Analysis of Relative Gene Expression Data Using Real-Time Quantitative PCR and the 2−ΔΔCT Method
Methods, 2001 · paper · Biomedicine
Explains the derivation, assumptions and applications of the 2−ΔΔCT method for calculating relative changes in gene expression from real-time quantitative PCR data, and presents two variations of it.
Checked: PDF from ffclrp.usp.br, fetched 5 Oct 2026. Page numbers are those of that PDF.
6 findings
Substance Table 2, Brain, Average row prints ΔCT "6.93 ± 0.16", but the six listed brain ΔCT values (7.31, 6.79, 7.03, 6.84, 7.17, 6.84) average 7.00 with SD 0.21; the kidney ΔΔCT "−2.47 ± 0.14" and fold value "5.5 (5.0–6.1)" are built on 6.93.
- p. 5 Table 2, Brain, Average row, ΔCT column
6.93 ± 0.16
- p. 5 Table 2, Brain, first row
7.31
- p. 5 Table 2, Kidney Average row
−2.47 ± 0.14
- p. 5 Table 2, Brain Average, ΔCT column
6.93 6 0.16
Only the authors can say what is right here.
Judge's note: Read Table 2 on the page 5 image. Each of the six brain ΔCT values equals c-myc CT minus GAPDH CT for its row. Their sum is 41.98 and their mean 6.997. The sum of squared deviations is 0.2212, giving a sample SD of 0.210 (0.19 with divisor n), not 0.16. Averaging the two CT columns first gives the same 7.00. The kidney block computed the same way reproduces the print (26.80/6 = 4.467, SD 0.14), so no other convention is in use. The text and footnote give no explanation, such as an excluded well. Either a printed brain CT value or the average and SD is misprinted; with 7.00 the kidney ΔΔCT would be about −2.53 and the fold value about 5.8. Only the authors can say which number is wrong.
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Substance Section 3: "the mean ± SD was 9.08 × 10−7 ± 1.33 × 10−7 with a CV of 13.5%"; the printed SD divided by the printed mean is 14.6%, not 13.5%.
- p. 7 Section 3, left column
the mean ± SD was 9.08 × 10−7 ± 1.33 × 10−7 with a CV of 13.5%
- p. 7 Section 3, left column
20.0 ± 0.194 with a CV of 0.971%
- p. 7 Section 3, paragraph 2
9.08 × 10−7 ± 1.33 × 10−7 with a CV of 13.5%
- p. 7 Section 3, last paragraph
9.08 ⫻ 10⫺7 ⫾ 1.33 ⫻ 10⫺7 with a CV of 13.5%
Only the authors can say what is right here.
Judge's note: Page 7 image shows 9.08 × 10^-7 ± 1.33 × 10^-7 and a CV of 13.5%. 1.33/9.08 = 14.65%; rounding of the mean and SD to three figures cannot bring this to 13.5%. The raw-CT figures in the same paragraph do agree (0.194/20.0 = 0.97%, printed 0.971%). No different sample set is described for the two calculations. In addition, the mean of 2^-CT over replicates cannot be below 2^-(mean CT), and 2^-20.0 is about 9.5 × 10^-7 (about 9.2 × 10^-7 even at a mean CT of 20.05), which is above the printed 9.08 × 10^-7. This suggests the mean is the misprinted figure (1.33/9.85 = 13.5%), but only the authors can say which of the three numbers is wrong.
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Substance Section 3 prints "the mean ± SD was 9.08 × 10^-7 ± 1.33 × 10^-7 with a CV of 13.5%"; the printed SD divided by the printed mean gives 14.6%, not 13.5%.
- p. 7 Section 3, last paragraph
9.08 3 1027 6 1.33 3 1027 with a CV of 13.5%
Only the authors can say what is right here.
Judge's note: Read the passage on the page image for PDF page 7, left column: mean 9.08 × 10^-7, SD 1.33 × 10^-7, CV 13.5%. SD/mean = 14.65%. Rounding of the printed three-figure values cannot reach 13.5%: the extremes are 1.325/9.085 = 14.58% and 1.335/9.075 = 14.71%. The sentence before it uses the same convention and is consistent (0.194/20.0 = 0.970%, printed 0.971%, reachable by rounding of the mean), so CV here is SD/mean. I searched the article text for another definition of CV or a different sample set for this figure and found none; the paper's other use of CV (Fig. 2, mean, SD and CV from triplicates) is the same quantity. At least one of the three printed numbers is misprinted, and only the authors can say which, hence author_query.
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Reference or label "Absolute quantification has been combined with real-time PCR and numerous reports have appeared in the literature (6–9)": refs 8 and 9 are cited elsewhere in the paper for mRNA decay and the serum response, and ref 8 is dated 1994, before the 1996 paper cited for real-time PCR (ref 4).
- p. 1 introduction, right column
ports have appeared in the literature (6–9) including
- p. 6 Section 2.2
induction is a commonly used model to study the decay of certain mRNAs (8)
- p. 7 References
8. Chen, C. Y., and Shyu, A. B. (1994) Mol. Cell. Biol. 14, 8471–8482.
- p. 1 Introduction, right column
the literature (5, 6)
Only the authors can say what is right here.
Judge's note: Read page 1, page 6 and the reference list on page 7. Section 2.2 cites ref 8 (Chen and Shyu 1994, Mol. Cell. Biol.) for "Serum starvation/induction is a commonly used model to study the decay of certain mRNAs (8)" and ref 9 (Iyer et al. 1999, Science) for "serum may alter the expression of numerous genes including standard housekeeping genes (9)". Ref 7 is the serum housekeeping-gene study reprinted as Fig. 3, and ref 6 is cited on page 1 as an example of the 2^-ΔΔCT method. The paper cites refs 4 (1996) and 5 for adapting real-time PCR to quantitative RT-PCR, so a 1994 paper is unlikely to be a real-time PCR absolute-quantification report. The range looks misnumbered; titles are not printed, so only the authors can say which references were meant.
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Reference or label "One difficulty is that CT is exponentially related to copy number (see Section 4 below)": Section 4 is "CONCLUDING REMARKS"; the topic is treated in Section 3, "STATISTICAL ANALYSIS OF REAL-TIME PCR DATA" ("CT is an exponential and not a linear term").
- p. 5 Section 1.4 continued, left column
(see Section 4 below)
- p. 6 Section 3 heading
3. STATISTICAL ANALYSIS OF REAL-TIME
- p. 7 Section 4 heading
4. CONCLUDING REMARKS
- p. 6 Section 3 (Statistical Analysis of Real-Time PCR Data)
CT is an exponential and not a linear term
Judge's note: Page 5 image shows the pointer "(see Section 4 below)". Page 6 image shows the Section 3 heading and its statement that CT is an exponential and not a linear term. Page 7 image shows Section 4 is the Concluding Remarks, which repeats the recommendation in its last sentence only. The pointer should read Section 3.
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Reference or label Table 2 column header "ΔCT (Avg. c-myc CT − Avg. GAPDH CT)" describes a difference of averages, but the column lists a ΔCT for each well and the text says "it makes sense to calculate ΔCT separately for each well. These ΔCT values can then be averaged".
- p. 5 Table 2, third column header
ΔCT (Avg. c-myc CT − Avg. GAPDH CT)
- p. 5 left column text
it makes sense to calculate ΔCT separately for each well. These ΔCT values can then be averaged
- p. 5 Table 2, third column header
Avg. GAPDH CT)
- p. 5 Section 1.4, left column
Therefore, it makes sense to calculate ΔCT separately
Only the authors can say what is right here.
Judge's note: Page 5 image: the Table 2 ΔCT column has one value per well, no average CT values are printed for either gene, and the header repeats Table 1's wording. The text on the same page says ΔCT is calculated per well and then averaged for the same-well design, and presents this as the difference from Table 1. The header mislabels what the column contains. The mean is the same either way, but the SD is not.
