PROTML:
        Maximum Likelihood Inference of Protein Phylogeny


             Jun Adachi 1)  and  Masami Hasegawa 2)


              1) Department of Statistical Science,
           The Graduate University for Advanced Study
         4-6-7 Minami-Azabu, Minato-ku, Tokyo 106, Japan

           2) The Institute of Statistical Mathematics
         4-6-7 Minami-Azabu, Minato-ku, Tokyo 106, Japan



                          INTRODUCTION


     PROTML is a PASCAL program for inferring evolutionary  trees
from protein (amino acid) sequences by using maximum likelihood.

     A maximum likelihood method for inferring trees from DNA  or
RNA  sequences  was  developed  by Felsenstein (1981). The method
does not impose any constraint on the constancy  of  evolutionary
rate  among lineages. He wrote a program (DNAML) implementing the
method, and included it  in  his  program  package,  PHYLIP.  The
program  has been used extensively and has proved of great use in
phylogenetic studies (Hasegawa and Yano, 1984a; Hasegawa et  al.,
1985,  1990a;  Hasegawa  and Kishino, 1989; Kishino and Hasegawa,
1989; Zillig et al., 1989; Hasegawa,  1990,  1991;  Golenberg  et
al.,  1990;  Adkins  and  Honeycutt,  1991; Doebley et al., 1991;
Edwards et al., 1991; Les et al.,  1991;  Ruvolo  et  al.,  1991;
Disotell   et   al.,  1992;  Lockhart  et  al.,  1992).  Computer
simulations have demonstrated that the method is highly efficient
in  estimating  a  true  tree  under various situations such as a
violation of rate constancy among lineages  (Hasegawa  and  Yano,
1984b; Hasegawa et al., 1991).

     DNAML, however, is confined to DNA or RNA sequence data, and
is  not  applicable  to  protein  sequence  data. In phylogenetic
studies of deep branchings, such as those among the  three  major
kingdoms  of eukaryotes, archaebacteria and eubacteria, and those
in the early evolution of eukaryotes, ribosomal RNA sequence data
has  been used widely (e.g., Woese, 1989; Sogin et al., 1989). In
spite of many works on the ribosomal RNAs, the universal root  of
all  contemporary  organisms  on  the earth including eukaryotes,
archaebacteria and eubacteria remained uncertain. Miyata and  his
coworkers   demonstrated  the  usefulness  of  using  amino  acid
sequence data encoded by duplicated genes  (duplicated  prior  to
the  divergence  among  the  major  kingdoms) in establishing the
universal root (Iwabe et  al.,  1989;  Hasegawa  et  al.,  1990b;
Miyata  et al., 1991). Furthermore, an evolutionary tree inferred
from  ribosomal  RNA  data  is  sometimes  misleading  when  base
composition  differs  widely  among lineages, and a tree inferred
from protein sequences is more reliable in such cases (Loomis and
Smith, 1990; Hasegawa et al., 1993).

     Because no program was available  for  inferring  a  protein
tree  by  maximum likelihood based on a reasonable model of amino
acid  substitutions,  many  authors  used  DNAML   in   analyzing
protein-encoding  DNA  sequences.  As  is  well  known, the third
position of codons evolve more rapidly than other positions,  and
therefore  DNAML  was  designed  so that a user could specify the
relative  rates  of  substitutions  in  several   categories   of
positions.  This approach seems to be good in many cases when one
is interested in phylogenetic relationships among closely related
species.

     Even if the rate difference among positions in a  codon  are
taken  into account, however, inclusion of the third positions in
the analysis can sometimes be  misleading  when  the  pattern  of
codon  usage  differs among lineages. Furthermore, the assumption
(in DNAML) of independent evolution among three  positions  of  a
codon  can  be a serious defect when one is interested in tracing
deep branchings, because a (negative) selection is likely  to  be
operating at the codon level, rather than at the individual sites
in the codon. Even if nucleotide frequencies of  protein-encoding
genes  differ  among  lineages,  amino  acid  frequencies may not
differ significantly (Adachi and Hasegawa, 1992).  Therefore,  if
the  amino  acid  substitution  process  can be represented by an
appropriate model, it seems to be better  to  handle  amino  acid
sequences  rather  than nucleotide sequences in estimating orders
of deep branchings from data  of  a  protein-encoding  gene,  and
there is an increasing demand for a maximum likelihood program to
infer protein phylogenies.

