Machine learning of functional class from phenotype data

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Machine learning of functional class from phenotype data
Amanda Clare
Ross D. King
Department of Computer Science,
University of Wales Aberystwyth, SY23 3DB, UK
1
Abstract
Motivation: Mutant phenotype growth experiments are an important novel source of
functional genomics data which have received
little attention in bioinformatics. We applied
supervised machine learning to the problem
of using phenotype data to predict the functional class of ORFs in S. cerevisiae. Three
sources of data were used: TRIPLES, EUROFAN and MIPS. The analysis of the data
presented a number of challenges to machine
learning: multi-class labels, a large number of
sparsely populated classes, the need to learn
a set of accurate rules (not a complete classification), and a very large amount of missing
values. We modified the algorithm C4.5 to deal
with these problems.
Results: Rules were learnt which are accurate and biologically meaningful. The rules
predict function of 83 ORFs of unknown function at an estimated accuracy of ≥ 80%.
Availability:
The
data
and
complete
results
are
available
at
http://users.aber.ac.uk/ajc99/phenotype/.
Contact: [email protected]
Introduction
Computational biology is playing an increasingly important role in determining the function of genes. Sequence similarity searches
such as PSI-BLAST (Altschul et al., 1997) are
generally the starting point for inferring function of new genes or ORFs (Open Reading
Frames). Moving on from sequence similarity,
the different types of data available for use in
functional genomics are growing each year, and
new techniques are needed to keep pace.
Computational techniques currently of use
in inferring function include using expression
data clustering (DeRisi, Iyer, and Brown,
1997; Eisen et al., 1998), structure prediction (CASP, 1999), and combined approaches
which can make use of several sources of data.
Marcotte et al. (1999) describe a scheme of
inter-linking yeast proteins according to various relations, including whether they are part
of the same pathway, have similar expression
patterns, or links from domain-fusion analysis.
Links between proteins of known and unknown
function can then be used to assign functions to
the unknowns. Three machine learning methods were used for prediction by des Jardins et
al. (1997), who predicted enzyme class of proteins from PDB and SwissProt using features
computed from amino acid sequence. King
et al. (2000; 2001) used data mining in the
form of Inductive Logic Programming and the
supervised machine learning program C4.5 to
1
as this MIPS catalogue, opens up the possibility of using supervised machine learning to predict the functional classification of ORFs (Kell
and King, 2000). Most work on classification
in computational biology has been with unsupervised learning/clustering classification algorithms (Eisen et al., 1998; Koonin et al., 1998;
Törönen et al., 1999). Few have made use of
the fact that we already have knowledge about
the functions of many of the ORFs. Supervised classification algorithms can make use
of this knowledge and are now beginning to
be used in bioinformatics (Brown et al., 2000;
des Jardins et al., 1997). For discussion of the
use of functional hierarchies and suitable types
of machine learning, see Kell and King (2000),
and for systems for categorising functions see
Riley (1998) and Andrade et al. (1999).
An ORF may have several different functions, and this is reflected in the MIPS classification scheme (where a single ORF can belong to up to 10 different functional classes).
This presents an unusual and interesting classification problem for machine learning. It is
a multi-label problem (as opposed to multiclass which usually refers to simply having
more than two possible disjoint classes for
the classifier to learn). There is only a limited literature on such problems, for example
(Karalic and Pirnat, 1991; McCallum, 1999;
Schapire and Singer, 2000). The simplest approach to the problem is to learn separate classifiers for each class (with all ORFs not belonging to a specific class used as negative examples
for that class). However this is clearly cumbersome and time-consuming when there are
many classes - as is the case in the functional
hierarchy in yeast. Also, in sparsely populated
classes there would be very few positive examples of a class and overwhelmingly many negative examples. We have therefore developed a
new algorithm based on the successful decision
tree algorithm C4.5 (Quinlan, 1993).
In summary our approach is to develop a
learn rules based on sequence, structure and
homology data from the M. tuberculosis and
E. coli genomes. These rules could then be directly applied to predict function of unknown
genes. Recently, other supervised learning algorithms have also been investigated. Support vector machines have been used to analyse yeast expression data (Brown et al., 2000),
and Pavlidis et al. (2001) have extended this
to learn from both expression and phylogenetic
data.
