Automated multidimensional phenotypic profiling using large public microarray repositories.
ABSTRACT Phenotypes are complex, and difficult to quantify in a high-throughput fashion. The lack of comprehensive phenotype data can prevent or distort genotype-phenotype mapping. Here, we describe "PhenoProfiler," a computational method that enables in silico phenotype profiling. Drawing on the principle that similar gene expression patterns are likely to be associated with similar phenotype patterns, PhenoProfiler supplements the missing quantitative phenotype information for a given microarray dataset based on other well-characterized microarray datasets. We applied our method to 587 human microarray datasets covering >14,000 samples, and confirmed that the predicted phenotype profiles are highly consistent with true phenotype descriptions. PhenoProfiler offers several unique capabilities: (i) automated, multidimensional phenotype profiling, facilitating the analysis and treatment design of complex diseases; (ii) the extrapolation of phenotype profiles beyond provided classes; and (iii) the detection of confounding phenotype factors that could otherwise bias biological inferences. Finally, because no direct comparisons are made between gene expression values from different datasets, the method can use the entire body of cross-platform microarray data. This work has produced a compendium of phenotype profiles for the National Center for Biotechnology Information GEO datasets, which can facilitate an unbiased understanding of the transcriptome-phenome mapping. The continued accumulation of microarray data will further increase the power of PhenoProfiler, by increasing the variety and the quality of phenotypes to be profiled.
- SourceAvailable from: PubMed Central[Show abstract] [Hide abstract]
ABSTRACT: Laboratory-based evolution and whole genome sequencing can link genotype and phenotype. We used evolution of acid resistance in exponential phase Escherichia coli to study resistance to a lethal stress. Iterative selection at pH 2.5 generated five populations that were resistant to low pH in early exponential phase. Genome sequencing revealed multiple mutations, but the only gene mutated in all strains was evgS, part of a two-component system that has already been implicated in acid resistance. All these mutations were in the cytoplasmic PAS domain of EvgS, and were shown to be solely responsible for the resistant phenotype, causing strong up-regulation at neutral pH of genes normally induced by low pH. Resistance to pH 2.5 in these strains did not require the transporter GadC, or the sigma factor RpoS. We found that EvgS-dependent constitutive acid resistance to pH 2.5 was retained in the absence of the regulators GadE or YdeO,. but was lost if the oxidoreductase YdeP was also absent. A deletion in the periplasmic domain of EvgS abolished the response to low pH, but not the activity of the constitutive mutants. On the basis of these results we propose a model for how EvgS may become activated by low pH.Molecular Microbiology 07/2014; · 5.03 Impact Factor
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ABSTRACT: Genome-wide binding assays can determine where individual transcription factors bind in the genome. However, these factors rarely bind chromatin alone, but instead frequently bind to cis-regulatory elements (CREs) together with other factors as protein complexes. Currently there are no integrative analytical approaches that can predict which complexes are formed on chromatin. Here, we describe a computational methodology to systematically capture protein complexes and infer their impact on gene expression. We applied our method to three human cell types, identified thousands of CREs, identified known or undescribed complexes recruited to these CREs, and determined the role of the complexes as activators or repressors. Importantly, we found that the predicted complexes have a higher number of physical interactions between their members than expected by chance. Our work provides a mechanism for developing hypotheses about gene regulation via binding partners, and deciphering the interplay between combinatorial binding and gene expression.Genome Research 04/2013; · 13.85 Impact Factor
