Modeling the Dynamics of a Family of Small Gene Regulatory Networks in which Single Edges Have Been Deleted Indicates Regulation by Hmo1, Msn2, and Cin5 Are Important for Controlling the Cold Shock Response in Saccharomyces cerevisiae

Abstract

A gene regulatory network (GRN) is a set of transcription factors which regulate the level of expression of genes encoding other transcription factors. The dynamics of a GRN show how gene expression in the network changes over time. Microarray data were obtained from the Saccharomyces cerevisiae wild type strain and five transcription factor deletion strains (Δcin5, Δgln3, Δhap4, Δhmo1, Δzap1) before cold shock at 13°C and 15, 30, and 60 minutes after cold shock (NCBI GEO Series GSE83656). Genes that showed a significant change in expression were submitted to the YEASTRACT database to determine which transcription factors regulated them and to generate a candidate GRN of 15 nodes (transcription factors) and 28 edges (regulatory relationships). The edges of this intact network were then systematically deleted one‐at‐a‐time to create a family of 28 additional networks to determine the importance of each edge in the network. We used the open source software, GRNmap ( http://kdahlquist.github.io/GRNmap/), to model the dynamics of these GRNs. GRNmap models the change in expression for each gene as the production of mRNA minus its degradation using differential equations with a sigmoidal production function. Given published mRNA degradation rates (Neymotin et al. 2014; doi: 10.1261/rna.045104.114) and cold shock microarray data, GRNmap then estimated the production rates and expression thresholds for each gene, and regulatory weights for each edge, which denote the direction (activation or repression) and strength of the regulatory relationships. Edge weights were then visualized with the open source software GRNsight (Dahlquist et al. 2014; doi: 10.7717/peerj‐cs.85; https://dondi.github.io/GRNsight/). Figure 1 shows the intact GRN. Red edges indicate activation; blue edges indicate repression. Node stripes left to right indicate gene expression at 15, 30, and 60 minutes of cold shock, red is increased expression; blue is decreased. To evaluate the goodness of fit of the model, GRNmap reports the least squares error (LSE) between the model and the microarray data. The LSE was compared to the minimum theoretical least squares error (minLSE) achievable due to variation in the data, to determine the model performance between networks. In the 28 edge‐deletion networks, LSE:minLSE ratios indicated that five networks performed better than the intact network, ten networks performed about the same, and thirteen performed worse. The edge‐deletions involving the Hmo1, Msn2, and Cin5 transcription factors resulted in a poor fit of the model to data, indicating that those edges represent important regulatory relationships in the cold shock response. K‐means clustering was performed on the edge weight values from the intact network and edge‐deletion networks. An examination of the clusters showed that weight values deviated from those of the intact network for 6 of 9 edge‐deletions involving Msn2, 4 of 5 edge‐deletions involving Hmo1, and 3 of 6 edge‐deletions involving Cin5, further reinforcing their importance in the network controlling the cold shock response in yeast.Support or Funding InformationLoyola Marymount University Rains Research Assistant Program (A.K.F.)Figure 1