A kinetic-based sigmoidal model for the polymerase chain reaction and its application to high-capacity absolute quantitative real-time PCR

Background

Based upon defining a common reference point, current real-time quantitative PCR technologies compare relative differences in amplification profile position. As such, absolute quantification requires construction of target-specific standard curves that are highly resource intensive and prone to introducing quantitative errors. Sigmoidal modeling using nonlinear regression has previously demonstrated that absolute quantification can be accomplished without standard curves; however, quantitative errors caused by distortions within the plateau phase have impeded effective implementation of this alternative approach.

Results

Recognition that amplification rate is linearly correlated to amplicon quantity led to the derivation of two sigmoid functions that allow target quantification via linear regression analysis. In addition to circumventing quantitative errors produced by plateau distortions, this approach allows the amplification efficiency within individual amplification reactions to be determined. Absolute quantification is accomplished by first converting individual fluorescence readings into target quantity expressed in fluorescence units, followed by conversion into the number of target molecules via optical calibration. Founded upon expressing reaction fluorescence in relation to amplicon DNA mass, a seminal element of this study was to implement optical calibration using lambda gDNA as a universal quantitative standard. Not only does this eliminate the need to prepare target-specific quantitative standards, it relegates establishment of quantitative scale to a single, highly defined entity. The quantitative competency of this approach was assessed by exploiting "limiting dilution assay" for absolute quantification, which provided an independent gold standard from which to verify quantitative accuracy. This yielded substantive corroborating evidence that absolute accuracies of ± 25% can be routinely achieved. Comparison with the LinReg and Miner automated qPCR data processing packages further demonstrated the superior performance of this kinetic-based methodology.

Conclusion

Called "linear regression of efficiency" or LRE, this novel kinetic approach confers the ability to conduct high-capacity absolute quantification with unprecedented quality control capabilities. The computational simplicity and recursive nature of LRE quantification also makes it amenable to software implementation, as demonstrated by a prototypic Java program that automates data analysis. This in turn introduces the prospect of conducting absolute quantification with little additional effort beyond that required for the preparation of the amplification reactions.     

A method for quantification of absolute amounts of nucleic acids by (RT)-PCR and a new mathematical model for data analysis

Accurate quantification of nucleic acids by competitive (RT)-PCR requires a valid internal standard, a reference for data normalization and an adequate mathematical model for data analysis. We report here an effective procedure for the generation of homologous RNA internal standards and a strategy for synthesizing and using a reference target RNA in quantification of absolute amounts of nucleic acids. Further, a new mathematical model describing the general kinetic features of competitive PCR was developed. The model extends the validity of quantitative competitive (RT)-PCR beyond the exponential phase. The new method eliminates the errors arising from different amplification efficiencies of the co-amplified sequences and from heteroduplex formation in the system. The high accuracy (relative error <2%) is comparable to the recently developed real time detection 5'-nuclease PCR. Also, corresponding computer software has been devised for practical data analysis.     

A method for quantification of absolute amounts of nucleic acids by (RT)–PCR and a new mathematical model for data analysis

Accurate quantification of nucleic acids by competitive (RT)–PCR requires a valid internal standard, a reference for data normalization and an adequate mathematical model for data analysis. We report here an effective procedure for the generation of homologous RNA internal standards and a strategy for synthesizing and using a reference target RNA in quantification of absolute amounts of nucleic acids. Further, a new mathematical model describing the general kinetic features of competitive PCR was developed. The model extends the validity of quantitative competitive (RT)–PCR beyond the exponential phase. The new method eliminates the errors arising from different amplification efficiencies of the co-amplified sequences and from heteroduplex formation in the system. The high accuracy (relative error <2%) is comparable to the recently developed real time detection 5′-nuclease PCR. Also, corresponding computer software has been devised for practical data analysis.     

