XRate: a fast prototyping, training and annotation tool for phylo-grammars.

Abstract

Recent years have seen the emergence of genome annotation methods based on the phylo-grammar, a probabilistic model combining continuous-time Markov chains and stochastic grammars. Previously, phylo-grammars have required considerable effort to implement, limiting their adoption by computational biologists.
We have developed an open source software tool, xrate, for working with reversible, irreversible or parametric substitution models combined with stochastic context-free grammars. xrate efficiently estimates maximum-likelihood parameters and phylogenetic trees using a novel "phylo-EM" algorithm that we describe. The grammar is specified in an external configuration file, allowing users to design new grammars, estimate rate parameters from training data and annotate multiple sequence alignments without the need to recompile code from source. We have used xrate to measure codon substitution rates and predict protein and RNA secondary structures.
Our results demonstrate that xrate estimates biologically meaningful rates and makes predictions whose accuracy is comparable to that of more specialized tools.

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BioMed Central
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BMC Bioinformatics
Open Access
Software
XRate: a fast prototyping, training and annotation tool for
phylo-grammars
Peter S Klosterman1, Andrew V Uzilov1, Yuri R Bendaña1, Robert K Bradley1,
Sharon Chao1, Carolin Kosiol2,3, Nick Goldman2 and Ian Holmes*1
Address: 1Department of Bioengineering, University of California, Berkeley CA, USA, 2European Bioinformatics Institute, Hinxton,
Cambridgeshire, UK and 3Department of Biological Statistics and Computational Biology, Cornell University, Ithaca NY, USA
Email: Peter S Klosterman - petek@accesscom.com; Andrew V Uzilov - andrew.uzilov@gmail.com; Yuri R Bendaña - ybendana@berkeley.edu;
Robert K Bradley - rbradley@berkeley.edu; Sharon Chao - schao@berkeley.edu; Carolin Kosiol - ck285@cornell.edu;
Nick Goldman - goldman@ebi.ac.uk; Ian Holmes* - ihh@berkeley.edu
* Corresponding author
Abstract
Background: Recent years have seen the emergence of genome annotation methods based on
the phylo-grammar, a probabilistic model combining continuous-time Markov chains and stochastic
grammars. Previously, phylo-grammars have required considerable effort to implement, limiting
their adoption by computational biologists.
Results: We have developed an open source software tool, xrate, for working with reversible,
irreversible or parametric substitution models combined with stochastic context-free grammars.
xrate efficiently estimates maximum-likelihood parameters and phylogenetic trees using a novel
"phylo-EM" algorithm that we describe. The grammar is specified in an external configuration file,
allowing users to design new grammars, estimate rate parameters from training data and annotate
multiple sequence alignments without the need to recompile code from source. We have used
xrate to measure codon substitution rates and predict protein and RNA secondary structures.
Conclusion: Our results demonstrate that xrate estimates biologically meaningful rates and makes
predictions whose accuracy is comparable to that of more specialized tools.
Background
Hidden Markov models [HMMs], together with related
probabilistic models such as stochastic context-free gram-
mars [SCFGs], are the basis of many algorithms for the
analysis of biological sequences [11,8,10,16]. An appeal-
ing feature of such models is that once the general struc-
ture of the model is specified, the parameters of the model
can be estimated from representative "training data" with
minimal user intervention (typically using the Expecta-
tion Maximization [EM] algorithm [14]). Combined with
the continuous-time Markov chain theory of likelihood-
based phylogeny, stochastic grammar approaches are
finding similarly broad application in comparative
sequence analysis, in particular the annotation of multi-
ple alignments [83,26,53,46,74,80] (and, in some cases,
simultaneous alignment and annotation [2,58]). This
combined model has been dubbed the phylo-grammar. By
contrast to the single-sequence case (for which there is
much prior art in the field of computational linguistics
[72,51]), the automated parameterization of phylo-gram-
mars from training data is somewhat uncharted territory,
partly because the application of the EM algorithm to phy-
Published: 03 October 2006
BMC Bioinformatics 2006, 7:428doi:10.1186/1471-2105-7-428
Received: 24 February 2006
Accepted: 03 October 2006
This article is available from: http://www.biomedcentral.com/1471-2105/7/428
© 2006 Klosterman et al; licensee BioMed Central Ltd.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0),
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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logenetics is a recent addition to the theoretical toolbox.
