Abstract

Background

Determination of polymerase chain reaction (PCR) efficiency for each primer pair is of key importance for correct evaluation and interpretation of quantitative PCR (qPCR) data [1–3]. Different approaches to determine efficiency have been developed, from the classical standard curve-based method to sophisticated methods that rely on fitting linear or non-linear models on individual amplification curves [4–7]. Occupying the middle ground between these two extremes is the dilution-replicate experimental design [8] that has remained underused, most probably due to the lack up to now of a dedicated software to apply the method. The dilution-replicate approach is based on multiple linear regression and offers a number of advantages. It requires fewer reactions and thus helps to reduce costs. In the traditional approach, standard curves are produced by a separate set of dilutions of a standard sample. In the dilution-replicate design (Fig. 1A), standard curves are determined from so-called dilution-replicates of experimental samples that serve both to control technical variance and to determine efficiency [8]. In this way, all samples contribute to the efficiency estimate and precision increases with the number of samples on a plate. Furthermore, the traditional approach requires that the linear dynamic range of the independent standard curve covers all sample Cq values. This requirement sometimes makes it necessary to repeat experiments using different dilutions. In contrast, with the dilution-replicate design it is guaranteed that the sample Cq values will be within range.

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Fig. 1

A Reaction setup according to the dilution-replicate design. B repDilPCR workflow. C An example of a completely automatically created plot from experimental data. The final plot displays 9 biological replicates per sample although only 3 biological replicates could be shown on the diagram in (A) for space reasons

The theoretical basis of the dilution-replicate method, including derivation of mathematical formulas, estimation of reaction efficiency by collinear fit of standard curves through multiple linear regression and estimation of relative changes in gene expression from Cq-Cq plots are described in the original article [8] and potential users of the method are advised to read it. For convenience, we have included the most important formulas in the Supplementary Information (Additional file 1). From a practical standpoint, the experimenter applying the dilution-replicate method should prepare three tubes with serial dilutions (usually fivefold) of each cDNA preparation. Three wells on a qPCR plate are necessary for every biological replicate / primer pair combination, analogous to the number of wells that one needs for technical replicates with the traditional approach. However, with the dilution-replicate method the amount of cDNA in each well is not the same but step-wise reduced (same volume from the different dilutions prepared in the tubes). No wells are necessary for separate standard curves. Control reactions in which no amplification is expected (no template, no reverse transcription and genomic DNA controls) should be performed with identical replicates as usual. It should be noted that analogous to the classical standard curve method, the dilution steps for the dilution-replicate method should be performed with a properly calibrated pipette, otherwise a bias would be introduced into the calculated efficiencies and relative quantities.

Our tool, repDilPCR, utilizes the described dilution-replicate analytical method [8] and extends it by adding the possibility to use multiple reference genes, a prerequisite for accurate qPCR expression profiling [9]. It also offers capabilities for performing statistical tests and plotting publication-ready graphs. The program has been designed with the philosophy to automate and speed up analysis of qPCR data (typically less than one minute from Cq values to publication-ready plots) and to help users select and perform the appropriate statistical tests, at least in the case of one-factor experimental designs. At the same time, the program allows experienced users to export intermediate data and perform more sophisticated analyses with external statistical software, e.g. if two-way analysis of variance (ANOVA) is necessary.

Although the primary goal of the program is to enable analysis of qPCR data via the dilution-replicate approach, the statistical and plotting functions can also be used with preprocessed data, i.e. with relative expression values obtained by usual assay designs and evaluation methods.

Implementation

repDilPCR is written in R/Shiny and can be used both as an ordinary R script on a local computer or as a Shiny app (either on a local computer or on a server) accessed through a web browser. A publicly available instance of the Shiny app is hosted at the German Cancer Research Center (DKFZ) in Heidelberg (https://repdilpcr.eu). This service is anonymous, does not require registration and complies with common standards for protection of user data: raw data uploaded by the user are processed on the server and used to generate results that can be downloaded by the user; after the user closes the session by closing the browser window all uploaded data and processed results are automatically deleted from the server (Warning: if you use a local installation of repDilPCR, do not store your data in the folder where repDilPCR is installed or they will be deleted!).

The source code of the program is organized in three separate files. repDilPCR_lib.R is the core of the program. It is a library of functions that is used by the other two scripts: app.R (the Shiny app) and repDilPCR.R (the executable R script) that can function independently of each other. Further details and installation instructions for users that would like to install the program locally are available in the Supplementary Information (Additional file 1), as well as on the GitHub page of the project: https://github.com/deyanyosifov/repDilPCR.

