TWO-LAYER MATHEMATICAL MODELING OF GENE EXPRESSION: INCORPORATING DNA-LEVEL INFORMATION AND SYSTEM DYNAMICS.

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.

A two-scale mathematical model for DNA transcription.

Unlike the earlier description of regulation of DNA transcription as a biological switch which simply turns on and off, scientists now understand that DNA transcription is a much more complex process. It can depend on several transcription factors (proteins) and DNA regulatory elements (transcription factor binding sites). The combination of these two groups of different scaled factors determines the transcription outcome.

Soluble electron shuttles can mediate energy taxis toward insoluble electron acceptors.

Shewanella species grow in widely disparate environments and play key roles in elemental cycling, especially in environments with varied redox conditions. To obtain a system-level understanding of Shewanella's robustness and versatility, the complex interplay of cellular growth, metabolism, and transport under conditions of limiting carbon sources, energy sources, and electron acceptors must be elucidated. In this paper, population-level taxis of Shewanella oneidensis MR-1 cells in the presence of a rate-limiting, insoluble electron acceptor was investigated.

Image processing and analysis for quantifying gene expression from early Drosophila embryos.

Correlation of quantities of transcriptional activators and repressors with the mRNA output of target genes is a central issue for modeling gene regulation. In multicellular organisms, both spatial and temporal differences in gene expression must be taken into account; this can be achieved by use of in situ hybridization followed by confocal laser scanning microscopy (CLSM). Here we present a method to correlate the protein levels of the short-range repressor Giant with lacZ mRNA produced by reporter genes using images of Drosophila blastoderm embryos taken by CLSM.

An optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systems.

Reaction-diffusion-chemotaxis systems have proven to be fairly accurate mathematical models for many pattern formation problems in chemistry and biology. These systems are important for computer simulations of patterns, parameter estimations as well as analysis of the biological systems. To solve reaction-diffusion-chemotaxis systems, efficient and reliable numerical algorithms are essential for pattern generations.

Numerical analysis of the flux and force generated by a correlation ratchet mechanism.

The correlation ratchet (CR) has been proposed as a possible mechanism for the operation of biomolecular motors. To test whether a CR mechanism is applicable to any particular motor, it is necessary to evaluate the unloaded velocity and the stall force of the CR mechanism. This paper is concerned with efficient numerical procedures for the determination of these quantities.