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Exploratory Analysis of the = Copy=20 Number Alterations in Glioblastoma Multiforme

Pablo Freire¹^,⁶,=20 Marco Vilela¹^,⁷,=20 Helena Deus¹^,⁷,=20 Yong-Wan Kim²,=20 Dimpy Koul²,=20 Howard Colman²,=20 Kenneth D. Aldape³,=20 Oliver Bogler⁴,=20 W. K. Alfred Yung²,=20 Kevin Coombes¹,=20 Gordon B. Mills⁵,=20 Ana T. Vasconcelos⁶,=20 Jonas S. Almeida¹^*

1 Department of Bioinformatics and = Computational=20 Biology, The University of Texas M. D. Anderson Cancer Center, Houston, = Texas=20 United States of America, 2 Department=20 of Neuro-Oncology, The University of Texas M. D. Anderson Cancer Center, = Houston, Texas United States of America, 3 Department of Pathology, The = University of=20 Texas M. D. Anderson Cancer Center, Houston, Texas United States of = America, 4 Department of Neurosurgery, = The=20 University of Texas M. D. Anderson Cancer Center, Houston, Texas United = States=20 of America, 5 Department = of Systems=20 Biology, The University of Texas M. D. Anderson Cancer Center, Houston, = Texas,=20 United States of America, 6=20 Laborat=C3=B3rio Nacional de Computa=C3=A7=C3=A3o Cient=C3=ADfica, = Laborat=C3=B3rio de Bioinform=C3=A1tica,=20 Petr=C3=B3polis, Rio de Janeiro, Brasil, 7=20 Instituto de Tecnologia Qu=C3=ADmica e Biol=C3=B3gica, Universidade Nova = de Lisboa,=20 Lisboa, Portugal

Abstract
Background The=20 Cancer Genome Atlas project (TCGA) has initiated the analysis of = multiple=20 samples of a variety of tumor types, starting with glioblastoma = multiforme. The=20 analytical methods encompass genomic and transcriptomic information, as = well as=20 demographic and clinical data about the sample donors. The data create = the=20 opportunity for a systematic screening of the components of the = molecular=20 machinery for features that may be associated with tumor formation. The = wealth=20 of existing mechanistic information about cancer cell biology provides a = natural=20 reference for the exploratory exercise.
Methodology/Principal=20 Findings Glioblastoma=20 multiforme DNA copy number data was generated by The Cancer Genome Atlas = project=20 for 167 patients using 227 aCGH experiments, and was analyzed to build a = catalog=20 of aberrant regions. Genome screening was performed using an information = theory=20 approach in order to quantify aberration as a deviation from a = centrality=20 without the bias of untested assumptions about its parametric nature. A = novel=20 Cancer Genome Browser software application was developed and is made = public to=20 provide a user-friendly graphical interface in which the reported = results can be=20 reproduced. The application source code and stand alone executable are = available=20 at http://code.google.com/p/c= ancergenome=20 and http://bioinformaticstation.org= /,=20 respectively.
Conclusions/Significance The=20 most important known copy number alterations for glioblastoma were = correctly=20 recovered using entropy as a measure of aberration. Additional = alterations were=20 identified in different pathways, such as cell proliferation, cell = junctions and=20 neural development. Moreover, novel candidates for oncogenes and tumor=20 suppressors were also detected. A detailed map of aberrant regions is=20 provided.

Citation: Freire P, Vilela M, Deus H, Kim Y-W, Koul = D, et=20 al. (2008) Exploratory Analysis of the Copy Number Alterations in = Glioblastoma=20 Multiforme. PLoS ONE 3(12): e4076. doi:10.1371/journal.pone.0004076

Editor: Andrea Califano, Columbia University, United = States=20 of America

Received: April 2, 2008; Accepted: = November=20 18, 2008; Published: December 30, 2008

Copyright: =C2=A9 2008 Freire et al. This is an = open-access=20 article distributed under the terms of the Creative Commons Attribution = License,=20 which permits unrestricted use, distribution, and reproduction in any = medium,=20 provided the original author and source are credited.

