Dynamical Systems Modeling of the Cold Shock Response in Saccharomyces cerevisiae
Authors:Nicholas A. Rohacz, Katrina Sherbina, Katrina Sherbina
- Kam D. Dahlquist, Associate Professor of Biology , Loyola Marymount University
- Ben G. Fitzpatrick, Professor of Mathematics, Loyola Marymount University
DNA microarray technology was used to measure the effect of cold shock on gene expression within Saccharomyces cerevisiae, budding yeast. Total RNA was purified from the wild type strain BY4741 and strains deleted for the Cin5, Gln3, Hmo1, and Zap1 transcription factors during growth at 30ºC, cold shock at 13ºC, and recovery at 30ºC. Four to five replicates were performed for each strain and time point. Total RNA was purified from each sample, fluorescently labeled and hybridized to a total of 103 DNA microarrays. Spatial and intensity biases present in the microarray data were corrected using Loess normalization and median absolute deviation scaling performed in the R Statistical computing environment using the limma package.
A gene regulatory network for the cold shock response was constructed consisting of 21 transcription factors chosen either because their target genes were enriched in a list of genes that had significant differential expression in the microarray data or because there was other experimental evidence suggesting their involvement in the cold shock response.
Expression of each gene in the network was modeled by a nonlinear differential equation describing the change in expression over time as the difference between the production rate and degradation rate. Solving the differential equation using both a sigmoid function and Michaelis-Menten kinetics to model production showed that the latter more accurately describes repression and the case of an OR transcriptional gate. The degradation rates in the model were taken from existing literature. The ode45 function in MATLAB was used to solve the differential equation model given a set of initial conditions. The fmincon function in MATLAB compared the model to the microarray data to find optimized weights and threshold constants by a nonlinear least squares fit criterion. The deletion strains were modeled by removing the gene from the dynamical system.