One new source of data which is of increasing
value in determining the function of ORFs is
phenotypic growth data. This is data from experiments about the sensitivity or resistance of
disruption mutants under various growth conditions. Novel experimental techniques have
made it possible to collect such data on a
genome-wide scale. This paper is, to the best
of our knowledge, the first on developing data
analysis methods for such data.
The best studied organism for phenotypic
growth data is S. cerevisiae. Despite this being one of the most extensively studied of all
organisms, the function of 30-40% of its ORFs
are currently unknown. The MIPS database
has several ORF functional classification
schemes for yeast, one of these being a hierarchical “Functional Classification Catalogue”
(http://mips.gsf.de/proj/yeast/catalogues/
funcat/). This catalogue classifies the functions of ORFs under various general classes,
such as “Metabolism”, “Energy”, “Transcription” and “Protein Synthesis”. Each of these
classes is then subdivided into more specific
classes, and these are in turn subdivided, and
then again subdivided, so the hierarchy is up
to 4 levels deep. An example of a subclass
of “Metabolism” is “amino-acid metabolism”,
and an example of a subclass of this is
“amino-acid biosynthesis”. An example of an
ORF in this subclass is YPR145w (gene name
ASN1, product “asparagine synthetase”).
The existence of functional hierarchies, such
2
The phenotype data has the form of attributevalue vectors: with the attributes being the
growth media, the values of the attributes
being the observed sensitivity or resistance
of the mutant compared with the wildtype,
and the class the functional class of the ORF.
Note that this data is not available for all
ORFs due to some mutants being inviable
or untested, and not all growth media were
tested/recorded for every ORF, so there were
many missing values in the data.
The values that the attributes could take
were the following: n = no data, w = wildtype (no phenotypic effect), s = sensitive (less
growth than for the wild-type), and r = resistance (better growth than for the wild-type).
There were 69 attributes, 68 of which
were the various growth media (e.g. calcofluor white, caffeine, sorbitol, benomyl), and
one which was a discretised count of how many
of the media this mutant had shown a reaction
to (i.e. for how many of the attributes this
mutant had a value of “s” or “r”).
specific machine learning method to learn rules
which map from phenotype data to functional
class. Rules are learnt and their accuracy estimated using phenotype data from deletion mutants of ORFs of known function. These rules
can then be applied to ORFs of unknown function for prediction.
2
2.1
Experimental method
Data
We used three separate sources of phenotypic
data: TRIPLES (Kumar et al., 2000), EUROFAN (Oliver, 1996) and MIPS (Mewes et al.,
1999).
• The TRIPLES (TRansposon-Insertion
Phenotypes, Localization and Expression
in Saccharomyces) data was generated by
randomly inserting transposons into the
yeast genome.
URLs: http://ygac.med.yale.edu/triples/
triples.htm, (raw data)
http://bioinfo.mbb.yale.edu/genome/
2.2 Algorithm
phenotypes/ (processed data)
The machine learning algorithm we chose to
• EUROFAN (European functional analy- adapt for the analysis of phenotype data was
sis network) is a large European network C4.5 (Quinlan, 1993). This is a well known deof research which has created a library of cision tree algorithm which is robust, and effideletion mutants by using PCR-mediated cient (Michie, Spiegelhalter, and Taylor, 1994).
gene replacement (replacing specific genes The output of C4.5 is a decision tree, or equivwith a marker gene (kanMX)). We used alently a set of symbolic rules. The use of symbolic rules allows the output to be interpreted
data from EUROFAN 1.
and compared with existing biological knowlURL: http://mips.gsf.de/proj/eurofan/
edge - this is not generally the case with other
• The MIPS (Munich Information Center machine learning methods, such as neural netfor Protein Sequences) database contains works, or support vector machines.
a catalogue of yeast phenotype data.
A decision tree is a tree where each node is
URL: http://mips.gsf.de/proj/yeast/
a test on the values of an attribute, and the
leaves represent the class of an item which satThe data from the three sources were con- isfies the tests. Rules can then be read off from
catenated together to form a unified dataset the tree by following a path from the root node
http://users.aber.ac.uk/ajc99/phenotype/.
to a leaf and using the nodes along the path as
3
preconditions for the rule, to predict the class
at the leaf. The rules can be pruned to remove
unnecessary preconditions and duplication.