     Kishino et al. (1990) developed a maximum likelihood  method
for  inferring  protein phylogenies that takes account of unequal
transition probabilities among pairs of amino acids by  using  an
empirical  transition  matrix  compiled by Dayhoff et al. (1978),
and the model is called  the  Dayhoff  model  (Hasegawa  et  al.,
1992).  Although  the  transition  matrix  was constructed from a
limited data set (accumulated up to 1978) of proteins encoded  in
nuclear  DNA,  the Dayhoff model is not necessarily specific only
to those proteins, but is appropriate in approximating the  amino
acid   substitutions   of   wider   protein   species   including
mitochondrial ones (Hasegawa et al., 1993; Adachi  and  Hasegawa,
1992; Adachi et al., 1992).

     The original program for  private  use  in  Kishino  et  al.
(1990), Mukohata et al. (1990), Hasegawa et al. (1990b), Iwabe et
al. (1991), and Miyata et al. (1991) was written in  FORTRAN  and
the  number  of  species  in  the maximum likelihood analysis was
confined to five. In writing this  program  "PROTML"  for  public
use,  we  took advantage of another computer language, PASCAL, to
represent the tree structure of the data. In this program,  there
is  no  limit  on the number of species, provided the computer is
big enough.

     Since the  number  of  possible  tree  topologies  increases
explosively  as  the  number  of  species increases (Felsenstein,
1978a), it is a serious problem to find the best tree  among  the
huge  number of alternatives. We have developed a novel algorithm
for searching tree topologies, called "star decomposition", which
seems to be effective in finding the best tree.

     The parsimony method  has  been  used  widely  in  molecular
phylogenetics,  but  it  may  be  positively  misleading when the
evolutionary rate differs among  lineages  (Felsenstein,  1978b).
PROTML  has  proved  of great use in inferring evolutionary trees
even in such situations (Hasegawa et al.,  1992),  and  has  been
applied  to several phylogenetic problems (Hasegawa et al., 1993;
Adachi and Hasegawa, 1992; Adachi et al., 1992; Hashimoto et al.,
1993).

     The overall structure  of  PROTML  is  similar  to  that  of
Felsenstein's  DNAML.  We  owe  very much to DNAML in the writing
PROTML, and have adopted several fundamental  routines  from  the
DNAML  program.  Furthermore, the input format of PROTML is quite
similar to that of DNAML.  Features  where  PROTML  differs  from
DNAML (up to version 3.4) are as follows:

   (1) Amino acid sequence data are analyzed based  on  Dayhoff's
   model(1978).
   (2) The likelihood of multifurcating trees can be estimated.
   (3) A novel method of topology search  ("star  decomposition")
   is adopted.
   (4) The Newton  method  is  adopted  in  the  maximization  of
   likelihood.
   (5)  Bootstrap  probabilities  of  candidate  trees   can   be
   estimated.



                  ALGORITHM FOR TOPOLOGY SEARCH

   Topological Data Structure

     Felsenstein considered a  data  structure  representing  the
unrooted tree, where each internal node (excluding external nodes
or tips)  is  decomposed  into  elements,  the  number  of  which
coincides  with  those  of  branches  stemming from the node. The
elements are connected circularly through the pointers.

     By adopting such a data structure, we can  store  a  partial
likelihood of a sub-tree stemming from the node. This means that,
when we  estimate  the  likelihood  of  the  tree,  we  need  not
calculate  likelihood through iteration of a loop by the times of
the number of nodes in  revising  the  estimate  of  each  branch
length, but need only revise the partial likelihoods of two nodes
of each branch.

     We extend this data structure so that a multifurcating  tree
can  be  represented. Since branches are connected dynamically by
pointers, the  data  structure  can  easily  be  revised  when  a
different  tree  topology  is  adopted,  and furthermore not only
bifurcating  trees  but  also   multifurcating   trees   can   be
represented  quite  easily. The extreme limit of a multifurcating
tree is the star-like tree.


