Supplemental material for K. A. Aiello, S. P. Ponnapalli and O. Alter, "Mathematically Universal and Biologically Consistent Astrocytoma Genotype Encodes for Transformation and Predicts Survival Phenotype," Applied Physics Letters (APL) Bioengineering 2 (3), Special Topic: Bioengineering of Cancer invited article 031909 (September 2018); doi: 10.1063/1.5037882.
Feature: A. J. Engler and D. E. Discher, "Rationally Engineered Advances in Cancer Research," Applied Physics Letters (APL) Bioengineering 2 (3), Special Topic: Bioengineering of Cancer preface 031601 (September 2018).
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 guanine-cytosine 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.
- The corresponding Mathematica 10.4.1 code file is:
- The corresponding WGS astrocytoma tumor and normal profiles are:
- Segments previously identified by the circular binary segmentation (CBS) in the GBM pattern, reproduced from Lee,* Alpert* et al.
- Segments identified by the CBS in significant tumor and normal arraylets revealed by the GSVD of the WGS astrocytoma datasets are: