Discovery of mechanisms from mathematical modeling of DNA microarray data:
computational prediction and experimental verification

17 October 2008

Orly Alter
Department of Biomedical Engineering
Institute for Cellular and Molecular Biology and
Institute for Computational Engineering and Sciences
University of Texas at Austin

Abstract

DNA microarrays make it possible to record the complete molecular biological signals that guide the progression of cellular processes on genomic scales. I will describe the ability of mathematical models, that were created from these data using matrix and tensor computations, to predict previously unknown biological as well as physical principles, which govern the activities of DNA and RNA [1].

First, I will describe the use of singular value decomposition to uncover "asymmetric Hermite functions," a generalization of the eigenfunctions of the quantum harmonic oscillator, in genome-wide mRNA lengths distribution data [2]. These patterns might be explained by a previously undiscovered asymmetry in RNA gel electrophoresis band broadening and hint at two competing evolutionary forces that determine the lengths of mRNA gene transcripts.

Second, I will describe the use of pseudoinverse projection [3, 4] and a higher-order singular value decomposition [5] to uncover independently equivalent genome-wide patterns of correlation between DNA replication initiation and mRNA expression. These patterns might be due to a previously unknown cellular mechanism of regulation.

Finally, I will describe recent DNA microarray experimental results that verify this computationally predicted mechanism.

References

1. O Alter, "Discovery of principles of nature from mathematical modeling of DNA microarray data", PNAS 103:16063-4 2006. Paper
2. O Alter, G H Golub, "Singular value decomposition of genome-scale mRNA lengths distribution reveals asymmetry in RNA gel electrophoresis band broadening", PNAS 103:11828-33 2006. PubMed Paper
3. O Alter, G H Golub, "Integrative analysis of genome-scale data using pseudoinverse projection predicts novel correlation between DNA replication and RNA transcription", PNAS 101:16577-82 2004. PubMed Paper
4. O Alter, G H Golub, P O Brown, D Botstein, "Novel genome-scale correlation between DNA replication and RNA transcription during the cell cycle in yeast is predicted by data-driven models", in M P Deutscher et al (eds) Proceedings of the Miami Nature Biotechnology Winter Symposium on the Cell Cycle, Chromosomes and Cancer, Volume 15, University of Miami School of Medicine, Miami, 2004. PDF
5. L Omberg, G H Golub, O Alter, "A tensor higher-order singular value decomposition for integrative analysis of DNA microarray data from different studies", PNAS 104:18371-6 2007. PubMed Paper