   Automatic Topology Search by Star Decomposition

     The straightforward approach to inferring a tree would be to
evaluate  all possible tree topologies one after another and pick
the one which gives the highest likelihood.  This  would  not  be
possible  for  more  than  a  small  number of species, since the
number of possible  tree  topologies  is  enormous  (Felsenstein,
1978a).

     The strategy that Felsenstein's DNAML employs is as follows:
the  species  are  taken in the order in which they appear in the
input file. The first three are taken and  an  unrooted  tree  is
constructed containing only those three. Then, the fourth species
is taken, and it is evaluated to see where it might best be added
to the tree. All possibilities (bifurcating trees) for adding the
fourth species are examined. The best one  under  the  likelihood
criterion  is chosen to be the basis for further operations. Then
the fifth species is added, and again the best placement of it is
chosen,  and  so on. At each step, local rearrangements of a tree
are examined. This procedure is  continued  until  a  bifurcating
tree connecting all the species is obtained (Felsenstein, 1992).

     The resulting tree from this procedure generally depends  on
the  order  of  the  input species. Hence, Felsenstein recommends
performing a number of runs with different orderings of the input
species.

     The alternative strategy which we employ  in  the  automatic
and  semi-automatic  search  options  of  PROTML  is called "star
decomposition". This is similar to the procedure employed in  the
neighbor-joining  method using a distance matrix (Saitou and Nei,
1987). This method starts with a star-like tree. Decomposing  the
star-like tree step by step, we finally obtain a bifurcating tree
if  all  multifurcations  can  be   resolved   with   statistical
confidence.  Since  the information from all of the species under
analysis is used from the beginning, the inference  of  the  tree
topology is likely to be stable by this procedure.

     Let be the number of species under  analysis.  At  first,  a
star-like tree containing species is constructed. Then, a pair of
species is separated from others.  Among  all  possible  pairwise
combinations  of  species,  a  pairing  that  gives  the  highest
likelihood is chosen. The resulting tree can  be  regarded  as  a
star-like  tree  with groups (a single species may form a group),
if the selected pair is regarded to form a group. This  procedure
is  continued  until  all  multifurcating nodes are resolved into
bifurcating ones.

     When the information content of the data is not large enough
to  discriminate  among alternative branching orders, it might be
misleading to resolve all the multifurcations into  bifurcations.
Hence,  by  using  "Akaike  Information  Criteria (AIC)" (Akaike,
1974), the program  decides  whether  the  multifurcation  should
further be resolved or not.



                       PROTML USER'S GUIDE

   Options

     The program allows various options that alter the amount  of
information the program is provided or what it is to be done with
the information. The program is notified that an option has  been
invoked  by  the  presence  of one or more letters after the last
number on the first line of the input file. These letters may  or
may  not  be  separated  from  each other by blanks, though it is
usually necessary to separate them from the number  by  a  blank.
They  can be in any order. Thus to invoke options U, W and B, the
input file starts with the line:

 19 409 UWB

or

   19  409   W  U  B

     This program  has  three  mode  of  topology  search;  i.e.,
Automatic mode, Semi-automatic mode and User tree (manual) mode.

   Automatic mode.
   Unless specified otherwise, the procedure uses automatic mode,
   so it starts with a star-like tree.

   "S" : Semi-automatic mode.
   Semi-automatic mode starts with a multifurcating tree  that  a
   user designates.

   "U" : User tree mode.
   User tree (manual) mode  is  similar  to  the  "U"  option  in
   Felsenstein's  DNAML.  This  mode calculates the likelihood of
   all  user  defined  topologies.  Different  from  DNAML,  this
   program allows multifurcating trees as user trees.

   "W" : Write option.
   Using this option, the program will produce  more  information
   than it dose for standard output.

   "B" : Bootstrap option.
   This option gives the approximate bootstrap  probabilities  of
   candidate trees by a resampling of estimated likelihood (RELL)
   method (Kishino et al., 1990).