The phylo-grammar approaches that have been used to
date have often used approximate and/or inefficient ver-
sions of EM to estimate parameters [59,81], or have been
limited to particular subclasses of model, e.g. reversible or
otherwise constrained models [9,38].
Previously, we showed how to apply the EM algorithm to
estimate substitution rates in a phylogenetic reversible
continuous-time Markov chain model [38]. This EM algo-
rithm is exact and without approximation, using an eigen-
vector decomposition of the rate matrix to estimate
summary statistics for the evolutionary history. We refer
to this version of EM as "phylo-EM".
Here, we report several extensions to the phylo-EM
method. Specifically, we give a version of the phylo-EM
algorithm for the fully general, irreversible substitution
model on a phylogenetic tree (noting that the irreversible
model is a generalisation of the reversible case). We then
present a flexible package for multiple alignment annota-
tion using phylo-HMMs and phylo-SCFGs that imple-
ments these algorithms and is similar, in spirit, to the
Dynamite package for generic dynamic programming
using HMMs [5].
Using this package, it is extremely easy to design, train and
apply a novel phylo-grammar, since new models can be
loaded from an external, user-specified grammar file. Our
hope is that the algorithms and software presented here
will aid in the establishment of phylo-grammars in bioin-
formatics and that such methods will be as widely
adopted for comparative genomics as HMMs and SCFGs
have been.
Overview
In 1981, Felsenstein published dynamic programming
(DP) recursions for computing the likelihood of a phylo-
genetic tree for aligned sequence data, given an underly-
ing substitution model [21]. Together with seminal
papers by Neyman [64] and DayhofF et al.[12,13], this
work heralded the widespread use probabilistic models in
bioinformatics and molecular evolution. Felsenstein's
underlying model is a finite-state continuous-time
Markov chain, as described e.g. by Karlin and Taylor [43].
It is characterised by an instantaneous rate matrix R
describing the instantaneous rates Rij of point substitu-
tions from residue i to j. In the unifying language of con-
temporary "Machine Learning" approaches, Felsenstein's
trees are recognisable as a form of graphical model [66] or
factor graph [50], and the DP recursions an instance of the
sum-product algorithm. (The connection to graphical
models has been made more explicit with recent
approaches that model other stochastic processes on phy-
logenetic trees, such as the evolution of molecular func-
tion [20].) Many parametric versions of this model have
been explored, such as the "HKY85" model [32].
Beginning in the late 1980s, another class of probabilistic
models for biological sequence analysis was developed.
These models included HMMs for DNA [11] and proteins
[8], and SCFGs for RNA [78,18]. Collectively, such models
form a subset of the stochastic grammars. Originally used
to annotate individual sequences, stochastic grammars
were soon also combined with phylogenetic models to
annotate alignments. Thus, trees have been combined
with HMMs and/or SCFGs to predict genes [68] and con-
served regions [23] in DNA sequences, secondary struc-
tures [83,26] and transmembrane topologies [53] in
protein sequences, and basepairing structures in RNA
sequences [46]. We refer to such hybrid models as phylo-
grammars. Associated with these advances were novel
methods to approximate context dependence of substitu-
tion models, such as CpG and other dinucleotide effects
[81,55]. The phylo-grammars can also be viewed as a sub-
class of the "statistical
[34,37,60,36], which are derived from more rigorous
assumptions about the underlying evolutionary model,
including indels [84].
alignment" grammars
A compelling attraction of stochastic grammars (and
probabilistic models in general) is that parameters can be
systematically "learned" from data by maximum likeli-
hood (ML). One reasonably good, general, albeit greedy
and imperfect, approximation to ML is the EM algorithm
[14]. EM applies to models which generate both "hidden"
and "observed" data; e.g., the transcriptional/translational
structure of a gene (hidden) and the raw genomic
sequence (observed). The applications of EM to training
HMMs (the Baum-Welch algorithm) [4] and SCFGs
(Inside-Outside) [51] are well-established (reviewed in
[16]), but what of phylo-grammars? While a limited ver-
sion of EM for substitution models was published in 1996
[9,31], the full derivation for the general reversible rate
matrix did not appear until 2002 [38]. The phylo-EM
algorithm for rate matrices has since been further devel-
oped [94,35]. (Various alternatives to phylo-EM, such as
eigenvector projections [3] and the "resolvent" [63], have
also been used to estimate rate matrices; some approxi-
mate versions of phylo-EM have also been described
[81,82].)
