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.
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. 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 and a higher-order singular value decomposition 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.