title: TWO-LAYER MATHEMATICAL MODELING OF GENE EXPRESSION: INCORPORATING DNA-LEVEL INFORMATION AND SYSTEM DYNAMICS.
abstract: High-throughput genome sequencing and transcriptome analysis have provided researchers with a quantitative basis for detailed modeling of gene expression using a wide variety of mathematical models. Two of the most commonly employed approaches used to model eukaryotic gene regulation are systems of differential equations, which describe time-dependent interactions of gene networks, and thermodynamic equilibrium approaches that can explore DNA-level transcriptional regulation. To combine the strengths of these approaches, we have constructed a new two-layer mathematical model that provides a dynamical description of gene regulatory systems, using detailed DNA-based information, as well as spatial and temporal transcription factor concentration data. We also developed a semi-implicit numerical algorithm for solving the model equations and demonstrate here the efficiency of this algorithm through stability and convergence analyses. To test the model, we used it together with the semi-implicit algorithm to simulate aDrosophilagene regulatory circuit that drives development in the dorsal-ventral axis of the blastoderm-stage embryo, involving three genes. For model validation, we have done both mathematical and statistical comparisons between the experimental data and the model's simulated data. Where protein andcis-regulatory information is available, our two-layer model provides a method for recapitulating and predicting dynamic aspects of eukaryotic transcriptional systems that will greatly improve our understanding of gene regulation at a global level.
authors.affiliation: Department of Mathematics, Harvey Mudd College, Claremont, CA 91711. This author's work was partly supported by a Teaching and Research Postdoctoral Fellowship at Harvey Mudd College.
authors.forename: Jacqueline M
authors.initials: JM
authors.lastname: Dresch
authors.affiliation: Department of Bioengineering, North Carolina Agricultural and Technical State University, Greensboro, NC27411.
authors.forename: Marc A
authors.initials: MA
authors.lastname: Thompson
authors.affiliation: Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, MI 48824. This author's work was partly supported by NIH grant GM056976.
authors.forename: David N
authors.initials: DN
authors.lastname: Arnosti
authors.affiliation: Department of Mathematics, Michigan State University, East Lansing, MI 48824.
authors.forename: Chichia
authors.initials: C
authors.lastname: Chiu
keywords: reaction-diffusion equation; thermodynamic equilibrium; transcriptional regulation