Funding: The authors thankfully acknowledge National = Institutes of Health (NIH) support through the Center for Clinical and=20 Translational Sciences under contract no. 1UL1RR024148 through awards=20 RO1CA123304, and RO1CA056041. P Freire and AT Vasconcelos also = acknowledge=20 funding from the Brazilian government programs and Institutions CAPES, = CNPq and=20 FAPERJ.

Competing interests: The authors have declared that = no=20 competing interests exist.

* E-mail: jalmeida@mdanderson.org

Introduction

Copy number = alterations=20 (CNAs) are known to be among the triggers of tumor formation [1],=20 [2].=20 Furthermore, tumor progression is associated with further variation in = the copy=20 number [3].=20 Although the association between chromosomal aberration and cancer has = been=20 known for a long time [4],=20 recent advances in array-based techniques allowed a more refined = description of=20 the genomic structure, thus yielding a better characterization of copy = number=20 events.

Beginning with BAC = and cDNA=20 arrays [5],=20 [6],=20 the resolution of the array techniques increased to the current = sensitivity=20 level capable of detecting events with a size of thousands of base pairs = [7],=20 [8].=20 As a consequence of ongoing methodological advancement, a growing number = of new=20 oncogenes and tumor suppressors have been identified [9].

During cancer = progression,=20 tumor cells undergo several genomic changes. Mutations that enhance = tumor=20 progression are most likely to be positive selected in the neoplasm = environment,=20 and the cells that carry these mutations tend to be dominant in the = tumor [10].=20 Due to the nature of CNAs, some mutations might carry genes that confer=20 selective advantage, along with genes that do not. This creates a = mutation=20 background that obfuscates the localization of the major players of = cancer [11].=20 Furthermore, tumor progression may take various routes as it occurs in = the=20 context of an individual genome and individual cell physiology. To track = this=20 variability, the analysis of several patients can be used to identify = the=20 recurrent regions of aberration (RRA).

Currently, most of = the=20 available mathematical tools for analyzing copy number data deal with=20 segmentation methods and breakpoint detection [12],=20 [13].=20 These techniques are used to define discrete regions in the genome that = have the=20 same copy number, analyzing each sample individually. However, few = studies have=20 addressed the detection of RRA, which are common amplification or = deletions that=20 occur in the same locus in a group of samples. One common approach to = detecting=20 RRA is to define arbitrary thresholds to identify amplifications and = deletions=20 [14],=20 using the frequency of events as a measure of abnormality for a given = region in=20 the genome. However, the signal from each experimental platform may = differ in=20 variance, which implies that a different threshold may be needed for = each new=20 analysis. Furthermore, tumor samples typically contain normal cells that = contaminate the tumor DNA, thus altering the amplitude of copy number=20 aberrations. Using absolute copy number values as thresholds to segment = CNAs=20 ignores both confounding effects. A number of other studies report more=20 sophisticated methodologies for RRA detection, but they still rely on = arbitrary=20 calling for amplifications and deletions [11],=20 [15]=E2=80=93[17].

In this study, we = propose a=20 new method for identifying RRA based on the information content of each = probe=20 position. The main goal is to provide an approach that detects aberrant = regions=20 while making minimal assumptions about their nature, scale or = prevalence.

Another aim of this = study is=20 to provide an exploratory framework for analyzing the data from = glioblastoma=20 multiforme (GBM) patients generated by The Cancer Genome Atlas project = (TCGA;[18]).=20 Despite the recent advances in the molecular pathology of GBM, the = underlying=20 mechanism of the origin and invasiveness of malignant glioma remains = obscure [19].

As often noted in = quality=20 analysis surveys [20],=20 data analysis results without dissemination of the applications that = generated=20 them are of unknown reproducibility. Therefore, an accompanying = graphical tool=20 is included to provide analysis of the copy number results as they are = made=20 available by the TCGA project and, more specifically, to allow the = reproduction=20 of the results reported here.

Results and=20 Discussion

Exploring = the=20 TCGA data

In order to = analyze=20 the data generated by the TCGA project, a new graphical tool was = developed, the=20 Cancer Genome Browser (CGB), which is freely available at http://code.google.com/p/= cancergenome/.=20 The rationale for this tool is to provide a client application that can = be used=20 for the visualization and data processing reported here. In the tool, = the input=20 data is directly accessed from a semantic database [21]=20 that provides the TCGA raw data in data structures designed to support = the=20 graphic representations reported here. The raw copy number data is = stored=20 alongside its preprocessed segmented values.

