Datasets

The sources of the datasets, including (1) gene expression data for TCGA GBM (separately analyzed as 3 batches: GBM1–3), OV (10), Phillips et al. dataset for GBM (GEO accession GSE4271) (8), and the reference dataset by Cahoy et al. for neuronal cells (GEO accession GSE9956) (11), (2) CNA data for GBM1–3, OV, (3) methylation data for GBM1, and (4) clinical data for these studies, are described in Supplemental Information (SI-1.1–1.4). Inferring Aneuploid Genome Proportion (AGP)

We performed logR and BAF-based segmentation and merged the two series of change points. For each segment we calculated the mean folded BAF and mean logR values, and used a least squared distance-based procedure to scan for the best fitting AGP values across the full range of canonical patterns (described in SI-2.1–2.5). The AGP values and associated confidence measures for each sample were extracted from the model as described in SI-2.6 and presented in Table S1.

Statistical analysis

K-means clustering, quantile normalization, t-tests, principal component analysis (PCA), and heatmap generation were performed using standard functions in R (12). Consensus Clustering was implemented using custom R codes. Survival analysis, including the log-rank test, Kaplan-Meier survival curves, Cox proportional hazard regression, and C-statistic (concordance measure) was performed using the R package survival. 3D scatter plots were generated using R package scatterplot3d. All scripts and processed data are available from the authors.

Genomic estimates of aneuploid-euploid mixing ratios

Allelic intensity data from SNP genotyping arrays provide quantitative copy number information of the two parental chromosomes: n_A and n_B. In a homogeneous cell population n_A and n_B are both integers, such that the logarithm of total intensity, logR=log(n_A+n_B), and the observed B allele frequency, BAF=n_B/(n_A+n_B), adopt a finite combination of discrete values, which can be shown as "canonical positions" in the BAF-LRR plot (Figure S1A). In a tumor sample, however, the population of aneuploid cells may be mixed with euploid cells, consequently logR and BAF of the former "contract" towards those of the latter; and different mixing ratios result in different degrees of contraction (Figure S1B). An example of such a mixed GBM sample is shown in Figure 1A. Based on this feature we developed an algorithm to quantitatively estimate genomewide mixing ratio from SNP data (see SI-2.1–2.5). By using experimental results for a series of aneuploid-euploid mixtures of known mixing ratios (GEO accession GSE11976) we confirmed that our method provides an unbiased estimate (Figure 1B, SI-2.7).

In this study we define Aneuploid Content, or synonymously, Aneuploid Genomic Proportion (AGP), as the parameter p in a mixture model consisting of two homogeneous populations: (1) aneuploid cells, at the fraction of p, and (2) euploid cells, at (1-p). Euploid cells carry a balanced set of parental chromosomes representing full-integer multiples of the haploid genome, and may include normal stromal cells surrounding the tumors as well as tumor cells without apparent genomic aberrations (e.g., only point mutations). Aneuploid cells, in contrast, carry CNAs at some chromosomes or subchromosomal intervals, resulting in an unbalanced set of genomic segments, each of which still contain an integer combination of parental DNA, e.g., n_A=2, and n_B=1 in a region of amplification. For many tumors, the two-way mixing model considered here is likely an over-simplification, as multiple subpopulations of tumor cells may exist, each carrying a different integer combination of parental segments. However, a mixture model with three or more subpopulations is computationally intractable using the observed averages of the entire population; and realistically, many tumors may contain a dominant aneuploid population. A two-way mixing model is the simplest scenario that could have generated the observed data regarding varying levels of contraction in different samples. We therefore applied this model for the first-order estimation of within-tumor heterogeneity; and we reported the goodness-of-fit by several quantitative indices (SI-2.6). This approach allowed us to (1) examine the impact of estimated aneuploid content in downstream analyses such as class discovery, (2) assess the adequacy of the model post hoc, and (3) refine the analyses by focusing on the subset of samples that were adequately explained by this simple model.

