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A new mathematical model for relative quantification in real-time RT–PCR

A new mathematical model for relative quantification in real-time RT–PCR © 2001 Oxford University Press Nucleic Acids Research, 2001, Vol. 29, No. 9 00 A new mathematical model for relative quantification in real-time RT–PCR MichaelW.Pfaffl* Institute of Physiology, FML-Weihenstephan, Center of Life and Food Sciences, Technical University of Munich, Germany Received December 18, 2000; Revised February 21, 2001; Accepted March 14, 2001 ABSTRACT fication types in real-time RT-PCR are possible. (i) A relative quantification based on the relative expression of a target gene Use of the real-time polymerase chain reaction (PCR) versus a reference gene. To investigate the physiological to amplify cDNA products reverse transcribed from changes in gene expression, the relative expression ratio is mRNA is on the way to becoming a routine tool in adequate for the most purposes. (ii) An absolute quantification, molecular biology to study low abundance gene based either on an internal or an external calibration curve expression. Real-time PCR is easy to perform, (1,3). Using such a calibration curve, the methodology has to provides the necessary accuracy and produces reli- be highly validated and the identical LightCycler PCR amplifi- cation efficiencies for standard material and target cDNA must able as well as rapid quantification results. But accu- be confirmed (4–6). Nevertheless, the generation of stable and rate quantification of nucleic acids requires a reliable standard material, either recombinant DNA or recom- reproducible methodology and an adequate mathe- binant RNA, is very time consuming and it must be precisely matical model for data analysis. This study enters quantified (2,7,8). Furthermore, a normalisation of the target into the particular topics of the relative quantification gene with an endogenous standard is recommended. Therefore, in real-time RT–PCR of a target gene transcript in mainly non-regulated reference genes or housekeeping genes like comparison to a reference gene transcript. There- glyceraldehyde-3-phosphate dehydrogenase (G3PDH or fore, a new mathematical model is presented. The GAPDH), albumin, actins, tubulins, cyclophilin, 18S rRNA or relative expression ratio is calculated only from the 28S rRNA (9) were applicable. Housekeeping genes are real-time PCR efficiencies and the crossing point present in all nucleated cell types since they are necessary for deviation of an unknown sample versus a control. basis cell survival. The mRNA synthesis of these genes is This model needs no calibration curve. Control levels considered to be stable and secure in various tissues, even under experimental treatments (9–11). But numerous studies were included in the model to standardise each reac- have already shown that the housekeeping genes are regulated tion run with respect to RNA integrity, sample and vary under experimental conditions (12–15). To circum- loading and inter-PCR variations. High accuracy and vent the high expenditure of design and production of standard reproducibility (<2.5% variation) were reached in material, as well as optimisation and validation of a calibration LightCycler PCR using the established mathematical curve based quantification model, and finally the need for model. normalisation of the target transcripts to an endogenous house- keeping transcript, a reliable and accurate relative quantifica- tion model in real-time RT–PCR is needed. INTRODUCTION This study enters into the particular topics of the relative Reverse transcription (RT) followed by the polymerase chain quantification of a target gene in comparison to a reference reaction (PCR) is the technique of choice to analyse mRNA gene. A new and simple mathematical model for data analysis expression derived from various sources. Real-time RT–PCR was established, the application of the new model was tested is highly sensitive and allows quantification of rare transcripts and compared with available mathematical calculation models. and small changes in gene expression. As well as this, it is easy Derived reproducibility, based on intra- and inter-test variation to perform, provides the necessary accuracy and produces of this relative quantification and accuracy of the model will be reliable as well as rapid quantification results. The simplest discussed. detection technique for newly synthesised PCR products in real-time PCR uses SYBR Green I fluorescence dye that binds MATERIALS AND METHODS specifically to the minor groove double-stranded DNA (1). The quantification method of choice depends on the target RNA source, total RNA extraction and RT sequence, the expected range of mRNA amount present in the tissue, the degree of accuracy required and whether quantifica- RNA extraction was performed as described previously (16) in tion needs to be relative or absolute (2). Generally two quanti- bacterial Escherichia coli culture grown either in M9 minimal *To whom correspondence should be addressed at present address: Institut für Physiologie, Weihenstephaner Berg 3, 85354 Freising, Weihenstephan, Germany. Tel: +49 8161 71 3511; Fax: +49 8161 71 4204; Email: [email protected] Nucleic Acids Research, 2001, Vol. 29, No. 9 00 PAGE 2003 OF 2007 Table 1. Intra-assay (test precision) and inter-assay variation (test variability) of LightCycler real-time RT–PCR Intra-assay variation (n = 3) Inter-assay variation (n =3) Mean CP CV Mean CP CV TyrA (sample) 15.020 0.06% 15.311 3.58% TyrA (control) 20.303 0.09% 20.426 2.98% PyrB (sample) 16.031 2.16% 16.289 3.91% PyrB (control) 11.720 1.32% 12.011 3.18% Gst (sample) 14.533 0.65% 14.371 2.26% Gst (control) 14.277 0.11% 13.997 2.62% Determination of variation was done in 20 ng reverse transcribed total RNA. Test variation is based on CP variation and expressed as mean CP with CV. media (sample preparation) or LB rich media (control prepara- tion), both with 0.4% glucose concentration (17). RNA integrity was electrophoretically verified by ethidium bromide staining and by OD /OD nm absorption ratio >1.95. Escherichia 260 280 coli total RNA (1 µ g) was reverse transcribed with 100 U of Superscript II