In C4.5 the tree is constructed top down.
For each node the attribute is chosen which
best classifies the remaining training examples.
This is decided by considering the information
gain, the difference between the entropy of the
whole set of remaining training examples and
the weighted sum of the entropy of the subsets
caused by partitioning on the values of that
attribute.
membership of each class ci has probability
p(ci ) the total number of bits needed for an
average example is given by
inf ormation gain(S, A) =
X |Sv |
entropy(S) −
∗ entropy(Sv )
|S|
v∈A
The resulting information after a partition
according to some attribute, can be calculated
as a weighted sum of the entropy for each
subset (calculated as above), where this time,
weighted sum means if an item appears twice
in a subset because it belongs to two classes
then we count it twice.
In allowing multiple labels per example we
have to allow leaves of the tree to potentially
be a set of class labels, i.e. the outcome of
a classification of an example can be a set of
classes. When we label the decision tree this
needs to be taken into account, and also when
we prune the tree. When we come to generate
rules from the decision tree, this can be done
in the usual way, except when it is the case
that a leaf is a set of classes, a separate rule
will be generated for each class, prior to the
rule-pruning part of the C4.5rules algorithm.
We could have generated rules which simply
output a set of classes - it was an arbitrary
choice to generate separate rules, chosen for
comprehensibility of the results.
−
N
X
(p(ci ) log p(ci )) + (q(ci ) log q(ci ))
i=1
where
p(ci ) = probability (relative frequency) of
class c
q(ci ) = 1 − p(c) = probability of not being
member of class c
where A is the attribute being considered, S
is the set of training examples being considered, and Sv is the subset of S with value v for
attribute A. The C4.5 algorithm is well documented and the code is open source, so this
allowed the algorithm to be extended.
Multiple labels are a problem for C4.5, and
almost all other learning methods, as it expects
each example to be labeled as belonging to just
one class. For yeast ORF function this is not
the case, as an ORF may belong to several different classes. In the case of a single class label
for each example the entropy for a set of examples is just
entropy(S) = −
N
X
p(ci ) log p(ci )
i=1
where p(ci ) is the probability (relative frequency) of class ci in this set.
We need to modify this formula for multiple classes. The information for an example is
now the number of bits needed to describe the
classes it belongs to. To estimate this we sum
the number of bits needed to describe membership or non-membership of each class. In
the general case where there are N classes and
2.3
Resampling
In most statistical and machine learning supervised classification problems the aim is to
maximise the prediction accuracy on the test
set. This is not the case for our problem. Instead, we wish to learn a set of rules which
4
We aimed to learn rules for predicting functional classes which could be interpreted biologically. To this end we evaluated splitting
the data set into 3 parts: training data, validation data to select the best rules from (rules
were chosen that had an accuracy of at least
50% and correctly covered at least 2 examples),
and test data. We used the validation data to
avoid overfitting rules to the data. However,
splitting the dataset into 3 parts means that
the amount of data available for training will
be even less. Similarly only a small amount will
be available for testing. Initial experiments
showed that the split of the data substantially
affected the rulesets produced, sometimes producing many good rules, and sometimes none.
The two standard methods for estimating accuracy under the circumstance of a small data
set are 10-fold cross-validation and the bootstrap method (Kohavi, 1995; Efron and Tibshirani, 1993). Because we are interested in
the rules themselves, and not just the accuracy,
we opted for the bootstrap method, because
a 10-fold cross validation would make just 10
rulesets, whereas bootstrap sampling can be
used to create hundreds of samples of the data
and hence hundreds of rulesets. We can then
examine these and see which rules occur regularly and are stable, not just artifacts of the
split of the data.
