Tensor GSVD of Patient- and Platform-Matched Tumor and Normal DNA Copy-Number Profiles Uncovers Chromosome Arm-Wide Patterns of Tumor-Exclusive Platform-Consistent Alterations Encoding for Cell Transformation and Predicting Ovarian Cancer Survival

The number of large-scale high-dimensional datasets recording different aspects of a single disease is growing, accompanied by a need for frameworks that can create one coherent model from multiple tensors of matched columns, e.g., patients and platforms, but independent rows, e.g., probes. We define and prove the mathematical properties of a novel tensor generalized singular value decomposition (GSVD), which can simultaneously find the similarities and dissimilarities, i.e., patterns of varying relative significance, between any two such tensors. We demonstrate the tensor GSVD in comparative modeling of patient- and platform-matched but probe-independent ovarian serous cystadenocarcinoma (OV) tumor, mostly high-grade, and normal DNA copy-number profiles, across each chromosome arm, and combination of two arms, separately. The modeling uncovers previously unrecognized patterns of tumor-exclusive platform-consistent co-occurring copy-number alterations (CNAs). We find, first, and validate that each of the patterns across only 7p and Xq, and the combination of 6p+12p, is correlated with a patient’s prognosis, is independent of the tumor’s stage, the best predictor of OV survival to date, and together with stage makes a better predictor than stage alone. Second, these patterns include most known OV-associated CNAs that map to these chromosome arms, as well as several previously unreported, yet frequent focal CNAs. Third, differential mRNA, microRNA, and protein expression consistently map to the DNA CNAs. A coherent picture emerges for each pattern, suggesting roles for the CNAs in OV pathogenesis and personalized therapy. In 6p+12p, deletion of the p21-encoding CDKN1A and p38-encoding MAPK14 and amplification of RAD51AP1 and KRAS encode for human cell transformation, and are correlated with a cell’s immortality, and a patient’s shorter survival time. In 7p, RPA3 deletion and POLD2 amplification are correlated with DNA stability, and a longer survival. In Xq, PABPC5 deletion and BCAP31 amplification are correlated with a cellular immune response, and a longer survival.

记录单一疾病不同维度的大规模高维数据集数量正持续增长，与此同时亟需能够从多组匹配列（如患者与检测平台）、独立行（如探针）的张量中构建统一模型的分析框架。我们定义并证明了一种新型张量广义奇异值分解（Tensor Generalized Singular Value Decomposition, GSVD）的数学性质，该方法可同时识别任意两组此类张量间的相似与差异模式，即相对重要性各异的特征模式。我们将该张量GSVD应用于卵巢浆液性囊腺癌（Ovarian Serous Cystadenocarcinoma, OV）的比较建模中，所用数据为仅匹配患者与检测平台、但探针独立的高级别为主的浆液性囊腺癌肿瘤与正常组织的DNA拷贝数谱，分别覆盖每条染色体臂以及任意两条染色体臂的组合。该建模分析揭示了此前未被发现的、肿瘤特异性且平台一致的拷贝数变异（Copy-Number Alterations, CNAs）共发生模式。我们首先发现并验证了三项结论：其一，仅覆盖7p、Xq的模式以及6p+12p的组合模式均与患者预后相关，且独立于迄今卵巢癌生存预测的最佳指标——肿瘤分期；将这些模式与分期结合后，其预测性能优于单独使用分期。其二，这些模式涵盖了定位于这些染色体臂的绝大多数已知OV相关CNAs，同时还包含若干此前未被报道但高频存在的局灶性CNAs。其三，差异表达的信使RNA（mRNA）、微小RNA（microRNA）与蛋白质的表达谱均与DNA CNAs存在显著关联。每种模式均呈现出清晰的统一图景，提示这些CNAs在OV发病机制与个性化治疗中发挥潜在作用。在6p+12p区域中，编码p21的CDKN1A与编码p38的MAPK14的缺失，以及RAD51AP1与KRAS的扩增，均参与人类细胞转化过程，并与细胞永生化以及患者更短的生存时间相关。在7p区域中，RPA3的缺失与POLD2的扩增与DNA稳定性及更长的生存时间相关。在Xq区域中，PABPC5的缺失与BCAP31的扩增与细胞免疫应答及更长的生存时间相关。