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Relative Quantification    or    Comparative Quantification in qPCR

Relative quantification determines the changes in steady-state mRNA levels of a gene across multiple samples and expresses it relative to the levels of an internal control RNA. This reference gene is often a housekeeping gene and can be co-amplified in the same tube in a multiplex assay or can be amplified in a separate tube. Therefore, relative quantification does not require standards with known concentrations and the reference can be any transcript, as long as its sequence is known. Relative quantification is based on the expression levels of a target gene versus one or more reference gene(s) and in many experiments it is adequate for investigating physiological changes in gene expression levels. To calculate the expression of a target gene in relation to an adequate reference gene various mathematical models are established. Calculations are based on the comparison of the distinct cycle determined by various methods, e.g. crossing points (CP) and cycle threshold values (Ct) at a constant level of fluorescence; or CP acquisition according to established mathematic algorithm. To date several calculation mathematical models have been developed calculating the relative expression ratio.

A new mathematical model for relative quantification in real-time RT-PCR
Pfaffl Michael W.
Nucleic Acids Res. 2001 29(9): E45

Use of the real-time polymerase chain reaction (PCR) to amplify cDNA products reverse transcribed from mRNA is on the way to becoming a routine tool in molecular biology to study low abundance gene expression. Real-time PCR is easy to perform, provides the necessary accuracy and produces reliable as well as rapid quantification results. But accurate quantification of nucleic acids requires a reproducible methodology and an adequate mathematical model for data analysis. This study enters into the particular topics of the relative quantification in real-time RT–PCR of a target gene transcript in comparison to a reference gene transcript. Therefore, a new mathematical model is presented. The relative expression ratio is calculated only from the real-time PCR efficiencies and the crossing point deviation of an unknown sample versus a control. This model needs no calibration curve. Control levels were included in the model to standardise each reaction run with respect to RNA integrity, sample loading and inter-PCR variations. High accuracy and reproducibility (<2.5% variation) were reached in LightCycler PCR using the established mathematical model.

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Absolute and relative real-time PCR in the quantification of tst gene expression among methicillin-resistant Staphylococcus aureus: evaluation by two mathematical models.
Chini V, Foka A, Dimitracopoulos G, Spiliopoulou I.
Lett Appl Microbiol. 2007 Nov;45(5):479-84.
Department of Microbiology, School of Medicine, University of Patras, Patras, Greece.

AIM: Absolute and relative quantitative real-time reverse transcriptase polymerase chain reaction (RT-PCR) by the use of two mathematical models were applied in order to study the expression of tst gene encoding the toxic shock syndrome toxin-1 (TSST-1), among methicillin-resistant Staphylococcus aureus (MRSA).
METHODS AND RESULTS: Thirteen epidemic MRSA belonging to different clones and carrying a variety of toxin genes were selected. tst gene expression was achieved by using absolute and relative quantitative real-time RT-PCR and the SYBR Green I. Absolute RT-PCR showed a statistically significant higher level of  tst expression among strains isolated from soft tissue infections. Relative quantification was performed in relation to 23S rRNA expression by the application of two mathematical models, the 2(-DeltaDeltaCt) and the Pfaffl analysis methods.
CONCLUSIONS: tst gene expression was best calculated by the relative real-time RT-PCR analysis applying the Pfaffl analysis method, taking into account the reactions' efficiencies. Level of tst expression was related to patients' infection and did not depend on the MRSA genetic profile.
SIGNIFICANCE AND IMPACT OF THE STUDY: The results indicate that the application of the Pfaffl analysis method in the evaluation of relative real-time RT-PCR is more adequate.
Real-Time PCR: Current Technology and Applications

Publisher: Caister Academic Press
Editor: Julie Logan, Kirstin Edwards and Nick Saunders Applied and Functional Genomics, Health Protection Agency, London (2009)
ISBN: 978-1-904455-39-4

Chapter 4 - Reference Gene Validation Software for Improved Normalization
J. Vandesompele, M. Kubista and M. W. Pfaffl  (2009)

Real-time PCR is the method of choice for expression analysis of a limited number of genes. The measured gene expression variation between subjects is the sum of the true biological variation and several confounding factors resulting in non-specific variation. The purpose of normalization is to remove the non-biological variation as much as possible. Several normalization strategies have been proposed, but the use of one or more reference genes is currently the preferred way of normalization. While these reference genes constitute the best possible normalizers, a major problem is that these genes have no constant expression under all experimental conditions. The experimenter therefore needs to carefully assess whether a certain reference gene is stably expressed in the experimental system under study. This is not trivial and represents a circular problem. Fortunately, several algorithms and freely available software have been developed to address this problem. This chapter aims to provide an overview of the different concepts.

