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
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from real-time quantitative PCR experiments. The purpose of this
treport is to present the derivation, assumptions, and applications
ito 2DDCT
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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
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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
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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,
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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
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B
16 0.00 6 0.16 1.0 (0.9±1.1)
K
14
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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-
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jected to real-time quantitative PCR using gene-specific primers for
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