The bootstrap is a method where data is
repeatedly sampled with replacement to make
hundreds of training sets. A classifier is constructed for each sample, and the accuracies of
all the classifiers can be averaged to give a final
measure of accuracy. First a bootstrap sample was taken from the original data. Items of
the original data not used in the sample made
up the test set. Then a new sample was taken
with replacement from the sample. This second
sample was used as training data, and items
that were in the first sample but not in the
second made up the validation set. All three
data sets are non-overlapping.
accurately predict functional class. This resembles in some respects association rule learning
in data mining. The problem is also unusual in
machine learning terms in that there are a very
large number of classes. For example there
are 99 potential classes represented in the data
for level 2 in the class hierarchy: in a typical
machine learning problem there are at most a
handful. These unusual features of the data
made it necessary for us to develop a complicated resampling approach to estimating rule
accuracy based on the bootstrap.
All accuracy measurements were made using
the m-estimate (Cestnik, 1990) which is a generalisation of the Laplace estimate, taking into
account the a priori probability of the class.
P
p + m P +N
M (r) =
p+n+m
where P = total number of positive examples, N = total number of negative examples,
p = number of positive examples covered by
rule r, n = number of negative examples covered by rule r.
Using this formula, the accuracy for rules
with zero coverage will be the a priori probability of the class. m is a parameter which can
be altered to weight the a priori probability.
We used m=1.
The data set in this case is small in machine
learning terms. We have 2452 ORFs with some
recorded phenotypes, of which 991 are classified by MIPS as “Unclassified” or “Classification not yet clear-cut”. These ORFs of unknown classification cannot be used in supervised learning (though we can later make predictions for them). This leaves just 1461, each
with many missing values. At the top level
of the classification hierarchy (the most general classes), there are many examples for each
class, but as we move to lower, more specific
levels, the classes become more sparsely populated, and machine learning becomes difficult.
5
functional catalogue) are all predictors for
the class “CELLULAR BIOGENESIS”. These
rules suggest that sensitivity to zymolase or
papulacandin b, or any reaction (sensitivity
or resistance) to calcofluor white is a general
property of mutants whose deleted ORFs belong to the CELLULAR BIOGENESIS class.
All correct ORFs matching these rules in fact
also belong to the subclass “biogenesis of cell
wall (cell envelope)”. The rules are far more
accurate than the prior probability of that class
would suggest should occur by chance.
Below are two of the rules regarding sensitivity/resistance to Calcofluor White.
We measured accuracy on the held-out test
set. We are aware that this will give a pessimistic measure of accuracy (i.e. the true accuracy on the whole data set will be higher),
but this is acceptable.
3
Results
We attempted to learn rules for all
classes in the MIPS functional hierarchy
http://mips.gsf.de/proj/yeast/catalogues/
funcat/, using the catalogue as it was on 27
September 1999. 500 bootstrap samples were
made, and so C4.5 was run 500 times and 500
rulesets were generated and tested. To discover which rules were stable and reliable we
counted how many times each rule appeared
across the 500 rulesets. Accurate stable rules
were produced for many of the classes at levels
1 and 2 in the hierarchy. At levels 3 and 4 (the
most specific levels with the least populated
classes) no useful rules were found. That is, at
the lower levels, few rules were produced and
these were not especially general or accurate.
The topic of learning within a class hierarchy
when child classes are sparsely populated, and
making good use of the hierarchy, is something
to consider in future experiments of this kind.
The good rules are generally very simple,
with just one or two conditions necessary to
discriminate the classes. This was expected,
especially since most mutants were only sensitive/resistant to a few media. Some classes
were far easier to recognise than others, for example, many good rules predicted class “CELLULAR BIOGENESIS” and its subclass “biogenesis of cell wall (cell envelope)”.
Some examples of the rules and their accuracies follow. The full set of rules can be seen
at http://users.aber.ac.uk/ajc99/phenotype/
along with the data sets used.