Chapter 5 - Data Analysis Software
M. W. Pfaffl, J. Vandesompele and M. Kubista  (2009)

Quantitative real-time RT-PCR (qRT-PCR) is widely and increasingly used in any kind of mRNA quantification, because of its high sensitivity, good reproducibility and wide dynamic quantification range. While qRT-PCR has a tremendous potential for analytical and quantitative applications, a comprehensive understanding of its underlying principles is important. Beside the classical RT-PCR parameters, e.g. primer design, RNA quality, RT and polymerase performances, the fidelity of the quantification process is highly dependent on a valid data analysis. This review will cover all aspects of data acquisition (trueness, reproducibility, and robustness), potentials in data modification and will focus particularly on relative quantification methods. Furthermore useful bioinformatical, biostatical as well as multi-dimensional expression software tools will be presented.

Real-Time PCR: Current Technology and Applications - Book reviews:

"... a comprehensive overview of the RT-PCR technology, which is as up-to-date as a book can be ..." Mareike Viebahn in Current Issues in Molecular Biology (2009)

"... a useful book for students ..." from J. Microbiological Methods

"provides a dual focus by aiming, in the early chapters, to provide both the theory and practicalities of this diverse and superficially simple technology, counter-balancing this in the later chapters with real-world applications, covering infectious diseases, biodefence, molecular haplotyping and food standards." from Microbiology Today
"a reference work that should be found both in university libraries and on the shelves of experienced applications specialists." from Microbiology Today

"a comprehensive guide to real-time PCR technology and its applications" from Food Science and Technology Abstracts (2009) Volume 41 Number 6

"This volume should be of utmost interest to all investigators interested and involved in using RT-PCR ... the RT-PCR protocols covered in this book will be of interest to most, if not all, investigators engaged in research that uses this important technique ... a well balanced book covering the many potential uses of real-time PCR ... valuable for all those interested in RT-PCR." from Doodys reviews (2009)
"provide the novice and the experienced user with guidance on the technology, its instrumentation, and its applications" from SciTech Book News June 2009 p. 64

"... written by international authors expert in specific technical principles and applications ... a useful compendium of basic and advanced applications for laboratory scientists. It is an ideal introductory textbook and will serve as a practical handbook in laboratories where the technology is employed." from Christopher J. McIver, Microbiology Department, Prince of Wales Hospital, New South Wales, Australia writing in Australian J. Med. Sci. 2009. 30(2): 59-60

Relative Expression Software Tool (REST©) for group wise comparison
and statistical analysis of relative expression results in real-time PCR.

Michael W. Pfaffl, Graham W. Horgan & Leo Dempfle (2002) 
Nucleic Acids Research 2002 30(9): E36


Use of the real-time polymerase chain reaction (PCR) to amplify cDNA products reverse transcribed from mRNA (RT) is on the way to become a routine tool used in molecular biology to study low abundant gene expression. Real-time PCR is easy to perform, provides the necessary exactness and produces reliable as well as rapid quantification results. But accurate quantification of nucleic acids requires a reproducible methodology and an adequate mathematical model for data analysis. This study enters into the particular topics of the relative quantification in real-time RT-PCR of a target gene transcript in comparison to a reference gene transcript. Therefore a new mathematical model is presented. The relative expression ratio is calculated only from the real-time PCR efficiencies and the crossing point deviation of an unknown sample versus a control. This model needs no calibration curve. Control levels were included in the model to standardise each reaction run with respect to RNA integrity, sample loading and inter-PCR variations. High accuracy and reproducibility (<2.5% variation) were reached in LightCycler PCRusing the established mathematical model.


The reverse transcription (RT) followed by polymerase chain reaction (PCR) is the technique of choice to analyse mRNA expression derived from various sources. Real-time RT-PCR is high sensitive and allow a quantification of rare transcripts and small changes in gene expression. Beside this it is easy to perform, provides the necessary exactness and produces reliable as well as rapid quantification results. The simplest detection technique of newly synthesized PCR products in real-time PCR uses SYBR Green I fluorescence dye, that bind specifically to the minor groove double-stranded DNA. The quantification method of choice depends on the target sequence, the expected range of the mRNA amount present in the tissue, the degree of accuracy required, and whether quantification needs to be relative or absolute.

