title: 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.
authors.affiliation: Department of Biology, Loyola Marymount University, 1 LMU Drive, MS 8888, Los Angeles, CA, 90045, USA. kdahlquist@lmu.edu.
authors.forename: Kam D
authors.identifier: http://orcid.org/0000-0003-1973-3311
authors.initials: KD
authors.lastname: Dahlquist
authors.affiliation: Department of Mathematics, Loyola Marymount University, 1 LMU Drive, UH 2700, Los Angeles, CA, 90045, USA.
authors.forename: Ben G
authors.initials: BG
authors.lastname: Fitzpatrick
authors.affiliation: School of Mathematical and Natural Sciences, Arizona State University, Mail Code 2352, P.O. Box 37100, Phoenix, AZ, 85069-7100, USA.
authors.forename: Erika T
authors.initials: ET
authors.lastname: Camacho
authors.affiliation: Department of Mathematics, Loyola Marymount University, 1 LMU Drive, UH 2700, Los Angeles, CA, 90045, USA.
authors.forename: Stephanie D
authors.initials: SD
authors.lastname: Entzminger
authors.affiliation: Department of Mathematics, Loyola Marymount University, 1 LMU Drive, UH 2700, Los Angeles, CA, 90045, USA.
authors.forename: Nathan C
authors.initials: NC
authors.lastname: Wanner
mesh_terms: D058639:Cold-Shock Response / Q000235:genetics; D053263:Gene Regulatory Networks; D016681:Genome, Fungal; D016018:Least-Squares Analysis; D055641:Mathematical Concepts; D008957:Models, Genetic; D020411:Oligonucleotide Array Sequence Analysis / Q000706:statistics & numerical data; D012441:Saccharomyces cerevisiae / Q000235:genetics*
keywords: Dynamic network model; Penalized least squares