> *******
> Discovery of Mechanisms from Mathematical Modeling of DNA Microarray
> Data: Computational Prediction and Experimental Verification
>
> Orly Alter
> Department of Biomedical Engineering,
> Institute for Cellular and Molecular Biology, and
> Institute for Computational Engineering and Sciences,
> University of Texas at Austin
>
> 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.
>        http://www.pnas.org/content/103/44/16063.full
> 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.
>        http://dx.doi.org/10.1073/pnas.0604756103
> 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.
>        http://dx.doi.org/10.1073/pnas.0406767101
> 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.
>        http://www.med.miami.edu/mnbws/documents/Alter-.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.
>        http://www.pnas.org/cgi/doi/10.1073/pnas.0709146104
>