Kinetic Outlier Detection (KOD) in real-time PCR

Real-time PCR is becoming the method of choice for precise quantification of minute amounts of nucleic acids. For proper comparison of samples, almost all quantification methods assume similar PCR efficiencies in the exponential phase of the reaction. However, inhibition of PCR is common when working with biological samples and may invalidate the assumed similarity of PCR efficiencies. Here we present a statistical method, Kinetic Outlier Detection (KOD), to detect samples with dissimilar efficiencies. KOD is based on a comparison of PCR efficiency, estimated from the amplification curve of a test sample, with the mean PCR efficiency of samples in a training set. KOD is demonstrated and validated on samples with the same initial number of template molecules, where PCR is inhibited to various degrees by elevated concentrations of dNTP; and in detection of cDNA samples with an aberrant ratio of two genes. Translating the dissimilarity in efficiency to quantity, KOD identifies outliers that differ by 1.3–1.9-fold in their quantity from normal samples with a P-value of 0.05. This precision is higher than the minimal 2-fold difference in number of DNA molecules that real-time PCR usually aims to detect. Thus, KOD may be a useful tool for outlier detection in real-time PCR.     

Simple absolute quantification method correcting for quantitative PCR efficiency variations for microbial community samples

Real-time quantitative PCR (qPCR) is a widely used technique in microbial community analysis, allowing the quantification of the number of target genes in a community sample. Currently, the standard-curve (SC) method of absolute quantification is widely employed for these kinds of analysis. However, the SC method assumes that the amplification efficiency (E) is the same for both the standard and the sample target template. We analyzed 19 bacterial strains and nine environmental samples in qPCR assays, targeting the nifH and 16S rRNA genes. The E values of the qPCRs differed significantly, depending on the template. This has major implications for the quantification. If the sample and standard differ in their E values, quantification errors of up to orders of magnitude are possible. To address this problem, we propose and test the one-point calibration (OPC) method for absolute quantification. The OPC method corrects for differences in E and was derived from the ΔΔC(T) method with correction for E, which is commonly used for relative quantification in gene expression studies. The SC and OPC methods were compared by quantifying artificial template mixtures from Geobacter sulfurreducens (DSM 12127) and Nostoc commune (Culture Collection of Algae and Protozoa [CCAP] 1453/33), which differ in their E values. While the SC method deviated from the expected nifH gene copy number by 3- to 5-fold, the OPC method quantified the template mixtures with high accuracy. Moreover, analyzing environmental samples, we show that even small differences in E between the standard and the sample can cause significant differences between the copy numbers calculated by the SC and the OPC methods.     

Amine-reactive isobaric tagging reagents: requirements for absolute quantification of proteins and peptides

Amine-reactive isobaric tagging reagents such as iTRAQ (isobaric tags for relative and absolute quantitation) have recently become increasing popular for relative protein quantification, cell expression profiling, and biomarker discovery. This is due mainly to the possibility of simultaneously identifying and quantifying multiple samples. The principles of iTRAQ may also be applied to absolute protein quantification with the use of synthetic peptides as standards. The prerequisites that must be fulfilled to perform absolute quantification of proteins by iTRAQ have been investigated and are described here. Three samples of somatropin were quantified using iTRAQ and synthetic peptides as standards, corresponding to a portion of the protein sequence. The results were compared with those obtained by quantification of the same protein solutions using double exact matching isotope dilution mass spectrometry (IDMS). To obtain reliable results, the appropriate standard peptides needed to be selected carefully and enzymatic digestion needed to be optimized to ensure complete release of the peptides from the protein. The kinetics and efficiency of the iTRAQ derivatization reaction of the standard peptides and digested proteins with isobaric tagging reagents were studied using a mixture of seven synthetic peptides and their corresponding labeled peptides. The implications of incomplete derivatization are also presented.     

Kinetics quality assessment for relative quantification by real-time PCR

For proper relative quantification by real-time PCR, compared samples should have similar PCR efficiencies. To test this prerequisite, we developed two quality tests: (i) adjustment of a test for kinetic outlier detection (KOD) to relative quantification; and (ii) comparison of the efficiency variance of test samples with the efficiency variance of samples with highly reproducible quantification. The tests were applied on relative quantification of two genes in 30 sets of 5 replicate samples (same treatment, different animals). Ten low-quality sets and 28 outliers were identified. The low-quality sets showed higher coefficient of variation (cv)% of DNA quantities in replicate experiments than high-quality sets (63% versus 26%; P = 0.001) and contained a higher proportion of outlying quantities (35% versus 5.9%; P = 0.001) when individual samples were detected by adjusted KOD. Outlier detection with adjusted KOD reduced the false detection of outliers by 2/3 compared with the previous, nonadjusted version of KOD (20% versus 5.9%; P = 0.001). We conclude that the presented tests can be used to assign technical reasons to outlying observations.     