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ABSTRACT: Calculation of voltages in a mine electrical distribution system using a power-flow program may fail to yield meaningful results if the iterative power-flow procedure fails to converge. A modified power-flow technique that converges for most of the mine electrical power-flow input data, even though the same input data do not yield a convergent solution with a traditional Newton power-flow algorithm, is presented. When no operable solution to the power-flow problem exists, the results tend to indicate the location of the modeling error that is responsible for nonconvergence. An extensive case study using data for a mine electrical power system is presented to demonstrate the robustness and error identification properties of the power-flow algorithmNeuron 01/1989; · 15.98 Impact Factor
Automated multidimensional phenotypic profiling
using large public microarray repositories
Min Xua,1, Wenyuan Lia,1, Gareth M. Jamesb, Michael R. Mehana, and Xianghong Jasmine Zhoua,2
aMolecular and Computational Biology, Department of Biological Sciences, andbMarshall School of Business, University of Southern California,
Los Angeles, CA 90089
Edited by Michael S. Waterman, University of Southern California, Los Angeles, CA, and approved June 1, 2009 (received for review January 26, 2009)
Phenotypes are complex, and difficult to quantify in a high-
throughput fashion. The lack of comprehensive phenotype data
can prevent or distort genotype–phenotype mapping. Here, we
describe ‘‘PhenoProfiler,’’ a computational method that enables in
silico phenotype profiling. Drawing on the principle that similar
gene expression patterns are likely to be associated with similar
phenotype patterns, PhenoProfiler supplements the missing quan-
titative phenotype information for a given microarray dataset
based on other well-characterized microarray datasets. We applied
our method to 587 human microarray datasets covering >14,000
samples, and confirmed that the predicted phenotype profiles are
highly consistent with true phenotype descriptions. PhenoProfiler
offers several unique capabilities: (i) automated, multidimensional
phenotype profiling, facilitating the analysis and treatment design
of complex diseases; (ii) the extrapolation of phenotype profiles
beyond provided classes; and (iii) the detection of confounding
phenotype factors that could otherwise bias biological inferences.
Finally, because no direct comparisons are made between gene
expression values from different datasets, the method can use the
entire body of cross-platform microarray data. This work has
produced a compendium of phenotype profiles for the National
Center for Biotechnology Information GEO datasets, which can
facilitate an unbiased understanding of the transcriptome-phe-
nome mapping. The continued accumulation of microarray data
will further increase the power of PhenoProfiler, by increasing the
variety and the quality of phenotypes to be profiled.
genotype–phenotype association ? phenotype prediction ?
the lack of phenotype data has become the bottleneck of this
process (1). Phenotyping, especially for human subjects, is a
laborious process (2). Moreover, researchers often gloss over the
complexity of human phenotypes by reporting only those traits
specifically relevant to their studies. For example, a given dataset
may provide survival information but not the patients’ ages.
Inferences derived from such data could be biased or even
invalidated by undocumented or poorly documented phenotypic
traits. Furthermore, most available phenotype characterizations
are qualitative (categorical) rather than quantitative (continu-
ous). This practice is problematic for 2 reasons: The boundaries
between categories are often vague or arbitrary (3), and any
phenotypic information distinguishing data within a category is
In this article, we address the above issues by developing
‘‘PhenoProfiler,’’ a computational framework for predicting the
quantitative phenotype information missing from a genomic
dataset. In particular, this method associates each sample of a
given dataset with the relative intensity of a specific phenotype
trait. The quantitative measures of samples across the whole
dataset is referred to as a ‘‘phenotype profile’’ (PP). Examples
include the body weights of individuals, degrees of malignancy in
he fundamental aim of modern genetics is linking genotype
are likely to be associated with similar phenotypic patterns (4).
Thus, we can supplement the (incomplete) phenotypic informa-
tion in a given genomics dataset with traits recorded in other
well-characterized datasets. In particular, we focus on the vast
accumulation microarray data. The National Center for Bio-
technology Information Gene Expression Omnibus (GEO) (5),
for example, currently contains ?2000 human microarray data-
sets that systematically document the transcriptome basis of
phenotypes as diverse as heart diseases, mental illness, infectious
diseases, and a variety of cancers.
