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]: 

Go to the input files for this example
Go to the output files for this example

Command line arguments

Create a distance matrix from a multiple sequence alignment
Version: EMBOSS:6.3.0

   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.

Input files for usage example

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.

Output files for usage example

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

Data files

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.

Diagnostic Error Messages

None.

Exit status

It always exits with status 0.

Known bugs

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.

Comments

None