荧光定量PCR定量方法之2-△△CT_Method

METHODS 25, 402±408 (2001) doi:10.1006/meth.2001.1262, available online at http://www.idealibrary.com on Analysis of Relative Gene Expression Data Using Real- Time Quantitative PCR and the 22DDC Kenneth J. Livak* and Thomas D. Schmittgen² *A f W o sre inti m to a o t sa b co p from real-time quantitative PCR experiments. The purpose of this treport is to present the derivation, assumptions, and applications ito 2DDCT sa u in Els t g q t re fr u s p a u fu d ti m q a a t p B q in b ti 33 40 f the 2 method. In addition, we present the derivation and pplications of two variations of the 22DDCT method that may be seful in the analysis of real-time, quantitative PCR data. q 2001 evier Science (USA) Key Words: reverse transcription polymerase chain reaction; uantitative polymerase chain reaction; relative quantification; al-time polymerase chain reaction; Taq Man. Reserve transcription combined with the polymer- se chain reaction (RT-PCR) has proven to be a power- l method to quantify gene expression (1±3). Real- me PCR technology has been adapted to perform uantitative RT-PCR (4, 5). Two different methods of nalyzing data from real-time, quantitative PCR ex- eriments exist: absolute quantification and relative uantification. Absolute quantification determines the pplied Biosystems, Foster City, California 94404; and ²Department o ashington State University, Pullman, Washington 99164-6534 The two most commonly used methods to analyze data from al-time, quantitative PCR experiments are absolute quantifica- on and relative quantification. Absolute quantification deter- ines the input copy number, usually by relating the PCR signal a standard curve. Relative quantification relates the PCR signal f the target transcript in a treatment group to that of another mple such as an untreated control. The 22DDCT method is a nvenient way to analyze the relative changes in gene expression sput copy number of the transcript of interest, usually ty relating the PCR signal to a standard curve. Rela- pve quantification describes the change in expression t o w t1 To whom requests for reprints should be addressed. Fax: (509) 5-5902. E-mail: Schmittg@mail.wsu.edu. a 2 T Method ,1 Pharmaceutical Sciences, College of Pharmacy, f the target gene relative to some reference group uch as an untreated control or a sample at time zero a time-course study. Absolute quantification should be performed in situ- tions where it is necessary to determine the absolute ranscript copy number. Absolute quantification has een combined with real-time PCR and numerous re- orts have appeared in the literature (6±9) including wo articles in this issue (10, 11). In some situations, may be unnecessary to determine the absolute tran- cript copy number and reporting the relative change gene expression will suffice. For example, stating hat a given treatment increased the expression of ene x by 2.5-fold may be more relevant than stating hat the treatment increased the expression of gene x om 1000 copies to 2500 copies per cell. Quantifying the relative changes in gene expression sing real-time PCR requires certain equations, as- umptions, and the testing of these assumptions to roperly analyze the data. The 22DDCT method may be sed to calculate relative changes in gene expression etermined from real-time quantitative PCR experi- ents. Derivation of the 22DDCT equation, including ssumptions, experimental design, and validation ests, have been described in Applied Biosystems User ulletin No. 2 (P/N 4303859). Analyses of gene expres- ion data using the 22DDCT method have appeared in he literature (5, 6). The purpose of this report is to resent the derivation of the 22DDCT method, assump- ions involved in using the method, and applications f this method for the general literature. In addition, e present the derivation and application of two varia- ions of the 22DDCT method that may be useful in the nalysis of real-time quantitative PCR data. 1046-2023/01 $35.00 q 2001 Elsevier Science (USA) All rights reserved. ANALYSIS OF REAL-TIME PCR DATA 403 or1. THE 22DDCT METHOD XN 3 (1 1 E )DCT 5 K, [6] 1.1. Derivation of the 22DDCT Method w (Xc c w Tn thm a i a T H w p w fo C r K r 2DDCT 1 w ec mE at Di F e i q t t T Fo sye ca ex tr fr re sa (C w The equation that describes the exponential amplifi- ation of PCR is Xn 5 X0 3 (1 1 EX)n, [1] here Xn is the number of target molecules at cycle of the reaction, X0 is the initial number of target olecules. EX is the efficiency of target amplification, nd n is the number of cycles. The threshold cycle (CT) ndicates the fractional cycle number at which the mount of amplified target reaches a fixed threshold. hus, XT 5 X0 3 (1 1 EX)CT,X 5 KX [2] here XT is the threshold number of target molecules, T,X is the threshold cycle for target amplification, and X is a constant. A similar equation for the endogenous eference (internal control gene) reaction is RT 5 R0 3 (1 1 