Generally two quantification types in real-time RT-PCR are possible:

A relative quantification based on the relative expression of a target gene versus 
a reference gene. To investigate the physiological changes in gene expression, 
the relative expression ratio is adequate for the most purposes.
An absolute quantification, based either on an internally or an externally calibration curve.
link => "absolute" quantification

Using such a calibration curve, the methododology has to be highly validated and the identical LightCycler PCR amplificationefficiencies for standard material and target cDNA must be confirmed. Nevertheless is the generation of stable and reliable standard material, either recombinant DNA or recombinant RNA, very time consuming and it must be precisely quantified. Further a normalisation of the target gene with an endogenous standard is recommended. Therefore mainly non regulated reference genes or house keeping genes like glyceraldehyde-3-phosphate dehydrogenase (G3PDH or GAPDH), albumin, actins, tubulins, cyclophilin, 18S rRNA or 28S rRNA were applicable. House keeping genes are present in all nucleated cell types since they are necessary for basis cell survival. The mRNA synthesis of these genes is considered to be stable and secure in various tissues, even under experimental treatments. But numerous studies have already shown that the mentioned house keeping genes are regulated and vary under experimental conditions. To circumvent the high expenditure of design and production of standard material, as well as optimisation and validation of a calibration curve based quantification model, and finally the needed normalisation of the target transcripts to an endogenous housekeeping transcript, an reliable and accurate relative quantification model in real-time (RT-) PCR is needed. This study enters into the particular topics of the relative quantification of a target gene in comparison to a reference gene. A new and simple mathematical model for data analysis was established, the application of the new model was tested and compared with available mathematical calculation models. Derived reproducibility, based on intra- and inter test variation of this relative quantification, and accuracy of the model will be discussed.

Real-time PCR amplification efficiencies and linearity

Real-time PCR efficiencies were calculated from the given slopes in LightCycler software. The corresponding real-time PCR efficiency (E) of one cycle in the exponential phase was calculated according to the equation: 

E = 10 ^[–1/slope]   (Figure 1)

Link => alternative efficiency calculation methods and algorithm

Investigated transcripts showed high real-time PCR efficiency rates for TyrA (E = 2.09), PyrB (E = 2.16) and Gst (E = 1.99) in the investigated range from 0.40 pg to 50 ng cDNA input (n = 3) with high linearity (Pearson cor. coef. r>0.95).


Intra-assay and inter-assay variation

To confirm precision and reproducibility of real-time PCR the intra-assay precision was determined in 3 repeats within one LightCycler run. Inter-assay variation was investigated in 3 different experiment runs performed on 3 days using 3 different premix cups of LightCycler – Fast Start DNA Master SYBR Green I kit (Roche Diagnostics). Determination of variation was done in 20 ng reverse transcribed total RNA (Table 1). Test reproducibility for all investigated transcripts was low in inter-test experiment (<3.91%) and even lower in intra-test experiment (<2.16%). The calculation of test precision and test variability is based on the CP variation from the CP mean value.

Mathematical model for relative quantification in real-time PCR
A new mathematical model was presented to determine the relative quantification of a target gene in comparison to a reference gene. The relative expression ratio ( R ) of a target gene is computed based on E and the CP deviation of a unknown sample versus a control (Equation 1), and expressed in comparison to a reference gene.

This reference gene could be a stable and secure unregulated transcript, e.g. a house keeping gene transcript. For the calculation of R, the individual real-time PCR efficiencies (E) and the CD deviation (delta CP) of the investigated transcripts must be known. Real-time PCR efficiencies were calculated, according to E = 10 [–1/slope] as shown in Figure 1 [Etarget = real-time PCR efficiency of target gene transcript;  Eref = real-time PCR efficiency of reference gene transcript]. CP deviations of  control cDNA minus sample of the target gene and reference genes were  calculated according to the derived CP values [delta CPtarget = CP of control - CP of sample;delta CPref = CP of control - sample]. Mean CP, variation of CP and delta CP values between control and sample of investigated transcripts are listed in Table 2. Beside this, the influence of differing cDNA input concentrations on delta CP are shown. Intended cDNA input concentration variation of control and sample were compared at different levels (low level: 3.2 ng, 4.0 ng, 4.8 ng cDNA; high level: 16 ng, 20 ng and 24 ng cDNA). They resulted in stable and constant delta CP cycle numbers. In Table 3 the correspondent ratios ( R ) of target genes in comparison to the reference gene were calculated, through to the established mathematical model (Equation 1). The expression ratios of target genes remain stable, even under intended –20% or +20% cDNA variation and low and high cDNA input levels, performed in two runs. A minimal coefficient of variation (CV) of 2.50% and 1.74% was observed, respectively.