In the first batch (GBM1), seven of 284 tumors had too few CNAs (including copy-neutral loss-of-heterozygosity events) for purity estimation, and were removed. The remaining 277 tumors had > 0.5% of the genome affected by CNAs, with an average Percent Changed (PC) of 37.3%, i.e., > 1/3 of the genome was altered in an "average" GBM. Across the 277 samples, the estimated AGPs ranged from 23% to 99% (mean ± SD: 76% ±17%), indicating significant admixture of euploid cells (average euploid content of 24%). To assess the goodness-of-fit for each sample we quantified the confidence interval (CI, 2.5–97.5%) of AGP and the fraction of CNAs that fall on canonical positions (PoP, Percent-on-Point) in the optimal two-way mixing model (SI-2.6, and Figure S1C–D). PoP values had a median of 92% among 277 GBMs, suggesting that it is indeed adequate to model a single dominant aneuploid cell population in most GBM samples.

Comparison of genomic estimates of aneuploid content with histopathologic reports

Histopathologic assessment of tumor purity provides basic information for clinical diagnosis, and is a key criterion in sample selection for research. In TCGA, for example, only GBM with >80% "tumor nuclei" were studied. We found, however, that aneuploid estimates based on SNP data were only moderately correlated with pathologists' report of "percent tumor cells" (Spearman's ρ = 0.14, P = 0.02, n=275), not correlated with "percent tumor nuclei" (ρ = 0.076, P = 0.21, n=275), and were lower than AGP by an average of 7% and 18%, respectively (Figure S2). The difference was not explained by tumors with worse fit in our model, or greater estimation uncertainty (SI-2.8). Our inferred AGP is therefore a novel feature extracted from molecular measurements, and can be complementary to the traditionally observed tumor purity.

Impact of aneuploid content on gene expression patterns

We examined 128 GBM1 samples with both gene expression and CNA data. First, samples of low AGP tend to cluster together in PCA of gene expression data, driving a strong correlation between the first principal component scores (PC1) and AGP (Pearson’s r = 0.62, P = 7.3×10⁻¹⁵, n = 128) (Figure 1C). PC2 was also correlated with AGP (r = 0.48, P = 1.1×10⁻⁸). This pattern suggests that within-tumor heterogeneity is a major driver of gene expression variation, and a factor overlooked in most previous studies. To see if the results for GBM extend to other tumor types, we applied a similar analysis to SNP and expression data for 509 ovarian (OV) tumors from TCGA (10), and observed a similar pattern (Figure S3), with a strong correlation between AGP and PC1 (r = 0.56, P < 2.2×10⁻¹⁶, n = 504). In contrast to AGP, clinically recorded purity values showed little correlation with PC1, r was 0.004 (P = 0.96) for "tumor nuclei", and 0.14 (P = 0.10) for "tumor cells", thus underscoring a key advantage of empirical measures of intra-tumor heterogeneity (13). Similar to mRNA, expression patterns of 504 microRNAs were also correlated with AGP (r = −0.26, P = 3.0×10⁻³ for PC1; r = −0.56, P = 1.7×10⁻¹¹ for PC2, n=125).

Combined use of DNA and mRNA patterns in class discovery

The results above raised the question of whether varying levels of euploid-aneuploid mixing could affect the detection of tumor subtypes. To answer this, we performed a joint classification analysis of DNA and mRNA data. In PCA of DNA copy number data, high-AGP samples had high and low PC1s, flanking low-AGP samples (Figure S4A), and this was mostly due to a split of Proneural samples (colored purple). Interestingly, PC1 for copy number and PC1 for expression data, when plotted together, showed a clear separation of two groups (Figure 1D), which, due to annotation efforts described below, we will call Non-Proneural and Proneural samples (even though the Proneural group defined here only partially overlaps with the previously defined Proneural group (5)). The two groups were not readily separable when either dataset was analyzed by itself. MicroRNA PC2 was highly correlated with PC1 of mRNA data (not shown); thus the joint use of this quantity with copy number PC1 also separated the two groups (Figure S4B). The Proneural class consisted of 20 high-AGP samples (AGP = 0.86 ± 0.11), of which all but one belonged to the Proneural group defined previously (5). Conversely, only 19 out of 38 previously defined Proneural samples (among the 128 analyzed) were Proneural here. Thus, our first revision of GBM classification is that the previously recognized Proneural group splits into two, about half becoming the newly recognized Proneural GBM, another half joining the Non-Proneural class. The Non-Proneural GBMs fell on a continuous distribution that parallels a gradient of AGP (range: 0.23–0.99), and span from the former Mesenchymal samples toward the Classical, Neural, and the rest of the former Proneural samples (Figure 1D).