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11 minor (typos and the like; most checked by the judge only)
Wording Fig. 1 title says "Amplification of cDNA synthesized from different amounts of RNA", while the legend and text describe serial dilutions of one cDNA preparation ("cDNA was synthesized from 1 μg total RNA"; "Serial dilutions of cDNA were amplified"; "a cDNA preparation was diluted over a 100-fold range").
- p. 2 Fig. 1 legend, title
Amplification of cDNA synthesized from different amounts of RNA
- p. 2 Fig. 1 legend
Serial dilutions of cDNA were amplified by
- p. 3 Section 1.2
results of an experiment where a cDNA preparation
Judge's note: Page 2 image: legend title, legend body and the x axis label "cDNA dilution". The page 3 passage was read in the text layer only. The title describes varying the RNA input to reverse transcription; the experiment described is a dilution of one cDNA preparation. The title may be shorthand for cDNA equivalent to different RNA amounts (the legend speaks of cDNA "derived from 1 ng of total RNA"), so this is a loose wording point.
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Wording Fig. 3 legend: "was calculated using Eq. [13], where ΔCT = (CT,Time x − CT,Time 0)" omits the prime; Eq. [13] is 2^−ΔC′T and the text defines "ΔC′T = CT,Time x − CT,Time 0", stating "The prime is used to distinguish this expression from the previous ΔCT calculation".
- p. 6 Fig. 3 legend
was calculated using Eq. [13], where ΔCT = (CT,Time x − CT,Time 0)
- p. 6 right column, top
equation where ΔC′T = CT,Time x − CT,Time 0
- p. 6 Section 2.1, after Eq. [12]
The prime is used to distinguish this expression from the previous ΔCT
- p. 6 Fig. 3 legend
was calculated using Eq. [13], where ΔCT = (CT,Time x − CT,Time 0) and
Judge's note: Page 6 image: the legend's definition prints ΔCT with no prime, while the legend title ("Application of the 2^−ΔC′T method"), Eq. [13] and the body text carry it. The text layer shows the same difference ("DCT" in the legend, "DC8T" elsewhere). The paper introduces the prime to separate this quantity from the target-minus-reference ΔCT, so the legend uses the wrong symbol. The meaning is recoverable from the definition given.
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Typo First sentence of the introduction reads "Reserve transcription combined with the polymerase chain reaction (RT-PCR)"; it should read "Reverse transcription".
- p. 1 first sentence of the introduction
Reserve transcription combined with the polymer-
Judge's note: Page 1 image shows "Reserve transcription" in print. The key words on the same page have "reverse transcription polymerase chain reaction".
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Typo Key words print "Taq Man." as two words; the text and Fig. 1 legend print "TaqMan" ("For real-time amplification using TaqMan probes").
- p. 1 Key Words
Taq Man.
- p. 2 Section 1.1
For real-time amplification using TaqMan probes
- p. 1 Key Words
real-time polymerase chain reaction; Taq Man.
- p. 2 Section 1.1
For real-time amplification using TaqMan probes, the
Judge's note: Page 1 image shows a clear word space in "Taq Man" in the key words. Page 2 image shows "TaqMan probes" in Section 1.1 and "TaqMan detection" in the Fig. 1 legend. Cosmetic inconsistency.
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Typo Fig. 2 legend prints "ΔΔCT = (CT,Target − C,Actin)Time x − (CT,Target − C,Actin)Time 0", with the subscript T missing from both actin terms, and writes "the Ct data" where the paper otherwise uses CT.
- p. 4 Fig. 2 legend
(CT,Target − C,Actin)Time x − (CT,Target − C,Actin)Time 0
- p. 4 Fig. 2 legend
the Ct data were imported
- p. 3 Section 1.4
(CT,Target − CT,Actin)Time x − (CT,Target − CT,Actin)Time 0
- p. 4 Fig. 2 legend
C,Actin)Time x
Judge's note: Page 4 image: the legend shows C with subscript ",Actin" and no T in both terms, and "Ct data" with a lower-case t. The text layer agrees ("C,Actin"). The same formula in Section 1.4 on page 3 has CT,Actin in the text layer; that page image was not opened.