Reverse transcription followed by PCR is the most powerful tool to amplify small amounts of mRNA. Because of its high ramping rates, limited annealing and elongation time, the rapid cycle PCR in the LightCycler system offers stringent reaction conditions to all PCR components and leads to a primer sensitive and template specific PCR. The application of fluorescence techniques to real-time PCR combines the PCR amplification, product detection and quantification of newly synthesised DNA, as well as the verification in the melting curve analysis. This led to the development of new kinetic RT-PCR methodologies that are revolutionising the possibilities of mRNA quantification.
We focused in this paper on the relative quantification of target gene transcripts in comparison to a reference gene transcript. A new mathematical model for data analysis was presented to calculate the relative expression ratio on the basis of the PCR efficiency and crossing point deviation of the investigated transcripts (Equation 1). The concept of the threshold fluorescence is the basis of an accurate and reproducible quantification using fluorescence based RT-PCR methodologies. Threshold fluorescence is defined as the point at which the fluorescence rises appreciably above the background fluorescence. In the used “Fit Point Method” the threshold fluorescence and therefore the DNA amount in the capillaries is identical for all samples. A linear relationship between the CP, crossing the threshold fluorescence, and the log of the start molecules input in the reaction is given. Therefore quantification will always occur during exponential phase, and it will be not affected by any reaction components becoming limited in the plateau phase. In the established model the relative expression ratio of an target gene is normalized with the expression of an endogenous desirable unregulated reference gene transcript to compensate inter PCR variations between the runs. Is the CP of the chosen reference gene equal in the control as well as in the sample (delta CP = 0), stable and constant reference gene mRNA levels are given. Under this considerations of an unregulated reference gene transcript no normalisation is needed and Equation 1 can be shortened to Equation 2 and 3

Two other mathematical models are available for the relative quantification during real-time PCR. The “Efficiency calibrated mathematical method for the relative expression ratio in real-time PCR” is presented by Roche Diagnostics in a truncated form in an internal publication. The complete equation is in principle the same and results in identical relative expression ratio like our model (Equation 4).

But, the way of calculation in the described mathematical model is hard to understand. The second model available, the “delta-delta Ct method” for comparing relative expression results between treatments in real-time PCR (Equation 4) is presented by PE Applied Biosystems (Perkin Elmer, Forster City, CA, USA). The model presumes an optimal and identical real-time amplification efficiencies of target and reference gene of E = 2. “Delta-delta Ct method” is only applicable for a quick estimation of the relative expression ratio. For such an quick estimation also equation 1 can be shortened and transferred in Equation 4

under the condition that 

Etarget  =  Eref  =  2 

Our presented formula 1 combines both models in order to better understanding 
the mode of CP data analysis and for a more reliable and exact relative gene expression.

Relative quantification is always based on an reference transcript. Normalisation of the target gene with an endogenous standard was done via the reference gene expression, to compensate inter-PCR variations. Beside this further control levels were included in the mathematical model to standardise each reaction run with respect to RNA integrity, RT efficiency or cDNA sample loading variations.The reproducibility of the RT step varies greatly between tissues, the applied RT isolation methodology (25) and the used RT enzymes (26). Different cDNA inputconcentrations were tested on low and high cDNA input ranges, to mimic different RT efficiencies (± 20%) at different quantification levels. In the applied two-step RT-PCR, using random hexamer primers, all possible interferences during RT will influence all target transcripts as well as the internal reference transcript in parallel. Occurring background interferences retrieved from extracted tissues components, like enzyme inhibitors, and cDNA synthesis efficiency were related to target and reference similarly. All products underwent identical reaction conditions during RT and variations only disappear during real-time PCR. Any source of error during RT will be compensated through the model itself. Widely distributed single-step RT-PCR models are not applicable, because in each reaction set-up and for each investigated factor individual and slightly different RT conditions will occur. Therefore the variation in a two-step RT-PCR will always be lower and the reproducibility of the assay will be higher, that in a single-step RT-PCR (8). Reproducibility of the developed mathematical model was dependent on the exact determination of real-time amplification efficiencies and on the given low LightCycler CP variability. In our mathematical model the needed reliability and reproducibility was given, which was confirmed by high accuracy and a relative error of <2.5% using low and high template concentration input.


LightCycler real-time PCR using SYBR Green I fluorescence dye is a rapid and sensitive method to detect low amounts of mRNA molecules and therefore offers important physiological insights on mRNA expression level. The established mathematical model is presented in order for a better understanding the mode of analysis in relative quantification in real-time RT-PCR. It is only dependent on DCP and amplification efficiency of the transcripts. No additional artificial nucleic acids, like recombinant nucleic acid constructs in external calibration curve models, are needed. Reproducibility of LightCycler RT-PCR in general and the minimal error rate of the model allows for an accurate determination of the relative expression ratio. Even different cDNA input resulted in minor variations. Relative expression is adequate for the most relevant physiological expression changes. In future it is not necessary to establish more complex and time consuming quantification models based on calibration curves. For the differential display of mRNA the relative expression ratio is an ideal and simple tool for the verification of RNA or DNA array chip technology results.

