distmat

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Function

Create a distance matrix from a multiple sequence alignment

Description

distmat calculates the evolutionary distance between every pair of sequences in a multiple sequence alignment. A variety of methods to estimate distance may be selected, and differ in how they correct the observed substitution rates to more accurately reflect the true evolutionary distance. An output file containing a distance matrix for the set of sequences is written. The distances are expressed in terms of the number of substitutions per 100 bases or amino acids.

Algorithm

For more divergent sequences, the probability of there being multiple substitutions at an alignment site increases. The distance will then be misestimate the true evolutionary distance between the sequences. A number of methods are available in distmat to correct the observed substitution rate to more accurately reflect the true evolutionary distance.

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 Create a distance matrix from a multiple sequence alignment Multiple substitution correction methods for proteins 0 : Uncorrected 1 : Jukes-Cantor 2 : Kimura Protein Method to use [0]: 2 Phylip distance matrix output file [pax.distmat]: ```

Command line arguments

 ```Create a distance matrix from a multiple sequence alignment Version: EMBOSS:6.4.0.0 Standard (Mandatory) qualifiers (* if not always prompted): [-sequence] seqset File containing a sequence alignment. * -nucmethod menu [0] Multiple substitution correction methods for nucleotides. (Values: 0 (Uncorrected); 1 (Jukes-Cantor); 2 (Kimura); 3 (Tamura); 4 (Tajima-Nei); 5 (Jin-Nei Gamma)) * -protmethod menu [0] Multiple substitution correction methods for proteins. (Values: 0 (Uncorrected); 1 (Jukes-Cantor); 2 (Kimura Protein)) [-outfile] outfile [*.distmat] Phylip distance matrix output file Additional (Optional) qualifiers (* if not always prompted): * -ambiguous boolean [N] Option to use the ambiguous codes in the calculation of the Jukes-Cantor method or if the sequences are proteins. * -gapweight float [0.] Option to weight gaps in the uncorrected (nucleotide) and Jukes-Cantor distance methods. (Any numeric value) * -position integer [123] 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) * -calculatea boolean [N] This will force the calculation of parameter 'a' in the Jin-Nei Gamma distance calculation, otherwise the default is 1.0 (see -parametera option). * -parametera float [1.0] User defined parameter 'a' 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 numeric value) Advanced (Unprompted) qualifiers: (none) Associated qualifiers: "-sequence" associated qualifiers -sbegin1 integer Start of each sequence to be used -send1 integer End of each sequence to be used -sreverse1 boolean Reverse (if DNA) -sask1 boolean Ask for begin/end/reverse -snucleotide1 boolean Sequence is nucleotide -sprotein1 boolean Sequence is protein -slower1 boolean Make lower case -supper1 boolean Make upper case -sformat1 string Input sequence format -sdbname1 string Database name -sid1 string Entryname -ufo1 string UFO features -fformat1 string Features format -fopenfile1 string Features file name "-outfile" associated qualifiers -odirectory2 string Output directory General qualifiers: -auto boolean Turn off prompts -stdout boolean Write first file to standard output -filter boolean Read first file from standard input, write first file to standard output -options boolean Prompt for standard and additional values -debug boolean Write debug output to program.dbg -verbose boolean Report some/full command line options -help boolean Report command line options and exit. More information on associated and general qualifiers can be found with -help -verbose -warning boolean Report warnings -error boolean Report errors -fatal boolean Report fatal errors -die boolean Report dying program messages -version boolean Report version number and exit ```

