Continuous Time Markov Chain Models of Gene Regulatory Networks under the Environmental Stress of Cold Shock in Saccharomyces cerevisiae
Authors:Nicholas Rohacz, Katrina Sherbina
- Ben Fitzpatrick, Professor of Mathematics, Loyola Marymount University
- Kam Dahlquist, Professor of Biology, Loyola Marymount University
In this presentation, we describe our recent efforts in building and analyzing a stochastic model of gene regulatory networks. By using continuous time Markov chains we are able to model complex interactions of regulatory dynamics. This model, coupled with stochastic approximation, allows for comparing the model to data.
DNA microarrays measuring gene expression in budding yeast (Saccharomyces cerevisiae) as it responds to a cold shock environmental stress were used. Four to five replicates of wild type strain BY4741 and strains deleted for the Cin5, Gln3, Hmo1, and Zap1 transcription factors were analyzed. Total RNA (labeled with Cy5) was purified from each sample, and hybridized with labeled aRNA from the t0 control time point (labeled with Cy3). Within-chip normalization was conducted using the limma package of the R Statistical computing environment and chip-to-chip normalization was conducted using median absolute deviation scaling.
A gene regulatory network for the cold shock response was constructed consisting of transcription factors chosen either because their target genes were enriched in a list of genes that either had significant differential expression in the microarray data or documented relationships arose in the YEASTRACT database. The state of each gene in the network is modeled in a discrete manner as being up-regulated, down-regulated, or unchanged under the stress condition, relative to the control condition. The states of the genes controlling each target gene, along with weighting parameters, determine the likelihood of the target making a transition from one state to another. As a complex, high-dimensional stochastic dynamical system, Monte Carlo simulation and stochastic approximation are used to compare the data and model. We have found that the agreement between model and data is very good for most strains. In some cases, however, the model’s variance is greater than that of the data.