BioInformatics - PCR Efficiency in real-time PCR

New added publications:

Quality control for quantitative PCR based on amplification compatibility test.
Tichopad A, Bar T, Pecen L, Kitchen RR, Kubista M, Pfaffl MW.
Methods. 2010 50(4): 308-312

Quantitative qPCR is a routinely used method for the accurate quantification of nucleic acids. Yet it may generate erroneous results if the amplification process is obscured by inhibition or generation of aberrant side-products such as primer dimers. Several methods have been established to control for pre-processing performance that rely on the introduction of a co-amplified reference sequence, however there is currently no method to allow for reliable control of the amplification process without directly modifying the sample mix. Herein we present a statistical approach based on multivariate analysis of the amplification response data generated in real-time. The amplification trajectory in its most resolved and dynamic phase is fitted with a suitable model. Two parameters of this model, related to amplification efficiency, are then used for calculation of the Z-score statistics. Each studied sample is compared to a predefined reference set of reactions, typically calibration reactions. A probabilistic decision for each individual Z-score is then used to identify the majority of inhibited reactions in our experiments. We compare this approach to univariate methods using only the sample specific amplification efficiency as reporter of the compatibility. We demonstrate improved identification performance using the multivariate approach compared to the univariate approach. Finally we stress that the performance of the amplification compatibility test as a quality control procedure depends on the quality of the reference set.

Efficiency clustering for low-density microarrays and its application to qPCR
Eric F Lock, Ryan Ziemiecke, J. S. Marron and Dirk P Dittmer
BMC Bioinformatics 2010, 11

Background

Pathway-targeted or low-density arrays are used more and more frequently in biomedical research, particularly those arrays that are based on quantitative real-time PCR. Typical QPCR arrays contain 96-1024 primer pairs or probes, and they bring with it the promise of being able to reliably measure differences in target levels without the need to establish absolute standard curves for each and every target. To achieve reliable quantification all primer pairs or array probes must perform with the same efficiency.

Results

Our results indicate that QPCR primer-pairs differ significantly both in reliability and efficiency. They can only be used in an array format if the raw data (so called CT values for real-time QPCR) are transformed to take these differences into account. We developed a novel method to obtain efficiency-adjusted CT values. We introduce transformed confidence intervals as a novel measure to identify unreliable primers. We introduce a robust clustering algorithm to combine efficiencies of groups of probes, and our results indicate that using n < 10 cluster-based mean efficiencies is comparable to using individually determined efficiency adjustments for each primer pair (N = 96-1024).

Conclusions

Careful estimation of primer efficiency is necessary to avoid significant measurement inaccuracies. Transformed confidence intervals are a novel method to assess and interprete the reliability of an efficiency estimate in a high throughput format. Efficiency clustering as developed here serves as a compromise between the imprecision in assuming uniform efficiency, and the computational complexity and danger of over-fitting when using individually determined efficiencies.

Shape based kinetic outlier detection in real-time PCR.
Sisti D, Guescini M, Rocchi MB, Tibollo P, D'Atri M, Stocchi V.
BMC Bioinformatics. 2010 12;11: 186

BACKGROUND:
Real-time PCR has recently become the technique of choice for absolute and relative nucleic acid quantification. The gold standard quantification method in real-time PCR assumes that the compared samples have similar PCR efficiency. However, many factors present in biological samples affect PCR kinetic, confounding quantification analysis. In this work we propose a new strategy to detect outlier samples, called SOD.
RESULTS:
Richards function was fitted on fluorescence readings to parameterize the amplification curves. There was not a significant correlation between calculated amplification parameters (plateau, slope and y-coordinate of the inflection point) and the Log of input DNA demonstrating that this approach can be used to achieve a "fingerprint" for each amplification curve. To identify the outlier runs, the calculated parameters of each unknown sample were compared to those of the standard samples. When a significant underestimation of starting DNA molecules was found, due to the presence of biological inhibitors such as tannic acid, IgG or quercitin, SOD efficiently marked these amplification profiles as outliers. SOD was subsequently compared with KOD, the current approach based on PCR efficiency estimation. The data obtained showed that SOD was more sensitive than KOD, whereas SOD and KOD were equally specific.
CONCLUSION:
Our results demonstrated, for the first time, that outlier detection can be based on amplification shape instead of PCR efficiency. SOD represents an improvement in real-time PCR analysis because it decreases the variance of data thus increasing the reliability of quantification.

A new real-time PCR method to overcome significant quantitative inaccuracy due to slight amplification inhibition.
BMC Bioinformatics. 2008 30;9: 326
Guescini M, Sisti D, Rocchi MB, Stocchi L, Stocchi V.

