Home | About | Journals | Submit | Contact Us | Français |

**|**PLoS One**|**v.5(7); 2010**|**PMC2908630

Formats

Article sections

Authors

Related links

PLoS One. 2010; 5(7): e11723.

Published online 2010 July 22. doi: 10.1371/journal.pone.0011723

PMCID: PMC2908630

Jens Magnus Bernth Jensen,^{1,}^{*} Mikkel Steen Petersen,^{1} Marc Stegger,^{2,}^{¤} Lars J. Østergaard,^{2} and Bjarne K. Møller^{1}

M. Thomas P. Gilbert, Editor^{}

Natural History Museum of Denmark, Denmark

* E-mail: kd.mr@nesnejej

Conceived and designed the experiments: JMBJ LØ BKM. Performed the experiments: JMBJ MS. Analyzed the data: JMBJ MSP. Contributed reagents/materials/analysis tools: JMBJ LØ BKM. Wrote the paper: JMBJ MSP MS LØ BKM. Deduced the principles: JMBJ.

Received 2010 February 15; Accepted 2010 June 23.

Copyright Bernth Jensen et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

This article has been cited by other articles in PMC.

Real-Time quantitative PCR is an important tool in research and clinical settings. Here, we describe two new approaches that broaden the scope of real-time quantitative PCR; namely, run-internal mini standard curves (RIMS) and direct real-time relative quantitative PCR (drqPCR). RIMS are an efficient alternative to traditional standard curves and provide both run-specific and target-specific estimates of PCR parameters. The drqPCR enables direct estimation of target ratios without reference to conventional control samples.

In this study, we compared RIMS-based drqPCR with classical quantifications based on external standard curves and the “comparative Ct method”. Specifically, we used a raw real-time PCR dataset as the basis for more than two-and-a-half million simulated quantifications with various user-defined conditions. Compared with classical approaches, we found that RIMS-based drqPCR provided superior precision and comparable accuracy.

The obviation of referencing to control samples is attractive whenever unpaired samples are quantified. This may be in clinical and research settings; for instance, studies on chimerism, TREC quantifications, copy number variations etc. Also, lab-to-lab comparability can be greatly simplified.

Real-time relative quantitative polymerase chain reaction (qPCR) has long been a favoured principle for relative quantifications of nucleic acid sequences. In essence, an undetectably low amount of a specific nucleic acid target sequence is expanded by PCR to a measurable level. Subsequently, the original amount of the target sequence is calculated from the parameters of the PCR. The basis of these calculations is the classical PCR equation:

(I.1)

*N*_{0} is the amount of the target sequence before PCR, *N _{Cq}* is the amount of target after

(I.2)

To solve the equation above, *N _{Cq}*s,

Despite the broad applicability of the technology, several methodological limitations have yet to be addressed. In this paper, we focus on two of these.

A general limitation is that **Eq.I.2** cannot be solved trivially offhand. The problem lies in the *N _{Cq,A}*/

(I.3)

The “double-ratio” above can be simplified, eliminating the *N _{Cq,A}*/

(I.4)

Although appropriate for paired samples, **Eq. I.4** is generally unsuitable if samples are unpaired: the ratio of *A* and *B* in a sample can be of immediate interest, and any reference to a control sample can be inconvenient or even meaningless. In these situations, **Eq. I.4** can still be useful if the control sample contains *A* and *B* in equal numbers. Nonetheless, two problems remain. First, such control samples are not necessarily available. Second, and more importantly, the sources of errors increases by the doubling of sample numbers to be determined with **Eq. I.4** compared with **Eq. I.2**. Ultimately, increased error of the final ratio-estimate is very likely. It may therefore be attractive to actually use **Eq. I.2** directly. If so, the inherent (*N _{Cq}*)

Another important limitation of conventional approaches concerns the use of low-capacity machinery. Conventionally, limited instrument capacity forces the investigator to estimate PCR unknowns (such as *E*) from standard curves analysed in separate runs or assuming a value of 1. This introduces a run-to-run variability that inevitably contributes to the error of *E*. As such, *E* varies considerably between replicate runs (e.g. >5% [10]). Even tiny errors of the *E*-estimate are critical. These errors induce disproportionately large errors of *R _{is}*/

We hypothesized that run-internal estimation of PCR unknowns (from small amounts of standard curve samples) is superior to run-external estimation. Also, by modifying the composition of standard curve samples, we hypothesized that target ratio estimates can be attained directly without reference to control samples.