A Bayesian method for calculating real-time quantitative PCR calibration curves using absolute plasmid DNA standards

Background  

In real-time quantitative PCR studies using absolute plasmid DNA standards, a calibration curve is developed to estimate an unknown DNA concentration. However, potential differences in the amplification performance of plasmid DNA compared to genomic DNA standards are often ignored in calibration calculations and in some cases impossible to characterize. A flexible statistical method that can account for uncertainty between plasmid and genomic DNA targets, replicate testing, and experiment-to-experiment variability is needed to estimate calibration curve parameters such as intercept and slope. Here we report the use of a Bayesian approach to generate calibration curves for the enumeration of target DNA from genomic DNA samples using absolute plasmid DNA standards.     

Experimental validation of novel and conventional approaches to quantitative real-time PCR data analysis

Real-time PCR is being used increasingly as the method of choice for mRNA quantification, allowing rapid analysis of gene expression from low quantities of starting template. Despite a wide range of approaches, the same principles underlie all data analysis, with standard approaches broadly classified as either absolute or relative. In this study we use a variety of absolute and relative approaches of data analysis to investigate nocturnal c-fos expression in wild-type and retinally degenerate mice. In addition, we apply a simple algorithm to calculate the amplification efficiency of every sample from its amplification profile. We confirm that nocturnal c-fos expression in the rodent eye originates from the photoreceptor layer, with around a 5-fold reduction in nocturnal c-fos expression in mice lacking rods and cones. Furthermore, we illustrate that differences in the results obtained from absolute and relative approaches are underpinned by differences in the calculated PCR efficiency. By calculating the amplification efficiency from the samples under analysis, comparable results may be obtained without the need for standard curves. We have automated this method to provide a means of streamlining the real-time PCR process, enabling analysis of experimental samples based upon their own reaction kinetics rather than those of artificial standards.     

Validation of real-time RT-PCR assays for mRNA quantification in baboons

Real-time RT-PCR has been used widely, both in fundamental research and in clinical diagnostics, for instance for quantification of RNA levels in human tissues and tissue biopsies. In the present study we provide a strategy to validate primers/probes for real-time RT-PCR quantification of baboon samples. The method is based on the TaqMan system and uses primers/probes that have been designed and validated for human real-time RT-PCR. A prerequisite for the accuracy of this strategy is a similar amplification efficiency between human and baboon PCR reactions. We propose two different methods, i.e. by calculating PCR efficiencies from the slope of a dilution curve or by using the linear regression method, to compare the amplification efficiency between human and baboon samples. In conclusion, by performing a simple validation experiment, real-time PCR assays based on human sequences, which are easily available, can be applied for analysis of baboon samples.     

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.     

Assessing the Performance Capabilities of LRE-Based Assays for Absolute Quantitative Real-Time PCR

Background

Linear regression of efficiency or LRE introduced a new paradigm for conducting absolute quantification, which does not require standard curves, can generate absolute accuracies of ±25% and has single molecule sensitivity. Derived from adapting the classic Boltzmann sigmoidal function to PCR, target quantity is calculated directly from the fluorescence readings within the central region of an amplification profile, generating 4–8 determinations from each amplification reaction.

Findings

Based on generating a linear representation of PCR amplification, the highly visual nature of LRE analysis is illustrated by varying reaction volume and amplification efficiency, which also demonstrates how LRE can be used to model PCR. Examining the dynamic range of LRE further demonstrates that quantitative accuracy can be maintained down to a single target molecule, and that target quantification below ten molecules conforms to that predicted by Poisson distribution. Essential to the universality of optical calibration, the fluorescence intensity generated by SYBR Green I (FU/bp) is shown to be independent of GC content and amplicon size, further verifying that absolute scale can be established using a single quantitative standard. Two high-performance lambda amplicons are also introduced that in addition to producing highly precise optical calibrations, can be used as benchmarks for performance testing. The utility of limiting dilution assay for conducting platform-independent absolute quantification is also discussed, along with the utility of defining assay performance in terms of absolute accuracy.

Conclusions

Founded on the ability to exploit lambda gDNA as a universal quantitative standard, LRE provides the ability to conduct absolute quantification using few resources beyond those needed for sample preparation and amplification. Combined with the quantitative and quality control capabilities of LRE, this kinetic-based approach has the potential to fundamentally transform how real-time qPCR is conducted.