Qualifier Type Description Allowed values Default
Standard (Mandatory) qualifiers
[-sequence]
(Parameter 1)
seqset File containing a sequence alignment. Readable set of sequences Required
-nucmethod list Multiple substitution correction methods for nucleotides.
 0 (Uncorrected) 1 (Jukes-Cantor) 2 (Kimura) 3 (Tamura) 4 (Tajima-Nei) 5 (Jin-Nei Gamma)
0
-protmethod list Multiple substitution correction methods for proteins.
 0 (Uncorrected) 1 (Jukes-Cantor) 2 (Kimura Protein)
0
[-outfile]
(Parameter 2)
outfile Phylip distance matrix output file Output file <*>.distmat
Additional (Optional) qualifiers
-ambiguous boolean Option to use the ambiguous codes in the calculation of the Jukes-Cantor method or if the sequences are proteins. Boolean value Yes/No No
-gapweight float Option to weight gaps in the uncorrected (nucleotide) and Jukes-Cantor distance methods. Any numeric value 0.
-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. Any integer value 123
-calculatea boolean This will force the calculation of parameter 'a' in the Jin-Nei Gamma distance calculation, otherwise the default is 1.0 (see -parametera option). Boolean value Yes/No No
-parametera float User defined parameter 'a' 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 numeric value 1.0
Advanced (Unprompted) qualifiers
(none)
Associated qualifiers
"-sequence" associated seqset qualifiers
-sbegin1
-sbegin_sequence
integer Start of each sequence to be used Any integer value 0
-send1
-send_sequence
integer End of each sequence to be used Any integer value 0
-sreverse1
-sreverse_sequence
boolean Reverse (if DNA) Boolean value Yes/No N
-sask1
-sask_sequence
boolean Ask for begin/end/reverse Boolean value Yes/No N
-snucleotide1
-snucleotide_sequence
boolean Sequence is nucleotide Boolean value Yes/No N
-sprotein1
-sprotein_sequence
boolean Sequence is protein Boolean value Yes/No N
-slower1
-slower_sequence
boolean Make lower case Boolean value Yes/No N
-supper1
-supper_sequence
boolean Make upper case Boolean value Yes/No N
-sformat1
-sformat_sequence
string Input sequence format Any string
-sdbname1
-sdbname_sequence
string Database name Any string
-sid1
-sid_sequence
string Entryname Any string
-ufo1
-ufo_sequence
string UFO features Any string
-fformat1
-fformat_sequence
string Features format Any string
-fopenfile1
-fopenfile_sequence
string Features file name Any string
"-outfile" associated outfile qualifiers
-odirectory2
-odirectory_outfile
string Output directory Any string
General qualifiers
-auto boolean Turn off prompts Boolean value Yes/No N
-stdout boolean Write first file to standard output Boolean value Yes/No N
-filter boolean Read first file from standard input, write first file to standard output Boolean value Yes/No N
-options boolean Prompt for standard and additional values Boolean value Yes/No N
-debug boolean Write debug output to program.dbg Boolean value Yes/No N
-verbose boolean Report some/full command line options Boolean value Yes/No Y
-help boolean Report command line options and exit. More information on associated and general qualifiers can be found with -help -verbose Boolean value Yes/No N
-warning boolean Report warnings Boolean value Yes/No Y
-error boolean Report errors Boolean value Yes/No Y
-fatal boolean Report fatal errors Boolean value Yes/No Y
-die boolean Report dying program messages Boolean value Yes/No Y
-version boolean Report version number and exit Boolean value Yes/No N

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.

File: pax.align