Assessment = of=20 aberration

We present a = new=20 mathematical method that uses Shannon's entropy as a measure of genomic=20 aberration. The entropy measures the deviation from the common state in = a=20 system. In the genomic context, the common state would be that all the = samples=20 have a copy number around 2. Any deviation from that state should be = reflected=20 in the entropy so that the more aberrant a region is, the lower the = entropy.

The = detection of=20 aberrant regions by the proposed procedure was first assessed using a = simulation=20 study (see Methods).=20 Goodness of classification was determined using the area under the = receiver=20 operating characteristic curve, with 1 indicating perfect recognition of = all=20 alterations and 0.5 indicating random classification of the variation. = Several=20 simulated datasets were tested, encompassing different combinations of=20 amplitudes and prevalences (the frequency of mutation in the = population). In=20 each one, a determined region of the genome had its copy number values = added=20 (amplified) by a certain amplitude value in a fraction of samples = (controlled by=20 the prevalence). The results were virtually the same when deletions were = tested=20 instead of amplifications (data not shown). The area under curve results = are=20 displayed in Figure=20 1, where it can be observed that, for amplitudes greater than 0.2, a = perfect=20 classification can be obtained if the prevalence is greater than 5%.

Figur= e 1.=20 Evaluation=20 of the entropy method performance by the area under the ROC curve from = simulated=20 datasets, accessing different amplitudes and prevalences of copy number=20 aberrations.

An=20 area under the ROC curve of 1 means a perfect separation between mutated = and=20 normal regions, while a value of 0.5 means a random = classification.
d= oi:10.1371/journal.pone.0004076.g001

There are = two main=20 forms of CNA [11]:=20 broad events, which can encompass several Mb or even the whole = chromosome, and=20 focal events, which are normally restricted to a few Mb. The search for = new=20 oncogenes and tumor suppressors in broad events can be extremely = difficult due=20 to the large number of genes within these regions. Therefore, we chose = to=20 analyze only the focal events and remove the influence of broad events = in the=20 entropy analysis. This was done by performing the analysis in each = chromosome=20 separately (thus nullifying the influence of whole chromosome = aberrations) and=20 applying baseline removal techniques to reduce the effects of other = broad events=20 in the entropy signal (see Methods).

GBM = analysis

A total of = 169 RRA=20 were found using the 167 tumor samples (Table=20 S1), being the majority of these regions annotated as copy number = variation=20 (CNV) that occurs in normal samples. CNV in normal cells has recently = been=20 described as a relatively common occurrence in the human genome [22].=20 To separate the mutations related to tumor progression from the normal = CNV, the=20 results were screened to identify the regions in which more than 50% of = the=20 probes were annotated as normal CNV or were detected in low-entropy = peaks in=20 normal samples. Thirty-one regions passed this test and were the objects = of=20 further analysis (Table=20 1 and Figure=20 2). The chromosomes X and Y were not analyzed. The entropy analyses = for each=20 chromosome are available on Figures=20 S1, S2,=20 S3,=20 S4,=20 S5,=20 S6,=20 S7,=20 S8,=20 S9,=20 S10,=20 S11,=20 S12,=20 S13,=20 S14,=20 S15,=20 S16,=20 S17,=20 S18,=20 S19,=20 S20,=20 S21,=20 S22.

Figur= e 2.=20 Entropy=20 analysis for the GBM data entire genome (A), chromosome 1(B) and = chromosome 7=20 (C).

The=20 segmented copy number values per sample are displayed as a heatmap on = the left,=20 with the tumor samples as columns; the entropy values are shown on the = right.=20 The gaps on the heatmap indicate genomic regions that lack coverage, = such as the=20 p arms of acrocentric chromosomes. The number in A corresponds to the = region=20 number in Table=20 1. Beside each region label, a plus sign indicates an amplification = and a=20 minus indicates a deletion. Note that a low-entropy region can be either = a=20 amplification or a deletion. The red line in the entropy plot shows the=20 threshold for defining an aberrant region, which is the 0.05 quantile of = the=20 bootstrap distribution of the entropy. Peaks that are below the = threshold but=20 have no region assigned are normal CNV. The cytoband annotation was = retrieved=20 using the UCSC Table Browser.
d= oi:10.1371/journal.pone.0004076.g002

Table=20 1. Amplifications=20 and deletions in the GBM data.

doi:10.1371/journal.pone.0004076.t001

Among those = 31=20 regions, there are 10 genes known to modulate cell proliferation in GBM: = EGFR,=20 MDM2, MDM4, CDK4, PTEN, PDFGRA, CDKN2A, CDKN2C, NF1 and CHD5 [23],=20 [24].=20 However, the total number of CNAs involved in cell proliferation is = still=20 unknown, and recent studies have added new genes to the pool of = oncogenes and=20 suppressors of GBM [11],=20 [24],=20 [25].

Amplitude = and=20 prevalence of the CNA

The = rationale of the=20 entropy method allows a straightforward interplay between the prevalence = and=20 amplitude of CNAs. Some of the detected mutations, such as MDM4 and = PTEN, have a=20 low prevalence in the population but high copy number amplitude. = Conversely,=20 other regions, such as #51, have relatively low amplitude and a high=20 prevalence.

Measures of = the=20 amplitude and prevalence directly on the log2 ratio copy number can lead = to bias=20 due to the whole chromosome variation and broad events. To avoid this = problem,=20 the amplification prevalence in an aberrant region was measured as the=20 proportion of probes within the region, considering all samples, with a = copy=20 number above the 0.975 quantile of all copy number values for all = samples at the=20 same chromosome. For deletions, the proportion of values below the 0.025 = quantile was used.

The = amplitude of a=20 given probe position was obtained in a similar way: considering all = samples and=20 all probes within the region, the 0.975 and 0.025 quantiles of the copy = number=20 of the aberrant region were obtained. Then the quantile of these values, = in=20 comparison with the copy number for all the probes in the same = chromosome, was=20 used as a measure of amplitude called QQ0.025 and QQ0.975. For instance, = let q=20 be the 0.975 quantile among all the copy number values from all samples = within a=20 determined aberrant region. The amplitude of amplification, QQ0.975, for = that=20 region will be the quantile relative to q when compared to all of the = copy=20 number values for the same chromosome. If the observed region was not = aberrant,=20 QQ0.975 would be around 0.975. Consequently, a QQ0.975 close to 1 = indicates=20 amplification, and a QQ0.025 close to 0 indicates deletion. To consider = an=20 aberration as an amplification or deletion alike, the one tailed area is = considered (which is to say, the area at either end of the two tailed=20 distribution) and the amplification amplitude is expressed as 1- = QQ0.975.=20 Interestingly, the known aberrations for GBM tend to have the most = extreme=20 values of amplitude and are therefore found at the end of the = distribution tails=20 with QQ0.025 and 1- QQ0.975 values close to 0 (Figure=20 3). The separation between amplification and deletion is done by = observing=20 each value, QQ0.025 or 1-QQ0.975, is close to 0.

Figur= e 3.=20 Interplay=20 between the amplitude, prevalence and entropy in deletions (A) and=20 amplifications (B).

The=20 prevalence measure adopted is the proportion of DNA probes on determined = regions=20 that have a log2 ratio above or below the 0.025 and 0.975 = quantiles.