dataset with known sample description of a phenotype P, for
each gene we can derive an association between its expression
profile and this phenotype P. We denote as ‘‘signature genes,’’
those genes whose expressions are strongly associated with the
phenotype in the training dataset. Given a new microarray
dataset that is known to be related to the phenotype P, but the
phenotype description of its individual samples are unknown, we
aim to estimate the PP by constructing a sample profile as a
real-valued vector that is most similar to the expression profiles
of those ‘‘signature genes’’ in the new dataset. Fig. 1 illustrates
Because the information we borrow from the training dataset
is only the association between the gene expressions and sample
phenotypes, we do not directly compare the expression values
between the training and prediction datasets, thus bypassing the
data incompatibility problem between cross-platform and cross-
laboratory microarray datasets. PhenoProfiler can therefore use
as many microarray datasets as possible in the public repositories
in the training stage, and construct a new dataset’s profiles for
a wide range of phenotypes.
We applied our method to 587 human microarray datasets,
covering ?14,000 microarray samples. The predicted phenotype
profiles were highly consistent with known phenotype descrip-
tions. We showed that PhenoProfiler can robustly provide
multidimensional characterization of the phenotypes missing
from a dataset, and can facilitate the discovery of confounding
factors for the transcriptome-phenotype mapping. The compre-
hensive phenotypic data generated by this approach will vastly
increase the value of published and forthcoming genomics data.
Overview of Method. As illustrated in Fig. 1, PhenoProfiler
consists of 2 steps: (i) Given a microarray dataset D1 whose
samples have known descriptions of the phenotype P, for each
gene i we calculate a coefficient withat indicates the degree of
Author contributions: M.X., W.L., G.M.J., and X.J.Z. designed research; M.X. and W.L.
performed research; M.X., W.L., M.R.M., and X.J.Z. analyzed data; and M.X., W.L., G.M.J.,
M.R.M., and X.J.Z. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
Freely available online through the PNAS open access option.
1M.X. and W.L. contributed equally to this work.
2To whom correspondence should be addressed. E-mail: firstname.lastname@example.org.
July 28, 2009 ?
vol. 106 ?
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association between its expression profile and the phenotype P.
The appropriate way to calculate widepends on the structure of
the phenotype descriptions. If the phenotype description is
binary, i.e., the dataset compares 2 phenotype groups, we can
simply use the 2-sample t statistic as wi. If the phenotype
phenotype values and the gene expression values as wi. Genes
with a large magnitude of wiare termed the signature genes of the
phenotype P. (ii) To predict the phenotype profile (PP) of a new
microarray dataset D2, we use the following constrained opti-
mization approach. For a dataset with m individual samples, the
PP is defined as a normalized, real-valued vector of m values (p1,
p2,. . ., pm)T(denoted p). We also define the normalized expres-
sion vector of the gene i as (ei1, ei2,. . ., eim)T, denoted ei; and we
denote the expression matrix containing all such expression
vectors as E. Given a set of coefficients widetermined from the
training data, the objective is to find a profile p that minimizes
the weighted least-squares difference min?i?wi??j(sgn(wi) eij?
pj)2. (The function sgn is ?1 or ?1 depending on the sign of its
argument; we want the phenotype profile p to be close to eiwhen
wiis positive, and close to ?eiwhen wiis negative.) A series of
matrix computations (see Methods) yields the optimal solution p ˆ,
which is essentially the normalized weighted (by wi) sum of gene
expression values across samples.
To assess whether the predicted profile p ˆ captures the expres-
sion trend of those signature genes, we calculate an association
score c ˆ, defined as the Pearson’s correlation between the coef-
ficients w and Ep ˆ (detailed explanation in Methods). To assess
the statistical significance of p ˆ, we compare the c ˆ to those
calculated using the same expression matrix E and 1,000 random
permutations of coefficients w.
An Illustrative Case: Reconstructing the Temporal Order of the Yeast
Log-to-Stationary Growth Transition. As an illustrative example,
consider the 2 microarray datasets GDS18 and GDS283. Both
study the log-to-stationary growth transition of yeast, but with
different microarray platforms. Both datasets measure gene
expression starting at the logarithmic phase and extending
in yeast phenotype from log to stationary transition, responding
samples serves as a good means of validating the prediction.
