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

<div><p>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.</p></div

Significant probelets and corresponding tumor and normal arraylets revealed by the GSVD of the LGA discovery datasets.

<p>(<i>a</i>) 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 [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164546#pone.0164546.ref008" target="_blank">8</a>]. 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 (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164546#pone.0164546.g003" target="_blank">Fig 3</a>). The GBM-associated LGA-shared focal CNAs (black) include, e.g., a gain of a segment on chromosome 1 containing <i>MDM4</i>. (<i>b</i>) 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 (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164546#pone.0164546.g004" target="_blank">Fig 4</a>). (<i>c</i>) Raster display of the tumor dataset shows the correspondence between the tumor profiles and the second LGA probelet and tumor arraylet. (<i>d</i>) Plot of the 53rd LGA normal arraylet, which is the most significant in the normal dataset, describes a deletion of the X chromosome. (<i>e</i>) 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 <i>P</i>-value is <10⁻¹³. (<i>f</i>) 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.</p

GSVD of the patient-matched LGA tumor and normal DNA copy-number profiles.

<p>The structure of the LGA discovery, tumor and normal datasets <i>D_i</i> 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 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164546#pone.0164546.e004" target="_blank">Eq (1)</a> simultaneously separates the datasets into a single set of normalized, not necessarily orthogonal probelets <i>V^T</i> (i.e., patterns of variation across the patients), which are identical for both datasets, but correspond to different sets of generalized singular values Σ_<i>i</i> (i.e., weights, or superposition coefficients) and orthonormal arraylets <i>U_i</i> (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 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164546#pone.0164546.e009" target="_blank">Eq (4)</a> 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 [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164546#pone.0164546.ref017" target="_blank">17</a>]. The inset bar chart shows that the angular distances largest in magnitude correspond to the first and second probelets, and are > 2<i>π</i>/15, whereas the magnitude of the angular distance that corresponds to the 53rd probelet is < <i>π</i>/16.</p

Survival analyses of the LGA patients classified by the LGA pattern and by treatment.

<p>(<i>a</i>) 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 (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164546#pone.0164546.g003" target="_blank">Fig 3</a>). 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 <i>P</i>-value <10⁻⁴. The univariate Cox proportional hazard ratio is >9. (<i>b</i>) 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. (<i>c</i>) 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. (<i>d</i>) 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. (<i>e</i>) 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. (<i>f</i>) 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.</p

GBM genome-wide pattern of co-occurring CNAs previously uncovered by the GSVD of GBM tumor and normal profiles.

<p>(<i>a</i>) Plot of the second most GBM tumor-exclusive tumor arraylet, which was previously uncovered by the GSVD [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164546#pone.0164546.ref008" target="_blank">8</a>], describes a genome-wide pattern of co-occurring CNAs across 212,696 Agilent probes. The GBM pattern, which encompasses the LGA pattern (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164546#pone.0164546.g002" target="_blank">Fig 2</a>), consists of LGA-shared (black) and GBM-specific (blue) CNAs, including, e.g., gains of segments on chromosome 1 containing <i>MDM4</i> and <i>AKT3</i>, respectively. (<i>b</i>) 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. (<i>c</i>) The LGA-shared CNAs, e.g., in <i>MDM4</i>, are visible across the 4,697 Affymetrix-matched consistently-aberrated Agilent probes. (<i>d</i>) The GBM-specific CNAs, e.g., in <i>AKT3</i>, are visible across the 3,405 remaining probes.</p

Survival analyses of the astrocytoma patients classified by treatment and by the GBM pattern.

<p>KM curves, log-rank test <i>P</i>-values, and Cox proportional hazard ratios of the 497 astrocytoma patients classified by (<i>a</i>) chemotherapy, (<i>b</i>) radiation, (<i>c</i>) the GBM pattern combined with chemotherapy, and (<i>d</i>) the GBM pattern combined with radiation.</p

Survival analyses of the LGA and GBM patients classified by the GBM pattern.

<p>KM curves, log-rank test <i>P</i>-values, and Cox proportional hazard ratios of (<i>a</i>) the GBM set of 364 patients, (<i>b</i>) the LGA discovery and validation sets of 133 patients, and (<i>c</i>) the LGA and GBM sets of 497 patients.</p

Survival analyses of the astrocytoma patients classified by the existing laboratory tests and by the GBM pattern.

<p>The 497 astrocytoma patients classified by (<i>a</i>) <i>MGMT</i> promoter methylation, (<i>b</i>) <i>IDH1</i> mutation, (<i>c</i>) the GBM pattern combined with <i>MGMT</i>, and (<i>d</i>) the GBM pattern combined with <i>IDH1</i>.</p

Survival analyses of the discovery and validation sets of patients, as well as only the platinum-based chemotherapy patients in the discovery and validation sets, classified by the 6p+12p, 7p, and Xq tensor GSVD combined.