Plus RNase H Reverse Trancriptase (Gibco BRL Life Technologies, Gaithersburg, MD) using 100 µ M random hexamer primers (Pharmacia Biotech, Uppsala, Sweden) according to the manufacturer’s instructions. Optimisation of RT–PCR Highly purified salt-free primer for target gene1 (TyrA, tryptophan operon: forward primer, AAG CGT CTG GAA CTG GTT GC; reverse primer, AAA CGC TGT GCG TAA TCG CC), target gene 2 (PyrB, aspartate transcarbamylase: forward primer, GCT CCA ACC AAC ATC CGA; reverse primer, TTC ACG Figure 1. Determination of real-time PCR efficiencies of reference gene (Gst), target gene 1 (TyrA) and target gene 2 (PyrB). CP cycles versus cDNA (reverse TTG GCG TAC TCG G) and reference gene (Gst, glutathione transcribed total RNA) concentration input were plotted to calculate the slope transferase: forward primer, CTT TGC CGT TAA CCC TAA (mean ± SD; n = 3). The corresponding real-time PCR efficiencies were calcu- [–1/slope] GGG; reverse primer, GCT GCA ATG TGC TCT AAC CC) lated according to the equation: E = 10 (18). were generated (MWG Biotech, Ebersberg, Germany) and optimised to an equal annealing temperature of 60°C. Condi- tions for all PCRs were optimised in a gradient cycler (Master- Cycler rotor. The following LightCycler experimental run cycler Gradient, Eppendorf, Germany) with regard to Taq DNA protocol was used: denaturation program (95°C for 10 min), polymerase (Roche Diagnostics, Basel, Switzerland), forward amplification and quantification program repeated 40 times and reverse primers, MgCl concentrations (Roche Diagnostics), (95°C for 15 s, 60°C for 10 s, 72°C for 60 s with a single dNTP concentrations (Roche Diagnostics) and various fluorescence measurement), melting curve program (60–95°C annealing temperatures (55–65°C). RT–PCR amplification with a heating rate of 0.1°C per second and a continuous fluo- products were separated on a 4% high resolution NuSieve rescence measurement) and finally a cooling step to 40°C. For agarose (FMC Bio Products, Rockland, ME) gel electro- the mathematical model it is necessary to determine the phoresis and analysed with the Image Master system (Pharmacia crossing points (CP) for each transcript. CP is defined as the Biotech). Optimised results were transferred on the following point at which the fluorescence rises appreciably above the LightCycler PCR protocol. background fluorescence. ‘Fit Point Method’ must be performed in the LightCycler software 3.3 (Roche Diagnostics), LightCycler real-time PCR at which CP will be measured at constant fluorescence level For LightCycler reaction a mastermix of the following reaction (18). components was prepared to the indicated end-concentration: 13 µ l water, 2.4 µ lMgCl (4 mM), 0.8 µ lforward primer RESULTS (0.4 µ M), 0.8 µ l reverse primer (0.4 µ M) and 2.0 µ lLightCyler (Fast Start DNA Master SYBR Green I; Roche Diagnostics). Confirmation of primer specificity LightCycler mastermix (19 µ l) was filled in the LightCycler glass capillaries and 1 µ l cDNA (3.2, 4.0, 4.8, 16, 20 or 24 ng Specificity of RT–PCR products was documented with high reverse transcribed total RNA) was added as PCR template. resolution gel electrophoresis and resulted in a single product Capillaries were closed, centrifuged and placed into the Light- with the desired length (TyrA, 978 bp; PyrB, 530 bp; and Gst, PAGE 2004 OF 2007 00 Nucleic Acids Research, 2001, Vol. 29, No. 9 402 bp). In addition a LightCycler melting curve analysis was performed which resulted in single product specific melting temperatures as follows: TyrA, 89.6°C; PyrB, 88.5°C; and Gst, 88.3°C. No primer-dimers were generated during the applied 40 real-time PCR amplification cycles. 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 [–1/slope] calculated according to the equation: E =10 (Fig. 1) (18). Investigated transcripts showed high real-time PCR efficiency rates; for TyrA, 2.09; PyrB, 2.16; and Gst, 1.99 in the investi- gated range from 0.40 to 50 ng cDNA input (n = 3) with high linearity (Pearson correlation coefficient r >0.95). Figure 2. Real-time RT–PCR SYBR Green I fluorescence history versus cycle Intra- and inter-assay variation number of target gene 1 (TyrA), target gene 2 (PyrB) and reference gene (Gst) in sample cDNA and control cDNA. CP determination was done at fluores- To confirm accuracy and reproducibility of real-time PCR the cence level 1. intra-assay precision was determined in three repeats within one LightCycler run. Inter-assay variation was investigated in three different experimental runs performed on 3 days using three different premix cups of LightCycler, Fast Start DNA cDNA input concentrations on ∆ CP are also shown. Intended Master SYBR Green I kit (Roche Diagnostics). Determination cDNA input concentration variation of control and sample of variation was done in 20 ng transcribed total RNA (Table 1). were compared at different levels (low level, 3.2, 4.0, 4.8 ng Test reproducibility for all investigated transcripts was low in cDNA; high level, 16, 20 and 24 ng cDNA). They resulted in inter-test experiments (<3.91%) and even lower in intra-test stable and constant ∆ CP cycle numbers. In Table 3 the corre- experiments (<2.16%). The calculation of test precision and sponding ratios of target genes in comparison to the reference test variability is based on the CP variation from the CP mean gene were calculated, through to the established mathematical value. model (equation 1). The expression ratios of target genes remain stable, even under intended ±20% cDNA variation and Mathematical model for relative quantification in real- low and high cDNA input levels, performed in two runs. A time PCR minimal coefficient of variation (CV) of 2.50 and 1.74% was A new mathematical model was presented to determine the observed, respectively. relative quantification of a target gene in comparison to a refer- Regulation of investigated gene transcripts ence gene. The relative expression ratio (R)ofatarget gene is calculated based on E and the CP deviation of an unknown All investigated transcript expressions were regulated diver- sample versus a control, and expressed in comparison to a gently (Table 3). The expression of Gst was constant, inde- reference gene. pendent of media conditions, and therefore was chosen as endogenous standard or reference gene transcript Fig. 2. TyrA ∆ CP() co n tro l – s am pl e target mRNA expression, measuredin 20ngcDNA, was up-regulated () E target 5.283 ratio = ---- -------- ------- -------- ------- -------- ------- -------- -------- --- 1 49.1-fold (2.09 ) in M9 minimal compared to LB rich ∆ CP() control – sample ref () E ref medium under high cDNA input conditions. Under the considera- tion of the reference gene expression the real up-regulation Equation 1 shows a mathematical model of relative expression ratio was, on average, 58.5-fold. PyrB mRNA expression was ratio in real-time PCR. The ratio of a target gene is expressed down-regulated under M9 minimal medium conditions by a 4.311 in a sample versus a control in comparison to a reference gene. factor of 27.6 (2.16 ). With the normalisation of the endog- E is the real-time PCR efficiency of target gene transcript; enous standard transcript, the exact relative expression ratio target E is the real-time PCR efficiency of a reference gene tran- can be calculated to 23.2. ref script; ∆ CP is the CP deviation of control – sample of the target target gene transcript; ∆ CP = CP deviation of control – ref DISCUSSION sample of reference gene transcript. The reference gene could be a stable and secure unregulated transcript, e.g. a house- RT followed by PCR is the most powerful tool to amplify keeping gene transcript. For the calculation of R, the individual small amounts of mRNA (19). Because of its high ramping real-time PCR efficiencies and the CD deviation (∆ CP)ofthe rates, limited annealing and elongation time, the rapid cycle investigated transcripts must be known. Real-time PCR PCR in the LightCycler system offers stringent reaction condi- [–1/slope] efficiencies were calculated, according to E =10 (18), as tions to all PCR components and leads to a primer sensitive shown in Figure 1. CP deviations of control cDNA minus and template specific PCR (20). The application of fluo- sample of the target gene and reference genes were calculated rescence techniques to real-time PCR combines the PCR according to the derived CP values. Mean CP, variation of CP amplification, product detection and quantification of newly and ∆ CP values between control and sample of investigated synthesised DNA, as well as verification in the melting curve transcripts are listed in Table 2. The influence of differing analysis. This led to the development of new kinetic RT–PCR Nucleic Acids Research, 2001, Vol. 29, No. 9 00 PAGE 2005 OF 2007 Table 2. Mean CP and CV of target gene 1 (TyrA) and target gene 2 (PyrB) in comparison to intended concentration variation of reference gene (Gst) low level (3.2, 4.0 and 4.8 ng per capillary) and high level cDNA input (16, 20 and 24 ng) cDNA input (ng) Mean CP (n =3) CV (%) ∆ CP (cycles) High cDNA input level TyrA (sample) 20 15.020 0.06 +5.283 TyrA (control) 20 20.303 0.09 PyrB (sample) 20 16.031 2.16 –4.311 PyrB (control) 20 11.720 1.32 Gst (sample) 16 14.290 0.73 –0.277 Gst (control) 16 14.013 0.39 Gst (sample) 20 14.533 0.65 –0.256 Gst (control) 20 14.277 0.11 Gst (sample) 24 14.957 1.29 –0.227 Gst (control) 24 14.730 1.14 Low cDNA input level TyrA (sample) 4.0 17.353 2.16 +5.487 TyrA (control) 4.0 22.840 1.26 PyrB (sample) 4.0 17.667 0.75 –4.277 PyrB (control) 4.0 13.390 0.12 Gst (sample) 3.2 16.927 0.643 –0.050 Gst (control) 3.2 16.877 1.81 Gst (sample) 4.0 16.750 2.31 –0.127 Gst (control) 4.0 16.623 1.04 Gst (sample) 4.8 16.297 1.68 –0.077 Gst (control) 4.8 16.220 0.69 methodologies that are revolutionising the possibilities of mRNA of a target gene is normalised with the expression of an endo- quantification (21). genous desirable unregulated reference gene transcript to compensate inter-PCR variations between the runs. The CP of In this paper, we focused on the relative quantification of the chosen reference gene is the same in the control and the target gene transcripts in comparison to a reference gene tran- sample (∆ CP = 0). Stable and constant reference gene mRNA script. A new mathematical model for data analysis was levels are given. Under these considerations of an unregulated presented to calculate the relative expression ratio on the basis reference gene transcript, no normalisation is needed and equa- of the PCR efficiency and crossing point deviation of the tion 1 can be shortened to equation 2. investigated transcripts (equation 1). The concept of threshold fluorescence is the basis of an accurate and reproducible quan- (co n tro l -sam pl e ) ∆ CP target tification using fluorescence-based RT–PCR methods (22). () E target ratio = ---- -------- ------- -------- ------- -------- ------- -------- -------- - - Threshold fluorescence is defined as the point at which the () E ref fluorescence rises appreciably above the background fluores- cence. In the Fit Point Method, the threshold fluorescence and () control -sa mp le ∆ CP target therefore the DNA amount in the capillaries is identical for all ratio =() E target samples. CP determination with the ‘Second Derivative Maximum Method’ is not adequate for our mathematical model, because quantification is done at the point of most effi- Equation 2 shows a mathematical model of relative expression cient real-time PCR where the second derivative is at its ratio in real-time PCR under constant reference gene expression. maximum (18). CP values in the sample and control are equal and represent A linear relationship between the CP, crossing the threshold ideal housekeeping conditions (∆ CP =0, E =1). ref ref fluorescence, and the log of the start molecules input in the Two other mathematical models are available for the relative reaction is given (18,23). Therefore, quantification will always quantification during real-time PCR. The ‘efficiency calibrated occur during the exponential phase, and it will not be affected mathematical method for the relative expression ratio in real- by any reaction components becoming limited in the plateau time PCR’ is presented by Roche Diagnostics in a truncated phase (7). In the established model the relative expression ratio form in an internal publication (24). The complete equation is, PAGE 2006 OF 2007 00 Nucleic Acids Research, 2001, Vol. 29, No. 9 in principle, the same and the results are in identical relative Table 3. Influence of variation in cDNA input (±20%) of control and sample (highand low level)onthe variationinrelativeexpression ratiobased on expression ratio like our model (equation 3). equation 1 and the error of mathematical model, expressed as CV of R CP CP Gst TyrA PyrB Sample Calibrator () E () E ref ref ratio = ---- -------- ------- -------- ------ - ÷ --- -------- ------- -------- ------- ----- - 3 E =1.99 E =2.09 E =2.16 CP CP Sample Calibrator () E () E target target High cDNA input level ∆ CP = +5.283 ∆ CP = –4.311 80% cDNA input ∆ CP = –0.277 R = 59.476 R = 0.04375 Efficiency calibrated mathematical method for the relative 100% cDNA input ∆ CP = –0.256 R = 58.625 R = 0.04312 expression ratio in real-time PCR presented by Soong et al. 120% cDNA input ∆ CP = –0.227 R = 57.459 R = 0.04226 (24). But the method of calculation in the described mathematical Mean of R 58.45900 0.04304 model is hard to understand. The second model available, the Error/CV of R 1.73% 1.74% ‘Delta–delta method’ for comparing relative expression results between treatments in real-time PCR (equation 4)ispresented by PE Applied Biosystems (Perkin Elmer, Forster City, CA). LowcDNAinput level ∆ CP = +5.487 ∆ CP = –4.277 –[] ∆ CP sample - ∆ CP control 16% cDNA input ∆ CP = –0.050 R = 59.104 R = 0.03844 ratio = 2 20% cDNA input ∆ CP = –0.127 R = 62.102 R = 0.04031 24% cDNA input DCP = –0.077 R = 60.208 R = 0.03914 –∆∆ CP ratio = 2 Mean of R 60.471 0.03930 Error/CV of R 2.50% 2.49% Equation 4 shows a mathematical delta–delta method for comparing relative expression results between treatments in real-time PCR developed by PE Applied Biosystems (Perkin Elmer). Optimal and identical real-time amplification efficiencies of target and reference gene of E =2are presumed. the developed mathematical model was dependent on the exact The delta–delta method is only applicable for a quick estima- determination of real-time amplification efficiencies and on tion of the relative expression ratio. For such a quick estima- the given low LightCycler CP variability. In our mathematical tion, equation 1 can be shortened and transferred into equation model the necessary reliability and reproducibility was given, 4, under the condition that E = E = 2. Our presented which was confirmed by high accuracy and a relative error of target ref formula combines both models in order to better understand <2.5% using low and high template concentration input. the mode of CP data analysis and for a more reliable and exact relative gene expression. CONCLUSION Relative quantification is always based on a reference tran- script. Normalisation of the target gene with an endogenous LightCycler real-time PCR using SYBR Green I fluorescence standard was done via the reference gene expression, to dye is a rapid and sensitive method to detect low amounts of compensate inter-PCR variations. Beside this further control mRNA molecules and therefore offers important physiological levels were included in the mathematical model to standardise insights on mRNA expression level. The established mathe- each reaction run with respect to RNA integrity, RT efficiency matical model is presented in order to better understand the or cDNA sample loading variations. The reproducibility of the mode of analysis in relative quantification in real-time RT– RT step varies greatly between tissues, the applied RT isola- PCR. It is only dependent on ∆ CP and amplification efficiency tion methodology (25) and the RT enzymes used (26). of the transcripts. No additional artificial nucleic acids, like Different cDNA input concentrations were tested on low and recombinant nucleic acid constructs in external calibration high cDNA input ranges, to mimic different RT efficiencies curve models, are needed. Reproducibility of LightCycler RT– (±20%) at different quantification levels. In the applied two- PCR in general and the minimal error rate of the model allows step RT–PCR, using random hexamer primers, all possible for an accurate determination of the relative expression ratio. interferences during RT will influence all target transcripts as Even different cDNA input resulted in minor variations. Rela- well as the internal reference transcript in parallel. Occurring tive expression is adequate for the most relevant physiological background interferences retrieved from extracted tissue expression changes. In future it is not necessary to establish components, like enzyme inhibitors, and cDNA synthesis more complex and time consuming quantification models efficiency were related to target and reference similarly. All based on calibration curves. For the differential display of products underwent identical reaction conditions during RT mRNA the relative expression ratio is an ideal and simple tool and variations only disappear during real-time PCR. Any for the verification of RNA or DNA array chip technology source of error during RT will be compensated through the results. 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 condi- ACKNOWLEDGEMENTS tions will occur. Therefore, the variation in a two-step RT–PCR will always be lower, and the reproducibility of the assay will The author thanks D.Schmidt for technical assistance. Primers, be higher, that in a single-step RT–PCR (8). Reproducibility of primer sequences and samples were kindly donated by Drs Nucleic Acids Research, 2001, Vol. 29, No. 9 00 PAGE 2007 OF 2007 13. Bereta,J. and Bereta,M. (1995) Stimulation of glyceraldehyde-3-phosphate S.Wegener and W.Mann in collaboration with the BioChip dehydrogenase mRNA levels by endogenous nitric oxide in cytokine-activated division of MWG Biotech in Ebersberg, Germany. endothelium. Biochem. Biophys. Res. Commun., 217, 363–369. 14. Chang,T.J., Juan,C.C., Yin,P.H., Chi,C.W. and Tsay,H.J. (1998) Up- regulation of β-actin, cyclophilin and GAPDH in N1S1 rat hepatoma. REFERENCES Oncol. Rep., 5, 469–471. 1. Morrison,T., Weis,J.J. and Wittwer,C.T. (1998) Quantification of low- 15. Zhang,J. and Snyder,S.H. (1992) Nitric oxide stimulates auto-ADP- copy transcripts by continuous SYBR Green I monitoring during ribosylation of glyceraldehydes 3 phosphate dehydrogenase. Proc. Natl amplification. Biotechniques, 24, 954–962. 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(1994) Comparison Comparison of the efficiency of M-MuLV reverse transcriptase, RNase H of glyceraldehyde-3-phosphate dehydrogenase and 28S-ribosomal RNA gene M-MuLV reverse transcriptase and AMV reverse transcriptase for the expression as RNA loading controls for northern blot analysis of cell lines of amplification of human immunglobulin genes. Biotechnol. Techniques, varying malignant potential. Anal. Biochem., 216, 223–226. 12, 485–489. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nucleic Acids Research Oxford University Press

