# Why is there a minus in the 2ˆ(–delta delta CT) method (qPCR)

Question: Why is there a minus in the 2ˆ(–delta delta CT) formula?

My line of thoughs:

Consider Ct values of some pPCR experiment (some gene of interest X and a reference gene REF is measured under some experiment condition and a control condition).

1. The delta CT (dCt) would correspond to normalized expression Ct of X against REF of both conditions. (dCt = X-REF)

2. The delta delta CT (ddCt) would then correspond the the difference of the dCt of the experiment condition minus the dCt of the control condition.

=> If ddCT > 0 then the gene of interest is upregulated downregulated (Ct is antiproportional to gene expression). (the difference of the dCt in the experiment condition is larger than in the control condition)

But now: the ratio R = 2ˆ(–delta delta CT) would then correspond to a value smaller than 1 (because of the minus).

"We see a 10% decrease of expression (R=0.9)..."

But actually the raw data clearly shows a upregulation... This is confusing since only the ratio R decreases by 10% but the this would correspond to an increase of raw expression...

I could interprete R as the ratio of the control against the gene of interest. But why not the other way around?

Edit: Ct is antiproportional to gene expression => dCt does not directly reflect the gene expression.

Sources:

https://bmcbioinformatics.biomedcentral.com/articles/10.1186/s12859-020-03696-y

"We can predict that a plant with a hormone concentration of 8.85 pg/mL would have an expression of Gene G that is 27% (𝑅̂ =0.73) lower than that of plants with average hormone concentration" (just below equation 8)

But clearly in Fig. 3a you can see that the expression at 8.85 is obviously higher than with average hormone concentration (x0 = 9.85)

• Perhaps this pdf of the ddCt package helps: bioconductor.org/packages/release/bioc/vignettes/ddCt/inst/doc/… . See equations 6, 7 and 8. – Peter Nov 25 '20 at 2:55
• ok I found the reason: Ct is antiproportional to the gene expression. Therefore the statements from the paper are correct. But thank you for your link, very nice derivation – Paul Nov 26 '20 at 14:29