Features and usage

The workflow is summarized in Fig. 1B. repDilPCR has been designed with the philosophy to automate and speed up data analysis. Once the input data have been uploaded in the correct format, the user can achieve all of the following with just a few clicks and within 1–2 min:

• Impute missing Cq values for reference genes (using the weighted predictive mean matching method from the R package mice [10]),

• Perform multiple linear regressions to get standard curves and Cq-Cq plots for all amplicons (based on Eq. 3 and 5 from the original article describing the dilution-replicate approach [8]),

• Identify possible outliers,

• Calculate relative quantities of the templates,

• Perform statistical tests to compare experimental groups,

• Prepare publication-ready plots (as in Fig. 1C),

• And download the results in a suitable format: Comma-Separated Values (CSV), Portable Document Format (PDF) or Portable Network Graphics (PNG).

Results and validation

We performed two validation qPCR experiments and analysed them using three different methods in parallel: the dilution-replicate approach with repDilPCR, the classical standard curve approach [2, 12] and LinRegPCR [6]. The standard curve approach uses a dilution series of single samples or of a pool of all samples to construct a standard curve for each amplicon and then determines its PCR efficiency from the slope of the curve according to the equation E=10^[−1/slope] [12]. These efficiencies are then used to determine the relative expression of each GOI versus reference genes according to the mathematical model published by Pfaffl or an equivalent model offered by Roche Diagnostics [2]. In contrast, the LinRegPCR program is based on an algorithm that estimates the baseline by reconstructing the log-linear phase downward from the early plateau phase of the PCR reaction [6]. PCR efficiency values are then determined per sample by fitting a regression line to a subset of data points in the log-linear phase. The relative expression of GOIs can then be estimated as described above for the standard curve approach.

The comparison of the three analysis methods showed that the obtained results were very similar when mRNA was used as a template in the reverse transcription step (Figs. 2 and ​and3;3; Additional file 1: Validation experiment 1). The differences in gene expression between undiluted and 1:1 diluted samples would be expected to be 1 unit on a log₂ scale and indeed these differences were close to 1 with all of the three analysis approaches and for both investigated GOIs: LGALS1 (Fig. 2) and VHL (Fig. S9). The goodness of the correlation between the methods is demonstrated quantitatively by the high coefficients of determination on the pairwise scatter plots (Fig. 3). Results from repDilPCR correlated a little bit better with results obtained via the standard curve method (R²=0.95–0.96) than with results from LinRegPCR (R²=0.91–0.95). Further details are given in the Supplementary Information (Additional file 1: Chapter 5.1, Fig. S9-S11, Table S1).

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Fig. 2

Relative expression of the galectin-1 gene (LGALS1) in different cell lines in Validation Experiment 1 as determined according to three different approaches: A standard curve; B LinRegPCR and C repDilPCR. Samples denoted by “(dil)” after the name of the cell line were diluted so that the expression values for LGALS1 would be half of those in the respective parent samples, i.e. the expected difference is 1 unit on a log₂ scale (see the Supplementary Data for details). Graphs A and B were prepared manually using Microsoft Excel. Graph C was prepared fully automatically by repDilPCR, starting from unprocessed Cq values. P-values are for comparisons with the HG-3 WT sample

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Fig. 3

Pairwise scatter plots comparing relative gene expression (on log₂ scale) determined by three different approaches in Validation Experiment 1. A Comparison of repDilPCR against the standard curve method. B Comparison of repDilPCR against LinRegPCR. C Comparison of LinRegPCR against the standard curve method. Each comparison was performed separately for the two genes of interest that were analysed: VHL and LGALS1. Each dot corresponds to a biological replicate in the experiment. The data were scaled to set the mean log₂(relative expression) to 0 to make comparisons possible. Linear regression was performed and the regression line with its 95%-confidence interval is shown for each comparison, as well as the p-value and the coefficient of determination (R²) of the model. Dashed lines indicate perfect correlation

In the second experiment, the aim was to assess expression levels of miRNAs (Additional file 1: Chapter 5.2, Validation experiment 2). Again, repDilPCR performed similarly to the standard curve method, however LinRegPCR did not always yield satisfactory results, probably because of the flatter amplification curves that made it difficult for the LinRegPCR program to reliably identify windows of linearity (Additional file 1: Fig. S12-S14). Accordingly, results from repDilPCR and the standard curve method correlated very well together (R²=0.98–1.0, Fig. 4A), whereas correlation was weaker for comparisons of LinRegPCR with the other two methods (Fig. 4B, ​B,C):C): R² was 0.69 for miR-17 and 0.99–1.0 for miR-155 but the regression lines for miR-155 were shifted away from the diagonal because several samples were not evaluable with LinRegPCR and the missing data interfered with the centering of the dataset around zero.

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Fig. 4

Pairwise scatter plots comparing relative gene expression (on log₂ scale) determined by three different approaches in Validation Experiment 2. A Comparison of repDilPCR against the standard curve method. B Comparison of repDilPCR against LinRegPCR. C Comparison of LinRegPCR against the standard curve method. Each comparison was performed separately for the two miRNAs that were analysed: miR-17 and miR-155. Each dot corresponds to a biological replicate in the experiment. The data were scaled to set the mean log₂(relative expression) to 0 to make comparisons possible. Linear regression was performed and the regression line with its 95%-confidence interval is shown for each comparison, as well as the p-value and the coefficient of determination (R²) of the model. Dashed lines indicate perfect correlation

In a third experiment, we verified the reproducibility of the dilution-replicate method by analysing the same samples in three separate PCR runs (Additional file 1: Chapter 5.3, Validation experiment 3, Fig. S15–17, Table S2). Furthermore, we demonstrated successful inter-run normalization using different multi-plate experiment designs—sample maximization or target maximization (Additional file 1: Fig. S18–23).