A new mathematical model for relative quantification in real-time RT–PCR

Nucleic Acids Research , Volume 29 (9) – May 1, 2001

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0305-1048
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1362-4962
DOI
10.1093/nar/29.9.e45
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Abstract

© 2001 Oxford University Press Nucleic Acids Research, 2001, Vol. 29, No. 9 00 A new mathematical model for relative quantification in real-time RT–PCR MichaelW.Pfaffl* Institute of Physiology, FML-Weihenstephan, Center of Life and Food Sciences, Technical University of Munich, Germany Received December 18, 2000; Revised February 21, 2001; Accepted March 14, 2001 ABSTRACT fication types in real-time RT-PCR are possible. (i) A relative quantification based on the relative expression of a target gene Use of the real-time polymerase chain reaction (PCR) versus a reference gene. To investigate the physiological to amplify cDNA products reverse transcribed from changes in gene expression, the relative expression ratio is mRNA is on the way to becoming a routine tool in adequate for the most purposes. (ii) An absolute quantification, molecular biology to study low abundance gene based either on an internal or an external calibration curve expression. Real-time PCR is easy to perform, (1,3). Using such a calibration curve, the methodology has to provides the necessary accuracy and produces reli- be highly validated and the identical LightCycler PCR amplifi- cation efficiencies for standard material and target cDNA must able as well as rapid quantification results. But accu- be confirmed (4–6). Nevertheless, the generation of stable and rate quantification of nucleic acids requires a reliable standard material, either recombinant DNA or recom- reproducible methodology and an adequate mathe- binant RNA, is very time consuming and it must be precisely matical model for data analysis. This study enters quantified (2,7,8). Furthermore, a normalisation of the target into the particular topics of the relative quantification gene with an endogenous standard is recommended. Therefore, in real-time RT–PCR of a target gene transcript in mainly non-regulated reference genes or housekeeping genes like comparison to a reference gene transcript. There- glyceraldehyde-3-phosphate dehydrogenase (G3PDH or fore, a new mathematical model is presented. The GAPDH), albumin, actins, tubulins, cyclophilin, 18S rRNA or relative expression ratio is calculated only from the 28S rRNA (9) were applicable. Housekeeping genes are real-time PCR efficiencies and the crossing point present in all nucleated cell types since they are necessary for deviation of an unknown sample versus a control. basis cell survival. The mRNA synthesis of these genes is This model needs no calibration curve. Control levels considered to be stable and secure in various tissues, even under experimental treatments (9–11). But numerous studies were included in the model to standardise each reac- have already shown that the housekeeping genes are regulated tion run with respect to RNA integrity, sample and vary under experimental conditions (12–15). To circum- loading and inter-PCR variations. High accuracy and vent the high expenditure of design and production of standard reproducibility (<2.5% variation) were reached in material, as well as optimisation and validation of a calibration LightCycler PCR using the established mathematical curve based quantification model, and finally the need for model. normalisation of the target transcripts to an endogenous house- keeping transcript, a reliable and accurate relative quantifica- tion model in real-time RT–PCR is needed. INTRODUCTION This study enters into the particular topics of the relative Reverse transcription (RT) followed by the polymerase chain quantification of a target gene in comparison to a reference reaction (PCR) is the technique of choice to analyse mRNA gene. A new and simple mathematical model for data analysis expression derived from various sources. Real-time RT–PCR was established, the application of the new model was tested is highly sensitive and allows quantification of rare transcripts and compared with available mathematical calculation models. and small changes in gene expression. As well as this, it is easy Derived reproducibility, based on intra- and inter-test variation to perform, provides the necessary accuracy and produces of this relative quantification and accuracy of the model will be reliable as well as rapid quantification results. The simplest discussed. detection technique for newly synthesised PCR products in real-time PCR uses SYBR Green I fluorescence dye that binds MATERIALS AND METHODS specifically to the minor groove double-stranded DNA (1). The quantification method of choice depends on the target RNA source, total RNA extraction and RT sequence, the expected range of mRNA amount present in the tissue, the degree of accuracy required and whether quantifica- RNA extraction was performed as described previously (16) in tion needs to be relative or absolute (2). Generally two quanti- bacterial Escherichia coli culture grown either in M9 minimal *To whom correspondence should be addressed at present address: Institut für Physiologie, Weihenstephaner Berg 3, 85354 Freising, Weihenstephan, Germany. Tel: +49 8161 71 3511; Fax: +49 8161 71 4204; Email: [email protected] Nucleic Acids Research, 2001, Vol. 29, No. 9 00 PAGE 2003 OF 2007 Table 1. Intra-assay (test precision) and inter-assay variation (test variability) of LightCycler real-time RT–PCR Intra-assay