d= oi:10.1371/journal.pone.0004076.g003

Genes = within=20 low-entropy regions

The = recurrence of an=20 aberration can be related to the influence of its genes in tumor = progression [10].=20 However, some regions can contain other genes that may not be related to = cancer.=20 In [11],=20 the genes that have influence on cancer are designated as = =E2=80=9Cdrivers=E2=80=9D and the=20 genes that are near the =E2=80=9Cdrivers=E2=80=9D but have no effect on = tumor progression are=20 designated as =E2=80=9Cpassengers.=E2=80=9D Most authors assign only one = =E2=80=9Cdriver=E2=80=9D per region [7],=20 [11],=20 [14],=20 but there may be other genes related to cancer within the same region. = For=20 instance, region # 100 in Table=20 1, which contains the known described tumor suppressor CDKN2A, also = contains=20 the gene ELAVL2, which is related to neuronal proliferation and = differentiation=20 [26].=20 A cluster of interferon genes is also present in this region and can = influence=20 tumor growth and progression [27].=20 Another example of a region with more than one =E2=80=9Cdriver=E2=80=9D = is region #117. Besides=20 the well-described oncogene CDK4, this region also contains = glioma-associated=20 gene 1, which has been described as affecting cell proliferation and=20 differentiation [28].=20 However, the CNA that is most likely to have multiple = =E2=80=9Cdrivers=E2=80=9D is the=20 well-known deletion of 1p36 [25],=20 [29].=20 This deletion is present in gliomas and neuroblastomas, but a single = =E2=80=9Cdriver=E2=80=9D=20 could not be defined [29]=20 in previous studies. Together with the tumor suppressor CDH5, analysis = of the=20 low-entropy regions shows that the genes TNFRSF9, CAMTA1 and AJAP1 are = among the=20 candidates for tumor suppressors. A complete list of genes found in = low-entropy=20 regions is available in Table=20 S2.

The gene = CDKN2C, a=20 well-known tumor suppressor [30],=20 was found in region #9 (Table=20 1). Being an important player in oligodrendroglioma and = medulloblastoma, the=20 deletion of CDKN2C was recently described in GBM [17].=20 Moreover, a deletion of gene NF1, a gene associated with = neurofibromatosis type=20 1 that appears to be a negative regulator of the Ras pathway [31],=20 was also detected.

Among the = candidates=20 for suppressors in GBM listed in Table=20 1 are the genes LSAMP and ACCN1. The former has been described as a = tumor=20 suppressor in renal carcinoma [32],=20 and the latter has been described as an inhibitor of glioma cell = proliferation=20 [33].=20 Some new candidates for oncogenes in GBM have also been found. The gene = ATOH8 is=20 a transcriptional regulator related to glial determination [34],=20 but has never been described as an oncogene. Finally, non-annotated = normal CNVs=20 might be the cause of some low-entropy peaks, as in regions #91 and 112, = which=20 are located close to known CNV events.

Paralog = regions may=20 contribute to the pool of detected of aberrant regions. An example of = the former=20 is region #79, which is paralog to the region 55715461=E2=80=9355763010 = on chromosome 7=20 [35],that=20 lies within the EGFR amplified area, The Pearson's correlation between = the copy=20 number values of the two paralog regions is 0.79.

Comparison = with=20 other methods

The = literature reports=20 two methods for the identification of RRA that were applied to the TCGA=20 glioblastoma dataset by the TCGA Research Network [36]:=20 GISTIC [11]=20 and GTS [17].=20 GISTIC uses an arbitrary threshold to define deletions and = amplifications and=20 calculates the q-value [37],=20 which is an upper bound to the false discovery rate, as a measure of = aberration.=20 GTS searches for RRA using a statistic that considers the number of = genes in=20 aberrant area and their copy number value. It also uses arbitrary = thresholds to=20 define aberrant regions.

Despite the=20 differences in the methods,=20 the main mutations in GBM (EGFR, CDKN2A, CDKN2C, PDGFRA, PTEN, CDK4, = MDM2 and=20 MDM4) were correctly recovered by the entropy method and the TCGA = Research=20 Network analysis, which used a combination of methods that included = GISTIC and=20 GTS. Confirming the simulation results, the entropy analysis was = insensitive to=20 mutations with low prevalence (<4=E2=80=935%). Some known oncogenes = and suppressors=20 in GBM were not detected by the entropy method, but were correctly = identified by=20 the combined GISTIC and GTS analysis (prevalence in parentheses): MET = (3%), CDK6=20 (1%), TP53 (1%), CCND2 (2%) and PIK3CA (2%). The tumor suppressor RB1 = was not=20 detected by entropy because it is located in the peak of a broad = deletion event=20 and is obfuscated by the baseline removal. However, low prevalence = mutations=20 will always represent a challenge for statistical methods that consider = the=20 whole population in the analysis. With arbitrary thresholds for = amplification=20 and deletion of 1.5 and =E2=88=921.5, respectively (log2 scale), some = mutations were not=20 detected by any method, such as CCNE1 and CCND3 (genes with a prevalence = less=20 than 1%).