Discussion

Here we introduce repDilPCR as a new tool for analysis of qPCR data that brings to the field a number of functions that up to now have not been available in existing software. repDilPCR is the first tool that can make use of the efficient dilution-replicate design for qPCR experiments [8] but is not limited to it and can also work with relative expression values calculated elsewhere. The dilution-replicate approach has important advantages like the guarantee that all samples are within the linear dynamic range of the standard curve and reduced costs due to the possibility to use a smaller number of reactions. We have shown that the results produced by this approach are in good agreement with established gold standard methods (standard curve and LinRegPCR) and hope that its ease of use will stimulate more researchers to abandon bad practices like indiscriminately applying the 2^–Cq method without efficiency corrections or using a single and unvalidated reference gene. The dilution-replicate method has two small disadvantages: it is not suitable for very diluted templates that are close to the limit of detection and it requires slightly more time to prepare the reactions due to the additional dilution steps. However, the last downside is completely offset by the fast analysis of the results when using repDilPCR. Our tool offers a fully automated workflow, including automatic choice of statistical tests to compare experimental groups and generation of publication-ready plots. These functions can also be used with relative expression values calculated by other methods.

Other freely available web servers for analysis of qPCR experiments include qRAT [13], SATQPCR [14], QPCR [15], PIPE-T (as a tool in Galaxy [16]), Auto-qPCR [17] and “Do my qPCR calculation” [18]. Most of these applications use the Cq model without efficiency corrections (qRAT, PIPE-T, Auto-q-PCR) or only offer the possibility for manual input of efficiency values calculated elsewhere (SATQPCR, “Do my qPCR calculation”). Only QPCR offers different methods for reaction efficiency determination from the input data. Although all of these tools perform differential expression analysis, the statistical functions in some of them are quite rudimentary and suboptimally implemented, e.g. using parametric tests on non-normally distributed linearly scaled expression values, rather than on log-transformed values (Auto-q-PCR, “Do my qPCR calculation”). These two tools also apply arithmetic averaging of reference genes although geometric averaging should be used. None of the aforementioned tools is able to insert statistical test results directly on the graphical output like repDilPCR. We find a lot of these tools difficult to use as they are not interactive and the user has to download the results before seeing them (SATQPCR, Auto-qPCR, “Do my qPCR calculation”), require uploading separate data files for each sample (PIPE-T) or do not offer an obvious way to group single samples in experimental groups (qRAT). Finally, our attempt to use “Do my qPCR calculation” revealed that the program returns erroneous results because it calculates the delta wrongly as the difference between Cq values of individual wells and the average Cq value for the same gene within an experimental group. On a positive note, some of these tools are able to directly use output files from a number of thermocyclers (qRAT, QPCR, Auto-qPCR) and perform interplate normalization (qRAT, QPCR).

Conclusions

repDilPCR is an easy-to-use and feature-rich tool for analysis of qPCR experiments that is freely available and can be installed locally or used as a web service. We plan to improve it further, e.g. by adding more helpful hints and error messages. Users can provide feedback and suggest new features in the Discussions tab of the GitHub page of the project.

Availability and requirements

Project name: repDilPCR.

Project home page: https://github.com/deyanyosifov/repDilPCR

Web server: https://repdilpcr.eu

Operating system(s): Platform independent.

Programming language: R, Shiny.

Other requirements: any modern web browser for accessing the web service; R≥3.6 and R packages (car, gridExtra, tidyverse, mice, PMCMRplus, scales, RColorBrewer, ggbeeswarm, ggsignif, shiny, shinycssloader and shinyalert) for local installations.

License: GPL-3, resp. GNU Affero General Public License when installed as server.

Any restrictions to use by non-academics: none.

Supplementary Information

Acknowledgements

Abbreviations

Author contributions

DYY conceived the project, developed the software, designed validation experiments and wrote the manuscript. MR designed and performed validation experiments. SS and DM provided guidance and supervised manuscript writing. All authors read and approved the final manuscript.

Funding

Open Access funding enabled and organized by Projekt DEAL. This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under collaborative research centre project SFB1074 (subprojects B1 and B2). The funding body had no role in study design, data collection, analysis and interpretation or approval of the work for publication.

Availability of data and materials

The web server is available at https://repdilpcr.eu, where also example datasets can be downloaded from within the program. The source code can be downloaded from https://github.com/deyanyosifov/repDilPCR, where users can also find answers to frequently asked questions. The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations

Footnotes

References