Mathematical model of real-time PCR kinetics

Several real-time PCR (rtPCR) quantification techniques are currently used to determine the expression levels of individual genes from rtPCR data in the form of fluorescence intensities. In most of these quantification techniques, it is assumed that the efficiency of rtPCR is constant. Our analysis of rtPCR data shows, however, that even during the exponential phase of rtPCR, the efficiency of the reaction is not constant, but is instead a function of cycle number. In order to understand better the mechanisms belying this behavior, we have developed a mathematical model of the annealing and extension phases of the PCR process. Using the model, we can simulate the PCR process over a series of reaction cycles. The model thus allows us to predict the efficiency of rtPCR at any cycle number, given a set of initial conditions and parameter values, which can mostly be estimated from biophysical data. The model predicts a precipitous decrease in cycle efficiency when the product concentration reaches a sufficient level for template-template re-annealing to compete with primer-template annealing; this behavior is consistent with available experimental data. The quantitative understanding of rtPCR provided by this model can allow us to develop more accurate methods to quantify gene expression levels from rtPCR data.     

Real-time PCR quantification of precursor and mature microRNA

microRNAs (miRNAs) are challenging molecules to amplify by PCR because the miRNA precursor consists of a stable hairpin and the mature miRNA is roughly the size of a standard PCR primer. Despite these difficulties, successful real-time RT-PCR technologies have been developed to amplify and quantify both the precursor and mature microRNA. An overview of real-time PCR technologies developed by us to detect precursor and mature microRNAs is presented here. Protocols describe presentation of the data using relative (comparative C(T)) and absolute (standard curve) quantification. Real-time PCR assays were used to measure the time course of precursor and mature miR-155 expression in monocytes stimulated by lipopolysaccharide. Protocols are provided to configure the assays as low density PCR arrays for high throughput gene expression profiling. By profiling over 200 precursor and mature miRNAs in HL60 cells induced to differentiate with 12-O-tetradecanoylphorbol-13-acetate, it was possible to identify miRNAs who's processing is regulated during differentiation. Real-time PCR has become the gold standard of nucleic acid quantification due to the specificity and sensitivity of the PCR. Technological advancements have allowed for quantification of miRNA that is of comparable quality to more traditional RNAs.     

New real-time quantitative PCR procedure for quantification of bifidobacteria in human fecal samples

The application of a real-time quantitative PCR method (5' nuclease assay), based on the use of a probe labeled at its 5' end with a stable, fluorescent lanthanide chelate, for the quantification of human fecal bifidobacteria was evaluated. The specificities of the primers and the primer-probe combination were evaluated by conventional PCR and real-time PCR, respectively. The results obtained by real-time PCR were compared with those obtained by fluorescent in situ hybridization, the current gold standard for intestinal microbiota quantification. In general, a good correlation between the two methods was observed. In order to determine the detection limit and the accuracy of the real-time PCR procedure, germfree rat feces were spiked with known amounts of bifidobacteria and analyzed by both methods. The detection limit of the method used in this study was found to be about 5 x 10(4) cells per g of feces. Both methods, real-time PCR and fluorescent in situ hybridization, led to an accurate quantification of the spiked samples with high levels of bifidobacteria, but real-time PCR was more accurate for samples with low levels. We conclude that the real-time PCR procedure described here is a specific, accurate, rapid, and easy method for the quantification of bifidobacteria in feces.     

New Real-Time Quantitative PCR Procedure for Quantification of Bifidobacteria in Human Fecal Samples

The application of a real-time quantitative PCR method (5′ nuclease assay), based on the use of a probe labeled at its 5′ end with a stable, fluorescent lanthanide chelate, for the quantification of human fecal bifidobacteria was evaluated. The specificities of the primers and the primer-probe combination were evaluated by conventional PCR and real-time PCR, respectively. The results obtained by real-time PCR were compared with those obtained by fluorescent in situ hybridization, the current gold standard for intestinal microbiota quantification. In general, a good correlation between the two methods was observed. In order to determine the detection limit and the accuracy of the real-time PCR procedure, germfree rat feces were spiked with known amounts of bifidobacteria and analyzed by both methods. The detection limit of the method used in this study was found to be about 5 × 10⁴ cells per g of feces. Both methods, real-time PCR and fluorescent in situ hybridization, led to an accurate quantification of the spiked samples with high levels of bifidobacteria, but real-time PCR was more accurate for samples with low levels. We conclude that the real-time PCR procedure described here is a specific, accurate, rapid, and easy method for the quantification of bifidobacteria in feces.     

