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

Kam D. Dahlquist, Ben G. Fitzpatrick, Erika Camacho, Stephanie D. Entzminger, Nathan C. Wanner

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1457-1492
Number of pages36
JournalBulletin of Mathematical Biology
Volume77
Issue number8
DOIs
StatePublished - Sep 29 2015

Fingerprint

Cold-Shock Response
Gene Regulatory Networks
Gene Regulatory Network
Saccharomyces Cerevisiae
Microarrays
Microarray Data
Yeast
Parameter estimation
Saccharomyces cerevisiae
Parameter Estimation
Shock
Transcription Factor
Transcription factors
Transcription Factors
Genes
gene
transcription factors
Activation
Weights and Measures
Saccharomycetales

Keywords

  • Dynamic network model
  • Penalized least squares

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Environmental Science(all)
  • Immunology
  • Mathematics(all)
  • Computational Theory and Mathematics
  • Neuroscience(all)
  • Pharmacology

Cite this

Parameter Estimation for Gene Regulatory Networks from Microarray Data : Cold Shock Response in Saccharomyces cerevisiae. / Dahlquist, Kam D.; Fitzpatrick, Ben G.; Camacho, Erika; Entzminger, Stephanie D.; Wanner, Nathan C.

In: Bulletin of Mathematical Biology, Vol. 77, No. 8, 29.09.2015, p. 1457-1492.

Research output: Contribution to journalArticle

Dahlquist, Kam D. ; Fitzpatrick, Ben G. ; Camacho, Erika ; Entzminger, Stephanie D. ; Wanner, Nathan C. / Parameter Estimation for Gene Regulatory Networks from Microarray Data : Cold Shock Response in Saccharomyces cerevisiae. In: Bulletin of Mathematical Biology. 2015 ; Vol. 77, No. 8. pp. 1457-1492.
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