Conceptually, EM is straightforward: one simply alter-
nates between imputing the hidden data (the "E-step")
and optimizing the parameters (the "M-step"). The E-step
typically results in a set of "expected counts" which are
intuitively easy to interpret. (For example, the E-step for
phylogenetic trees returns the number of times each sub-
stitution is expected to have occurred on each branch.)
The EM algorithm has been intensely scrutinized and has

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been shown to be versatile, adaptable and fast [25,57],
particularly the special case of phylo-EM [94]. We there-
fore argue that there are strong advantages to combining
the form of EM used to train stochastic grammars (i.e. the
Baum-Welch and Inside-Outside algorithms [16]) with
the phylo-EM form used for parameterizing substitution
models on phylogenetic trees [38].
Previous applications of phylo-grammars
The program we have developed can handle a broad class
of phylo-grammars within one framework. The following
is a brief review of prior work that either uses phylo-gram-
mars, or is ideally suited to the phylo-grammar frame-
work.
This section is subclassified according to the complexity of
the grammar, beginning with the simplest. Generally
speaking, a phylo-grammar can be used to annotate a
multiple sequence alignment in any context where a sto-
chastic grammar could be used to annotate an individual
sequence. The applications span DNA, RNA and protein
sequence annotation.
Point substitution models
A subset of the class of phylo-grammars is the class of
homogeneous substitution models, where the mutation
rate is not a function of position but rather is identical for
every site. Such models can be represented as a single-state
phylo-HMM. Examples include
The Jukes-Cantor model [41], Kimura's two-parameter
model [44], the HKY85 model [32], the general reversi-
ble model [92], and the general irreversible model [91].
In the case of the Kimura and HKY85 models, the rate
matrices are formulated para-metrically: that is, each sub-
stitution rate is expressed as a function of a small set of
rate and/or probability parameters (e.g. in Kimura's
model, there are two rate parameters: the transition rate
and the transversion rate).
Variable-rate models, where the evolutionary rate is
allowed to vary from site to site [90]. Yang used a finite
number of discrete, fixed rate categories to approximate a
continuous gamma distribution over site-specific rates. In
essence, this can be viewed as special cases of the phylo-
HMM of Felsenstein and Churchill [23], with the autocor-
relation explicitly set to zero.
Hidden-state models [48,38]. A relative of the variable-
rate model, the hidden-state model allows a variety of dif-
ferent substitution rate matrices to be used, depending on
a hidden state variable that specifies the structural context
of the site [48]. For example, a hydrophobically-inclined
rate matrix might be used for buried amino acids and a
hydrophilic matrix for exposed amino acids. An extension
to the hidden-state model allows the hidden state variable
itself to change over time at some slow rate, modeling rare
changes in structural context [38]. An alternative exten-
sion allows correlations between hidden state variables at
adjacent sites: this is essentially the idea behind the phylo-
HMM, described below.
Models for synonymous/nonsynonymous substitution
ratio measurement; empirical rate matrices for codon
evolution [27,87]. Codon substitution matrices such as
WAG [87] can be used to measure the ratio r of synony-
mous to nonsynonymous substitution rates, which may
be indicative of purifying (r < 1), neutral (r = 1) or diver-
sifying (r > 1) selection. These models are also related to
the exon prediction phylo-HMMs in EVOGENE [68] and
EXONIPHY [80], described below.
Amino acid substitution models [12,28]. Likelihood cal-
culations using these models can, as with the other substi-
tution models discussed above, be viewed as trivial
applications of phylo-grammars.
Context-sensitive substitution models [81]. Siepel and
Haussler introduced several alternate approximations for
calculating the likelihood of alignments assuming a near-
est neighbor substitution model, suitable for capturing
the context-sensitivity of the substitution process that is
observed in real sequence alignments (most notoriously
in genomes wherein CpG methylation is used as a mech-
anism of epigenetic regulation, leading to elevated rates
for the mutations CpG→TpG and CpG→ApG). Siepel and
Haussler's method ignores longer-range correlations
induced by nearest-neighbor effects, but is effective in
practice. (It may be regarded as an approximation to the
more rigorous analysis of Lunter and Hein [55].)
Many of these models can be expressed using the General
Parametric Substitution Model, which we define as the
substitution model wherein all substitution rates and ini-
tial probabilities can be expressed as simple functions of a
(reduced) set of rate and probability parameters. As an
example, Kimura's two-parameter model [44] is shown
(see figure 1) along with the HKY85 six-parameter model
[32] (see figure 2).