Statistical methods for efficiency adjusted real-time PCR quantification

The statistical treatment for hypothesis testing using real-time PCR data is a challenge for quantification of gene expression. One has to consider two key factors in precise statistical analysis of real-time PCR data: a well-defined statistical model and the integration of amplification efficiency (AE) into the model. Previous publications in real-time PCR data analysis often fall short in integrating the AE into the model. Novel, user-friendly, and universal AE-integrated statistical methods were developed for real-time PCR data analysis with four goals. First, we addressed the definition of AE, introduced the concept of efficiency-adjusted Delta Delta Ct, and developed a general mathematical method for its calculation. Second, we developed several linear combination approaches for the estimation of efficiency adjusted Delta Delta Ct and statistical significance for hypothesis testing based on different mathematical formulae and experimental designs. Statistical methods were also adopted to estimate the AE and its equivalence among the samples. A weighted Delta Delta Ct method was introduced to analyze the data with multiple internal controls. Third, we implemented the linear models with SAS programs and analyzed a set of data for each model. In order to allow other researchers to use and compare different approaches, SAS programs are included in the Supporting Information. Fourth, the results from analysis of different statistical models were compared and discussed. Our results underline the differences between the efficiency adjusted Delta Delta Ct methods and previously published methods, thereby better identifying and controlling the source of errors introduced by real-time PCR data analysis.     

Evaluation of quantification methods for real-time PCR minor groove binding hybridization probe assays

Real-time PCR data analysis for quantification has been the subject of many studies aimed at the identification of new and improved quantification methods. Several analysis methods have been proposed as superior alternatives to the common variations of the threshold crossing method. Notably, sigmoidal and exponential curve fit methods have been proposed. However, these studies have primarily analyzed real-time PCR with intercalating dyes such as SYBR Green. Clinical real-time PCR assays, in contrast, often employ fluorescent probes whose real-time amplification fluorescence curves differ from those of intercalating dyes. In the current study, we compared four analysis methods related to recent literature: two versions of the threshold crossing method, a second derivative maximum method, and a sigmoidal curve fit method. These methods were applied to a clinically relevant real-time human herpes virus type 6 (HHV6) PCR assay that used a minor groove binding (MGB) Eclipse hybridization probe as well as an Epstein-Barr virus (EBV) PCR assay that used an MGB Pleiades hybridization probe. We found that the crossing threshold method yielded more precise results when analyzing the HHV6 assay, which was characterized by lower signal/noise and less developed amplification curve plateaus. In contrast, the EBV assay, characterized by greater signal/noise and amplification curves with plateau regions similar to those observed with intercalating dyes, gave results with statistically similar precision by all four analysis methods.     

实时荧光定量PCR的发展和数据分析

实时荧光定量PCR技术是基因时代一项用于检测mRNA的常用技术,是临床检测和基础研究中不可缺少的重要研究方法,包括绝对定量PCR和相对定量PCR。该技术的特点是可以减少PCR后操作,在比较不同浓度的mRNA方面具有非常宽的动力学范围。我们就目前实时荧光定量PCR的发展及数据的分析进行综述。     

基于SYBR Green I的双链DNA定量方法

摘要 基于SYBR Green I荧光染料与双链DNA（dsDNA）结合产生荧光的原理,建立一种高精度、高通量的双链DNA 定量方法。将梯度稀释后的基因组DNA及已知浓度的?DNA与等体积的SYBR Green I（4×）充分混合后,利用荧光定量PCR仪采集荧光信号,以ROX（1×）作为校正染料进行定量分析;同时利用紫外分光光度计对样品进行平行测定,比较该方法与紫外分光光度法的检测限与准确度。紫外分光光度法的检测限为2 ng/?l,而SYBR Green I荧光定量法的检测限可达到0.015 ng/?l,并且在0.015~2 ng/?l范围内,SYBR Green I荧光强度与?DNA浓度呈线性关系（R2=0.9999）,比紫外分光光度法灵敏100倍以上,并可准确定量低纯度的DNA样品。此方法具有重复性好、高通量的特点,仅需少量的生物样本即可满足定量要求,为分子生物学研究及临床检验等多个领域提供了一种可靠的dsDNA定量方法。     