   Format of input data file

     We have tried to adhere to a rather stereotyped input format
similar  to  that of Felsenstein's programs. The simplest version
of the input file looks something like this:

     4   40   W
 species1 ARNDCQEGHILKAFPMTWYVARNDCQEGHISKMFGWTWYV
 species2 ARNHNQCGHILKMFPMTSYVARNCCAEHHILKHFPSTWIV
 species3 AINDCQEGHHLKMFPMTMYSVRNRIQEMHIQKHCPHTHYV
 species4 AINHCQCEHILWMFPSTPYVARNDIQNYHILKMPPSTWWV

     The first line of the input  file  contains  the  number  of
species  and  the length of amino acid sequences, in free format,
separated by blanks. The information for  each  species  follows,
starting  with  a  ten-character  species name (which can include
punctuation marks), and continuing with the characters  for  that
species.

     An input file has three  parts  of  data;  i.e.,  arguments,
sequences and topologies.

   1. Arguments
   The first line of the file gives number of  species,  sequence
   length, and options.

   2. Sequences
   The following lines give species names and amino acid sequence
   data.  The  amino  acids  must  be specified by the one letter
   codes  adopted  by   IUPAC-IUB   Commission   on   Biochemical
   Nomenclature  (1968).  The  amino acid code must be one of the
   twenty.

   3. Topologies
   If one specifies User  or  Semi-automatic  options,  one  mast
   specify  the  number  of topologies followed by the topologies
   themselves.

     This program allows the option U, which signals  that  user-
defined  tree(s)  are provided. The topologies of these trees are
supplied AFTER the species and sequence data, rather than  before
them.  The  letter U appears on the first line of the file. After
the species and sequence data, a line containing  the  number  of
user-defined  trees  appears.  Each user-defined tree starts on a
new line. Here is an example with three user-defined trees:

     5   40   U   B
 species1 ARNDCQEGHILKAFPMTWYVARNDCQEGHISKMFGWTWYV
 species2 ARNHNQCGHILKMFPMTSYVARNCCAEHHILKHFPSTWIV
 species3 AINDCQEGHHLKMFPMTMYSVRNRIQEMHIQKHCPHTHYV
 species4 AINHCQCEHILWMFPSTPYVARNDIQNYHILKMPPSTWWV
 species5 AINDCSCGHHLWMFPSLCYVRRNECQGGHIWKMFPLTVCA
     3
 (((species1,species2),species3),species4,species5)
 ((species1,species2),(species3,species4),species5)
 (species1,(species2,species3),(species4,species5))

     An example of semi-auto mode is as follows:

     5   40   S
 species1 ARNDCQEGHILKAFPMTWYVARNDCQEGHISKMFGWTWYV
 species2 ARNHNQCGHILKMFPMTSYVARNCCAEHHILKHFPSTWIV
 species3 AINDCQEGHHLKMFPMTMYSVRNRIQEMHIQKHCPHTHYV
 species4 AINHCQCEHILWMFPSTPYVARNDIQNYHILKMPPSTWWV
 species5 AINDCSCGHHLWMFPSLCYVRRNECQGGHIWKMFPLTVCA

 ((species1,species2,species3),species4,species5)

     The  tree  topology  is  specified  by   nested   pairs   of
parentheses,  enclosing  species  names  and separated by commas.
Trailing blanks in the name may be omitted. The  pattern  of  the
parentheses indicates the pattern of the tree by having each pair
of parentheses enclose all the members of a  monophyletic  group.
The  entire tree is enclosed in an outermost pair of parentheses.
Note that the tree is an unrooted one,  and  therefore  its  base
must  be  multifurcation  with  a multiplicity of greater than or
equal to three. A specification of a tree ends with  a  semicolon
which may be omitted.


