Parameter Estimation for Gene Regulatory Networks from Microarray Data: Cold Shock Response in Saccharomyces cerevisiae

Abstract

We investigated the dynamics of a gene regulatory network controlling the cold shock response in budding yeast, Saccharomyces cerevisiae. The medium-scale network, derived from published genome-wide location data, consists of 21 transcription factors that regulate one another through 31 directed edges. The expression levels of the individual transcription factors were modeled using mass balance ordinary differential equations with a sigmoidal production function. Each equation includes a production rate, a degradation rate, weights that denote the magnitude and type of influence of the connected transcription factors (activation or repression), and a threshold of expression. The inverse problem of determining model parameters from observed data is our primary interest. We fit the differential equation model to published microarray data using a penalized nonlinear least squares approach. Model predictions fit the experimental data well, within the 95 % confidence interval. Tests of the model using randomized initial guesses and model-generated data also lend confidence to the fit. The results have revealed activation and repression relationships between the transcription factors. Sensitivity analysis indicates that the model is most sensitive to changes in the production rate parameters, weights, and thresholds of Yap1, Rox1, and Yap6, which form a densely connected core in the network. The modeling results newly suggest that Rap1, Fhl1, Msn4, Rph1, and Hsf1 play an important role in regulating the early response to cold shock in yeast. Our results demonstrate that estimation for a large number of parameters can be successfully performed for nonlinear dynamic gene regulatory networks using sparse, noisy microarray data.Electronic supplementary materialThe online version of this article (doi:10.1007/s11538-015-0092-6) contains supplementary material, which is available to authorized users.

GRNsight: a web application and service for visualizing models of small- to medium-scale gene regulatory networks

“…There are several other 4node chains that originate at CIN5, MAC1, PHD1, SKN7, and YAP1. Finally, there are two rather complex feedforward motifs involving CIN5, ROX1, and YAP6 and SKN7, YAP1, and ROX1 (Dahlquist et al, 2015).…”

“…It is noticeable that none of the edges that represent activation are as thick as the ABF1-to-MSN1 edge; only RAP1-to-RPH1 and HAL9-to-MSN4 are close with weights of 1.50 and 1.43, respectively. Because of this visualization of the weight parameters, one can make some interesting observations about the behavior of the network (Dahlquist et al, 2015). Taking the arrowhead type, thickness, and color into consideration, one can, by visual inspection, group edges by type and relative influence into four activation and four repression bins.…”

“…GRNsight also has the capability of importing and exporting files in SIF and GraphML formats. Although GRNsight was originally developed for use with the GRNmap modeling software, and has provided useful insight into the interpretation of the gene regulatory network model described in Dahlquist et al (2015), it has general applicability for displaying any small, unweighted or weighted network with directed edges for systems biology or other application domains. Thus, GRNsight inhabits a niche not satisfied by other software, doing "one thing well".…”

“…gives a side-by-side view of the same adjacency matrices laid out by GRNsight and by hand.Figures 5A, 5B, and 5C are derived from Demo #3: Unweighted GRN (21 genes, 31 edges), and Figures 5D, 5E, and 5F are derived from Demo #4: Weighted GRN (21 genes, 31 edges,Schade et al 2004 data).Figures 5A and 5Dshow examples of the automatic layout performed by GRNsight.Figures 5C and 5Fshow the same adjacency matrices laid out by hand in Adobe Illustrator, corresponding toFigure 1andFigure 8ofDahlquist et al (2015), respectively.Figures 5B and 5Estarted with the automatic layout from GRNsight and then were manually manipulated from within GRNsight to lay them out similarly toFigures 5C and 5F,…”

Peer Review #2 of "GRNsight: a web application and service for visualizing models of small- to medium-scale gene regulatory networks (v0.1)"

“…A gene regulatory network consists of genes, transcription factors, and the regulatory connections between them which govern the level of expression of mRNA and protein from genes. Our group has developed a MATLAB program to perform parameter estimation and forward simulation of the dynamics of an ordinary differential equations model of a medium-scale GRN with 21 nodes and 31 edges (Dahlquist et al, 2015;http://kdahlquist.github.io/GRNmap/). GRNmap accepts a Microsoft Excel workbook as input, with multiple worksheets specifying the different types of data needed to run the model.…”