genetics, mathematics, physics

Postdoctoral and Graduate Positions at the Genomic Signal Processing Lab

NCI U01 CA-202144: Multi-Tensor Decompositions for Personalized Cancer Diagnostics and Prognostics

In the Genomic Signal Processing Lab, we are breaking new ground in mathematics, genetics, and at the interface between the two fields, since our highly cited¹ invention of the "eigengene."^2,3

At the interface, we pioneered both matrix^4,5,6 and tensor^7,8 modeling of large-scale molecular biological data, which, as we demonstrated, can be used to correctly predict previously unknown physical,^9,10,11 cellular,^{12,13,14,15,16} and evolutionary^17,18 mechanisms that govern the activity of DNA and RNA.^19,20,21

In mathematics, we developed the only framework that can create a single coherent model from multiple two-dimensional datasets, by extending the generalized singular value decomposition (GSVD) from two to more than two matrices.^22,23,24

In genetics, our recent GSVD and tensor GSVD comparisons of the genomes of tumor and normal cells from the same sets of glioblastoma and lower-grade astrocytoma brain^25,26,27 and, separately, ovarian^{28,29,30,31,32,33,34} cancer patients uncovered patterns of DNA copy-number alterations that were found to be correlated with a patient's survival and response to chemotherapy. For three decades prior, the best predictor of ovarian cancer survival was the tumor's stage; more than a quarter of ovarian tumors are resistant to the platinum-based chemotherapy, the first-line treatment, yet no diagnostic existed to distinguish resistant from sensitive tumors before the treatment. For five decades prior, the best prognostic indicator of glioblastoma was the patient's age at diagnosis. The ovarian and brain cancer data were published, but the patterns remained unknown until we applied our mathematical frameworks.

Currently, our work is supported by a five-year, three million-dollar National Cancer Institute (NCI) Physical Sciences in Oncology U01 project grant.^35,36 Additional support for our work comes from the Utah Science, Technology, and Research (USTAR) Initiative.

Aiello KA, Alter O, 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. PLoS One 2016;11(10):e0164546

Sankaranarayanan P, Schomay TE, Aiello KA, Alter O, 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. PLoS One 2015;10(4):e0121396

Bertagnolli NM, Drake JA, Tennessen JM, Alter O, SVD identifies transcript length distribution functions from DNA microarray data and reveals evolutionary forces globally affecting GBM metabolism. PLoS One 2013;8(11):e78913

Lee CH, Alpert BO, Sankaranarayanan P, Alter O, GSVD comparison of patient-matched normal and tumor aCGH profiles reveals global copy-number alterations predicting glioblastoma multiforme survival. PLoS One 2012;7(1):e30098

Ponnapalli SP, Saunders MA, Van Loan CF, Alter O, A higher-order generalized singular value decomposition for comparison of global mRNA expression from multiple organisms. PLoS One 2011;6(12):e28072

Muralidhara C, Gross AM, Gutell RR, Alter O, Tensor decomposition reveals concurrent evolutionary convergences and divergences and correlations with structural motifs in ribosomal RNA. PLoS One 2011;6(4):e18768

Omberg L, Meyerson JR, Kobayashi K, Drury LS, Diffley JF, Alter O, Global effects of DNA replication and DNA replication origin activity on eukaryotic gene expression. Mol Syst Biol 2009;5:312

Omberg L, Golub GH, Alter O, A tensor higher-order singular value decomposition for integrative analysis of DNA microarray data from different studies. Proc Natl Acad Sci U S A 2007 Nov 20;104(47):18371-6

Alter O, Genomic signal processing: from matrix algebra to genetic networks. Methods Mol Biol 2007;377:17-60

Alter O, Discovery of principles of nature from mathematical modeling of DNA microarray data. Proc Natl Acad Sci U S A 2006 Oct 31;103(44):16063-4

Alter O, Golub GH, Singular value decomposition of genome-scale mRNA lengths distribution reveals asymmetry in RNA gel electrophoresis band broadening. Proc Natl Acad Sci U S A 2006 Aug 8;103(32):11828-33

Alter O, Golub GH, Reconstructing the pathways of a cellular system from genome-scale signals by using matrix and tensor computations. Proc Natl Acad Sci U S A 2005 Dec 6;102(49):17559-64

Alter O, Golub GH, Integrative analysis of genome-scale data by using pseudoinverse projection predicts novel correlation between DNA replication and RNA transcription. Proc Natl Acad Sci U S A 2004 Nov 23;101(47):16577-82

Alter O, Brown PO, Botstein D, Generalized singular value decomposition for comparative analysis of genome-scale expression data sets of two different organisms. Proc Natl Acad Sci U S A 2003 Mar 18;100(6):3351-6

Nielsen TO, West RB, Linn SC, Alter O, Knowling MA, O'Connell JX, Zhu S, Fero M, Sherlock G, Pollack JR, Brown PO, Botstein D, van de Rijn M, Molecular characterisation of soft tissue tumours: a gene expression study. Lancet 2002 Apr 13;359(9314):1301-7

Alter O, Brown PO, Botstein D, Singular value decomposition for genome-wide expression data processing and modeling. Proc Natl Acad Sci U S A 2000 Aug 29;97(18):10101-6