We sought to validate these findings in the second batch of GBM (GBM2) (SI-3.1), using 154 samples having both DNA and mRNA data. AGP estimates were generated as above, showing a similar distribution of AGP in PCA plots of CNA and gene expression data (Figure S5A–B). Just as in GBM1, combined analysis revealed two well separated classes (Figure S5C), with 15 Proneural samples.

Molecular and clinical features of Proneural GBMs (Proneural/G-CIMP+)

To provide biological annotation of Non-Proneural and Proneural samples, we first note that they carried distinct CNA patterns. Non-Proneural GBMs carried recurrent gains in chromosomes 7, 19, 20, recurrent losses in chromosomes 9p and 10, and a gradient of CNA intensities due to varying AGP (Figure 2A). Proneural tumors, in contrast, lacked most of the Non-Proneural features described above and had high AGP values. They carried a more diverse set of CNAs, including 11p15.2 deletions (n=12 out of 20), 8q24.21 amplification (n=7), and 10p11.23 amplifications (n=14). Two of the Proneural samples showed co-occurrence of chr1p loss and chr19q loss (bottom of Figure 2A), each of which was rarely seen in other samples, yet this co-deletion has been reported as a key feature in anaplastic oligodendrogliomas (14, 15). Proneural GBMs had more IDH1 mutation, a hallmark of secondary GBM (16–18). They showed higher frequencies of mutations in TP53, lower frequencies of mutations in PTEN, fewer deletions of CDKN2A - these are also signatures of secondary GBM reported previously (17, 19). They also showed fewer amplifications and over-expression of EGFR, high expression of PDGFRA, and lower expression of FAS and MDM2 (Figure 2B and Table S2).

We also compared clinical outcome between the two groups. Compared to Non-Proneural GBM, patients with Proneural GBM were younger at diagnosis (Figure 2C) and had longer survival time (Figure 2D). Notably, while the Proneural group defined here has a better outcome, the other half of the former Proneural group (which we assigned to non-Proneural), is significantly worse than the rest of the Non-Proneural group (P=0.0059). Thus, lumping the two dissimilar types of GBM in the previously defined Proneural class would have missed a clinically relevant distinction.

A recent study of methylation patterns in TCGA samples revealed a subclass of GBM with glioma-CpG island methylator phenotype (G-CIMP+), an epigenetic signature associated with secondary or recurrent GBM and with IDH1 mutations (6). Of the 20 Proneural samples we identified, 15 were G-CIMP+ (Figure 2B); whereas of the 108 Non-Proneural samples none was G-CIMP+, strongly supporting Proneural GBM as a biologically distinct subtype. Indeed, 3-way analysis of CNA, gene expression, and DNA methylation data revealed consistent separation between Proneural and Non-Proneural GBMs (Figure S6). Proneural samples also match the Proneural GBMs defined in Phillips et al. (8) (SI-3.2, Table S3). As the term "Proneural" was applied differently in Verhaak et al. and Phillips et al. we renamed the Proneural group as Proneural/G-CIMP+ (or PN/G-CIMP+). PN/G-CIMP+ samples carry signatures resembling those of secondary GBM or low-grade gliomas (16), despite the fact that all but four samples in TCGA have been designated as primary (three of these were PN/G-CIMP+). These results suggest that a fraction (20 of 128 analyzed, ~16%) of the apparently primary GBM cases recruited in TCGA may in fact be latent secondary cases.

Three subclasses within Non-Proneural GBMs: Molecular and clinical signatures

After Proneural/G-CIMP+ GBMs were recognized, we sought to identify subclasses within the remaining, Non-Proneural GBMs. The reason for removing an already recognized group (i.e., Proneural/G-CIMP+) when studying the fine structure inside another (Non-Proneural) is that the markers distinguishing the two main groups may not be most informative for the within-group analyses, and could confound the latter. We applied a two-step method that emphasizes GBM1-GBM2 mutual validation (SI-3.1 and Figure S7, S8) and discovered three Non-Proneural classes. By comparing with the class assignments reported in Verhaak et al. and the annotated features in Phillips et al. we named the three classes as Classical, Proliferative, and Mesenchymal (we chose to apply similar terminology as in previous work even though many samples were reassigned, and the revised subtypes took on new characteristics). Of the 108 samples, 70 (65%) had one-to-one mapping to the previous NL, CL, and MES classes (SI-3.2 and Figure S9); thus 35% of GBM1 samples received revised assignments. We similarly analyzed the 46 Non-Proneural samples in Phillips et al. (Figure S10–11), and found that the former Proliferative group was split into the new Proliferative and Classical groups, and 11 (24%) were reassigned into or out of the MES group.