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Typo Table 1 column header "ΔCT (Avg. c-myc CT − Avg. GAPDH CT" has no closing parenthesis; the same header in Table 2 is closed ("Avg. GAPDH CT)").
- p. 4 Table 1, third column header
Avg. GAPDH CT
- p. 5 Table 2, third column header
Avg. GAPDH CT)
Judge's note: Page 4 image: the Table 1 header ends "Avg. GAPDH CT" with no parenthesis, while the next header is closed ("− Avg. ΔCT,Brain)"). Page 5 image: the Table 2 header is closed.
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Typo "Thus, the target gene and the endogenous reference are one in the same." should read "one and the same".
- p. 6 Section 2.1 continued, left column
target gene and the endogenous reference are one in
Judge's note: Page 6 image, left column, shows "are one in the same".
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Typo Section 4 summary of steps prints "and (iii) PCR on perform dilutions of RNA or cDNA for both the target and internal control genes"; the words are transposed (evidently "perform PCR on dilutions of RNA or cDNA").
- p. 7 Section 4, right column
and (iii) PCR on perform dilutions of RNA or cDNA
- p. 7 Section 4, summary of steps
PCR on perform dilutions of RNA or cDNA
- p. 7
PCR on perform dilutions of RNA or cDNA for both the target
Judge's note: Read the full page image for PDF page 7, right column. The text is printed as "(iii) PCR on / perform dilutions of RNA or cDNA" across a line break within the same column, so it is not a column-interleaving artefact of extraction (the text layer interleaves the two columns, which is why the quote was not found as one string). The wording is ungrammatical as typeset.
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Typo Reference 2 prints the last author as "Von-Hoff, D. D., and Robinson, I. B. (1990) Proc. Natl. Acad. Sci. USA 87, 7160–7164"; the last author of the cited paper is reported to be I. B. Roninson.
- p. 7 Reference 2
Von-Hoff, D. D., and Robinson, I. B. (1990)
- p. 7 Reference list, entry 2
Von-Hoff, D. D., and Robinson, I. B. (1990) Proc. Natl. Acad. Sci.
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that the last author of Noonan et al., Proc. Natl. Acad. Sci. USA 87, 7160–7164 (1990) is I. B. Roninson, not Robinson. The page image for PDF page 7 does print "Robinson, I. B." in reference 2, as quoted. Nothing in the files gives the cited paper's author list, so the spelling cannot be verified here; it should be checked against the journal record.
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Typo Reference 10 prints the fourth author as "Giulietti, A., Overbergh, L., Valckx, D., Decallone, B., Bouillon, R., and Mathieu, C. (2001) Methods 25, 386–401"; the author's name is reported to be Decallonne.
- p. 7 Reference 10
Decallone, B.
- p. 7 Reference list, entry 10
10. Giulietti, A., Overbergh, L., Valckx, D., Decallone, B., Bouillon,
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that the fourth author of Giulietti et al., Methods 25, 386–401 (2001) is B. Decallonne (double n). The page image for PDF page 7 does print "Decallone, B." in reference 10, as quoted. The files do not contain the cited article, so the spelling cannot be verified here; it should be checked against the journal record.
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Typo Reference 5 gives an abbreviated page range, "Anal. Biochem. 270, 41–9.", while every other entry in the list gives the last page in full (e.g. "194–204", "69–81", "986–994").
- p. 7 Reference 5
Anal. Biochem. 270, 41–9.
Judge's note: Read the reference list on the page image for PDF page 7. All ten other entries print full first and last pages; only reference 5 shortens the end page to "9". This is a formatting inconsistency within the list, not a wrong value: "41–9" is a recognised abbreviation of 41–49, so the reference remains findable.
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