Exploring the TCGA data

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

Assessment of aberration

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

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

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

An area under the ROC curve of 1 means a perfect separation between mutated and normal regions, while a value of 0.5 means a random classification.

https://doi.org/10.1371/journal.pone.0004076.g001

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

GBM analysis

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

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

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

https://doi.org/10.1371/journal.pone.0004076.g002

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Table 1. Amplifications and deletions in the GBM data.

https://doi.org/10.1371/journal.pone.0004076.t001

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

Amplitude and prevalence of the CNA

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

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

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

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Figure 3. Interplay between the amplitude, prevalence and entropy in deletions (A) and amplifications (B).

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

https://doi.org/10.1371/journal.pone.0004076.g003

Genes within low-entropy regions

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

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

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

Paralog regions may contribute to the pool of detected of aberrant regions. An example of the former is region #79, which is paralog to the region 55715461–55763010 on chromosome 7 [35],that lies within the EGFR amplified area, The Pearson's correlation between the copy number values of the two paralog regions is 0.79.

Comparison with other methods

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

Despite the differences in the methods, the main mutations in GBM (EGFR, CDKN2A, CDKN2C, PDGFRA, PTEN, CDK4, MDM2 and MDM4) were correctly recovered by the entropy method and the TCGA Research Network analysis, which used a combination of methods that included GISTIC and GTS. Confirming the simulation results, the entropy analysis was insensitive to mutations with low prevalence (<4–5%). Some known oncogenes and suppressors in GBM were not detected by the entropy method, but were correctly identified by the combined GISTIC and GTS analysis (prevalence in parentheses): MET (3%), CDK6 (1%), TP53 (1%), CCND2 (2%) and PIK3CA (2%). The tumor suppressor RB1 was not detected by entropy because it is located in the peak of a broad deletion event and is obfuscated by the baseline removal. However, low prevalence mutations will always represent a challenge for statistical methods that consider the whole population in the analysis. With arbitrary thresholds for amplification and deletion of 1.5 and −1.5, respectively (log2 scale), some mutations were not detected by any method, such as CCNE1 and CCND3 (genes with a prevalence less than 1%).

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

Tumor vs. normal samples

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

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Figure 4. Log2 ratio of copy number of the 58 tumor-normal sample pairs.

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

https://doi.org/10.1371/journal.pone.0004076.g004

In a comparison between the low-entropy regions on the normal samples (Table S3) and the regions annotated in the CNV databases (described in Methods), 62% of the DNA probes of the low-entropy regions in normal samples are also located in known CNV regions. Moreover, some of the low-entropy regions are located close to a CNV, and it might be reasonable to assume that they are part of the CNV, once it is difficult to achieve a precise definition of the boundaries of a CNV with array techniques [38]. This observation suggests incompleteness of the current databases for normal CNV. Indeed, some of the low-entropy regions in normal samples (e.g. region 85219839–85227131 on chromosome 12) were later confirmed by sequencing to be CNVs [38]. Experimental artifacts may also be underlying reason for the low-entropy regions in normal samples.

Conclusion

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

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

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

Source data

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

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

Data analysis method

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

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

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

The amount of information associated with an “aberration” is inversely proportional to the entropy S. If a determined region is recurrently amplified or deleted, it should have a higher information content, and thus a lower entropy, when compared to the overall distribution of the entropy.

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

[n,m] = size(X);

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

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

Detecting the regions of interest

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

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

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

Identifying normal CNV

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

Simulation of aberrant regions

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

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