variation (n = 3) Inter-assay variation (n =3) Mean CP CV Mean CP CV TyrA (sample) 15.020 0.06% 15.311 3.58% TyrA (control) 20.303 0.09% 20.426 2.98% PyrB (sample) 16.031 2.16% 16.289 3.91% PyrB (control) 11.720 1.32% 12.011 3.18% Gst (sample) 14.533 0.65% 14.371 2.26% Gst (control) 14.277 0.11% 13.997 2.62% Determination of variation was done in 20 ng reverse transcribed total RNA. Test variation is based on CP variation and expressed as mean CP with CV. media (sample preparation) or LB rich media (control prepara- tion), both with 0.4% glucose concentration (17). RNA integrity was electrophoretically verified by ethidium bromide staining and by OD /OD nm absorption ratio >1.95. Escherichia 260 280 coli total RNA (1 µ g) was reverse transcribed with 100 U of Superscript II Plus RNase H Reverse Trancriptase (Gibco BRL Life Technologies, Gaithersburg, MD) using 100 µ M random hexamer primers (Pharmacia Biotech, Uppsala, Sweden) according to the manufacturer’s instructions. Optimisation of RT–PCR Highly purified salt-free primer for target gene1 (TyrA, tryptophan operon: forward primer, AAG CGT CTG GAA CTG GTT GC; reverse primer, AAA CGC TGT GCG TAA TCG CC), target gene 2 (PyrB, aspartate transcarbamylase: forward primer, GCT CCA ACC AAC ATC CGA; reverse primer, TTC ACG Figure 1. Determination of real-time PCR efficiencies of reference gene (Gst), target gene 1 (TyrA) and target gene 2 (PyrB). CP cycles versus cDNA (reverse TTG GCG TAC TCG G) and reference gene (Gst, glutathione transcribed total RNA) concentration input were plotted to calculate the slope transferase: forward primer, CTT TGC CGT TAA CCC TAA (mean ± SD; n = 3). The corresponding real-time PCR efficiencies were calcu- [–1/slope] GGG; reverse primer, GCT GCA ATG TGC TCT AAC CC) lated according to the equation: E = 10 (18). were generated (MWG Biotech, Ebersberg, Germany) and optimised to an equal annealing temperature of 60°C. Condi- tions for all PCRs were optimised in a gradient cycler (Master- Cycler rotor. The following LightCycler experimental run cycler Gradient, Eppendorf, Germany) with regard to Taq DNA protocol was used: denaturation program (95°C for 10 min), polymerase (Roche Diagnostics, Basel, Switzerland), forward amplification and quantification program repeated 40 times and reverse primers, MgCl concentrations (Roche Diagnostics), (95°C for 15 s, 60°C for 10 s, 72°C for 60 s with a single dNTP concentrations (Roche Diagnostics) and various fluorescence measurement), melting curve program (60–95°C annealing temperatures (55–65°C). RT–PCR amplification with a heating rate of 0.1°C per second and a continuous fluo- products were separated on a 4% high resolution NuSieve rescence measurement) and finally a cooling step to 40°C. For agarose (FMC Bio Products, Rockland, ME) gel electro- the mathematical model it is necessary to determine the phoresis and analysed with the Image Master system (Pharmacia crossing points (CP) for each transcript. CP is defined as the Biotech). Optimised results were transferred on the following point at which the fluorescence rises appreciably above the LightCycler PCR protocol. background fluorescence. ‘Fit Point Method’ must be performed in the LightCycler software 3.3 (Roche Diagnostics), LightCycler real-time PCR at which CP will be measured at constant fluorescence level For LightCycler reaction a mastermix of the following reaction (18). components was prepared to the indicated end-concentration: 13 µ l water, 2.4 µ lMgCl (4 mM), 0.8 µ lforward primer RESULTS (0.4 µ M), 0.8 µ l reverse primer (0.4 µ M) and 2.0 µ lLightCyler (Fast Start DNA Master SYBR Green I; Roche Diagnostics). Confirmation of primer specificity LightCycler mastermix (19 µ l) was filled in the LightCycler glass capillaries and 1 µ l cDNA (3.2, 4.0, 4.8, 16, 20 or 24 ng Specificity of RT–PCR products was documented with high reverse transcribed total RNA) was added as PCR template. resolution gel electrophoresis and resulted in a single product Capillaries were closed, centrifuged and placed into the Light- with the desired length (TyrA, 978 bp; PyrB, 530 bp; and Gst, PAGE 2004 OF 2007 00 Nucleic Acids Research, 2001, Vol. 29, No. 9 402 bp). In addition a LightCycler melting curve analysis was performed which resulted in single product specific melting temperatures as follows: TyrA, 89.6°C; PyrB, 88.5°C; and Gst, 88.3°C. No primer-dimers were generated during the applied 40 real-time PCR amplification cycles. 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 [–1/slope] calculated according to the equation: E =10 (Fig. 1) (18). Investigated transcripts showed high real-time PCR efficiency rates; for TyrA, 2.09; PyrB, 2.16; and Gst, 1.99 in the investi- gated range from 0.40 to 50 ng cDNA input (n = 3) with high linearity (Pearson correlation coefficient r >0.95). Figure 2. Real-time RT–PCR SYBR Green I fluorescence history versus cycle Intra- and inter-assay variation number of target gene 1 (TyrA), target gene 2 (PyrB) and reference gene (Gst) in sample cDNA and control cDNA. CP determination was done at fluores- To confirm accuracy and reproducibility of real-time PCR the cence level 1. intra-assay precision was determined in three repeats within one LightCycler run. Inter-assay variation was investigated in three different experimental runs performed on 3 days using three different premix cups of LightCycler, Fast Start DNA cDNA input concentrations on ∆ CP are also shown. Intended Master SYBR Green I kit (Roche Diagnostics). Determination cDNA input concentration variation of control and sample of variation was done in 20 ng transcribed total RNA (Table 1). were compared at different levels (low level, 3.2, 4.0, 4.8 ng Test reproducibility for all investigated transcripts was low in cDNA; high level, 16, 20 and 24 ng cDNA). They resulted in inter-test experiments (<3.91%) and even lower in intra-test stable and constant ∆ CP cycle numbers. In Table 3 the corre- experiments (<2.16%). The calculation of test precision and sponding ratios of target genes in comparison to the reference test variability is based on the CP variation from the CP mean gene were calculated, through to the established mathematical value. model (equation 1). The expression ratios of target