Our objective was to deduce the optimal composition of standard curve samples to remedy the limitations of classical qPCR. In the process, we wanted to compare the precision and accuracy of our approach to classical approaches.

Blunt-ended PCR products of parts of Human Endogenous retrovirus 1 (ERV1) and TUP-like enhancer of SPLIT 1 (TUPLE1) were produced from genomic DNA by conventional PCRs (Platinum Pfx DNA Polymerase (InVitrogen)). Primer sequences were obtained from Overhauser J et al [11] and Weksberg R et al [12]. PCR products were gel electrophorized. Single bands of expected lengths were excised and PCR products purified (Illustra GFX™ PCR DNA and Gel Band Purification Kit, GE Healthcare). TUPLE1 PCR products were 5′-dephosphorylated with rAPID Alkaline Phospatase in supplied buffer (Roche) and purified. Blunt-ended ERV1 PCR products- and 5′-dephosphorylated TUPLE1 PCR products were ligated (T4 DNA Ligase in T4 DNA Ligase Buffer, New England Biolabs) and purified. Hundred-fold diluted fused PCR products were expanded by standard PCR (ERV1 forward and TUPLE1 reverse primers, respectively). Reactions were gel electrophorized; and single bands consistent with the expected length of the fused PCR product were obtained, purified, and diluted 100-fold before an additional round of PCR, isolation, purification, and dilution. The PCR products were validated by sequencing.

The diluted fusion-PCR product was thoroughly mixed and stored in aliquots (−20°C). On three separate days, an aliquot was thawed and used for a 10-fold dilution series in eight steps. Weight data of the pipetted volumes were sampled while the dilution series were made. Each dilution step was performed three times into the same tube (to minimize impact of stochastic errors).

Each dilution series was analyzed by real-time PCR with the primer pairs for ERV1 and TUPLE1. Each primer pair was used in separate runs. Reactions of 20 µl were set up in LightCycler capillaries: 10 µl 2× QuantiTect SYBR Green PCR mix (Qiagen), 0.5 µM primers and 8 µl template. PCRs were conducted on a LightCycler 1.0 Instrument (Roche) with the following settings: 15 min at 95°C, 45 amplification cycles (each 15 seconds at 94°C, 20 seconds annealing at 57°C, and 20 seconds at 72°C with endpoint fluorescence detection). Each of the eight concentrations of the dilution series was analysed in four replicates. Six preliminary data sets containing 32 data points each were thus generated.

We estimated *C _{q}*s for the six preliminary data sets by the fit-points-approach, which gave more linear standard curves than the second derivative maximums-method (see

Data handling was done in Microsoft Excel 2007. Sampled *C _{q}*- and

(M.1)

Regarding LOG (*N*_{0}) as the outcome variable and *C _{q}* as the predictor variable is opposite of the conventional approach and may seem awkward. However, as

(M.2)

With *α* and *β* being intercept and slope, respectively. Data of the six 28-sample- standard curves generated from fusion-PCR products are presented in **Table 1**.

To examine the usability of RIMS and RIMS-based drqPCR, we simulated a large number of individual quantifications from actual real-time PCR data. First, we combined the raw data (*C _{q}* and

The constructed RIMS were used in simulations of 2,500,848 direct relative quantifications (i.e. quantifications without reference to a control sample). To simplify, unicate quantifications were applied (only one *C _{q}*-measurement of each target per quantification). The

For the evaluation of double-ratio drqPCR, a combined measure of concentration difference between interest- and virtual control sample in the individual quantification was calculated:

(M.3)

Double-ratio-based quantification was used (**Eq. I.4**, *E _{A}*=

The external-SC-based quantifications were done as the 2* ^{ΔΔCq}*-based quantifications, but with efficiency corrections based on external SCs of

