Future discovery and control in biology and medicine will come from
the mathematical modeling of large-scale molecular biological data,
such as DNA microarray data, just as Kepler discovered the laws of
planetary motion by using mathematics to describe trends in
astronomical data. In this talk, I will demonstrate that
mathematical modeling of DNA microarray data can be used to correctly
predict previously unknown mechanisms that govern the activities of
DNA and RNA.
First, I will describe the computational prediction of a mechanism of
regulation, by using the pseudoinverse projection and a higher-order
singular value decomposition to uncover a genome-wide pattern of
correlation between DNA replication initiation and RNA expression
during the cell cycle. Then, I will describe the recent
experimental verification of this computational prediction, by
analyzing global expression in synchronized cultures of yeast under
conditions that prevent DNA replication initiation without delaying
cell cycle progression. Finally, I will describe the use of the
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 gene transcripts.