genes remain stable, even under intended ±20% cDNA variation and Mathematical model for relative quantification in real- low and high cDNA input levels, performed in two runs. A time PCR minimal coefficient of variation (CV) of 2.50 and 1.74% was A new mathematical model was presented to determine the observed, respectively. relative quantification of a target gene in comparison to a refer- Regulation of investigated gene transcripts ence gene. The relative expression ratio (R)ofatarget gene is calculated based on E and the CP deviation of an unknown All investigated transcript expressions were regulated diver- sample versus a control, and expressed in comparison to a gently (Table 3). The expression of Gst was constant, inde- reference gene. pendent of media conditions, and therefore was chosen as endogenous standard or reference gene transcript Fig. 2. TyrA ∆ CP() co n tro l – s am pl e target mRNA expression, measuredin 20ngcDNA, was up-regulated () E target 5.283 ratio = ---- -------- ------- -------- ------- -------- ------- -------- -------- --- 1 49.1-fold (2.09 ) in M9 minimal compared to LB rich ∆ CP() control – sample ref () E ref medium under high cDNA input conditions. Under the considera- tion of the reference gene expression the real up-regulation Equation 1 shows a mathematical model of relative expression ratio was, on average, 58.5-fold. PyrB mRNA expression was ratio in real-time PCR. The ratio of a target gene is expressed down-regulated under M9 minimal medium conditions by a 4.311 in a sample versus a control in comparison to a reference gene. factor of 27.6 (2.16 ). With the normalisation of the endog- E is the real-time PCR efficiency of target gene transcript; enous standard transcript, the exact relative expression ratio target E is the real-time PCR efficiency of a reference gene tran- can be calculated to 23.2. ref script; ∆ CP is the CP deviation of control – sample of the target target gene transcript; ∆ CP = CP deviation of control – ref DISCUSSION sample of reference gene transcript. The reference gene could be a stable and secure unregulated transcript, e.g. a house- RT followed by PCR is the most powerful tool to amplify keeping gene transcript. For the calculation of R, the individual small amounts of mRNA (19). Because of its high ramping real-time PCR efficiencies and the CD deviation (∆ CP)ofthe rates, limited annealing and elongation time, the rapid cycle investigated transcripts must be known. Real-time PCR PCR in the LightCycler system offers stringent reaction condi- [–1/slope] efficiencies were calculated, according to E =10 (18), as tions to all PCR components and leads to a primer sensitive shown in Figure 1. CP deviations of control cDNA minus and template specific PCR (20). The application of fluo- sample of the target gene and reference genes were calculated rescence techniques to real-time PCR combines the PCR according to the derived CP values. Mean CP, variation of CP amplification, product detection and quantification of newly and ∆ CP values between control and sample of investigated synthesised DNA, as well as verification in the melting curve transcripts are listed in Table 2. The influence of differing analysis. This led to the development of new kinetic RT–PCR Nucleic Acids Research, 2001, Vol. 29, No. 9 00 PAGE 2005 OF 2007 Table 2. Mean CP and CV of target gene 1 (TyrA) and target gene 2 (PyrB) in comparison to intended concentration variation of reference gene (Gst) low level (3.2, 4.0 and 4.8 ng per capillary) and high level cDNA input (16, 20 and 24 ng) cDNA input (ng) Mean CP (n =3) CV (%) ∆ CP (cycles) High cDNA input level TyrA (sample) 20 15.020 0.06 +5.283 TyrA (control) 20 20.303 0.09 PyrB (sample) 20 16.031 2.16 –4.311 PyrB (control) 20 11.720 1.32 Gst (sample) 16 14.290 0.73 –0.277 Gst (control) 16 14.013 0.39 Gst (sample) 20 14.533 0.65 –0.256 Gst (control) 20 14.277 0.11 Gst (sample) 24 14.957 1.29 –0.227 Gst (control) 24 14.730 1.14 Low cDNA input level TyrA (sample) 4.0 17.353 2.16 +5.487 TyrA (control) 4.0 22.840 1.26 PyrB (sample) 4.0 17.667 0.75 –4.277 PyrB (control) 4.0 13.390 0.12 Gst (sample) 3.2 16.927 0.643 –0.050 Gst (control) 3.2 16.877 1.81 Gst (sample) 4.0 16.750 2.31 –0.127 Gst (control) 4.0 16.623 1.04 Gst (sample) 4.8 16.297 1.68 –0.077 Gst (control) 4.8 16.220 0.69 methodologies that are revolutionising the possibilities of mRNA of a target gene is normalised with the expression of an endo- quantification (21). genous desirable unregulated reference gene transcript to compensate inter-PCR variations between the runs. The CP of In this paper, we focused on the relative quantification of the chosen reference gene is the same in the control and the target gene transcripts in comparison to a reference gene tran- sample (∆ CP = 0). Stable and constant reference gene mRNA script. A new mathematical model for data analysis was levels are given. Under these considerations of an unregulated presented to calculate the relative expression ratio on the basis reference gene transcript, no normalisation is needed and equa- of the PCR efficiency and crossing point deviation of the tion 1 can be shortened to equation 2. investigated transcripts (equation 1). The concept of threshold fluorescence is the basis of an accurate and reproducible quan- (co n tro l -sam pl e ) ∆ CP target tification using fluorescence-based RT–PCR methods (22). () E target ratio = ---- -------- ------- -------- ------- -------- ------- -------- -------- - - Threshold fluorescence is defined as the point at which the () E ref fluorescence rises appreciably above the background fluores- cence. In the Fit Point Method, the threshold fluorescence and () control -sa mp le ∆ CP target therefore the DNA amount in the capillaries is identical for all ratio =() E target samples. CP determination with the ‘Second Derivative Maximum Method’ is not adequate for our mathematical model, because quantification is done at the point of most effi- Equation 2 shows a mathematical model of relative expression cient real-time PCR where the second derivative is at its ratio in real-time PCR under constant reference gene expression. maximum (18). CP values in the sample and control are equal and represent A linear relationship