LEMming: A Linear Error Model to Normalize Parallel Quantitative Real-Time PCR (qPCR) Data as an Alternative to Reference Gene Based Methods

BackgroundGene expression analysis is an essential part of biological and medical investigations. Quantitative real-time PCR (qPCR) is characterized with excellent sensitivity, dynamic range, reproducibility and is still regarded to be the gold standard for quantifying transcripts abundance. Parallelization of qPCR such as by microfluidic Taqman Fluidigm Biomark Platform enables evaluation of multiple transcripts in samples treated under various conditions. Despite advanced technologies, correct evaluation of the measurements remains challenging. Most widely used methods for evaluating or calculating gene expression data include geNorm and ΔΔCt, respectively. They rely on one or several stable reference genes (RGs) for normalization, thus potentially causing biased results. We therefore applied multivariable regression with a tailored error model to overcome the necessity of stable RGs.ResultsWe developed a RG independent data normalization approach based on a tailored linear error model for parallel qPCR data, called LEMming. It uses the assumption that the mean Ct values within samples of similarly treated groups are equal. Performance of LEMming was evaluated in three data sets with different stability patterns of RGs and compared to the results of geNorm normalization. Data set 1 showed that both methods gave similar results if stable RGs are available. Data set 2 included RGs which are stable according to geNorm criteria, but became differentially expressed in normalized data evaluated by a t-test. geNorm-normalized data showed an effect of a shifted mean per gene per condition whereas LEMming-normalized data did not. Comparing the decrease of standard deviation from raw data to geNorm and to LEMming, the latter was superior. In data set 3 according to geNorm calculated average expression stability and pairwise variation, stable RGs were available, but t-tests of raw data contradicted this. Normalization with RGs resulted in distorted data contradicting literature, while LEMming normalized data did not.ConclusionsIf RGs are coexpressed but are not independent of the experimental conditions the stability criteria based on inter- and intragroup variation fail. The linear error model developed, LEMming, overcomes the dependency of using RGs for parallel qPCR measurements, besides resolving biases of both technical and biological nature in qPCR. However, to distinguish systematic errors per treated group from a global treatment effect an additional measurement is needed. Quantification of total cDNA content per sample helps to identify systematic errors.

背景
基因表达分析是生物学与医学研究的核心组成部分。实时定量聚合酶链反应（quantitative real-time PCR，qPCR）以优异的灵敏度、动态范围与重现性为显著特征，至今仍是转录本丰度定量的金标准。通过微流体Taqman Fluidigm Biomark平台等方式实现qPCR的并行化，可对不同处理条件下的样本中的多种转录本进行检测评估。尽管相关技术已较为先进，但对检测结果的准确评估仍存在挑战。目前应用最为广泛的基因表达数据评估与定量方法分别为geNorm法与ΔΔCt法，这类方法均依赖一个或多个稳定的持家基因（reference genes，RGs）进行归一化处理，因此可能引入偏差，导致结果失真。为此，本研究采用搭载定制化误差模型的多变量回归方法，以摆脱对稳定持家基因的依赖。

结果
本研究开发了一种不依赖持家基因的并行qPCR数据归一化方法，基于定制化线性误差模型，命名为LEMming。该方法假设：经相似实验处理的各组样本内，其平均Ct值相等。我们选取三组具有不同持家基因稳定性特征的数据集，对LEMming的性能进行验证，并与geNorm归一化法的结果展开对比。数据集1的结果表明：当存在可用的稳定持家基因时，两种方法的输出结果高度一致。数据集2中的持家基因虽符合geNorm的稳定性判定标准，但通过t检验分析归一化后的数据时发现，这些基因出现了差异表达现象。经geNorm归一化的数据呈现出「每个基因在各处理条件下的均值发生偏移」的特征，而经LEMming归一化的数据则无此异常。对比原始数据经geNorm与LEMming归一化后的标准差降幅，LEMming的归一化效果更优。数据集3中，基于geNorm计算得到的平均表达稳定性与配对变异值，理论上存在可用的稳定持家基因，但原始数据的t检验结果却与此相悖。使用持家基因进行归一化会导致数据失真，与已有文献结论相悖，而经LEMming归一化后的结果则无此问题。

结论
若持家基因存在共表达现象，且其表达水平并非不受实验条件影响，则基于组间与组内变异的稳定性判定标准将失效。本研究开发的线性误差模型方法LEMming，不仅解决了并行qPCR检测对持家基因的依赖问题，同时还可校正qPCR检测中存在的技术与生物学偏差。不过，若要区分各处理组的系统误差与全局处理效应，仍需开展额外的检测实验。对每个样本的总cDNA含量进行定量，有助于识别系统误差。