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

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.

Candidate genes for chromosomes 6 and 10 quantitative trait loci for age-related retinal degeneration in mice.

PURPOSE: In a previous study, several quantitative trait loci (QTL) that influence age-related degeneration (ageRD) were identified in a cross between the albino strains B6(Cg)-Tyr(c-2J)/J (B6a) and BALB/cByJ (C). The Chromosome (Chr) 6 and Chr 10 QTL were the strongest and most highly significant loci and both involved B6a protective alleles. The QTL were responsible for 21% and 9% of the variance in phenotypes, respectively. We focused on these two QTL to identify candidate genes. METHODS: DNA microarrays were used for the two mouse strains at four and eight months of age to identify genes that are differentially regulated and map to either QTL. Gene Ontology (GO) analysis of the differentially expressed genes was performed to identify possible processes and pathways associated with ageRD. To identify additional candidates, database analyses (Positional Medline or PosMed) were used. Based on differential expression, PosMed, and the presence of reported polymorphisms, five genes per QTL were selected for further study by sequencing analysis and qRT-PCR. Tumor necrosis factor, alpha- induced protein 3 (Tnfaip3; on a C57BL/6J (B6) background) was phenotypically tested. Single nucleotide polymorphisms (SNPs) flanking this gene were correlated with outer nuclear layer thickness (ONL), and eight-month-old Tnfaip3(+/-) mice were tested for ageRD. RESULTS: Polymorphisms were found in the coding regions of eight genes. Changes in gene expression were identified by qRT-PCR for Hexokinase 2 (Hk2) and Docking protein 1 (Dok1) at four months and for Dok1 and Tnfaip3 at eight months. Tnfaip3 was selected for phenotypic testing due to differential expression and the presence of two nonsynonymous mutations. However, when ONL thickness was compared in eight-month-old congenic Tnfaip3(+/-) and Tnfaip3(+/+) mice, no differences were found, suggesting that Tnfaip3 is not the quantitative trait gene (QTG) for the Chr 10 QTL. The GO analysis revealed that GO terms associated with stress and cell remodeling are overrepresented in the ageRD-sensitive C strain compared with the B6a strain with age (eight months). In the ageRD-resistant B6a strain, compared with the C strain, GO terms associated with antioxidant response and the regulation of blood vessel size are overrepresented with age. CONCLUSIONS: The analyses of differentially expressed genes and the PosMed database yielded candidate genes for the Chr 6 and Chr 10 QTL. HtrA serine peptidase 2 (Htra2), Dok1, and Tnfaip3 were deemed most promising because of their known roles in apoptosis and our finding of nonsynonymous substitutions between B6a and C strains. While Tnfaip3 was excluded as the QTG for the Chr 10 QTL, Dok1 and Htra2 remain good candidates for the Chr 6 QTL. Finally, the GO term analysis further supports the general hypothesis that oxidative stress is involved in ageRD.

GenMAPP 2: new features and resources for pathway analysis.

BACKGROUND: Microarray technologies have evolved rapidly, enabling biologists to quantify genome-wide levels of gene expression, alternative splicing, and sequence variations for a variety of species. Analyzing and displaying these data present a significant challenge. Pathway-based approaches for analyzing microarray data have proven useful for presenting data and for generating testable hypotheses. RESULTS: To address the growing needs of the microarray community we have released version 2 of Gene Map Annotator and Pathway Profiler (GenMAPP), a new GenMAPP database schema, and integrated resources for pathway analysis. We have redesigned the GenMAPP database to support multiple gene annotations and species as well as custom species database creation for a potentially unlimited number of species. We have expanded our pathway resources by utilizing homology information to translate pathway content between species and extending existing pathways with data derived from conserved protein interactions and coexpression. We have implemented a new mode of data visualization to support analysis of complex data, including time-course, single nucleotide polymorphism (SNP), and splicing. GenMAPP version 2 also offers innovative ways to display and share data by incorporating HTML export of analyses for entire sets of pathways as organized web pages. CONCLUSION: GenMAPP version 2 provides a means to rapidly interrogate complex experimental data for pathway-level changes in a diverse range of organisms.

Using GenMAPP and MAPPFinder to view microarray data on biological pathways and identify global trends in the data.

GenMAPP (Gene MicroArray Pathway Profiler) is a free, stand-alone computer program designed for viewing and analyzing gene expression data on MAPPs representing biological pathways or any other functional grouping of genes. A MAPP is a special file format produced with the graphics tools in GenMAPP that depicts the biological relationship between genes or gene products. When a MAPP is linked to an expression dataset, GenMAPP automatically and dynamically color-codes the genes on the MAPP according to criteria supplied by the user. MAPPFinder is an accessory program that works with GenMAPP and the annotations from the Gene Ontology (GO) Consortium to identify global biological trends in gene expression data. MAPPFinder relates the microarray dataset to the GO hierarchy and calculates a percentage and statistical score for genes meeting the user's criterion for a meaningful gene expression change for each GO biological process, cellular component, and molecular function term.

MAPPFinder: using Gene Ontology and GenMAPP to create a global gene-expression profile from microarray data.

MAPPFinder is a tool that creates a global gene-expression profile across all areas of biology by integrating the annotations of the Gene Ontology (GO) Project with the free software package GenMAPP http://www.GenMAPP.org. The results are displayed in a searchable browser, allowing the user to rapidly identify GO terms with over-represented numbers of gene-expression changes. Clicking on GO terms generates GenMAPP graphical files where gene relationships can be explored, annotated, and files can be freely exchanged.

Regression approaches for microarray data analysis.

A variety of new procedures have been devised to handle the two-sample comparison (e.g., tumor versus normal tissue) of gene expression values as measured with microarrays. Such new methods are required in part because of some defining characteristics of microarray-based studies: (i) the very large number of genes contributing expression measures which far exceeds the number of samples (observations) available and (ii) the fact that by virtue of pathway/network relationships, the gene expression measures tend to be highly correlated. These concerns are exacerbated in the regression setting, where the objective is to relate gene expression, simultaneously for multiple genes, to some external outcome or phenotype. Correspondingly, several methods have been recently proposed for addressing these issues. We briefly critique some of these methods prior to a detailed evaluation of gene harvesting. This reveals that gene harvesting, without additional constraints, can yield artifactual solutions. Results obtained employing such constraints motivate the use of regularized regression procedures such as the lasso, least angle regression, and support vector machines. Model selection and solution multiplicity issues are also discussed. The methods are evaluated using a microarray-based study of cardiomyopathy in transgenic mice.