protmethod Multiple substitution correction methods for proteins.
   0 (Uncorrected)
   1 (Jukes-Cantor)
   2 (Kimura Protein)
   0
   [-outf]
   (Parameter 2) Enter a name for the distance matrix Output file
   <sequence>.distmat
   Optional qualifiers Allowed values Default
   -ambiguous Option to use the abiguous codes in the calculation of the
   Jukes-Cantor method or if the sequences are proteins. Yes/No No
   -gapweight Option to weight gaps in the uncorrected (nucleotide) and
   Jukes-Cantor distance methods. Any integer value 0.
   -position Choose base positions to analyse in each codon i.e. 123 (all
   bases), 12 (the first two bases), 1, 2, or 3 individual bases. Any
   integer value 123
   -calculatea This will force the calculation of the a-parameter in the
   Jin-Nei Gamma distance calculation, otherwise the default is 1.0 (see
   -parametera option). Yes/No No
   -parametera User defined a parameter to be use in the Jin-Nei Gamma
   distance calculation. The suggested value to be used is 1.0 [Jin et
   al.] and this is the default. Any integer value 1.0
   Advanced qualifiers Allowed values Default
   (none)
   
Input file format

   It reads in a normal multiple sequence alignment file.
   
   The quality of the alignment is of paramount importance in obtaining
   meaningful information from this analysis.
   
Output file format

   The output from the program is a file containing a matrix of the
   calculated distances between each of the input aligned sequences. The
   distances are expressed in terms of the number of substitutions per
   100 bases or amino acids.
   
   The output from the example usage above is:
     _________________________________________________________________
   
Distance Matrix
---------------

Using the Kimura correction method
Gap weighting is 0.000000

            1       2       3       4       5       6       7       8       9
     10
          0.00   96.10  137.41  128.65  161.04  160.26  157.46  154.14  164.22
 152.59          PAX4_HUMAN 1
                  0.00  111.86  109.96  156.25  149.70  143.75  135.71  150.60
 146.87          PAX6_HUMAN 2
                          0.00   26.21  131.54  143.54  162.95  151.39  163.56
 159.78          PAX3_HUMAN 3
                                  0.00  145.45  138.76  158.79  149.96  167.26
 161.82          PAX7_HUMAN 4
                                          0.00   44.29  120.84  123.00  131.69
 130.22          PAX1_HUMAN 5
                                                  0.00  123.56  130.21  131.64
 130.17          PAX9_HUMAN 6
                                                          0.00   36.43   53.12
  64.32          PAX2_HUMAN 7
                                                                  0.00   60.88
  73.82          PAX5_HUMAN 8
                                                                          0.00
  20.37          PX8A_HUMAN 9
     _________________________________________________________________
   
Data files

   None.
   
Notes

   None.
   
References

   See the following for details of the methods used:
   
    1. "Phylogenetic Inference", Swofford, Olsen, Waddell, and Hillis, in
       Molecular Systematics, 2nd ed., Sinauer Ass., Inc., 1996, Ch. 11.
    2. F. Tajima and M. Nei, Mol. Biol. Evol. 1984, 1, 269.
    3. M. Kimura, J. Mol. Evol. 1980, 16, 111.
    4. K. Tamura, Mol. Biol. Evol. 1992, 9, 678.
    5. L. Jin and M. Nei, Mol. Biol. Evol. 1990, 7, 82.
    6. M. Kimura, The Neutral Theory of Molecular Evolution, Camb. Uni.
       Press, Camb., 1983.
       
Warnings

   The quality of the alignment is of paramount importance in obtaining
   meaningful information from this analysis.
   
Diagnostic Error Messages

   None.
   
Exit status

   It always exits with status 0.
   
Known bugs

   None.
   
See also

   Program name Description
   
Author(s)

   This application was written by Tim Carver (tcarver@hgmp.mrc.ac.uk)
   
History

   Written (March 2001) - Tim Carver
   
Target users

   This program is intended to be used by everyone and everything, from
   naive users to embedded scripts.
   
Comments