=>   Relative Expression Software Tool ( REST © )   <=

=>   download  REST ©    <=

 Analysis of relative gene expression data using real-time quantitative PCR and the
2^[ -delta delta Ct ] method.

Livak KJ  & Schmittgen TD.   Methods  2001 Dec;25(4): 402-408 

Applied Biosystems, Foster City, California 94404, USA.

The two most commonly used methods to analyze data from real-time, quantitative PCR experiments are absolute quantification and relative quantification. Absolute quantification determines the input copy number, usually by relating the PCR signal to a standard curve. Relative quantification relates the PCR signal of the target transcript in a treatment group to that of another sample such as an untreated control. The 2(-delta delta Ct) method is a convenient way to analyze the relative changes in gene expression from real-time quantitative PCR experiments. The purpose of this report is to present the derivation, assumptions, and applications of the 2(-delta delta Ct) method. In addition, we present the derivation and applications of two variations of the 2(-delta delta Ct) method that may be useful in the analysis of real-time, quantitative PCR data.

A quantitative real-time PCR method for detection of B-Lymphocyte Monoclonality
by comparison of kappa and
lambda Immunoglobulin Light Chain Expression

Anders Stahlberg,1 Pierre Aman, Börje Ridell, Petter Mostad, and Mikael Kubista

Clinical Chemistry 49(1): 51-59

Background: An abnormal IgL kappa / IgLlambda ratio has long been used as a clinical criterion for Hodgkin B-cell lymphomas. As a first step towards a quantitative real-time PCR based multi marker diagnostic analysis of lymphomas, we have developed a method for determination of IgL kappa / IgLlambda ratio in clinical samples.
Methods: Light-up probe based real-time PCR was used to quantify ,IgL kappa and IgLlambda cDNA from 20 clinical samples. The samples were also investigated by routine immunohistochemical analysis and flow cytometry analysis.
Results: The classification of patient samples by Q-PCR correlated well with the routine diagnostic data. To account for sample and template specific PCR inhibition in the biological samples, we developed a method for in situ calibration to determine sample specific Q-PCR efficiencies of the reactions being compared. This increased considerably the accuracy of the Q-PCR method. We also designed an approach to classify patient samples based on average PCR efficiencies. This allowed faster and more cost efficient classification suitable for a first gross classification in high throughput screens.
Conclusions: This work is a first step towards analyzing clinical samples using quantitative light-up probe based real-time PCR. Our results shows that Q-PCR based methods are highly suitable for high throughput screens of suspected tumor samples by determining anomalous gene expression that are characteristic for tumor cells.

Real-Time PCR Technology for Cancer Diagnostics
Philip S. Bernard and Carl T. Wittwer
Clinical Chemistry 48: 8  1178–1185 (2002)

Background: Advances in the biological sciences and technology are providing molecular targets for diagnosing and treating cancer. Current classifications in surgical pathology for staging malignancies are based primarily on anatomic features (e.g., tumor-nodemetastasis) and histopathology (e.g., grade). Microarrays together with clustering algorithms are revealing a molecular diversity among cancers that promises to form a new taxonomy with prognostic and, more importantly, therapeutic significance. The challenge for pathology will be the development and implementation of these molecular classifications for routine clinical practice. in the clinical laboratory. Quantitative real-time PCR can determine gene duplications or deletions. Furthermore, melting curve analysis immediately after PCR can identify small mutations, down to single base changes. These techniques are becoming easier and faster and can be multiplexed. Real-time PCR methods are a favorable option for the analysis of cancer markers.
Approach: This article discusses the benefits, challenges, and possibilities for solid-tumor profiling in the clinical laboratory with an emphasis on DNA-based PCR techniques. Content: Molecular markers can be used to provide accurate prognosis and to predict response, resistance, or toxicity to therapy. The diversity of genomic alterations involved in malignancy necessitates a variety of assays for complete tumor profiling. Some new molecular classifications of tumors are based on gene expression, requiring a paradigm shift in specimen processing to preserve the integrity of RNA for analysis. More stable markers (i.e., DNA and protein) are readily handled.  
Summary: There is a need to translate recent discoveries in oncology research into clinical practice. This requires objective, robust, and cost-effective molecular techniques for clinical trials and, eventually, routine use. Real-time PCR has attractive features for tumor profiling in the clinical laboratory