As long as each parameter in a parametric substitution
model can be interpreted either as a rate (such as Kimura's
transition and transversion rates) or a probability (such as
the HKY85 equilibrium distribution over nucleotides),
the phylo-EM algorithm can be adapted to estimate such
parameters via the computation of expected event counts.
A formal description of the sets of allowable rate and
probability functions is given in the Supplementary Mate-
rial [see Additional file 1].

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Although the particular models used above (Kimura and
HKY85) are reversible, matrices of allowable rate func-
tions can in general be irreversible. Our General Paramet-
ric Model may thus be regarded as a generalisation of the
General Irreversible Model.
Phylo-HMMs
Phylo-HMMs form a class of models slightly more com-
plex than point substitution models. In a phylo-HMM,
each column (or group of adjacent columns) is associated
with a hidden state, representing the evolutionary context
of the site. Each hidden state is conditionally dependent
upon the immediately preceding state (the Markov prop-
erty).
Tasks that have been addressed using phylo-HMMs
include:
Measurement of variation of evolutionary rate among
sites in DNA [23]. Felsenstein and Churchill construct an
HMM with three states. Each state generates an alignment
column according to a point substitution process on a tree
[21]. The overall evolutionary rate for the column
depends on the state from which it is emitted: each state
thus corresponds to a "rate category" (the relative rates for
the three states are 0.3, 2.0 and 10.0). The use of an HMM
allows for an autocorrelated model of rate variation.
Modeling site-specific residue usage in proteins[9,31].
While site-specific profiles are familiar tools in bioinfor-
matics, early tools such as Gribskov profiles [29] and hid-
den Markov models [8] ignored phylogenetic correlations
in the dataset, leading to biased sampling. Phylo-gram-
mars incorporate these correlations directly. In these
papers, Bruno et al. introduced an initial EM algorithm for
estimating rate matrices.
Prediction of secondary structure in proteins[83,26]. In
a similar manner to Felsenstein and Churchill, a three-
state HMM is constructed wherein each state emits an
alignment column using a substitution rate matrix. Here,
however, the states correspond to different units of sec-
ondary structure (loop, α-helix and β-sheet). The substitu-
tion rate matrix for each state reflects the frequency
distribution and substitution patterns for that secondary
structural class. The method performs less well than estab-
lished secondary structure prediction algorithms, but
shows promise, in particular given the simplicity of the
model (three states only). Later work expanded the
number of states in the phylo-HMM to eight (correspond-
ingly increasing the number of parameters). Note that, as
more parameters are introduced into this kind of phylo-
HMM, the problem of "training" those parameters grows
in importance.
Prediction of exons and protein-coding gene structures
in DNA [68,80]. The basis for the gene prediction pro-
grams EVOGENE and EXONIPHY, respectively, these
phylo-HMMs are based on substitution models for codon
triplets with 43 = 64 states. The paper by Siepel and Haus-
sler introduced the term "phylo-HMM" and used an
approximate version of the EM algorithm introduced by
Holmes and Rubin for parameterization [38].
Detection, modeling and annotation of transcription
factor binding sites in DNA [62]. Here, the EM algorithm
and other formulae of Bruno and Halpern [9,31] is used
to model site-specific residue frequencies in alignments of
promoter regions (rather than proteins, as addressed by
Bruno and Halpern).
Detection of conserved regions in multiple alignments
of genomic DNA [79]. Phylo-HMMs to detect conserved
regions can be viewed as extensions of Felsenstein and
Churchill's original model with more rate categories. This
approach has been used to detect highly-conserved
regions in vertebrate, insect, nematode and yeast
genomes. Approaches measuring the substitution rate per
Kimura's two-parameter model
Figure 1
Kimura's two-parameter model. The state order is {A, C, G,
T}. Each entry is a function of the reduced parameter set (α,
β) where α and β are rates.
Hasegawa et al's six-parameter model
Figure 2
Hasegawa et al's six-parameter model. The state order is {A,
C, G, T}. The negative on-diagonal elements have been omit-
ted for brevity (they are constrained by the requirement that
each row sums to zero). Each entry is a function of the
reduced parameter set (α, β, πA, πC, πG, πT) where (α, β) are
rates and (πA, πC, πG, πT) are probabilities.

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site [79,85], the local indel rate [54] and/or the CpG
mutation bias [81,55] have all shown merit.