ER)CT,R 5 KR, [3] here RT is the threshold number of reference mole- ules, R0 is the initial number of reference molecules, R is the efficiency of reference amplification, CT,R is he threshold cycle for reference amplification, and KR s a constant. Dividing XT by RT gives the expression XT RT 5 X0 3 (1 1 EX)CT,X R0 3 (1 1 ER)CT,R 5 KX KR 5 K. [4] or real-time amplification using TaqMan probes, the xact values of XT and RT depend on a number of factors ncluding the reporter dye used in the probe, the se- uence context effects on the fluorescence properties of he probe, the efficiency of probe cleavage, purity of he probe, and setting of the fluorescence threshold. herefore, the constant K does not have to be equal to ne. Assuming efficiencies of the target and the refer- nce are the same, EX 5 ER 5 E, X0 R0 3 (1 1 E )CT,X2CT,R 5 K, [5] amount of target 5 2 . [9] .2. Assumptions and Applications of the 22DDCT Method For the DDCT calculation to be valid, the amplification fficiencies of the target and reference must be approxi- ately equal. A sensitive method for assessing if two mplicons have the same efficiency is to look at how CT varies with template dilution. Figure 1 shows the IG. 1. Validation of the 22DDCT method: Amplification of cDNA nthesized from different amounts of RNA. The efficiency of amplifi- tion of the target gene (c-myc) and internal control (GAPDH) was amined using real-time PCR and TaqMan detection. Using reverse anscriptase, cDNA was synthesized from 1 mg total RNA isolated om human Raji cells. Serial dilutions of cDNA were amplified by al-time PCR using gene-specific primers. The most concentrated mple contained cDNA derived from 1 ng of total RNA. The DCT T,c2myc 2 CT,GAPDH) was calculated for each cDNA dilution. The data ere fit using least-squares linear regression analysis (N 5 3). here XN is equal to the normalized amount of target 0 /R0) and DCT is equal to the difference in threshold ycles for target and reference (CT,X 2 CT,R). Rearranging gives the expression XN 5 K 3 (1 1 E )2DCT. [7] he final step is to divide the XN for any sample q by e XN for the calibrator (cb): XN,q XN,cb 5 K 3 (1 1 E )2DCT,q K 3 (1 1 E )2DCT,cb 5 (1 1 E )2DDCT. [8] ere 2DDCT 5 2(DCT,q 2 DCT,cb). For amplicons designed to be less than 150 bp and for hich the primer and Mg2+ concentrations have been roperly optimized, the efficiency is close to one. There- re, the amount of target, normalized to an endogenous eference and relative to a calibrator, is given by LIVAK AND SCHMITTGEN404 results of an experiment where a cDNA preparation change in gene expression relative to an untreated con- trol, for example, if one wanted to determine the expres-was diluted over a 100-fold range. For each dilution sample, amplifications were performed using primers sion of a particular mRNA in an organ. In these cases, ta a in dt t R aI e a bl t m so a T vI t a pa A m 1r m 1 g 2 y e i s mv s o en t c Tm w (C xm d s Cp A w wm d n t p (F do t p cm g s mg t t so t g ht f rc t t es p t o nd fluorogenic probes for c-myc and GAPDH. The aver- ge CT was calculated for both c-myc and GAPDH and he DCT (CT,myc 2 CT,GAPDH) was determined. A plot of he log cDNA dilution versus DCT was made (Fig. 1). f the absolute value of the slope is close to zero, the fficiencies of the target and reference genes are simi- ar, and the DDCT calculation for the relative quantifica- ion of target may be used. As shown in Fig. 1, the slope f the line is 0.0471; therefore, the assumption holds nd the DDCT method may be used to analyze the data. f the efficiencies of the two amplicons are not equal, hen the analysis may need to be performed via the bsolute quantification method using standard curves. lternatively, new primers can be designed and/or opti- ized to achieve a similar efficiency for the target and eference amplicons. .3. Selection of Internal Control and Calibrator for the 2DDCT Method The purpose of the internal control gene is to normal- ze the PCRs for the amount of RNA added to the re- erse transcription reactions. We have found that tandard housekeeping genes usually suffice as inter- al control genes. Suitable internal controls for real- ime quantitative PCR include GAPDH, b -actin, b2- icroglobulin, and rRNA. Other housekeeping genes ill undoubtedly work as well. It is highly recom- ended that the internal control gene be properly vali- ated for each experiment to determine that gene ex- ression is unaffected by the experimental treatment. method to validate the effect of experimental treat- ent on the expression of the internal control gene is escribed in Section 2.2. The choice of calibrator for the 22DDCT method de- ends on the type of gene expression experiment that ne has planned. The simplest design is to use the un- reated control as the calibrator. Using the 22DDCT ethod, the data are presented as the fold change in ene expression normalized to an endogenous reference ene and relative