title: Statistical modelling of transcript profiles of differentially regulated genes.
abstract: BACKGROUND
  The vast quantities of gene expression profiling data produced in microarray studies, and the more precise quantitative PCR, are often not statistically analysed to their full potential. Previous studies have summarised gene expression profiles using simple descriptive statistics, basic analysis of variance (ANOVA) and the clustering of genes based on simple models fitted to their expression profiles over time. We report the novel application of statistical non-linear regression modelling techniques to describe the shapes of expression profiles for the fungus Agaricus bisporus, quantified by PCR, and for E. coli and Rattus norvegicus, using microarray technology. The use of parametric non-linear regression models provides a more precise description of expression profiles, reducing the "noise" of the raw data to produce a clear "signal" given by the fitted curve, and describing each profile with a small number of biologically interpretable parameters. This approach then allows the direct comparison and clustering of the shapes of response patterns between genes and potentially enables a greater exploration and interpretation of the biological processes driving gene expression.
  
  
  RESULTS
  Quantitative reverse transcriptase PCR-derived time-course data of genes were modelled. "Split-line" or "broken-stick" regression identified the initial time of gene up-regulation, enabling the classification of genes into those with primary and secondary responses. Five-day profiles were modelled using the biologically-oriented, critical exponential curve, y(t) = A + (B + Ct)Rt + epsilon. This non-linear regression approach allowed the expression patterns for different genes to be compared in terms of curve shape, time of maximal transcript level and the decline and asymptotic response levels. Three distinct regulatory patterns were identified for the five genes studied. Applying the regression modelling approach to microarray-derived time course data allowed 11% of the Escherichia coli features to be fitted by an exponential function, and 25% of the Rattus norvegicus features could be described by the critical exponential model, all with statistical significance of p < 0.05.
  
  
  CONCLUSIONS
  The statistical non-linear regression approaches presented in this study provide detailed biologically oriented descriptions of individual gene expression profiles, using biologically variable data to generate a set of defining parameters. These approaches have application to the modelling and greater interpretation of profiles obtained across a wide range of platforms, such as microarrays. Through careful choice of appropriate model forms, such statistical regression approaches allow an improved comparison of gene expression profiles, and may provide an approach for the greater understanding of common regulatory mechanisms between genes.
authors.affiliation: Warwick HRI, University of Warwick, Wellesbourne, Warwickshire, CV35 9EF, UK. daniel.eastwood@warwick.ac.uk
authors.forename: Daniel C
authors.initials: DC
authors.lastname: Eastwood
authors.forename: Andrew
authors.initials: A
authors.lastname: Mead
authors.forename: Martin J
authors.initials: MJ
authors.lastname: Sergeant
authors.forename: Kerry S
authors.initials: KS
authors.lastname: Burton
mesh_terms: D000364:Agaricus / Q000235:genetics; D000818:Animals; D015152:Blotting, Northern; D004926:Escherichia coli / Q000235:genetics; D020869:Gene Expression Profiling / Q000706:statistics & numerical data*; D005786:Gene Expression Regulation / Q000235:genetics*; D005796:Genes / Q000235:genetics; D007700:Kinetics; D015233:Models, Statistical; D020411:Oligonucleotide Array Sequence Analysis; D012333:RNA, Messenger / Q000032:analysis; D051381:Rats / Q000235:genetics; D012044:Regression Analysis
chemical_list: D012333:RNA, Messenger