Discovery of Mechanisms from Mathematical Modeling of DNA Microarray Data: Computational Prediction and Experimental Verification

Abstract

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 [1]. 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 developing generalizations of the matrix and tensor computations that underlie theoretical physics and using them to uncover a genome-wide pattern of correlation between DNA replication initiation and RNA expression during the cell cycle [2,3]. Second, 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 [4]. Third, 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 [5]. 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. Finally, I will describe ongoing work in the development of tensor algebra algorithms (as well as viusal correlation tools), the integrative and comparative modeling of DNA microarray data (as well as rRNA sequence data), and the discovery of mechanisms that regulate cell division, cancer and evolution. 1. Alter, PNAS 103, 16063 (2006). 2. Alter & Golub, PNAS 101, 16577 (2004). 3. Omberg, Golub & Alter, PNAS 104, 18371 (2007). 4. Omberg, Meyerson, Kobayashi, Drury, Diffley & Alter, Nature MSB 5, 312 (2009). 5. Alter & Golub, PNAS 103, 11828 (2006).