Constructing Mathematical Models of Gene Regulatory Networks for the Yeast Cell Cycle and Other Periodic Processes

Abstract

We work on constructing mathematical models of gene regulatory networks for periodic processes, such as the cell cycle in budding yeast, using biological data sets and applying or developing analysis methods in the areas of mathematics, statistics, and computer science. We identify genes with periodic expression and then the interactions between periodic genes, which defines the structure of the network. This network is then translated into a mathematical model, using Ordinary Differential Equations (ODEs), to describe these entities and their interactions. The models currently describe gene regulatory interactions, but we are expanding to capture other events, such as phosphorylation and ubiquitination. To model the behavior, we must then find appropriate parameters for the mathematical model that allow its dynamics to approximate the biological data. This pipeline for model construction is not focused on a specific algorithm or data set for each step, but instead on leveraging several sources of data and analysis from several algorithms. For example, we are incorporating data from multiple time series experiments, genome-wide binding experiments, computationally predicted binding, and regulation inference to identify potential regulatory interactions.These approaches are designed to be applicable to various periodic processes in different species. While we have worked most extensively on models for the cell cycle in Saccharomyces cerevisiae, we have also begun working with data sets for the metabolic cycle in S. cerevisiae, and the circadian rhythm in Mus musculus.