The 4 most frequently appearing rules
at level 1 (the most general level in the
if
the ORF deletant is sensitive to calcofluor
white and
the ORF deletant is sensitive to zymolyase
then its class is "biogenesis of cell
wall (cell envelope)"
Mean accuracy:
90.9%
Prior prob of class: 9.5%
Std dev accuracy:
1.8%
Mean no. matching orfs: 9.3
if
the ORF deletant is resistant to calcofluor
white
then its class is "biogenesis of cell
wall (cell envelope)"
Mean accuracy:
43.8%
Prior prob of class: 9.5%
Std dev accuracy:
14.4%
Mean no. matching orfs: 6.7
These rules confirm that Calcofluor White is
useful for detecting cell wall mutations (Ram
et al., 1994; Lussier et al., 1997). Calcofluor
White is a negatively charged fluorescent dye
that does not enter the cell wall. Its main
mode of action is believed to be through binding to chitin and prevention of microfibril formation and so weakening the cell wall. The explanation for disruption mutations in the cell
wall having increased sensitivity to Calcofluor
White is believed to be that if the cell wall is
weak, then the cell may not be able to withstand further disturbance. The explanation for
6
resistance is less clear, but the disruption mutations may cause the dye to bind less well to
the cell wall. Zymolase is also known to interfere with cell wall formation (Lussier et al.,
1997). Neither rule predicts the function of any
ORF of currently unassigned function. This is
not surprising given the previous large scale
analysis of the Calcofluor White on mutants.
One rule that does predict a number of
ORFs of unknown function is:
if the ORF deletant is sensitive to
hydroxyurea
then its class is "nuclear organization"
Mean accuracy:
40.2%
Prior prob of class: 21.5%
Std dev accuracy:
6.6%
Mean no. matching orfs: 33.4
This rule predicts 27 ORFs of unassigned
function. The rule is not of high accuracy
but it is statistically highly significant. Hydoxyurea is known to inhibit DNA replication
(Sugimoto et al., 1995), so the rule is biologically consistent.
include YMR035W (mitochondrial inner membrane protease subunit) and YNR045W (translational activator, mitochondrial). The 9/24
ORFs that this rule wrongly predicted include YCL040W (aldohexose specific glucokinase) and YCR012W (phosphoglycerate kinase), both associated with gluconeogenesis/glycolysis. YCR012W (phosphoglycerate
kinase) has no known isoenzyme and would
therefore be expected to be essential for growth
on glycerol. The sensitivity of the YCL040W
(aldohexose specific glucokinase) deletant mutant is less clear and therefore perhaps more
interesting. The functions of the the other
wrongly predicted ORFs, such as YMR188C
(weak similarity to bacterial ribosomal protein
S17), have no known connection with carbon
metabolism and the reason for the sensitivity
to growth on glycerol is unclear.
The rules can appear in several similar
forms, some more general than others. This
rule about sensitivity to YPGlyc appears in
various forms with other conditions (usually
that the mutant ORF is equally as sensitive as
the wildtype to various media). This leads to
very specific rules supporting the general rule,
such as the following:
if the ORF deletant is sensitive to YPGlyc
and the number of media the ORF deletant
is sensitive or resistant to is low
then its class is "mitochondrial
if the ORF deletant is
organization"
as sensitive as wildtype to EGTA
Mean accuracy:
52.2%
and as sensitive as wildtype to SDS
Prior prob of class: 7.9%
and sensitive to YPGlyc
Std dev accuracy:
11.8%
and as sensitive as wildtype to calcofluor_white
Mean no. matching orfs: 8.2
and as sensitive as wildtype to hygromycin_b
then its class is "mitochondrial organization"
51.9%
To grow aerobically on Glycerol as a sole Mean accuracy:
carbon source yeast requires functioning mi- Prior prob of class: 7.9%
20.8%
tochondria. YPGlyc is a growth media with Std dev accuracy:
Mean no. matching orfs: 12.667
glycerol as sole carbon source, therefore it is
consistent that mutants lacking ORFs involved
The following rule shows a very low accuin mitochondrial organization will be sensitive racy, no better than the a priori probability,
to growth in this medium. This rule is more due to few examples.
than 6 times more accurate than the a priori
probability would suggest by chance. Exam- if the ORF deletant is sensitive to canavanine
then its class is "stress response"
ples of ORFs that this rule correctly predicted
7
Mean accuracy:
5.0%
Prior prob of class: 6.0%
Std dev accuracy:
1.6%
Mean no. matching orfs: 0.3
estimated
accuracy
≥ 80%
≥ 70%
≥ 50%
Lack of statistical significance does not necessarily mean that the rule is not biologically
interesting. Canavanine is an analogue of arginine, and cells which have this present will take
up canavanine instead of synthesising arginine. They will then have short lives. Ubiquitin overexpression is known to increase tolerance to canavanine (Chen and Piper, 1995),
so mutants which affect ubiquitin may be expected to be more sensitive than the wildtype.