<p>(<i>a</i>) KM curves of the discovery set of 249 patients classified by combination of the 6p+12p, 7p, and Xq <i>x</i>-probelet coefficients, show median survival times of 86, 52, and 36 months for the groups A, B, and C, respectively, with the corresponding log-rank test <i>P</i>-value < 10⁻³. (<i>b</i>) KM survival analysis of only the 218, i.e., ∼ 88% platinum-based chemotherapy patients in the discovery set, classified by combination of the three tensor GSVDs, gives qualitatively the same and quantitatively similar results to those of the analyses of 100% of the patients. This means that the combination of the three tensor GSVDs predicts survival in the platinum-based chemotherapy patient population. (<i>c</i>) KM curves of the validation set of 148 stage III-IV patients classified by combination of the 6p+12p, 7p, and Xq arraylet correlation coefficients, show median survival times of 72, 57, and 33 months for the groups A, B, and C, respectively, with the corresponding log-rank test <i>P</i>-value < 10⁻³. This validates the survival analyses of the discovery set of 249 patients. (<i>d</i>) KM survival analysis of only the 140, i.e., ∼ 95% platinum-based chemotherapy patients in the validation set, classified by combination of the three tensor GSVDs.</p

Significant probelets and corresponding tumor and normal arraylets uncovered by GSVD of the patient-matched GBM and normal aCGH profiles.

<p>(<i>a</i>) Plot of the second tumor arraylet describes a global pattern of tumor-exclusive co-occurring CNAs across the tumor probes. The probes are ordered, and their copy numbers are colored, according to each probe's chromosomal location. Segments (black lines) identified by circular binary segmentation (CBS) <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098-Olshen1" target="_blank">[20]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098-Venkatraman1" target="_blank">[21]</a> include most known GBM-associated focal CNAs (black), e.g., <i>EGFR</i> amplification. CNAs previously unrecognized in GBM (red) include an amplification of a segment containing the biochemically putative drug target-encoding <i>TLK2</i>. (<i>b</i>) Plot of the second most tumor-exclusive probelet, which is also the most significant probelet in the tumor dataset (Figure S1<i>a</i> in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098.s001" target="_blank">Appendix S1</a>), describes the corresponding variation across the patients. The patients are ordered and classified according to each patient's relative copy number in this probelet. There are 227 patients (blue) with high (0.02) and 23 patients (red) with low, approximately zero, numbers in the second probelet. One patient (gray) remains unclassified with a large negative (−0.02) number. This classification significantly correlates with GBM survival times (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone-0030098-g003" target="_blank">Figure 3<i>a</i></a> and Table S1 in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098.s001" target="_blank">Appendix S1</a>). (<i>c</i>) Raster display of the tumor dataset, with relative gain (red), no change (black) and loss (green) of DNA copy numbers, shows the correspondence between the GBM profiles and the second probelet and tumor arraylet. Chromosome 7 gain and losses of chromosomes 9p and 10, which are dominant in the second tumor arraylet (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone-0030098-g002" target="_blank">Figure 2<i>a</i></a>), are negligible in the patients with low copy numbers in the second probelet, but distinct in the remaining patients (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone-0030098-g002" target="_blank">Figure 2<i>b</i></a>). This illustrates that the copy numbers listed in the second probelet correspond to the weights of the second tumor arraylet in the GBM profiles of the patients. (<i>d</i>) Plot of the 246th normal arraylet describes an X chromosome-exclusive amplification across the normal probes. (<i>e</i>) Plot of the 246th probelet, which is approximately common to both the normal and tumor datasets, and is the second most significant in the normal dataset (Figure S1<i>b</i> in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098.s001" target="_blank">Appendix S1</a>), describes the corresponding copy-number amplification in the female (red) relative to the male (blue) patients. Classification of the patients by the 246th probelet agrees with the copy-number gender assignments (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone-0030098-t001" target="_blank">Table 1</a> and Figure S9 in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098.s001" target="_blank">Appendix S1</a>), also for three patients with missing TCGA gender annotations and three additional patients with conflicting TCGA annotations and copy-number gender assignments. (<i>f</i>) Raster display of the normal dataset shows the correspondence between the normal profiles and the 246th probelet and normal arraylet. X chromosome amplification, which is dominant in the 246th normal arraylet (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone-0030098-g002" target="_blank">Figure 2<i>d</i></a>), is distinct in the female but nonexisting in the male patients (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone-0030098-g002" target="_blank">Figure 2<i>e</i></a>). Note also that although the tumor samples exhibit female-specific X chromosome amplification (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone-0030098-g002" target="_blank">Figure 2<i>c</i></a>), the second tumor arraylet (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone-0030098-g002" target="_blank">Figure 2<i>a</i></a>) exhibits an unsegmented X chromosome copy-number distribution, that is approximately centered at zero with a relatively small width.</p