Regression analysis was based on least-squares methods and *t*-distributions. Probability testing of variance similarity () was based on the *F*-distribution: *F _{obs}*=largest variance estimate/smallest variance estimate, degrees of freedom being (

To estimate *R _{is}* directly (without reference to a control sample), the unknown (

(R.1)

The benefit of using regression estimates is that simple statistics can be applied to determining errors of LOG (*R _{is}*) (see

The accuracy of **Eq. R.1** hinges on use of valid estimates of slopes and intercepts. These parameters can vary significantly between targets but also between PCR runs of the same target (**Tabel I**). Therefore, target-specific and run-specific parameters are preferable. We hypothesized that internal standard curves based on fewer samples are preferable over larger, external standard curves. This hypothesis was confronted as follows:

Initially, we sought an optimal sample composition strategy for RIMSs. The composition should minimize the errors of regression estimates of LOG ((*N _{0}*)

Next, we investigated the quantitative precision and accuracy of our two approaches when used in combination. In total, 2,500,848 unicate quantifications were determined from the raw data of the six 28-sample data sets. The quantitative precision is summarized in **Figure 2**. Increases in *C* and RIMS-sample replicate numbers both generally conferred significant precision improvements. However, the effect of using four as opposed to three RIMS-sample replicates was insignificant. The accuracy was unaffected by *C* or RIMS-sample replicate number and ranged between 94% and 110% of the true target ratios. **Double-ratio drqPCR** as argued in the introduction, the double-ratio approach (**Eq. I.4**) can provide *R _{is}*-estimates

(R.2)

A prerequisite is that *α*s and *β*s are constant between interest and control samples for each target.

Some heterogeneity is evident in a comparison of single-ratio to double-ratio based drqPCR (**Eq. R.1** and **Eq. R.2**). Fewer different samples are required in the former approach. This confers fewer sources of errors to *R _{is}*. However, erroneous

(R.3)

We compared the precision and accuracy of quantification by single- and double-ratio drqPCR in the 1,190,880 possible quantifications from the six 28-samplestandard curve data sets (*C*≥10^{3}). We expected that increasing the Δ*C _{q}* of interest sample and virtual control sample would decrease the precision of double-ratio drqPCR. Data were therefore split according to

The data of the six 28-samplestandard curves were used to generate 61,236 and 244,944 different quantifications by the 2* ^{ΔΔCq}*-approach and based on external standard curves, respectively. Quantifications were based on

Real-time relative quantitative PCR in clinical settings is hampered by a lack of accurate and precise approaches to estimate the ratio between nucleic acid sequences without reference to a control sample. Also, conventional approaches for estimating internal PCR parameters are problematic in low capacity PCR machines. This paper concerns the establishment and examination of two new approaches for real-time quantitative PCR; namely RIMS and drqPCR. RIMS concerns estimation of run-internal specific PCR parameters, such as efficiency, from a minimum of samples. The drqPCR is a universal strategy for estimation of ratios directly in the sample, alleviating the need for control samples and therefore ideal for analysis of unpaired samples. We compared RIMS and drqPCR with conventional methods on a common data set. This data set was generated from samples with known target ratios. Therefore, both the precision and accuracy of the approaches could be evaluated.

Separately, RIMS gives target-specific and run-specific estimates of the standard curve's slope and intercept (measures of *N _{Cq}* and

From Real-Time PCR data, we produced 8,694 individual RIMS. Not surprisingly, the number of RIMS-sample replicates and the value of *C* were of immense importance for precision (**Figure 1**). Compared with standard curves, RIMS provided the potential for attaining estimates of the highest precision. Obviously, a potential explanation could be large run-run external standard curve-variation in our study. Rutledge and Cote [10] used a model comparable to ours, in which a PCR product was serially diluted and subjected to real-time PCR with two different primer sets five times. They reported *E* CVs of 2.2% and 2.1% for five repeated standard curves for each of two targets. In comparison, *E* CVs of our study were 2.9% (ERV1) and 2.5% (TUPLE1). The CVs of *N _{Cq}* in the study of Rutledge and Cote were 19.0% and 14.7%.