   Program Constants

     The CONSTants in program that may be changed by a user are:

 CONST
 maxsp     : maximum number of species
 maxnode   : maxsp * 2 - 3
 maxpair   : maxsp * (maxsp-1) / 2
 maxsite   : maximum number of sites
 maxptrn   : maximum number of different site patterns
 maxtree   : maximum number of user trees
 maxsmooth : number of smoothing algorithm
 maxiterat : number of iterates of Newton method
 epsilon   : stopping value of error
 minarc    : lower limit on number of substitutions per branch
 maxarc    : upper limit on number of substitutions per branch
 prprtn    : proprtion of branch length
 maxboot   : number of bootstrap replications
 maxexe    : number of jobs
 maxline   : length of sequence output per line
 maxname   : maximum number of characters in species name
 maxami    : number of amino acids
 minreal   : if job is in underflow error, increase this value
 seqfname  : input file of sequence data
 tpmfname  : input file of transition probability
 lklfname  : output file of log-likelihood


   Output Format

     The output usually consists of
   (1) the name of the program and its version number,
   (2) the input information printed out, and
   (3) a series of trees,
some with associated information indicating how much change there
was in each character or on each part of the tree.

     The tree grows from left to right and has branches that  are
approximately  proportional  in  length  to  the lengths that the
program estimates. In some cases when branches are  estimated  to
be  very  short,  the output makes them three spaces long so that
the topology is clearly shown. Here is what a typical tree  looks
like:

   :-----------1.Tabac.chl
  0:
   :        :-------2.Prochloro
   :   :----6
   :   :    :---3.Anacystis
   :---7
   :   :------------------5.Synechocy
   :
   :------4.Fremyella

  No.            number   Length       S.E.
  ----------------------------------------------
      Tabac.chl     1     9.44861  (  1.63423 )
      Prochloro     2     5.69634  (  1.30862 )
      Anacystis     3     1.57704  (  0.74325 )
      Fremyella     4     4.92061  (  1.24297 )
      Synechocy     5    16.05818  (  2.24639 )
                    6     2.13260  (  0.86082 )
                    7     1.01070  (  0.63908 )
  ----------------------------------------------
   ln L : -1813.614 (  66.205 )  AIC : 3641.229
  ----------------------------------------------

     Length refers to the estimated number of  substitutions  per
100  amino  acid  sites  along the branch leading to the node (or
leaf) indicated by the number, and S.E. refers  to  its  standard
error estimated by the formula of Kishino and Hasegawa (1989).



           Installing PROTML and Executive Environment


     Personal computer with MS-DOS + Turbo Pascal(Borland):  e.g.
IBM  PCs  and  compatibles,  NEC  PC-98x. Please remove or change
comments marked as shown below:

 (*  <statements>  TURBO Pascal *)

     UNIX Workstation  +  standard  Pascal  compiler:  e.g.  SUN.
Please remove or change comments marked as shown below:

 (*  <statements>  SUN Pascal *)

     Mainframe computer (IBM and compatibles) +  standard  Pascal
compiler. For example, JCL (Job Control Language) of batch job.

 //USERIDB    JOB  PATHWORD
 //STEP       EXEC OPASCLG
 //PASC.SYSIN DD   DSN='USERID.PROTML.PASCAL',DISP=SHR
 //GO.SEQFILE DD   DSN='USERID.SEQFILE.DATA',DISP=SHR



                    How to contact developers


     The best way to contact developers is to send an E-mail.

          E-mail: adachi@ism.ac.jp

If you prefer, write a letter with your comments and send it to

          Jun Adachi
          Department of Statistical Science,
          The Graduate University for Advanced Study,
          4-6-7 Minami-Azabu, Minato-ku, Tokyo 106, Japan
          FAX: +81-3-3446-1695

     Please send a mail with the following information

          1. Computer brand, model.
          2. The brand and version number of Pascal compiler.
          3. Operating system and version number.
          4. The input file of sequence data.
          5. The output file.



                        Acknowledgements


     We  are  particularly  grateful  to  Dr.  H.   Kishino   for
invaluable  advices during the course of this work, and to Dr. J.
Felsenstein for generously  permitting  us  to  use  routines  in
DNAML. We also thank Drs. T. Hashimoto, T. Miyata and T. Yano for
discussions and comments. This work was  carried  out  under  the
Institute of Statistical Mathematics Cooperative Research Program
(90-ISM-57, 91-ISM-69), and was  supported  by  grants  from  the
Ministry of Education, Science, and Culture of Japan.



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