 ```PileUp MSF: 603 Type: P Check: 9004 .. Name: PAX4_HUMAN oo Len: 603 Check: 6594 Weight: 11.2 Name: PAX6_HUMAN oo Len: 603 Check: 7176 Weight: 9.1 Name: PAX3_HUMAN oo Len: 603 Check: 7760 Weight: 9.5 Name: PAX7_HUMAN oo Len: 603 Check: 4677 Weight: 13.7 Name: PAX1_HUMAN oo Len: 603 Check: 9671 Weight: 8.7 Name: PAX9_HUMAN oo Len: 603 Check: 565 Weight: 12.0 Name: PAX2_HUMAN oo Len: 603 Check: 9553 Weight: 8.7 Name: PAX5_HUMAN oo Len: 603 Check: 448 Weight: 11.2 Name: PX8A_HUMAN oo Len: 603 Check: 6763 Weight: 7.5 Name: PX8D_HUMAN oo Len: 603 Check: 5797 Weight: 7.9 // PAX4_HUMAN .......... .......... .........M HQDGISSMNQ LGGLFVNGRP PAX6_HUMAN .......... .......... .......... MQNSHSGVNQ LGGVFVNGRP PAX3_HUMAN MTTLAGAVPR MMRPGPGQNY PRSGFPLEVS TPLGQGRVNQ LGGVFINGRP PAX7_HUMAN MAALPGTVPR MMRPAPGQNY PRTGFPLEVS TPLGQGRVNQ LGGVFINGRP PAX1_HUMAN .......... .......... .......... MEQTYGEVNQ LGGVFVNGRP PAX9_HUMAN .......... .......... .......... MEPAFGEVNQ LGGVFVNGRP PAX2_HUMAN .......... ........MD MHCKADPFSA MHPGHGGVNQ LGGVFVNGRP PAX5_HUMAN .......... ........MD LEKNYPTPRT SRTGHGGVNQ LGGVFVNGRP PX8A_HUMAN .......... .......... .....MPHNS IRSGHGGLNQ LGGAFVNGRP PX8D_HUMAN .......... .......... .....MPHNS IRSGHGGLNQ LGGAFVNGRP PAX4_HUMAN LPLDTRQQIV RLAVSGMRPC DISRILKVSN GCVSKILGRY YRTGVLEPKG PAX6_HUMAN LPDSTRQKIV ELAHSGARPC DISRILQVSN GCVSKILGRY YETGSIRPRA PAX3_HUMAN LPNHIRHKIV EMAHHGIRPC VISRQLRVSH GCVSKILCRY QETGSIRPGA PAX7_HUMAN LPNHIRHKIV EMAHHGIRPC VISRQLRVSH GCVSKILCRY QETGSIRPGA PAX1_HUMAN LPNAIRLRIV ELAQLGIRPC DISRQLRVSH GCVSKILARY NETGSILPGA PAX9_HUMAN LPNAIRLRIV ELAQLGIRPC DISRQLRVSH GCVSKILARY NETGSILPGA PAX2_HUMAN LPDVVRQRIV ELAHQGVRPC DISRQLRVSH GCVSKILGRY YETGSIKPGV PAX5_HUMAN LPDVVRQRIV ELAHQGVRPC DISRQLRVSH GCVSKILGRY YETGSIKPGV PX8A_HUMAN LPEVVRQRIV DLAHQGVRPC DISRQLRVSH GCVSKILGRY YETGSIRPGV PX8D_HUMAN LPEVVRQRIV DLAHQGVRPC DISRQLRVSH GCVSKILGRY YETGSIRPGV PAX4_HUMAN IGGSKPR.LA TPPVVARIAQ LKGECPALFA WEIQRQLCAE GLCTQDKTPS PAX6_HUMAN IGGSKPR.VA TPEVVSKIAQ YKRECPSIFA WEIRDRLLSE GVCTNDNIPS PAX3_HUMAN IGGSKPKQVT TPDVEKKIEE YKRENPGMFS WEIRDKLLKD AVCDRNTVPS PAX7_HUMAN IGGSKPRQVA TPDVEKKIEE YKRENPGMFS WEIRDRLLKD GHCDRSTVPS PAX1_HUMAN IGGSKPR.VT TPNVVKHIRD YKQGDPGIFA WEIRDRLLAD GVCDKYNVPS [Part of this file has been deleted for brevity] PX8A_HUMAN VSSSSSTPSS LSSSAFLDLQ QVGSGVPPFN AFPHAASVYG QFTGQALLSG PX8D_HUMAN ....KSAPGS RPS....... .....MP... .FPMLPPCTG SSRARPSSQG PAX4_HUMAN .......... .......... .....ERCLS DTPPKACLKP CWDCGSFLLP PAX6_HUMAN .......... .......... .SFTMANNLP MQPPVPSQTS SYSCMLPTSP PAX3_HUMAN NGL.SPQVM. .......... GLLTNHGGVP HQPQTDYALS PLTGGLEPTT PAX7_HUMAN NGL.SPQVM. .......... SILGNPSAVP PQPQADFSIS PLHGGLDSAT PAX1_HUMAN .......... .......... GAGVAVHGGE LAAAMTFKHR EGTDRKPP.. PAX9_HUMAN .......... .......... ......HNCD IPASLAFKGM QAARE..... PAX2_HUMAN .......... .......... GSYPTSTLAG MVPGSEFSGN