between the CP, crossing the threshold ideal housekeeping conditions (∆ CP =0, E =1). ref ref fluorescence, and the log of the start molecules input in the Two other mathematical models are available for the relative reaction is given (18,23). Therefore, quantification will always quantification during real-time PCR. The ‘efficiency calibrated occur during the exponential phase, and it will not be affected mathematical method for the relative expression ratio in real- by any reaction components becoming limited in the plateau time PCR’ is presented by Roche Diagnostics in a truncated phase (7). In the established model the relative expression ratio form in an internal publication (24). The complete equation is, PAGE 2006 OF 2007 00 Nucleic Acids Research, 2001, Vol. 29, No. 9 in principle, the same and the results are in identical relative Table 3. Influence of variation in cDNA input (±20%) of control and sample (highand low level)onthe variationinrelativeexpression ratiobased on expression ratio like our model (equation 3). equation 1 and the error of mathematical model, expressed as CV of R CP CP Gst TyrA PyrB Sample Calibrator () E () E ref ref ratio = ---- -------- ------- -------- ------ - ÷ --- -------- ------- -------- ------- ----- - 3 E =1.99 E =2.09 E =2.16 CP CP Sample Calibrator () E () E target target High cDNA input level ∆ CP = +5.283 ∆ CP = –4.311 80% cDNA input ∆ CP = –0.277 R = 59.476 R = 0.04375 Efficiency calibrated mathematical method for the relative 100% cDNA input ∆ CP = –0.256 R = 58.625 R = 0.04312 expression ratio in real-time PCR presented by Soong et al. 120% cDNA input ∆ CP = –0.227 R = 57.459 R = 0.04226 (24). But the method of calculation in the described mathematical Mean of R 58.45900 0.04304 model is hard to understand. The second model available, the Error/CV of R 1.73% 1.74% ‘Delta–delta method’ for comparing relative expression results between treatments in real-time PCR (equation 4)ispresented by PE Applied Biosystems (Perkin Elmer, Forster City, CA). LowcDNAinput level ∆ CP = +5.487 ∆ CP = –4.277 –[] ∆ CP sample - ∆ CP control 16% cDNA input ∆ CP = –0.050 R = 59.104 R = 0.03844 ratio = 2 20% cDNA input ∆ CP = –0.127 R = 62.102 R = 0.04031 24% cDNA input DCP = –0.077 R = 60.208 R = 0.03914 –∆∆ CP ratio = 2 Mean of R 60.471 0.03930 Error/CV of R 2.50% 2.49% Equation 4 shows a mathematical delta–delta method for comparing relative expression results between treatments in real-time PCR developed by PE Applied Biosystems (Perkin Elmer). Optimal and identical real-time amplification efficiencies of target and reference gene of E =2are presumed. the developed mathematical model was dependent on the exact The delta–delta method is only applicable for a quick estima- determination of real-time amplification efficiencies and on tion of the relative expression ratio. For such a quick estima- the given low LightCycler CP variability. In our mathematical tion, equation 1 can be shortened and transferred into equation model the necessary reliability and reproducibility was given, 4, under the condition that E = E = 2. Our presented which was confirmed by high accuracy and a relative error of target ref formula combines both models in order to better understand <2.5% using low and high template concentration input. the mode of CP data analysis and for a more reliable and exact relative gene expression. CONCLUSION Relative quantification is always based on a reference tran- script. Normalisation of the target gene with an endogenous LightCycler real-time PCR using SYBR Green I fluorescence standard was done via the reference gene expression, to dye is a rapid and sensitive method to detect low amounts of compensate inter-PCR variations. Beside this further control mRNA molecules and therefore offers important physiological levels were included in the mathematical model to standardise insights on mRNA expression level. The established mathe- each reaction run with respect to RNA integrity, RT efficiency matical model is presented in order to better understand the or cDNA sample loading variations. The reproducibility of the mode of analysis in relative quantification in real-time RT– RT step varies greatly between tissues, the applied RT isola- PCR. It is only dependent on ∆ CP and amplification efficiency tion methodology (25) and the RT enzymes used (26). of the transcripts. No additional artificial nucleic acids, like Different cDNA input concentrations were tested on low and recombinant nucleic acid constructs in external calibration high cDNA input ranges, to mimic different RT efficiencies curve models, are needed. Reproducibility of LightCycler RT– (±20%) at different quantification levels. In the applied two- PCR in general and the minimal error rate of the model allows step RT–PCR, using random hexamer primers, all possible for an accurate determination of the relative expression ratio. interferences during RT will influence all target transcripts as Even different cDNA input resulted in minor variations. Rela- well as the internal reference transcript in parallel. Occurring tive expression is adequate for the most relevant physiological background interferences retrieved from extracted tissue expression changes. In future it is not necessary to establish components, like enzyme inhibitors, and cDNA synthesis more complex and time consuming quantification models efficiency were related to target and reference similarly. All based on calibration curves. For the differential display of products underwent identical reaction conditions during RT mRNA the relative expression ratio is an ideal and simple tool and variations only disappear during real-time PCR. Any for the verification of RNA or DNA array chip technology source of error during RT will be compensated through the results. 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 condi- ACKNOWLEDGEMENTS tions will occur. Therefore, the variation in a two-step RT–PCR will always be lower, and the reproducibility of the assay will The author thanks D.Schmidt for technical assistance. 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Nucleic Acids ResearchOxford University Press

Published: May 1, 2001

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