YBR082C (E2 ubiquitin-conjugating enzyme)
and YER125W (ubiquitin-protein ligase) are
two of the ORFs matching this rule, both in
the “stress response” class, so it is possible that
this rule is correct, but we just do not have the
number of examples needed for statistical confidence. However, analysis of the biological explanation for this rule can still be interesting.
Tables 1 and 2 show the number of ORFs
of unassigned function predicted by the learnt
rules at levels 1 and 2 in the functional hierarchy. These are plotted as a function of the estimated accuracy of the predictions and the significance (how many standard deviations the
estimated accuracy is from the prior probability of the class). These figures record ORFs
predicted by rules that have appeared at least
5 times during the bootstrap process.
estimated
accuracy
≥ 80%
≥ 70%
≥ 50%
std. deviations
from prior
2
3
4
63
63
63
77
77
77
133 126 126
Table 2: Number of ORFs of unknown function
predicted at Level 2.
It can be seen that analysis of the phenotype
growth data allows the prediction of the functional class of many of the ORFs of currently
unassigned function.
When we compare our results with other
work in supervised learning of function, it can
be seen that we have similar levels of prediction and accuracy. For example Marcotte et al
(1999) used a nearest-neighbour type method
on 5 different types of data, including expression data and metabolic pathways. They predicted 15% of the ORFs of unknown function
at high accuracy (and 62% at lower accuracy).
des Jardins et al. (1997) report an accuracy
of 74% in prediction of level 1 of the enzyme
classification, and 68% at level 2. Pavlidis et al.
(2001) built separate classifiers for each of 27 of
the MIPS functional classes, chosen after preliminary investigation into learnability of the
data. However, they do not make predictions.
Most other work on prediction of function has
been either through unsupervised learning, or
by choosing a very small number of classes to
predict, such as in Brown et al. (2000).
std. deviations
from prior
2
3
4
83
72 35
209 150 65
211 150 65
4
Discussion and conclusion
Many accurate and simple rules have
Table 1: Number of ORFs of unknown function been found which can predict an ORF’s
functional class from mutant phenotype
predicted at Level 1.
experiments.
Biological relevance for
several of the rules has been discussed.
8
this required us to use an unusual rule
selection procedure, and also led to our
choice of the bootstrap to give a clearer
picture of the rules themselves.
The full set of rules can be found at
http://users.aber.ac.uk/ajc99/phenotype/.
The technique can be added to the toolbox of
biologists and computational biologists when
making hypotheses about the roles of ORFs
within a genome, and the method should be
easily portable to other genomes for which mutant phenotype data can be collected.
The rules are also useful as they show
future experimenters which media provide
the most discrimination between functional
classes. Many types of growth media are
shown to be highly informative for identifying the functional class of disruption mutants
(e.g. Calcofluor White), others are of little
value (e.g. sodium chloride). The nature of the
C4.5 algorithm is always to choose attributes
which split the data in the most informative
way. This knowledge can be used in the next
round of phenotypic experiments.
It is also interesting to note that different
functional classes are predicted better by different types of data. For example here we have
seen that this phenotypic data is a very good
predictor of class “biogenesis of cell wall (cell
envelope)”. In their investigations with SVMs,
Pavlidis et al. (2001) also acknowledge that
some classes are easier to learn than others.
With expression data it would seem to be ribosomal proteins that are easy to learn, and
with phylogenetic data, transporter proteins
are predictable (we have also found these results in our current work). This independence
in functional genomics data will be a great help
in determining the functions of ORFs.
Working with the phenotypic growth data
highlighted several machine learning issues
which are interesting:
Our work illustrates the value of crossdisciplinary work. Functional genomics is enriched by a technique for improved prediction
of the functional class of ORFs: and machine
learning is enriched by provision of new data
analysis challenges.
Acknowledgments: We would like to thank
Ugis Sarkans for initial collection of the data and
Stephen Oliver and Douglas Kell for useful discussions. Amanda Clare was supported by MRC grant
G78/6609.
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