PYSHPQYTAY PAX5_HUMAN .......... .......... GSYSAPTLTG MVPGSEFSGS PYSHPQYSSY PX8A_HUMAN REMVGPTLPG YPPHIPTSGQ GSYASSAIAG MVAGSEYSGN AYGHTPYSSY PX8D_HUMAN ERWWGPRCP. .......... DTHPTSPPAD RAAMPPLPSQ AWWQEVN... PAX4_HUMAN VIAPSCVDVA WP.CLDASLA HHLIGGAGKA TPTHFS.... .......... PAX6_HUMAN SVNGRSYDTY TPPHMQTHMN SQPMGTSGTT STGLISPGVS VPVQVPGSEP PAX3_HUMAN TVSASCSQRL DHMKSLDSLP TSQSYCPPTY STTGYSMDPV TGYQYGQYGQ PAX7_HUMAN SISASCSQRA DSIKPGDSLP TSQAYCPPTY STTGYSVDPV AGYQYGQYGQ PAX1_HUMAN ..SSGSKAPD ALSSLH.... ....GLPIPA STS....... .......... PAX9_HUMAN ..GSHSVTAS AL........ .......... .......... .......... PAX2_HUMAN NEAWRFSNPA LLSSPYYYSA APR.SAPAAR AAAYDRH... .......... PAX5_HUMAN NDSWRFPNPG LLGSPYYYSA AARGAAPPAA ATAYDRH... .......... PX8A_HUMAN SEAWGFPNSS LLSSPYYYSS TSRPSAPPTT ATAFDHL... .......... PX8D_HUMAN ..TLAMPMAT PPTPP..... TARPGASPTP AC........ .......... PAX4_HUMAN .....HWP.. .......... .......... .......... .......... PAX6_HUMAN DMS.QYWPRL Q......... .......... .......... .......... PAX3_HUMAN S...KPWTF. .......... .......... .......... .......... PAX7_HUMAN SECLVPWASP VPIPSPTPRA SCLFMESYKV VSGWGMSISQ MEKLKSSQME PAX1_HUMAN .......... .......... .......... .......... .......... PAX9_HUMAN .......... .......... .......... .......... .......... PAX2_HUMAN .......... .......... .......... .......... .......... PAX5_HUMAN .......... .......... .......... .......... .......... PX8A_HUMAN .......... .......... .......... .......... .......... PX8D_HUMAN .......... .......... .......... .......... .......... PAX4_HUMAN ... PAX6_HUMAN ... PAX3_HUMAN ... PAX7_HUMAN QFT PAX1_HUMAN ... PAX9_HUMAN ... PAX2_HUMAN ... PAX5_HUMAN ... PX8A_HUMAN ... PX8D_HUMAN ... ```

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.

File: pax.distmat

 ```Distance Matrix --------------- Using the Kimura correction method Gap weighting is 0.000000 1 2 3 4 5 6 7 8 9 10 0.00 96.15 137.48 128.72 161.14 160.37 157.55 154.23 164.32 152.68 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 0.00 PX8D_HUMAN 10 ```

None.

Notes

The input sequences must of course be aligned before running this program. The quality of the alignment is of paramount importance in obtaining meaningful information from this analysis.

For nucleotides, the -position flag selects base positions to analyse in each codon, i.e. 123 (all bases), 12 (the first two bases), 1, 2, or 3 individual bases.

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.

None.

Exit status

It always exits with status 0.

None.

See also

Program name Description

Author(s)

Tim Carver formerly at:
MRC Rosalind Franklin Centre for Genomics Research Wellcome Trust Genome Campus, Hinxton, Cambridge, CB10 1SB, UK

Please report all bugs to the EMBOSS bug team (emboss-bug © emboss.open-bio.org) not to the original author.

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.

None