Using one dataset for training, we computed the Spearman’s
rank correlation between individual gene expression profiles and
the temporal order of the samples. These statistics are used as
the training coefficients. In the other dataset, we then predicted
the phenotype response profile based on gene expressions,
hoping to recover the correct temporal order of samples. In both
cases, the predicted PP was highly consistent with the actual
sequence of samples (Spearman’s rank correlation was 0.83 and
0.79, depending on which dataset was used for training). Fig. 2
shows the predicted and the original sample order of dataset
GDS18. Two subgroups are visible in the predicted profile,
of gene expression is indicated by a color scale running from green (low) to red (high). From the training dataset (at left), we obtain for each gene i a coefficient
widescribing the degree of association between its expression level and the phenotype. Here, genes 1 and 2 have high positive coefficients. Gene 3 shows no
clear association with the phenotype, so its coefficient is close to zero. Gene 4 has a high negative coefficient. Therefore, genes 1, 2, and 4 are signature genes
of the phenotype. Given a new dataset, for each sample we aim to estimate the relative intensity of the association between this sample and the phenotype
such that the derived intensity values of all samples are most similar to the expression values of signature genes. We term such a sample profile a phenotype
that of gene 4 is anti-correlated.
The principles of PhenoProfiler. Each row of an expression matrix corresponds to a gene, and each column corresponds to a sample. The magnitude
www.pnas.org?cgi?doi?10.1073?pnas.0900883106Xu et al.
accurately reflecting the logarithmic and stationary phases. The
sole exception is at the transition between the 2 phases.
Intriguingly, experiment GDS283 stopped taking measure-
ments only 17 h after the yeast entered the stationary phase.
Experiment GDS18, however, continued measurements for an-
other 12 days. So it is remarkable that a phenotype signature
derived from GDS283 can accurately sort the phenotype pro-
gression of GDS18. This result demonstrates that the essential
physiological changes occurring within and between the loga-
rithmic and stationary growth phases can be extrapolated and
Large-Scale Prediction of Phenotype Profiles. To test the general
applicability of our method, we performed a large-scale analysis
of 587 human microarray datasets (see Methods for details on
data collection and processing). Datasets containing at least 2
(P and P?), each with at least 10 samples, were selected as
training datasets (D1). If a dataset contains n sample groups, we
can generate (2
type values in these datasets are categorical, we use the 2-sample
t statistic as coefficients w. By setting the threshold P value for
the predicted PP to 0.001 and the association score c ˆ ? 0.25, a
total of 37,852 PPs were associated to the 587 datasets.
To validate the method, for each training dataset D1we also
need a testing dataset D2that contains the sample descriptions
on exactly the same phenotypes P and P?. Among all 587
datasets, we only identified 4 training-testing dataset pairs
meeting this criterion, in which each of the testing datasets also
contains 2 sample groups of P and P?. To assess whether the
predicted phenotype profile is consistent with the known distri-
bution of phenotypes P and P? in the testing dataset, we used the
Wilcoxon rank sum test. Specifically, in the testing dataset, the
2 sample groups’ (P and P?) predicted phenotype values are
compared using the Wilcoxon rank sum test. A small Wilcoxon
P value indicates that there is a significant difference between
the distributions of predicted phenotype values for the 2 groups,
therefore the predicted profile is consistent with known pheno-
type information. Among the 4 training-testing pairs, all pre-
dicted PPs were highly consistent with the known phenotype
groups (Wilcoxon P ? 10?4).
n) distinct training datasets. Because the pheno-
To obtain a general assessment using more validation data, we
relaxed the requirement that the description of the testing
dataset exactly matches the training data phenotypes. In fact, if
the phenotypes of a given dataset were even moderately similar
to the training phenotype, the predicted profiles were found to
agree well with known phenotype groups in the testing dataset.
This implies a strong interdepedence among related phenotypes.
