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. 2016 Oct 31;11(10):e0164546.
doi: 10.1371/journal.pone.0164546. eCollection 2016.

Platform-Independent Genome-Wide Pattern of DNA Copy-Number Alterations Predicting Astrocytoma Survival and Response to Treatment Revealed by the GSVD Formulated as a Comparative Spectral Decomposition

Katherine A Aiello  1   2 , Orly Alter  1   2   3   4
Affiliations

Platform-Independent Genome-Wide Pattern of DNA Copy-Number Alterations Predicting Astrocytoma Survival and Response to Treatment Revealed by the GSVD Formulated as a Comparative Spectral Decomposition

Katherine A Aiello et al. PLoS One. .

Abstract

We use the generalized singular value decomposition (GSVD), formulated as a comparative spectral decomposition, to model patient-matched grades III and II, i.e., lower-grade astrocytoma (LGA) brain tumor and normal DNA copy-number profiles. A genome-wide tumor-exclusive pattern of DNA copy-number alterations (CNAs) is revealed, encompassed in that previously uncovered in glioblastoma (GBM), i.e., grade IV astrocytoma, where GBM-specific CNAs encode for enhanced opportunities for transformation and proliferation via growth and developmental signaling pathways in GBM relative to LGA. The GSVD separates the LGA pattern from other sources of biological and experimental variation, common to both, or exclusive to one of the tumor and normal datasets. We find, first, and computationally validate, that the LGA pattern is correlated with a patient's survival and response to treatment. Second, the GBM pattern identifies among the LGA patients a subtype, statistically indistinguishable from that among the GBM patients, where the CNA genotype is correlated with an approximately one-year survival phenotype. Third, cross-platform classification of the Affymetrix-measured LGA and GBM profiles by using the Agilent-derived GBM pattern shows that the GBM pattern is a platform-independent predictor of astrocytoma outcome. Statistically, the pattern is a better predictor (corresponding to greater median survival time difference, proportional hazard ratio, and concordance index) than the patient's age and the tumor's grade, which are the best indicators of astrocytoma currently in clinical use, and laboratory tests. The pattern is also statistically independent of these indicators, and, combined with either one, is an even better predictor of astrocytoma outcome. Recurring DNA CNAs have been observed in astrocytoma tumors' genomes for decades, however, copy-number subtypes that are predictive of patients' outcomes were not identified before. This is despite the growing number of datasets recording different aspects of the disease, and due to an existing fundamental need for mathematical frameworks that can simultaneously find similarities and dissimilarities across the datasets. This illustrates the ability of comparative spectral decompositions to find what other methods miss.

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Conflict of interest statement

OA is a co-founder of and an equity holder in Eigengene, Inc. This does not alter our adherence to PLOS ONE policies on sharing data and materials.