Since any new method could lead to a different classification, we pursued an important question: are the biological features of the new classes more robust than in the old system? Many marker genes highlighted in previous studies were consistently observed (SI-3.3 and Table S4). In CNA patterns (Figure 3A), while Non-Proneural samples shared the chr7 gains and chr10 losses, Proliferative samples carried additional deletions in chr14 and chr15 rarely seen in Classical samples (Student t test for chromosome-wide averaged copy number: P=2.6×10⁻³ and 3.1×10⁻⁴, for chr14 and chr15, respectively), whereas Classical samples carried more amplifications in chr19 (P=1.1×10⁻⁶) and chr20 (P=3.6×10⁻⁶) than in Proliferative samples. Interestingly, many MES samples carried both the chr14–15 deletions and the chr19–20 gains, although with varying intensities due to lower aneuploid content, and with significantly more chr13 deletions compared with non-MES tumors (P=9.6×10⁻³). For Proliferative and MES samples, chr14q and 15 deletions tended to be mutually exclusive (mean Pearson’s r = −0.23 for Prolif and −0.26 for MES); whereas for Classical samples, chr19 gains tended to co-occur with chr20 gains (mean Pearson’s r = 0.46). These results showed that in addition to the CNA differences between Non-Proneural and PN/G-CIMP+ (Figure 2A), the three Non-Proneural classes carried different patterns of genomic aberration, possibly reflecting their differences in cell lineage, transcriptome patterns, and patient outcome.

The three Non-Proneural classes also showed significant differences in survival time in a three-way comparison in GBM1 (Figure 3B, log-rank test P=0.011). This is in contrast to the previous class assignments (5), for which the three-way comparison was not significant (Figure 3C). For individual pairs of classes, five out of six pairwise comparisons were significant in the revised system, while only one of six was significant in the previous system (Figure S12). The revised classes for Phillips' dataset also had significant survival differences in the three-way comparison (P = 0.033, log-rank test) and in the four-way comparison that included the PN/G-CIMP+ group (P = 0.014).

To directly compare the relative hazard across the four GBM subtypes and incorporate relevant patient characteristics, we performed a Cox proportional hazard regression analysis using our four-class assignments as explanatory covariates, and including patient age and the Karnofsky Performance Status (KPS) scores. First, for the entire set of 128 GBM1 samples, with the PN/G-CIMP+ subtype used as the reference category, the three non-Proneural subtypes had higher hazard ratios in the revised system (Figure S13A) than in the previous system (Figure S13B). Second, when we focused only on the three non-Proneural subtypes, using Classical as the reference, the 108 samples in the revised system (Figure S13C) showed higher hazard ratios than the 98 samples in the previous system (Figure S13D). To compare concordance between tumor classification and patient outcomes, we computed the C-statistics (20) for the 128 GBM1 dataset using the Cox regression model with age, KPS and subtypes as covariates. Revised classification had a concordance score of 0.668, higher than using age and KPS alone (0.643) by 2.5%, whereas the previous system had a concordance of 0.651, higher than using age and KPS alone (0.643) by only 0.8%, indicating that the revised system had improved predictive power for patient outcome.

Validation of survival time differences in an independent cohort

The Non-Proneural classes described above were defined by mutual validation of GBM1 and GBM2, thus having used information from both cohorts. To validate the survival time differences in a new, independent dataset, we analyzed a third batch of 144 TCGA samples (GBM3). As before, we identified 26 PN/G-CIMP+ samples using expression data and CNA data. After "locking down" the class assignment in GBM1 and GBM2 we selected 651 genes as the most informative predictors of the three Non-Proneural GBM classes (Table S5), and applied them in supervised class assignment of Non-Proneural samples in GBM3 (SI-4). Survival time differences were indeed validated in GBM3, with five out of six pairwise comparisons showing significant differences (Table 1A). To compare with the previous system, we used the 840 markers suggested by Verhaak et al. to classify the GBM3 samples and found that only one of six pairwise comparisons was significant (Table 1B).

