Mathematically universal and biologically consistent astrocytoma genotype encodes for transformation and predicts survival phenotype

Abstract

DNA alterations have been observed in astrocytoma for decades. A copy-number genotype predictive of a survival phenotype was only discovered by using the generalized singular value decomposition (GSVD) formulated as a comparative spectral decomposition. Here, we use the GSVD to compare whole-genome sequencing (WGS) profiles of patient-matched astrocytoma and normal DNA. First, the GSVD uncovers a genome-wide pattern of copy-number alterations, which is bounded by patterns recently uncovered by the GSVDs of microarray-profiled patient-matched glioblastoma (GBM) and, separately, lower-grade astrocytoma and normal genomes. Like the microarray patterns, the WGS pattern is correlated with an approximately one-year median survival time. By filling in gaps in the microarray patterns, the WGS pattern reveals that this biologically consistent genotype encodes for transformation via the Notch together with the Ras and Shh pathways. Second, like the GSVDs of the microarray profiles, the GSVD of the WGS profiles separates the tumor-exclusive pattern from normal copy-number variations and experimental inconsistencies. These include the WGS technology-specific effects of guaninecytosine content variations across the genomes that are correlated with experimental batches. Third, by identifying the biologically consistent phenotype among the WGS-profiled tumors, the GBM pattern proves to be a technology-independent predictor of survival and response to chemotherapy and radiation, statistically better than the patient’s age and tumor’s grade, the best other indicators, and MGMT promoter methylation and IDH1 mutation. We conclude that by using the complex structure of the data, comparative spectral decompositions underlie a mathematically universal description of the genotype-phenotype relations in cancer that other methods miss.

GSVD- and tensor GSVD-uncovered patterns of DNA copy-number alterations predict adenocarcinomas survival in general and in response to platinum

“…Only recently, a copy-number genotype predictive of a brain astrocytoma survival phenotype was discovered only by using the GSVD 42 . In comparisons of astrocytoma tumor and patient-matched normal genomes, the GSVD invariably separated the tumor-exclusive genotype and phenotype from those that occur in the normal genomes and from experimental batch effects, independent of the astrocytoma type and the profiling technology.…”

The GSVD: Where are the ellipses?, Matrix Trigonometry, and more

“…In a series of beautiful applications of the GSVD, Alter, et.al. [2,27,28,30,1] propose an approach towards data reconstruction and classification. In their case [2], the A and B are two DNA microarrays, one from humans and the other from yeast.…”

“…The cosine matrix C ∈ IR m1×r matrix puts the c i on the diagonal starting with c 1 in the (1,1) position. If we run out of room, by not having enough rows, we drop some of the 0 cosines.…”

“…One may expect that there may always be a relation between the gsvd of A, B and the svd of AB † . For example, in the matlab documentation 1 it is stated that the generalized singular values are the ratios of the diagonal elements of C and S in a given example. One might infer from the documentation that this is always the case.…”

Rationally engineered advances in cancer research

“…The considerable engineering advances that profoundly reduced the costs of sequencing are now producing tera-bytes of such data for an increasing number of patients—as was the vision of physicists and engineers in the Department of Energy who first conceived of the Human Genome Project decades ago in order to sequence DNA for radiation-induced mutations 35 . In this issue, Alter and coworkers 17 analyzed patient-matched astrocytomas and non-malignant tissues using generalized singular value decomposition and uncovered patterns in genes within Notch, Ras, and Shh pathways. Compared to age or tumor grade, the patterns provide more accurate predictors of recurrence free survival and response to chemotherapy and radiation therapy.…”