The absence = of any=20 unique pattern on the GBM genotype and the influence of low prevalence = mutations=20 suggest that a better description of the copy number data can be = achieved if=20 individual characteristics of each sample is considered instead of a = summary for=20 the whole population. In that context, the entropy method should be used = as an=20 initial scan of the copy number data due to its speed, in the order of = seconds,=20 robustness and lack of parameter calibration. Future versions of the CGB = tool=20 will include GTS and GISTIC, thus allowing the integration of different = methods=20 of RRA detection with heatmap visualization and data exporting.

Tumor = vs. normal=20 samples

In this = study, normal=20 samples were used for identifying germline CNV (see Metods). However, = the=20 comparison of the paired normal and tumor samples reveals mutations that = are=20 only present in the normal samples, which contradicts the common = assumption that=20 blood samples contain only germline CNV (Figure=20 4). A detailed analysis of these mutations indicates that most of = them are=20 artifacts of the segmentation procedure, which creates very small = segments in=20 the normal samples that are not present in the tumor samples. Also, the = samples=20 from patient TCGA-06-0178 appears to be mislabeled; while the tumor = sample has=20 almost no mutation, the blood sample contains several CNAs, including = the=20 oncogene CDK4.

Figur= e 4.=20 Log2=20 ratio of copy number of the 58 tumor-normal sample = pairs.

The=20 values in the diagonal line correspond to variations similarly observed = in tumor=20 and normal tissue. The values in the horizontal line correspond to=20 amplifications (right) and deletions (left) observed only in the tumor=20 samples.

d= oi:10.1371/journal.pone.0004076.g004

In a = comparison=20 between the low-entropy regions on the normal samples (Table=20 S3) and the regions annotated in the CNV databases (described in Methods),=20 62% of the DNA probes of the low-entropy regions in normal samples are = also=20 located in known CNV regions. Moreover, some of the low-entropy regions = are=20 located close to a CNV, and it might be reasonable to assume that they = are part=20 of the CNV, once it is difficult to achieve a precise definition of the=20 boundaries of a CNV with array techniques [38].=20 This observation suggests incompleteness of the current databases for = normal=20 CNV. Indeed, some of the low-entropy regions in normal samples (e.g. = region=20 85219839=E2=80=9385227131 on chromosome 12) were later confirmed by = sequencing to be=20 CNVs [38].=20 Experimental artifacts may also be underlying reason for the low-entropy = regions=20 in normal samples.

Conclusion
This study = presents a=20 new method for detecting RRA that uses low entropy as an indicator. A=20 stand-alone graphic application is provided for the exploration of the = TCGA data=20 and the replication of the detection of low-entropy regions presented = here.

From a = dataset of 167=20 GBM samples from the TCGA project, 31 aberrant regions were found, = including 10=20 known CNAs in GBM, namely the genes EGFR, MDM2, MDM4, CDK4, PDGFRA, = PTEN,=20 CDKN2A, CDKN2C, NF1 and CHD5. Also, candidates that were never described = as=20 being major players in cancer, such as the glial differentiation gene = ATOH8 and=20 the transcription factor NCOA1, were detected in aberrant regions. The = unusual=20 level of enrichment of the list of candidate oncogenes and tumor = suppressors=20 lends considerable expectation to those few regions for which neither=20 variability nor association with tumor formation could be found.

The analysis = of the=20 entropy in the blood (non-tumor) samples showed that only 62% of the = aberrant=20 regions were previously annotated as normal CNV regions. The expansion = of the=20 CNV databases may refine the separation between normal CNV and copy = number=20 aberrations that have influence on cancer.

Methods

Source = data

A total of = 227=20 normalized array comparative genomic hybridization (aCGH) results for = GBM=20 patients were retrieved from the TCGA data portal (http://tcga-data.nci.nih.gov/)= . The=20 aCGH experiments were performed by the Memorial Sloan-Kettering Cancer = Center=20 using the Agilent Human Genome CGH Microarray 244A (Agilent = Technologies, Inc.,=20 Santa Clara, California) platform. From the 227 samples (Table=20 S4), 167 were tumor samples and 60 were blood samples. When there = was more=20 than one sample of the same tissue for a patient, one sample was = randomly=20 selected (see Supplementary Material for a sample list). Of the 167 = tumor=20 samples, 58 had a paired blood sample from the same patient.