BACKGROUND:
Real-time PCR analysis is a sensitive DNA quantification technique that has recently gained considerable attention in biotechnology, microbiology and molecular diagnostics. Although, the cycle-threshold (Ct) method is the present "gold standard", it is far from being a standard assay. Uniform reaction efficiency among samples is the most important assumption of this method. Nevertheless, some authors have reported that it may not be correct and a slight PCR efficiency decrease of about 4% could result in an error of up to 400% using the Ct method. This reaction efficiency decrease may be caused by inhibiting agents used during nucleic acid extraction or copurified from the biological sample. We propose a new method (Cy0) that does not require the assumption of equal reaction efficiency between unknowns and standard curve.
RESULTS:
The Cy0 method is based on the fit of Richards' equation to real-time PCR data by nonlinear regression in order to obtain the best fit estimators of reaction parameters. Subsequently, these parameters were used to calculate the Cy0 value that minimizes the dependence of its value on PCR kinetic. The Ct, second derivative (Cp), sigmoidal curve fitting method (SCF) and Cy0 methods were compared using two criteria: precision and accuracy. Our results demonstrated that, in optimal amplification conditions, these four methods are equally precise and accurate. However, when PCR efficiency was slightly decreased, diluting amplification mix quantity or adding a biological inhibitor such as IgG, the SCF, Ct and Cp methods were markedly impaired while the Cy0 method gave significantly more accurate and precise results.
CONCLUSION:
Our results demonstrate that Cy0 represents a significant improvement over the standard methods for obtaining a reliable and precise nucleic acid quantification even in sub-optimal amplification conditions overcoming the underestimation caused by the presence of some PCR inhibitors.

Amplification efficiency: linking baseline and bias in the analysis of quantitative PCR data.
Ruijter JM, Ramakers C, Hoogaars WM, Karlen Y, Bakker O, van den Hoff MJ, Moorman AF.
Nucleic Acids Res. 2009 37(6): e45

Despite the central role of quantitative PCR (qPCR) in the quantification of mRNA transcripts, most analyses of qPCR data are still delegated to the software that comes with the qPCR apparatus. This is especially true for the handling of the fluorescence baseline. This article shows that baseline estimation errors are directly reflected in the observed PCR efficiency values and are thus propagated exponentially in the estimated starting concentrations as well as 'fold-difference' results. Because of the unknown origin and kinetics of the baseline fluorescence, the fluorescence values monitored in the initial cycles of the PCR reaction cannot be used to estimate a useful baseline value. An algorithm that estimates the baseline by reconstructing the log-linear phase downward from the early plateau phase of the PCR reaction was developed and shown to lead to very reproducible PCR efficiency values. PCR efficiency values were determined per sample by fitting a regression line to a subset of data points in the log-linear phase. The variability, as well as the bias, in qPCR results was significantly reduced when the mean of these PCR efficiencies per amplicon was used in the calculation of an estimate of the starting concentration per sample.

Assessing the performance capabilities of LRE-based assays for absolute quantitative real-time PCR.
Rutledge RG, Stewart D.
PLoS One. 2010 Mar 17;5(3):e9731.

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.

Bias in the Cq value observed with hydrolysis probe based quantitative PCR can be corrected with the estimated PCR efficiency value.
Tuomi JM, Voorbraak F, Jones DL, Ruijter JM.
Methods. 2010 Apr;50(4): 313-22

For real-time monitoring of PCR amplification of DNA, quantitative PCR (qPCR) assays use various fluorescent reporters. DNA binding molecules and hybridization reporters (primers and probes) only fluoresce when bound to DNA and result in the non-cumulative increase in observed fluorescence. Hydrolysis reporters (TaqMan probes and QZyme primers) become fluorescent during DNA elongation and the released fluorophore remains fluorescent during further cycles; this results in a cumulative increase in observed fluorescence. Although the quantification threshold is reached at a lower number of cycles when fluorescence accumulates, in qPCR analysis no distinction is made between the two types of data sets. Mathematical modeling shows that ignoring the cumulative nature of the data leaves the estimated PCR efficiency practically unaffected but will lead to at least one cycle underestimation of the quantification cycle (C(q) value), corresponding to a 2-fold overestimation of target quantity. The effect on the target reference ratio depends on the PCR efficiency of the target and reference amplicons. The leftward shift of the C(q) value is dependent on the PCR efficiency and with sufficiently large C(q) values, this shift is constant. This allows the C(q) to be corrected and unbiased target quantities to be obtained.