We quantify the similarity between the training and testing
phenotype with 2 measures: (i) the percentage ? of Unified
Medical Language System (UMLS) concepts of the merged
sample group descriptions of D1shared with the dataset descrip-
tion of D2; and (ii) the similarity between the descriptions of
corresponding sample groups in D1and D2, denoted as s. The
latter is defined as the cosine of the angle between 2 term
frequency-inverse document frequency (tf-idf) vectors of
mapped UMLS terms (see Methods for details). Using these
measurements, we identified 32 training-testing dataset pairs
with similarity thresholds s ? 0.4 and ? ? 0.6. Among these, 81%
of predicted phenotype profiles were consistent with prior
phenotype descriptions (Wilcoxion test P ? 0.05). This result
highlights the effectiveness of our method in exploiting the
interdependence of similar phenotypes.
We further studied the robustness of our method against the
perturbation of the training dataset. We randomly selected a
training dataset and a testing dataset, and then calculated the
correlation between the PP constructed with the original train-
ing dataset and that with a certain amount of training samples
randomly removed. Repeating this test 10,000 times with 10%
(and 20%) sample removal produced an average correlation of
0.98 (and 0.95) between the resulting PPs and those without any
samples removed. Even for those training datasets with a small
size of 10 samples in each of the 2 phenotype groups, the
obtained PP correlations were still ?0.9 for both 10% and 20%
sample removal, demonstrating the robustness of our method.
Multidimensional Profiling of Complex Phenotypes. As previously
587 datasets. On average, each dataset is assigned 65 PPs. In
some cases, related training datasets generated highly correlated
PPs, further enhancing our confidence in the prediction. Two
examples are described below.
Dataset GDS2855 studies various forms of muscular dystro-
phy. Three training sets (GDS609, 610, and 612) generated
highly correlated PPs (average correlation 0.88) for GDS2855.
All 3 training datasets describe the difference between Duch-
enne muscular dystrophy and normal muscle tissues, although
they were measured with different platform technologies.
Furthermore, all 3 predicted PPs were highly consistent with
the original sample description of GDS2855 (Wilcoxion test
P ? 10?6).
Dataset GDS1962 studies gliomas of different grades, and was
assigned 4 highly correlated PPs (average correlation 0.9) by
datasets GDS1975, GDS1976, GDS1815, and GDS1816. All 4
training datasets focused on comparing grade III and grade IV
glioma samples. Remarkably, the predicted PPs not only did a
good job of separating grade III from grade IV samples in the
testing dataset, but also separated grade II from grade III
grades. This example shows that our method captures the
essential difference between high- and low-grade tumors, and
thus can be extrapolated to tumors of grades beyond those
represented in the training data. This ability to extrapolate from
the training dataset represents a significant advantage over
traditional classification methods.
A testing dataset is often (78% of cases) assigned multiple
uncorrelated PPs (correlation ?0.1) describing different prop-
erties of a complex phenotype. For example, dataset GDS843
contains 49 samples comparing patients with abnormal karyo-
profile of GDS18 closely matches the original temporal order of the samples.
Using GDS283 as the training dataset, the predicted phenotype
Xu et al.PNAS ?
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types to patients with normal karyotypes to study adult acute
myeloid leukemia (AML). The samples were collected from
peripheral blood or bone marrow. Its predicted phenotypes
include 3 uncorrelated profiles (see Fig. 3), which are detailed
1. Training dataset GDS842 also studied abnormal versus nor-
mal karyotypes in adult AML patients. The derived pheno-
type profile is consistent with the known sample description
of this phenotype in the testing dataset (Wilcoxon P ? 0.04),
thus validating our method.