to the untreated control. For the un- reated control sample, DDCT equals zero and 20 equals ne, so that the fold change in gene expression relative o the untreated control equals one, by definition. For he treated samples, evaluation of 22DDCT indicates the old change in gene expression relative to the untreated ontrol. Similar analysis could be applied to study the ime course of gene expression where the calibrator ample represents the amount of transcript that is ex- ressed at time zero. Situations exist where one may not compare the he calibrator may be the expression of the same mRNA another organ. Table 1 presents mean CT values etermined for c-myc and GAPDH transcripts in total NA samples from brain and kidney. The brain was rbitrarily chosen as the calibrator in this example. The mount of c-myc, normalized to GAPDH and relative to rain, is reported. Although the relative quantitative ethod can be used to make this type of tissue compari- on, biological interpretation of the results is complex. he single relative quantity reported actually reflects ariation in both target and reference transcripts across variety of cell types that might be present in any articular tissue. .4. Data Analysis Using the 22DDCT Method The CT values provided from real-time PCR instru- entation are easily imported into a spreadsheet pro- ram such as Microsoft Excel. To demonstrate the anal- sis, data are reported from a quantitative gene xpression experiment and a sample spreadsheet is de- cribed (Fig. 2). The change in expression of the fos±glo± yc target gene normalized to b -actin was monitored ver 8 h. Triplicate samples of cells were collected at ach time point. Real-time PCR was performed on the orresponding cDNA synthesized from each sample. he data were analyzed using Eq. [9], where DDCT 5 T,Target 2 CT,Actin)Time x 2 (CT,Target 2 CT,Actin)Time 0. Time is any time point and Time 0 represents the 13 expres- ion of the target gene normalized to b -actin. The mean T values for both the target and internal control genes ere determined at time zero (Fig. 2, column 8) and ere used in Eq. [9]. The fold change in the target gene, ormalized to b -actin and relative to the expression at ime zero, was calculated for each sample using Eq. [9] ig. 2, column 9). The mean, SD, and CV are then etermined from the triplicate samples at each time oint. Using this analysis, the value of the mean fold hange at time zero should be very close to one (i.e., ince 20 5 1). We have found the verification of the ean fold change at time zero to be a convenient method o check for errors and variation among the triplicate amples. A value that is very different from one sug- ests a calculation error in the spreadsheet or a very igh degree of experimental variation. In the preceding example, three separate RNA prepa- ations were made for each time point and carried hrough the analysis. Therefore, it made sense to treat ach sample separately and average the results after he 22DDCT calculation. When replicate PCRs are run n the same sample, it is more appropriate to average ANALYSIS OF REAL-TIME PCR DATA 405 CT data before performing the 22DDCT calculation. Ex- (GAPDH) were amplified in separate wells. There is no reason to pair any particular c-myc well with anyactly how the averaging is performed depends on if the target and reference are amplified in separate wells particular GAPDH well. Therefore, it makes sense to F r PCR and the Ct data were imported into Microsoft Excel. The mean fold change in expression of the target gene at each time point was c et a alculated using Eq. [9], where DDCT 5 (CT,Target 2 C,Actin)Time x 2 (CT,Targ s is a sample calculation for the fold change using 22DDCT (black box). 2 C,Actin)Time 0. The mean CT at time zero are shown (colored boxes) IG. 2. Sample spreadsheet of data analysis using the 22DDCT method. The fold change in expression of the target gene ( fos±glo±myc) elative to the internal control gene (b -actin) at various time points was studied. The samples were analyzed using real-time quantitative average the c-myc and GAPDH CT values separatelyor in the same well. Table 1 presents data from an experiment where the target (c-myc) and reference before performing the DCT calculation. The variance TABLE 1 Treatment of Replicate Data Where Target and Reference Are Amplified in Separate Wellsa DCT (Avg. c-myc CT 2 DDCT (Avg. DCT Normalized c-myc amount Tissue c-myc CT GAPDH CT Avg. GAPDH CT 2 Avg. DCT,Brain) relative to brain 22DDCT Brain 30.72 23.70 30.34 23.56 30.58 23.47 30.34 23.65 30.50 23.69 30.43 23.68 Average 30.49 6 0.15 23.63 6 0.09 6.86 6 0.17 0.00 6 0.17 1.0 (0.9±1.1) Kidney 27.06 22.76 27.03 22.61 27.03 22.62 27.10 22.60 26.99 22.61 26.94 22.76 Average 27.03 6 0.06 22.66 6 0.08 4.37 6 0.10 22.50 6 0.10 5.6 (5.3±6.0) a Total RNA from human brain and kidney were purchased from Clontech. Using reverse transcriptase, cDNA was synthesized from 1 mg total RNA. Aliquots