Inference of cell type composition of GBM classes

We attempted to deduce the possible cell type composition of the four GBM classes to shed light on the cellular origins of this heterogeneous cancer. To do so, we compared GBM expression data with a reference dataset, GEO accession GSE9566 (11), for 38 samples that represent four main cell types in the central nervous system: acutely isolated astrocytes, neurons, oligodendrocytes, and cultured astroglia. The 38 samples formed four well-separated clusters, in agreement with their known identity (Figure S14). Cross-correlations of Non-Proneural GBM samples with the 38 reference samples, when grouped by class (for GBM) and cell type (for reference samples), showed recognizable mapping of GBM classes to known neural cell types, for GBM1 (N=128), GBM2 (N=154), and Phillips’ dataset (N=56) (Figure 4A–C). Both PN/G-CIMP+ and Proliferative samples showed high correlations with neurons and oligodendrocytes, suggesting that they both resemble oligodendrogliomas. The Classical samples were similar to the astrocytes, suggesting that they may be related to astrocytomas. Lastly, the Mesenchymal samples showed high similarities with the cultured astroglia samples, which had an "immature or reactive phenotype" (11), consistent with the MES signatures of angiogenesis and inflammatory infiltration (5, 8, 21). The observed resemblance to known cell types were generally consistent with what was reported previously (5), but with important differences (SI-3.4).

As most of the low-AGP samples fell in the Mesenchymal group, we attempted to clarify the cell lineage of the aneuploid and euploid populations. If the aneuploid cells were derived from one of the reference cell types, there should be a positive correlation between (1) the correlation between samples of that particular cell type and individual MES tumors and (2) the MES tumors' AGP values, which measure how much aneuploid cells they contain. We calculated the correlation coefficients r, for each of the 38 reference samples, between its correlation coefficients with the MES samples and the AGP values of the MES samples, and found consistent and positive r values for Cultured Astrocytes (Figure 4D), suggesting that the aneuploid cells in MES share gene expression features, and possible common lineage, with reactive astrocytes (11).

As no other cell type in the reference set showed negative correlations, the identity of the euploid cells in MES remained unexplained. MES tumors carry angiogenic and inflammatory signatures, and some microglia markers are highly expressed in MES samples (5). We therefore hypothesize that the euploid fraction may be related to microglia/macrophage infiltration. To test this hypothesis, we searched public databases for gene expression data for microglia samples (SI-1.1.2), and found data for tumor-infiltrating microglia/macrophage isolated from freshly excised brain tumors ("TI. microglia", in GEO accession GSE25289) (22) and for microglia fraction from postoperative GBM tissue ("G. microglia", in GSE16119) (21). The correlation of these cells with MES tumors showed negative correlations with AGP (Figure 4D), suggesting that expression signatures of MES euploid cells are similar to microglia/macrophage. Moreover, two microglia/macrophage-specific transcripts, integrin alpha M (ITGAM) (23) and allograft inflammatory factor-1 (AIF1) (24), were negatively correlated with AGP (r = −0.58, P = 6.3×10⁻⁶ for ITGAM; r = −0.53, P = 5.3×10⁻⁵ for AIF1), further supporting microglia/macrophage as the probable source of euploid population in MES.

Hierarchical classification of GBM

The new understanding of GBM genomic landscape led to our proposal of a cohesive stepwise classification procedure (Figure 5). First, Proneural/G-CIMP+ GBMs can be identified with joint analyses of copy number and mRNA profiles, along with clinical data such as patient age. Even if a case was recorded as primary GBM due to the apparent lack of antecedent tumors, it could be recognized as Proneural/G-CIMP+ by features such as younger age, IDH1 mutations, lack of PTEN mutations, hyper-methylation patterns, and lack of chr7 gains and chr10 losses. Among the remaining, Non-Proneural samples, MES samples can be separated from the Classical and Proliferative samples by lower AGP values, necrosis signatures, higher expression of FAS and CHI3L1, etc. These tumors experienced more infiltration of non-cancerous cells, containing aneuploid reactive astrocyte-like cells intermingled with cells such as microglia/macrophage that lack CNAs. Lastly, Classical and Proliferative samples can be distinguished by gene expression patterns that resemble different neural cell types. Known markers highlighted by previous studies (Table S4), such as PCNA and TOPA2A overexpression in Proliferative samples, can also be incorporated in this step.