2. Training dataset GDS2118 compared individuals with refrac-
tory anemia to normal individuals. The PP trained by this
comparison is highly correlated (correlation ?0.9) with two
other PPs that also come from training datasets that studied
refractory anemia. In fact, the recently proposed WHO
classification of hematologic malignancies merged the disease
‘‘refractory anemia with excess blasts in transformation’’
(RAEB-T) into the category AML. However, this new dis-
ease classification is controversial. Although RAEB-T and
AML share similar clinical parameters, a study pointed out
that their biological bases are different (e.g., RAEB-T is
distinguished from AML by a significant increase in apopto-
sis), and it suggested that RAEB-T should be regarded as a
distinct disease entity (6). Therefore, the derived PP may
uncover hidden patient information and possibly help to
differentiate RAEB-T from AML, which could further lead
to improved treatment design.
3. Training set GDS1221 studies the patient response to the
drug Imatinib. Imatinib was designed to treat chronic myeloid
leukemia by reducing the tyrosine kinase activity of the
well-known bcr–abl fusion gene. Our phenotype profile could
therefore be used to identify patients that would be more
likely to respond to Imatinib treatment.
In summary, although the first PP serves as an internal
validation of the method, the other two PPs provide insights into
the pathologic and therapeutic properties of sample phenotypes
in the dataset GDS843. The specific phenotype properties
represented by the above PPs can be further confirmed by
examining genes whose expressions are significantly correlated
(P ? 0.001) with these profiles. For example, the AML PP
(number 1 above), has 10 significantly correlated genes that are
known to be associated with the UMLS concept ‘‘Leukemia,
Myelocytic, Acute.’’ A particularly interesting gene is FLT3. A
study suggested that in patients with karyotype alterations, a
reciprocal translocation was not sufficient to cause acute pro-
myelocytic leukemia, and that an additional mutation in FTL3
there are 12 significantly correlated genes known to be involved
in ‘‘Anemia.’’ These include 3 Fanconi Anemia genes (FANCA,
FANCD2, FANCG) and TGFB1, which may affect the progres-
sion of refractory anemia specifically (8). Among the genes
correlated with the Imatinib response profile, three are tyrosine
kinases, which is consistent with the target of Imatinib (9).
Discovery of Hidden Confounding Factors in Microarray Studies. Due
to the scarcity of phenotype information in many microarray
datasets, confounding phenotype variables may not be well
documented. Thus, caution should be exercised in deriving
inferences from microarray datasets. The following cases pro-
vide representative scenarios.
Dataset GDS1673 examines normal lung tissue from 23
donors, including smoking and nonsmoking individuals. Inter-
estingly, we found that a predicted PP trained on male vs. female
skeletal muscle samples (dataset GDS914) was able to separate
the smoking and nonsmoking samples of GDS1673 (Wilcoxon
P ? 0.0002). After obtaining additional phenotype information
on the GDS1673 subjects, it turns out that among nonsmokers,
which made up almost 2/3 of the sample, females outnumbered
males by ?2:1, whereas among smokers the numbers of the 2
genders were approximately equal. Thus, simply comparing the
expression profiles of the smoking versus nonsmoking groups
would not derive the signature of smoking, but rather the mixed
signatures of smoking and gender.
As another example, the goal of the GDS1887 study was to
build a prognosis model for rectal cancer cells responding to
Studies of adult acute myeloid leukemia
Responsive to imatinib vs. unresponsive
-2 -1 0
1 2 3
010 20 304050
Refractory anemia vs. normal
3Normal karyotype vs. aberrant karyotype
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| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Three different training datasets produced mutually uncorrelated phenotype profiles (black curves) that could be assigned to GDS843. The 3 most significantly
are ordered according to the first PP, and the expression profiles of negatively correlated expression profiles have been reversed.