of cDNA were used as template for real-time PCR reactions containing either primers and probe for c-myc or primers and probe for GAPDH. Each reaction contained cDNA derived from 10 ng total RNA. Six replicates of each reaction were performed. LIVAK AND SCHMITTGEN406 estimated from the replicate CT values is carried of an arbitrary constant. This gives results equivalent to those reported in Fig. 2 where CT values for nonrepli-through to the final calculation of relative quantities using standard propagation of error methods. One diffi- cated samples were carried through the entire 22DDCT Such situations include when only limited amounts ofIn Tables 1 and 2, the estimated error has not been i R oD p n ea t t E c T B 16 0.00 6 0.16 1.0 (0.9±1.1) K 14 p G a B yc a ncreased in proceeding from the DCT column to the DCT column. This is because we have decided to dis- lay the data with error shown both in the calibrator nd in the test sample. Subtraction of the average DCT,cb o determine the DDCT value is treated as subtraction TABL Treatment of Replicate Data Where Target and c-myc DCT (Avg. c-my issue CT GAPDH CT Avg. GAPDH rain 32.38 25.07 7.31 32.08 25.29 6.79 32.35 25.32 7.03 32.08 25.24 6.84 32.34 25.17 7.17 32.13 25.29 6.84 Average 6.93 6 0. idney 28.73 24.30 4.43 28.84 24.32 4.52 28.51 24.31 4.20 28.86 24.25 4.61 28.86 24.34 4.52 28.70 24.18 4.52 Average 4.47 6 0. a An experiment like that described in Table 1 was performed exce APDH. The probe for c-myc was labeled with the reporter dye FAM ecause of the different reporter dyes, the real-time PCR signals for c-m re occurring in the same well. 22.47 6 0.14 5.5 (5.0±6.1) t the reactions contained primers and probes for both c-myc and nd the probe for GAPDH was labeled with the reporter dye JOE. and GAPDH can be distinguished even though both amplifications NA are available or when high-throughput processing f many samples is desired. It is possible, though, to ormalize to some measurement external to the PCR xperiment. The most common method for normaliza- ion is to use UV absorbance to determine the amount 2 Reference are Amplified in the Same Wella CT 2 DDCT (Avg. DCT Normalized c-myc amount CT) 2 Avg. DCT,Brain) relative to brain 22DDCT calculation before averaging. Alternatively, it is possi-culty is that CT is exponentially related to copy number (see Section 4 below). Thus, in the final calculation, the ble to report results with the calibrator quantity defined as 13 without any error. In this case, the error esti-error is estimated by evaluating the 22DDCT term using DDCT plus the standard deviation and DDCT minus the mated for the average DCT,cb value must be propagated into each of the DDCT values for the test samples. Instandard deviation. This leads to a range of values that is asymmetrically distributed relative to the average Table 1, the DDCT value for the kidney sample would become 22.50 6 0.20 and the normalized c-myc amountvalue. The asymmetric distribution is a consequence of converting the results of an exponential process into a would be 5.63 with a range of 4.9 to 6.5. Results for brain would be reported as 13 without any error.linear comparison of amounts. By using probes labeled with distinguishable reporter dyes, it is possible to run the target and reference ampli- fications in the same well. Table 2 presents data from 2. THE 22DC8T METHOD an experiment where the target (c-myc) and reference (GAPDH) were amplified in the same well. In any par- 2.1. Derivation of the 22DC8T Methodticular well, we know that the c-myc reaction and the GAPDH reaction had exactly the same cDNA input. Normalizing to an endogenous reference provides a method for correcting results for differing amounts ofTherefore, it makes sense to calculate DCT separately for each well. These DCT values can then be averaged input RNA. One hallmark of the 22DDCT method is that it uses data generated as part of the real-time PCRbefore proceeding with the 22DDCT calculation. Again, the estimated error is given as an asymmetric range of experiment to perform this normalization function. This is particularly attractive when it is not practicalvalues, reflecting conversion of an exponential variable to a linear comparison. to measure the amount of input RNA by other methods. ANALYSIS OF REAL-TIME PCR DATA 407 of RNA added to a cDNA reaction. PCRs are then set equation where DC8T 5 CT,Time x 2 CT,Time 0 (Fig. 3). A sta- tistically significant relationship exists between theup using cDNA derived from the same amount of input RNA. One example of using this external normalization treatment and expression of GAPDH but not for b2- mi e m st t p tt a g 3 PR o p N C c r w t c v e r 2 d t d t i Fo we o h s S ma jected to real-time quantitative PCR using gene-specific primers for s b a w isa frd t G t wg s to study the effect of experimental treatment on the xpression of an endogenous reference to determine if he internal control is affected