In our examination of the precision of RIMS-based estimates, the estimates were compared to the corresponding estimate of the internal standard curves. We found a close approximation (that is, a high precision) of the large-*C*-based RIMS estimates to the 28-sample internal standard curves' (**Figure 1**). We perceive this as indicative of RIMS potential for high accuracy. Furthermore, the result illustrates the redundancy of the intervening data points. RIMS may therefore also be considered as a cost-saving alternative in high-capacity machinery.

The following points should be considered when constructing the RIMS in practice. First, RIMS samples should be selected from the dilution series based on a preliminary standard curve to maximize *C* (≥10^{5}) while preserving linearity. Second, very dilute samples should be avoided completely (**Appendix S1**, section 1). Third, the chosen samples should be aliquoted and stored. Fourth, two or more replicate *C _{q}*-estimations of each RIMS sample are preferable. Fifth, the type of template (e.g. PCR-product, cDNA, or genomic DNA) chosen for RIMS-samples should permit appropriately sized

Instead, we advocate approaches based on internal, relative standard curves (derived from samples containing the targets of interest in equal amounts) and use of regression estimates. This ensures both target-specific and run-specific corrections of the underlying variable (*N _{Cq}*)

We evaluated drqPCR based on RIMS in quantifications of samples containing the quantified targets in known stoichiometry. This model permitted us to evaluate both quantitative precision and accuracy. Not surprisingly, we found that increasing *C* and the number of RIMS replicates increased the precision significantly (**Figure 2****–****3**). However, *C* was the most important parameter for improving precision. More than two replicates of each RIMS-sample conferred only minimal improvements of precision. Accuracy was within ±8%. Finally, we compared precision and accuracy of drqPCR based on the 2* ^{ΔΔCq}*-approach, external standard curves, and RIMS. RIMS-based drqPCR demonstrated the largest potential for precision (

Use of drqPCR has other beneficial side-effects. The principle renders calibrator samples (or reference-control samples) superfluous. Calibrators are a necessity when interest and control samples are not in the same PCR-run [3]. Their purpose is to correct for run-to-run differences of targets *N _{q}*-value. Briefly, the calibrator sample contains the targets-to-be-quantified and is PCR-expanded both in runs of controls and interest samples. Subsequently, interest and control data are made comparable by dividing each with the calibrator data of their respective runs. In drqPCR, data of control and interest samples are always immediately comparable, provided that the same RIMS samples are used in runs. Avoidance of calibrators is attractive to minimize the sources of errors of

In summary, we suggest that RIMS and drqPCR be used separately or combined for relative quantifications of high precision and accuracyThe drqPCR allows determination of *R _{is}* directly in the sample, and RIMS can replace external standard curves.

The association of replicate-*C _{q}* spread and

(0.21 MB TIF)

Click here for additional data file.^{(203K, tif)}

Precision of RIMS based single-ratio drqPCR with *C _{q}*-sampling by SDM and FP (black and white bars, respectively) for different values of

(0.11 MB TIF)

Click here for additional data file.^{(106K, tif)}

Precision of double-ratio-based qPCR by the 2* ^{ΔΔCq}*-approach (black and dark grey bars) or from external standard curves (light grey and white bars) for variable sizes of

(0.18 MB TIF)

Click here for additional data file.^{(176K, tif)}

Quantitative precision of single-ratio drqPCR based on RIMS (duplicate analysis) with estimations of *C* based on pipetted weights (white and dark grey bars) or volumes (black and light grey). Weight as opposed to volume based *C*-estimation provided minute improvements of precision for all *C*s regardless of *C _{q}*-sampling approach (SDM: black and dark grey, FP: light grey and white). However, improvements were insignificant except where indicated by an asterisk (

(0.13 MB TIF)

Click here for additional data file.^{(131K, tif)}

Algorithm for practical use of RIMS based drqPCR.

