Gene regulation networks are composed of transcription factors, their interactions, and targets. It is of great interest to reconstruct and study these regulatory networks from genomics data. Ordinary differential equations (ODEs) are popular tools to model the dynamic system of gene regulation networks. Although the form of ODEs is often provided based on expert knowledge, the values for ODE parameters are seldom known. It is a challenging problem to infer ODE parameters from gene expression data, because the ODEs do not have analytic solutions and the time-course gene expression data are usually sparse and associated with large noise. In this chapter, we review how the generalized profiling method can be applied to obtain estimates for ODE parameters from the time-course gene expression data. We also summarize the consistency and asymptotic normality results for the generalized profiling estimates.
Dynamic system Gene regulation network Generalized profiling method Spline smoothing Systems biology Time-course gene expression
This is a preview of subscription content, log in to check access.
Springer Nature is developing a new tool to find and evaluate Protocols. Learn more
Qi and Zhao’s research is supported by NIH grant GM 59507 and NSF grant DMS-0714817. Cao’s research is supported by a discovery grant of the Natural Sciences and Engineering Research Council (NSERC) of Canada. The authors thank the invitation from the editors of this book.
Alon U (2007) An introduction to systems biology. Chapman & Hall/CRC, London.Google Scholar
Sun N, Zhao H (2009) Reconstructing transcriptional regulatory networks through genomics data. Statistical Methods in Medical Research 18:595–617.PubMedCrossRefGoogle Scholar
Mangan S, Alon U (2003) Structure and function of the feed-forward loop network motif. Proceeding of the National Academy of Sciences 100:11980–11985.CrossRefGoogle Scholar
Stolovitzky G, Monroe D, Califano A (2007) Dialogue on reverseengineering assessment and methods: The dream of high-throughput pathway inference. Annals of the New York Academy of Sciences 1115:11–22.Google Scholar
Stolovitzky G, Prill RJ, Califano A (2009) Lessons from the dream2 challenges. Annals of the New York Academy of Sciences 1158:159–195.PubMedCrossRefGoogle Scholar
Prill RJ, Marbach D, Saez-Rodriguez J et al (2010) Towards a rigorous assessment of systems biology models: the dream3 challenges. PLoS One 5:e9202.PubMedCrossRefGoogle Scholar
Chen J, Wu H (2008) Efficient local estimation for time-varying coefficients in deterministic dynamic models with applications to HIV-1 dynamics. Journal of the American Statistical Association 103(481):369–383.CrossRefGoogle Scholar
Ramsay JO, Hooker G, Campbell D et al (2007) Parameter estimation for differential equations: a generalized smoothing approach (with discussion). Journal of the Royal Statistical Society, Series B 69:741–796.CrossRefGoogle Scholar
Qi X, Zhao H (2010) Asymptotic efficiency and finite-sample properties of the generalized profiling estimation of parameters in ordinary differential equations. The Annals of Statistics 38:435–481.CrossRefGoogle Scholar
Wang R, Wang Y, Zhang X et al (2007) Inferring transcriptional regulatory networks from high-throughput data. Bioinformatics 23:3056–3064.PubMedCrossRefGoogle Scholar
Rogers S, Khanin R, Girolami M (2007) Bayesian model-based inference of transcription factor activity. BMC Bioinformatics 8:1–11.CrossRefGoogle Scholar
Gao P, Honkela A, Rattray M et al (2008) Genomic expression programs in the response of yeast cells to environmental changes. Bioinformatics 24:i70–i75.PubMedCrossRefGoogle Scholar
Aijo T, Lahdesmaki H (2009) Learning gene regulatory networks from gene expression measurements using non-parametric molecular kinetics. Bioinformatics 25:2937–2944.PubMedCrossRefGoogle Scholar
Kirk PDW, Stumpf MPH (2009) Gaussian process regression bootstrapping: exploring the effects of uncertainty in time course data. Bioinformatics 25:1300–1306.PubMedCrossRefGoogle Scholar
Gennemark P, Wedelin D (2009) Benchmarks for identification of ordinary differential equations from time series data. Bioinformatics 25:780–786.PubMedCrossRefGoogle Scholar