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