(1.26 MB XLS)

Click here for additional data file.^{(1.2M, xls)}

The authors thank laboratory technician Erik Hagen for performing the sequencing of the TUPLE1-ERV1 fusion PCR product and PhD Martin Roelsgaard for technical discussions.

**Competing Interests: **The authors have declared that no competing interests exist.

**Funding: **The authors have no support or funding to report.

1. Livak KJ. ABI prism 7700 sequence detection system, user bulletin 2. PE Applied Biosystems 12-11-1997

2. Vandesompele J, De Preter K, Pattyn F, Poppe B, Van Roy N, et al. Accurate normalization of real-time quantitative RT-PCR data by geometric averaging of multiple internal control genes. Genome Biol. 2002;3(7):RESEARCH0034. [PMC free article] [PubMed]

3. Wong ML, Medrano JF. Real-time PCR for mRNA quantitation. BioTechniques. 2005;39(1):75–85. [PubMed]

4. VanGuilder HD, Vrana KE, Freeman WM. Twenty-five years of quantitative PCR for gene expression analysis. BioTechniques. 2008;44(5):619–626. [PubMed]

5. Higuchi R, Fockler C, Dollinger G, Watson R. Kinetic PCR analysis: Real-time monitoring of DNA amplification reactions. Biotechnology (N Y) 1993;11(9):1026–1030. [PubMed]

6. Schmittgen TD, Livak KJ. Analyzing real-time PCR data by the comparative C(T) method. Nat Protoc. 2008;3(6):1101–1108. [PubMed]

7. Livak KJ, Schmittgen TD. Analysis of relative gene expression data using real-time quantitative PCR and the 2(-delta delta C(T)) method. Methods. 2001;25(4):402–408. [PubMed]

8. Pfaffl MW. A new mathematical model for relative quantification in real-time RT-PCR. Nucleic Acids Res. 2001;29(9):e45. [PMC free article] [PubMed]

9. Zipper H, Brunner H, Bernhagen J, Vitzthum F. Investigations on DNA intercalation and surface binding by SYBR green I, its structure determination and methodological implications. Nucleic Acids Res. 2004;32(12):e103. [PMC free article] [PubMed]

10. Rutledge RG, Cote C. Mathematics of quantitative kinetic PCR and the application of standard curves. Nucleic Acids Res. 2003;31(16):e93. [PMC free article] [PubMed]

11. Overhauser J, Mewar R, Rojas K, Lia K, Kline AD, et al. STS map of genes and anonymous DNA fragments on human chromosome 18 using a panel of somatic cell hybrids. Genomics. 1993;15(2):387–391. [PubMed]

12. Weksberg R, Hughes S, Moldovan L, Bassett AS, Chow EW, et al. A method for accurate detection of genomic microdeletions using real-time quantitative PCR. BMC Genomics. 2005;6:180. [PMC free article] [PubMed]

13. Hellemans J, Mortier G, De Paepe A, Speleman F, Vandesompele J. qBase relative quantification framework and software for management and automated analysis of real-time quantitative PCR data. Genome Biol. 2007;8(2):R19. [PMC free article] [PubMed]

14. Yuan JS, Wang D, Stewart CN., Jr Statistical methods for efficiency adjusted real-time PCR quantification. Biotechnol J. 2008;3(1):112–123. [PubMed]

15. Ruijter JM, Ramakers C, Hoogaars WM, Karlen Y, Bakker O, et al. Amplification efficiency: Linking baseline and bias in the analysis of quantitative PCR data. Nucleic Acids Res. 2009;37(6):e45. [PMC free article] [PubMed]

16. Bustin SA. Absolute quantification of mRNA using real-time reverse transcription polymerase chain reaction assays. J Mol Endocrinol. 2000;25(2):169–193. [PubMed]

Articles from PLoS ONE are provided here courtesy of **Public Library of Science**

PubMed Central Canada is a service of the Canadian Institutes of Health Research (CIHR) working in partnership with the National Research Council's national science library in cooperation with the National Center for Biotechnology Information at the U.S. National Library of Medicine(NCBI/NLM). It includes content provided to the PubMed Central International archive by participating publishers. |