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. CONCLUSION 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.

中文翻译：

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差异调节基因转录谱的统计建模。

背景技术在微阵列研究中产生的大量基因表达谱数据以及更精确的定量PCR，通常没有充分发挥其潜力进行统计分析。以前的研究已经使用简单的描述性统计、基本方差分析 (ANOVA) 和基于适合其表达谱随时间推移的简单模型的基因聚类来总结基因表达谱。我们报告了统计非线性回归建模技术的新应用，以描述真菌双孢蘑菇（通过 PCR 量化）和大肠杆菌和褐家鼠（使用微阵列技术）的表达谱形状。参数非线性回归模型的使用提供了更精确的表达谱描述，减少了“噪音” 原始数据以产生由拟合曲线给出的清晰“信号”，并用少量生物学可解释参数描述每个轮廓。这种方法可以直接比较和聚类基因之间反应模式的形状，并有可能对驱动基因表达的生物过程进行更大的探索和解释。结果 对基因的定量逆转录酶 PCR 衍生的时间进程数据进行建模。“分割线”或“折线”回归确定了基因上调的初始时间，从而能够将基因分类为具有初级和次级反应的基因。使用面向生物学的临界指数曲线，y(t) = A + (B + Ct)Rt + epsilon 对五天剖面进行建模。这种非线性回归方法允许在曲线形状、最大转录水平的时间以及下降和渐近反应水平方面比较不同基因的表达模式。为研究的五个基因确定了三个不同的调节模式。将回归建模方法应用于微阵列衍生的时间过程数据允许 11% 的大肠杆菌特征由指数函数拟合，25% 的褐家鼠特征可以由临界指数模型描述，所有这些都具有统计显着性p < 0.05。结论 本研究中提出的统计非线性回归方法提供了个体基因表达谱的详细生物学导向描述，使用生物学变量数据生成一组定义参数。这些方法可应用于建模和更好地解释在各种平台（例如微阵列）上获得的配置文件。通过仔细选择合适的模型形式，这种统计回归方法可以改进基因表达谱的比较，并可能为更好地理解基因之间的共同调控机制提供一种方法。