Analogously to some of the point substitution models,
many phylo-HMMs can be expressed parametrically. An
example of such a model is the one used by Siepel's
PHASTCONS program, whose phylo-HMM has ten states
ranging from slow to fast overall substitution rate. Moving
from one state to another, the relative substitution rates
between different nucleotides do not change (i.e. the ratio
Rij/Rkl is constant for any i, j, k, l ∈ {A, C, G, T}); only the
overall substitution rate varies (i.e. the absolute value Rij is
not constant). Such consistency across states can be
achieved by writing the rate matrices for the ten states as
k1R, k2 × R, k3 × R... k10 × R where the ki are scalar multipli-
ers and R is a relative rate matrix shared by all the states.
Similarly, the rate matrices of Felsenstein and Churchill's
three-state phylo-HMM can be written 0.3 × R, 2 × R and
10 × R. Both are examples of the general parametric
phylo-HMM.
Phylo-SCFGs
The most complex class of phylo-grammar considered
here is the phylo-SCFG. Most commonly used to model
RNA secondary structure, these grammars are capable of
modeling covariation between paired sites. In an SCFG,
covarying sites must be strictly nested, allowing the mod-
eling of foldback structures but not pseudoknots, kissing
loops or other topologi-cally elaborate RNA structures
[45].
Tasks that have been addressed using phylo-SCFGs
include:
Prediction of RNA secondary structure [46,47]. The
Pfold program in this paper introduced the first phylo-
SCFG, combining stochastic context-free grammars (used
to model RNA structure) with evolutionary substitution
models. Since HMMs are a subset of SCFGs, the frame-
work of phylo-SCFGs includes the previously discussed
phylo-HMMs. The Pfold program also allowed for user-
specified grammars; however, it lacked a fast EM-like algo-
rithm for estimating grammar parameters from data (by
contrast, the non-phylogenetic SCFGs used elsewhere in
bioinformatics can be rapidly trained using the Inside-
Outside algorithm [16]). A key feature of these models is
the use of 16-state "basepair models" for modeling the
simultaneous coevolution of functional base-pairs in RNA
structures. Again, fast and effective parameterization of
the model is an important issue.
Detection of noncoding RNA genes [67]. A similar
model to Pfold was used by the Evofold program, which
uses a phylo-SCFG to parse genomic alignments into non-
coding RNA and other features [67].
Detection of RNA secondary structure within exons
[69]. The RNA-Decoder program uses a parametric phylo-
SCFG to model exonic regions in which there is simulta-
neous selection on both the translated protein sequence
and the secondary structure of the pre-mRNA. Such
regions have been found in viral genomes and hypothe-
sized to fulfil a regulatory role [69]. Due to the complexity
of these models and the sparsity of training data, paramet-
ric rate functions are required to limit the number of free
parameters that must be estimated.
Detection of accelerated selection in human noncoding
RNA [70]. Pollard et al used phylo-HMMs and phylo-
SCFGs to identify a neurally-expressed RNA gene, HARF1,
that had undergone recent accelerated evolution in the
lineage separating humans from the human-chimp ances-
tor.
Implementation
In practice, users of phylo-grammars need to do a similar
core set of tasks in order to perform data analysis. These
tasks may include model development, structured param-
eterization, estimation of parameter values and applica-
tion of the model to annotate alignments. Using the
framework of phylo-grammars, an implementation ena-
bling all these tasks is possible. The EM algorithm pro-
vides a general and consistent approach to parameter
estimation, while standard "parsing" algorithms (the
Viterbi and Cocke-Younger-Kasami (CYK) algorithms
[16]) address the problem of annotation.
We have implemented EM and Viterbi/CYK parsing algo-
rithms in our software. The general irreversible phylo-EM
algorithm, using eigenvector decompositions, is described
in the Supplementary Material to this paper [see Addi-
tional file 1]. (Note that this model is more general than
the "general reversible model" [92], which can be
regarded as a special case wherein the rates obey a detailed
balance symmetry so that πiRij = πjRji.) The main advance
over previous descriptions of this algorithm [38,81] is a
complete closed-form solution for the M-step of EM for
irreversible models, including a full algebraic treatment of
the complex conjugate eigenvector pairs [see Additional
file 1]. This closed-form solution for the M-step eliminates
the need for numerical optimization code as part of EM.
The Viterbi and CYK algorithms are described in full else-
where [16].
The essential idea of EM is iteratively to maximize the
expected log-likelihood with respect to the rate parameters,
where the expectation is taken over the posterior distribu-
tion of the missing data using the current parameters. In
the case of phylo-EM, the missing data are the sequences
ancestral to the observed sequence data.