The = normalized copy=20 number data obtained from the 227 samples were mapped into the human = genome=20 using the Build 18 (NCBI 36) assembly with an annotation file provided = by the=20 manufacturer (http://www.chem.agilent.com/). = The array=20 normalization procedure was performed by Memorial Sloan Kettering Cancer = Center=20 with their in=E2=80=93house algorithm that corrects for CG contents bias = (see TCGA Data=20 portal; http://tcga.cancer.gov/datapor= tal).=20 The copy number data was filtered using the Circular Binary Segmentation = (CBS)=20 algorithm as implemented in the R package DNAcopy with the default = parameter=20 settings [12].

Data = analysis=20 method

The = detection of=20 aberrations was pursued here as that of an unqualified deviation. As a=20 consequence of this critical concern with untested null models, the = choice of=20 method must satisfy two concerns about possible bias. First, it must = make no=20 assumptions about a reference non-deviant signal. Secondly, it must make = no=20 assumptions about the shape of the variation. These non-parametric = requirements=20 are satisfied by approaches that use the density of observed measures to = assess=20 the information content of the signal. The individual signal is thus = assessed by=20 the probability, p, of the deviation in the context of observed = signals.=20 Shannon's entropy (Eq. 1) was calculated for each of the DNA probe = positions, i=20 =3D 1,=E2=80=A6,n.
(1)

The = probability,=20 p_ij, for each copy number value was determined as the = fraction=20 of the kernel density, K, observed in all samples, j =3D = 1,=E2=80=A6m, at that=20 position (Eq. 2).
(2)

The Parzen = window=20 method [39]=20 with the Gaussian kernel function was used to approximate the = probability=20 density value K of the log2 ratio of copy numbers observed at = that=20 position, CN_i,j. This technique considers that every = element=20 in the population is a center of a Gaussian curve, and that the = probability=20 density value for a given point is the sum of all Gaussian values at = that point.=20 The calculation of the kernel density for all DNA probes would have = required a=20 large amount of computational effort. Therefore, the kernel density was = sampled=20 in 100 equally-distributed points, KS, ranging from the minimum to the = maximum=20 value of the copy number log2 ratio (Eq. 3). The probability density = value,=20 K(CN_ij), was then obtained by interpolation with the = vector=20 KS. The parameter =CF=83, relative to the bandwidth of the = kernel, was defined=20 as the standard deviation of the raw data inside each segment summarized = for all=20 segments in all samples. Methods for bandwidth estimation that were = designed for=20 Gaussian populations yielded a bandwidth parameter that was too short, = which=20 resulted in several peaks in the probability density distribution (data = not=20 shown). Our bandwidth selection criteria resulted in a unimodal = probability=20 density centered at 0. Since most of the important CNAs have high = amplitudes,=20 and consequently low probably densities, the detection of aberrant = regions is=20 relatively insensitive to large bandwidth parameters.
(3)

The amount = of=20 information associated with an =E2=80=9Caberration=E2=80=9D is inversely = proportional to the=20 entropy S. If a determined region is recurrently amplified or deleted, = it should=20 have a higher information content, and thus a lower entropy, when = compared to=20 the overall distribution of the entropy.

The = implementation of=20 this three step procedure is detailed using Matlab's m-code :

[n,m] =3D = size(X);

Generate=20 reference distribution
[f,xi]=20 =3D ksdensity(X(:), bandwidth);
and=20 replace each value by its density (Eq. 3)
P=20 =3D X;P(:) =3D interp1(xi,f,X(:));
Calculate=20 the actual probability now as the proportion of row density (Eq. = 2)
P=20 =3D P./repmat(max(sum(P,2)),1,m);
Calculate=20 Shannon's entropy (Eq. 1)
H=20 =3D =E2=88=92sum(P.*log2(P),2);

Although = applied to=20 aCGH experiments in this work, the entropy method is suitable for any=20 array-based copy number platform.