Multidimensional profiling of the dataset GDS843 that compares patients of adult AML with abnormal karyotypes to those with normal karyotypes.
www.pnas.org?cgi?doi?10.1073?pnas.0900883106Xu et al.
radio therapy. According to the GEO annotation, its 46 samples
had been separated into training and test groups for model
construction and validation. Surprisingly, we found that the
orignal training and test samples from this study could be well
separated (average Wilcoxon P ? 0.001) by 4 highly correlated
PPs (average correlation 0.95). All of those 4 PPs come from
training datasets that compare the cancer to normal tissue or
that compare cancers of different malignancies. This strongly
suggests that there were systematic differences in cancer malig-
nancy between the training and testing samples, even though
they were supposed to be generated by random partition. Any
such sampling bias would negatively impact the accuracy of the
Of course, sampling bias can often be traced to the very
limited availability of phenotype data in the first place. Our
compendium of predicted phenotype profiles (http://zhoulab.us-
c.edu/PhenoProfiler) provides a comprehensive description of a
large proportion of the datasets in the GEO database. This
knowledge can facilitate an unbiased understanding of the
transcriptome-phenome mapping. It can also serve as the start-
ing point for the identification of molecular mechanisms shared
by different diseases and phenotypes.
Phenotypes are complex, and difficult to quantify in a high-
throughput fashion. The lack of comprehensive phenotype data
describes a unique approach to perform in silico phenotype
profiling. Our method provides numerous advantages, which we
outline here. (i) For most datasets we were able to predict
multiple phenotype profiles, which could help researchers to
reveal different aspects of complex diseases and facilitate treat-
ment design. (ii) We can provide a quantitative phenotype
description of the sample characteristics. Although ‘‘categorical’’
phenotype description is prevalent, in reality phenotypes con-
stitute a continuous spectrum. (iii) Our method can extrapolate
the profiling to classes beyond those represented in the training
data, as illustrated in the glioma case study. This is an advantage
over traditional classification methods. (iv) PhenoProfiler avoids
direct comparison of gene expression values from different
datasets, and thus can use almost all available microarray data
regardless of platform or laboratory. In contrast, traditional
regression methods cannot be directly applied to microarray
datasets from different platforms.
The continued accumulation of microarray data will further
increase the power of PhenoProfiler in 2 aspects: the variety of
phenotypes to be profiled, and the confidence of its predictions.
The latter benefit derives from having several mutually corre-
be easily applied to other types of genomics data (e.g., proteom-
ics or metabolomics) as they become increasingly available. The
present work focuses on linear gene-phenotype associations, but
more complex relationships can be devised depending on the
Our univariate method for constructing the gene coefficients
from the training samples is only one of many possible ap-
proaches. For example, one could consider constructing coeffi-
cients using a multivariate procedure that takes into account
correlations among the gene expression levels, such as Fisher’s
linear discriminant procedure (i.e., discriminant function anal-
ysis for 2 groups). However, such an approach requires estimat-
ing a covariance matrix for the gene expressions which is not
practical given that there are thousands of genes and a limited
number of samples (typically on the order of 10) per dataset. Fan
is high, a univariate 2-sample t test procedure, similar to our
approach, is often superior to a multivariate method. Alterna-
tively, when the important phenotype information can be char-
acterized using a small number of linear combinations of the
genes, dimension reduction techniques like Nonnegative Matrix
Factorization (11, 12) may also produce meaningful phenotype
Predicting Phenotype Profiles by Constrained Optimization. From a training
microarray dataset, we derive a vector w ? (w1,w2,. . .,wn)Tthat contains the
n genes and m samples, and the normalized gene expression matrix E ?
wherePPisanormalized,real-valuedvectorp?(p1,p2,. . .,pm)Tthatshowhigh
similarity to the expression profiles of those genes that have high magnitude
of gene-phenotype association coefficients w (signature genes)
d?E, w, p? ??
m ? 1?
Let b ? (b1, b2,. . ., bm)Tbe the weighted sum of gene expression values for
each sample, bj? ?iwieij. The following theorem provides the solution to the
Theorem. The solution p ˆ to problem Q1is a vector that is the normalized form
of b. That is,
p ˆ ?b ? b?
where b?and ?(b) are the mean and standard deviation of b respectively.
terms are fixed. So the minimization problem Q1can be simplified to an
equivalent maximization problem:
2? 2?iwi?jeijpj. Because p is normalized and E and w are fixed, the first 2
c?E, w, p? ? wTEp
pT1 ? 0
pTp ? m ? 1
where 1 is the vector whose elements are all 1.