Enhanced analysis of real-time PCR data by using a variable efficiency model: FPK-PCR

Current methodology in real-time Polymerase chain reaction (PCR) analysis performs well provided PCR efficiency remains constant over reactions. Yet, small changes in efficiency can lead to large quantification errors. Particularly in biological samples, the possible presence of inhibitors forms a challenge. We present a new approach to single reaction efficiency calculation, called Full Process Kinetics-PCR (FPK-PCR). It combines a kinetically more realistic model with flexible adaptation to the full range of data. By reconstructing the entire chain of cycle efficiencies, rather than restricting the focus on a 'window of application', one extracts additional information and loses a level of arbitrariness. The maximal efficiency estimates returned by the model are comparable in accuracy and precision to both the golden standard of serial dilution and other single reaction efficiency methods. The cycle-to-cycle changes in efficiency, as described by the FPK-PCR procedure, stay considerably closer to the data than those from other S-shaped models. The assessment of individual cycle efficiencies returns more information than other single efficiency methods. It allows in-depth interpretation of real-time PCR data and reconstruction of the fluorescence data, providing quality control. Finally, by implementing a global efficiency model, reproducibility is improved as the selection of a window of application is avoided.     

Another formula for calculating the gene change rate in real-time RT-PCR

Relative quantification real-time PCR has become a routine method in molecular biology research to study the small amount gene expression. There are a few mathematical models for relative quantification data analysis in real-time PCR, and the formula 2^−∆∆CT is one of the most frequently used method. In this paper, we are to present another equation which directly calculates the change rate (R _c) of gene expression, and give a example to compare the application of this model with 2^−∆∆CT.     

Development of a temperature sensor array chip and a chip-based real-time PCR machine for DNA amplification efficiency-based quantification

A temperature sensor array chip was developed to monitor the thermal cycling profiles of a polymerase chain reaction (PCR). DNA amplification efficiency of each cycle was estimated through temperature data to fit the stochastic model. A fluorescence detector system was constructed to detect the PCR amplifications of latter cycles, at which the fluorescence intensity passed the optical detection threshold. Through monitoring of both temperature and fluorescence, DNA amplification efficiency curve was completed for quantification. The F?rster resonance energy transfer (FRET) was employed to detect the measurements of the PCR product amount at the reaction endpoint. The chip-based, real-time PCR machine was constructed to perform the amplification efficiency curve-based quantification method. This novel method achieved the absolute quantification of the Hepatitis B virus (HBV) DNA using a single sample without the construction of the standard curve. The coefficient of variation (CV) of the 15 replicates inter assay experiments was less than 5.87%. Compared with the CV values obtained from the commercial machine in the range of 4.33-14.56%, it is noted that CV values of the prototype with respect to the samples of different initial concentration ranging from 10(7) to 10(3)copies/ml are almost equable.     

Real-time quantification of microRNAs by stem-loop RT-PCR

A novel microRNA (miRNA) quantification method has been developed using stem-loop RT followed by TaqMan PCR analysis. Stem-loop RT primers are better than conventional ones in terms of RT efficiency and specificity. TaqMan miRNA assays are specific for mature miRNAs and discriminate among related miRNAs that differ by as little as one nucleotide. Furthermore, they are not affected by genomic DNA contamination. Precise quantification is achieved routinely with as little as 25 pg of total RNA for most miRNAs. In fact, the high sensitivity, specificity and precision of this method allows for direct analysis of a single cell without nucleic acid purification. Like standard TaqMan gene expression assays, TaqMan miRNA assays exhibit a dynamic range of seven orders of magnitude. Quantification of five miRNAs in seven mouse tissues showed variation from less than 10 to more than 30,000 copies per cell. This method enables fast, accurate and sensitive miRNA expression profiling and can identify and monitor potential biomarkers specific to tissues or diseases. Stem-loop RT-PCR can be used for the quantification of other small RNA molecules such as short interfering RNAs (siRNAs). Furthermore, the concept of stem-loop RT primer design could be applied in small RNA cloning and multiplex assays for better specificity and efficiency.