Genomic instabilities, amplifications, deletions and translocations are often observed in tumor cells. In the process of cancer pathogenesis cells acquire multiple genomic alterations, some of which drive the process by triggering overexpression of oncogenes and by silencing tumor suppressors and DNA repair genes.
We present data analysis methods designed to study the overall transcriptional effects of DNA copy number alterations. Alterations can be measured using several techniques including microarray based hybridization assays. The data have unique properties due to the strong dependence between measurement values in close genomic loci. To account for this dependence in studying the correlation of DNA copy number to expression levels we develop versions of standard correlation methods that apply to genomic regions and methods for assessing the statistical significance of the observed results. In joint DNA copy number and expression data we define significantly altered submatrices as submatrices where a statistically significant correlation of DNA copy number to expression is observed. We develop heuristic approaches to identify these structures in data matrices. We apply all methods to several datasets, highlighting results that can not be obtained by direct approaches or without using the regional view.
In the paper [1] we define two scores for identifying significant correlations in joint DNA copy number and gene expression data: The Regional Correlation score and significantly altered Genomic Continuous Submatrices (GCSMs). Here we present updated forms of these scores.
Regional Correlation
Given a gene
with a vector of gene expression
levels over a set of samples
we wish to find a genomic segment
containing
, such that the correlation of
with all DNA copy number vectors
of genes
in this segment are consistently
and significantly high. If this set of correlation values significantly
deviates from the values that are expected at random, we will suspect that the
expression of
is affected by a genomic
aberration in the genomic interval that corresponds to
. Since we do not assume that we have a-priori knowledge of the exact location
of the interval
with the best correlation to
, we would like to consider all possible intervals, and locate the most
significantly correlating one.
Let
, where Corr is some correlation function (e.g. the Pearson correlation
coefficient). The Regional Correlation of the gene
is defined as:
A high regional correlation score may arise
due to significant correlation between the expression vector
and
the DNA copy number vectors
within a interval
,
but it may also arise due to random (insignificant) correlation between and DNA copy number vectors
that are very highly correlated between themselves. In order
to identify only significant correlation score, we compute a p-value for
by considering alrage number of random instances of the expression vector.
Genomic Continouous Submatrices (GCSMs)
A GCSM is defined by a continuous genomic segment G
and a subset of the samples S. These determine a submatrix of the DNA
copy number measurement matrix C, and a submatrix of the gene
expression matrix E. We denote these matrices
and
, respectively.
We would like to score the degree to which the DNA copy
numbers and expression levels of the genes
support the existence of an
amplification (or deletion) in M.
Given k – the
number of positive entries in
, p – the fraction of positive entries in the data and
, we score the overabundance of positive entries in M as:
Similarly, we would like
to score the overabundance of measurements in E that suggest that M
is indeed aberrant. Unlike the DNA copy number values, we do not expect the
expression measurements of all genes
to support M since the
expression level of any gene incident to the aberration may or may not be
modified depending on different factors that determine regulation.
Accordingly, we define a score
that reflects the overabundance of genes in
that are significantly
differentially expressed, comparing
and
, in the correct direction (higher in
than in
). A TNoM (Threshold Number of Misclassifications) score may be assigned to
each gene according to its performance as a
versus
classifier. For a more detailed
description of differential expression overabundance please see [2].
A total score for an amplification in M is then defined as:
Although
and
both arise from statistical
significance considerations, since
is expected to be supported by
more data than
, we use a weighting factor a
to balance their contributions to the total score.
Algorithmic methods for locating high-scoring GCSMs are described in [1].
We demonstrate the use the use of Regional correaltion and significantly-altered GCSMs on breast cancer data of Pollack et al [3]. The dataset contains parallel DNA copy number and gene expression measurements of 6,095 genes on 41 breast tumor and cell-line samples.
The
following Figure depicts the genomic locations of significant aberrations
located in the breast cancer dataset. Pink marks depcit significantly altered
GCSMs (S(M;C,E) >40) where the embedded yellow
marks denote the positions of resident genes that are significantly
differentially expressed (TNoM<7). with relation to the respective
partition. Genes with significant regional correlation score (R(i,*)>1.3,
pval<10-3) are depicted
above by yellow marks, where the surrounding light blue marks depict the
genomic intervals for against which the maximum regional correaltion was
attained.
Note the high degree of agreement between the two scores, although
high-scoring GCSMs may be found even when no transcriptional effect is
detected.
A table that summarizes the information for significantly-altered GCSMs
A table that summarizes the information for genes with significant Regional Correlation
D. Lipson, A. Ben-Dor, E. Dehan and Z. Yakhini, Joint Analysis of DNA Copy Numbers and Gene Expression Levels, in Proceedings of WABI '04, LNCS Vol. 3240/2004, p.135, Springer, 2004.
A. Ben-Dor, L. Bruhn, N. Friedman, I. Nachman, M. Schummer, and Z. Yakhini, Tissue classification with gene expression profiles, in Proceedings of RECOMB '02, pp. 54–64, 2000.
- J.R. Pollack, T. Sorlie, C.M. Perou, C.A. Rees, S.S. Jeffrey, P.E. Lonning, R. Tibshirani, D. Botstein, A. Borresen-Dale, and P.O. Brown. Microarray analysis reveals a major direct role of DNA copy number alteration in the transcriptional program of human breast tumors, PNAS, 99(20):12963–8, 2002.