Detecting = the=20 regions of interest

As discussed = in [11],=20 there are two main forms of CNAs in tumor cells: broad events, which can = contain=20 several Mb of nucleotides and encompass numerous genes; and focal = events, which=20 are much more localized. Focal events inside broad events represent a = challenge=20 for methods that are based on thresholds for the binary calling of=20 amplifications and deletions, once the entire broad region can be = considered=20 significant, hence hidden the focal events. However, some methods for = RRA=20 detection, while relying on arbitrary thresholds, use the amplitude to = separate=20 these nested focal events [11],=20 [17].

Even though = broad=20 events can be prevalent in the cancer genome [14],=20 their applicability for finding new oncogenes or tumor suppressors is = limited=20 due to the large number of genes present in those regions. Thus, in this = paper=20 the detection of RRA was limited to the focal events. To remove the = influence of=20 entire chromosome amplification or deletion, the kernel density was = calculated=20 individually for each chromosome. Moreover, to diminish the effects of = broad=20 events on the entropy, the baseline of the entropy signal was removed = using a=20 Whitaker filter [40]=20 (smoothing). For each probe position, the value of the entropy was = determined as=20 follows: Final entropy =3D Original entropy=E2=88=92Smoothed entropy. = Therefore, only=20 peaks in the entropy, which represent focal events, remained in the = signal.=20 Finally, a threshold for the entropy was obtained using the 0.05 = quantile of the=20 bootstrap distribution of the entropy. The regions that had a final = entropy=20 lower than the threshold were considered RRA. Regions represented by = only one=20 probe were not considered.

In the CGB = tool, the=20 baseline removal is given as an option to the user. Therefore, it is = possible to=20 deactivate this procedure in order to analyze broad events as well. = Since the=20 entropy method does not consider the size of the events, it is capable = of=20 detecting broad events such arm-size or even whole chromosome events. = For whole=20 chromosome events, the entropy should be measured in the whole genome = instead of=20 individually on each chromosome.

Identifying = normal CNV

CNV in = normal cells=20 has recently been described as a relatively common occurrence in the = human=20 genome [22].=20 To detect whether an RRA is a normal copy number variation or an = aberrant=20 alteration that promotes cell proliferation, the regions were compared = to the=20 entries of the Database of Genomic Variants (http://projects.tcag.ca/varia= tion/;=20 version 18v1; [22])=20 and the =E2=80=9CStructural Variants=E2=80=9D annotations in the UCSC = Genome Browser [41].=20 Also, the entropy was calculated for the 60 normal samples using the = same=20 procedure described above. The low-entropy regions in normal samples = were not=20 used when analyzing the tumor dataset.

Simulation = of=20 aberrant regions

One hundred=20 simulations were performed to analyze the behavior of the entropy = according to=20 variations in the amplitude and the prevalence of CNAs. The length of = each=20 aberration was not changed since our method considers each position=20 independently.

A set with = 100=20 artificial patients was built using randomly sampled copy number values = from the=20 GBM data. The simulated CNA amplitude ranged from 0 to 0.4 (log2 ratio = scale)=20 with a prevalence from 0 to 25%. The area under the receiver operator=20 characteristic curve (ROC) was used for performance evaluation in each = simulated=20 condition. The analysis of the simulation is described in the Results=20 section.

Supporting=20 Information

Figure=20 S1. (0.26 MB TIF) Entropy=20 analysis of chromosome 1, containing the copy number heatmap (on the = right) and=20 the entropy signal (left). The threshold for determining aberrant = regions is=20 displayed in the entropy plot as a red line, and it is defined by the = quantile=20 0.05 of the bootstrap distribution of entropy. Only tumor samples are = included.=20 The assignments of the regions is the same on the Table=20 1 of the manuscript and peaks that don't have any regions assigned = represent=20 normal CNV or low-entropy regions in normal samples.

Figure=20 S2. (0.34 MB TIF) Entropy=20 analysis of chromosome 2, containing the copy number heatmap (on the = right) and=20 the entropy signal (left). The threshold for determining aberrant = regions is=20 displayed in the entropy plot as a red line, and it is defined by the = quantile=20 0.05 of the bootstrap distribution of entropy. Only tumor samples are = included.=20 The assignments of the regions is the same on the Table=20 1 of the manus