Figures

Fig 1
Fig 1. GSVD of the patient-matched LGA tumor and normal DNA copy-number profiles.
The structure of the LGA discovery, tumor and normal datasets Di is that of two matrices of 59 matched columns (i.e., patients), and 933,827, not necessarily matched or equal in numbers, rows (i.e., tumor and normal genomic regions, or Affymetrix probes). The GSVD of Eq (1) simultaneously separates the datasets into a single set of normalized, not necessarily orthogonal probelets VT (i.e., patterns of variation across the patients), which are identical for both datasets, but correspond to different sets of generalized singular values Σi (i.e., weights, or superposition coefficients) and orthonormal arraylets Ui (i.e., patterns of variation across the genome) in each dataset. The GSVD is depicted in a raster display, with relative DNA copy-number gain (red), no change (black), and loss (green), which explicitly shows only the first through the 10th, and the 50th through the 59th probelets and corresponding tumor and normal arraylets, and tumor and normal generalized singular values. The angular distances of Eq (4) define the significance of each probelet in the tumor dataset relative to its significance in the normal dataset in terms of the ratio of the corresponding tumor to normal generalized singular values [17]. The inset bar chart shows that the angular distances largest in magnitude correspond to the first and second probelets, and are > 2π/15, whereas the magnitude of the angular distance that corresponds to the 53rd probelet is < π/16.
Fig 2
Fig 2. Significant probelets and corresponding tumor and normal arraylets revealed by the GSVD of the LGA discovery datasets.
(a) Plot of the second most LGA tumor-exclusive tumor arraylet describes a genome-wide pattern of co-occurring CNAs across 933,827 Affymetrix probes. The probes are ordered, and their copy numbers are colored, according to each probe’s chromosomal location. This LGA pattern is encompassed in a GBM pattern, which was previously uncovered by the GSVD [8]. Segments (black lines) that were identified in the GBM pattern, and are amplified or deleted in the LGA pattern, are also amplified or deleted in the GBM pattern, respectively, and at a greater magnitude (Fig 3). The GBM-associated LGA-shared focal CNAs (black) include, e.g., a gain of a segment on chromosome 1 containing MDM4. (b) Plot of the second LGA probelet describes the variation of the weight, or superposition coefficient of the LGA pattern in the tumor profiles of the 59 patients. The second probelet classifies the patients into two groups of low (red) and high (blue) weights, which are of statistically significantly different prognoses (Fig 4). (c) Raster display of the tumor dataset shows the correspondence between the tumor profiles and the second LGA probelet and tumor arraylet. (d) Plot of the 53rd LGA normal arraylet, which is the most significant in the normal dataset, describes a deletion of the X chromosome. (e) Plot of the 53rd LGA probelet, which is approximately common to the tumor and normal datasets, describes a classification of the patients by gender into females (red) and males (blue). The corresponding hypergeometric P-value is <10−13. (f) Raster display of the normal dataset shows the male-specific X chromosome deletion across the normal genomes. This biological variation is conserved in the patient-matched LGA tumor genomes. The GSVD separates this variation from the second LGA tumor arraylet.
Fig 3
Fig 3. GBM genome-wide pattern of co-occurring CNAs previously uncovered by the GSVD of GBM tumor and normal profiles.
(a) Plot of the second most GBM tumor-exclusive tumor arraylet, which was previously uncovered by the GSVD [8], describes a genome-wide pattern of co-occurring CNAs across 212,696 Agilent probes. The GBM pattern, which encompasses the LGA pattern (Fig 2), consists of LGA-shared (black) and GBM-specific (blue) CNAs, including, e.g., gains of segments on chromosome 1 containing MDM4 and AKT3, respectively. (b) Both LGA-shared and GBM-specific CNAs are visible across the 8,102 Affymetrix-matched Agilent probes, even though these are <4% of the probes that constitute the GBM pattern. (c) The LGA-shared CNAs, e.g., in MDM4, are visible across the 4,697 Affymetrix-matched consistently-aberrated Agilent probes. (d) The GBM-specific CNAs, e.g., in AKT3, are visible across the 3,405 remaining probes.
Fig 4
Fig 4. Survival analyses of the LGA patients classified by the LGA pattern and by treatment.
(a) KM curves of the discovery set of 59 patients classified by the weights, or superposition coefficients of the LGA pattern in their tumor profiles, as listed in the second probelet (Fig 3). The 63-month KM median survival time of the group of patients with low coefficients is >3 times greater than that of the group of patients with high coefficients, with the corresponding log-rank test P-value <10−4. The univariate Cox proportional hazard ratio is >9. (b) Among the 29 patients in the discovery set treated by chemotherapy, the median survival time of the patients with low coefficients is ∼3.5 times greater than that of the patients with high coefficients. (c) Among the patients treated by radiation, the median survival times of patients with low and high coefficients are the same as among the chemotherapy-treated patients. (d) KM curves of the validation set of 74 patients classified by the Pearson correlation of the LGA pattern with their tumor profiles. The 73-month median survival time of the patients with low correlations is >3.5 times greater than that of the patients with high correlations, consistent with the median survival times of the patients in the discovery set. (e) The median survival times of the 46 chemotherapy-treated validation patients with low and high correlations are the same as those of the 74 validation patients, and consistent with those of the 27 chemotherapy-treated discovery patients. (f) The median survival times of the radiation-treated validation patients are the same as those of the validation patients, and consistent with those of the radiation-treated discovery patients.
Fig 5
Fig 5. Survival analyses of the LGA and GBM patients classified by the GBM pattern.
KM curves, log-rank test P-values, and Cox proportional hazard ratios of (a) the GBM set of 364 patients, (b) the LGA discovery and validation sets of 133 patients, and (c) the LGA and GBM sets of 497 patients.
Fig 6
Fig 6. Survival analyses of the astrocytoma patients classified by treatment and by the GBM pattern.
KM curves, log-rank test P-values, and Cox proportional hazard ratios of the 497 astrocytoma patients classified by (a) chemotherapy, (b) radiation, (c) the GBM pattern combined with chemotherapy, and (d) the GBM pattern combined with radiation.
Fig 7
Fig 7. Survival analyses of the astrocytoma patients classified by the patient’s age at diagnosis and the tumor’s grade, and by the GBM pattern.
The 497 astrocytoma patients classified by (a) the patient’s age, (b) the tumor’s grade, (c) the GBM pattern combined with age, and (d) the GBM pattern combined with grade.
Fig 8
Fig 8. Survival analyses of the astrocytoma patients classified by the existing laboratory tests and by the GBM pattern.
The 497 astrocytoma patients classified by (a) MGMT promoter methylation, (b) IDH1 mutation, (c) the GBM pattern combined with MGMT, and (d) the GBM pattern combined with IDH1.
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