Let b ? ETw. Let the Lagrangian function for Q2be.
L?p, ?1, ?2? ? bTp ? ?1pT1 ? ?2?pTp ? ?m ? 1??
where ?1and ?2are Lagrangian multipliers. According to the Karush–Kuhn–
Tuker conditions (13) (as the functions bTp, pT1, and pTp are all convex), the
solution to Eq. 1 contains the global optimum of Q2,
?L?p, ?1, ?2? ? 0
Eq. 1 results in 2 solutions: p ? ?(b ? b?)/?(b). Because Q2is a maximization
problem, it is easy to show that the solution of Q2is p ˆ ? (b ? b?)/?(b), and so
is the solution of Q1.
p ˆ isregardedasthePPofthenewdatasetbecauseamongallvectorsin?m,
p ˆ is the one that most resembles the normalized expression profiles of the
signature genes that were defined by the training data. We calculate an
association score c ˆ as the Pearson correlation between w and Ep ˆ. The score is
derived from the maximization problem Q2. Ep ˆ provides the association
between expression profiles and the predicted phenotype profile in the
testingdataset.Thus,higherc ˆ indicateshigherconsistencyofgene-phenotype
associations derived from the training and testing datasets.
Xu et al.PNAS ?
July 28, 2009 ?
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Data Collection and Processing. We collected 587 human microarray datasets,
each containing at least 5 samples, from the National Center for Biotechnol-
the Affymetrix platforms, we increased any values ?10 to 10 and performed
a log transform of the gene expression values. For genes with multiple
probesets present, the expression values of those probesets were averaged.
gene to Z scores (zero mean and unit variance). The 587 datasets yielded 537
When performing PP prediction, we discarded those training-testing dataset
pairs that share ?100 genes in common.
Automatic Processing of Phenotype Annotations. In GEO, a dataset is usually
annotated by a short description paragraph; a sample group is annotated by
a word or a short phrase; and a sample is usually annotated by 1 sentence. To
systematically categorize the phenotype information associated with each
15). We mapped the dataset description, sample group descriptions, and
sample descriptions onto UMLS concepts via the MetaMap Transfer program
(16). To reduce noise we focused on disease-related concepts, including the
MeSH vocabulary and the semantic types ‘‘Pathologic Function,’’ ‘‘Injury or
Poisoning,’’ ‘‘Anatomical Abnormality,’’ ‘‘Body Part, Organ, or Organ Com-
hierarchy, the broader is the concept. Disease concepts at the fine granularity
level may be associated with more clinical significance. To infer higher-order
Measuring Phenotype Annotation Similarity. We measure phenotype similarity
between sample groups (the 2 groups of a training dataset and the 2 groups
of a testing dataset) by the following procedure. (i) For each group, we map
its title and member sample descriptions onto UMLS concepts. (ii) We then
each sample group. (iii) Suppose that U11and U12are 2 tf-idf vectors corre-
sponding to the 2 sample groups in the training dataset, and that U21and U22
are tf-idf vectors corresponding to the 2 sample groups in the testing data-
set. The similarity between the sample groups is then calculated as
max(?U11, U21? ? ?U12, U22?, ?U11, U22? ? ?U12, U21?), where ?a, b? denotes the
cosine similarity (18) of 2 vectors a and b, calculated as a normalized dot
product ?a, b? ? (aTb)/(?a???b?). Essentially, this measure identifies the best
match between the sample groups in the training dataset and testing dataset
while taking into account the possibility that the groups could be matched in
phenotype profile compendium and Chao Cheng, Caleb Finch, Huanying Ge,
tions. This work was supported by National Institutes of Health Grants
R01GM074163, P50HG002790, and U54CA112952 and NSF Grants 0515936,
0747475 and DMS-0705312. X.J.Z. is an Alfred Sloan Fellow.
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