<p>Question: Why is there a minus in the <code>2ˆ(–delta delta CT)</code> formula?</p>
<p>My line of thoughs:</p>
<p>Consider <code>Ct</code> 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).</p>
<ol>
<li><p>The delta CT (<code>dCt</code>) would correspond to normalized <s>expression</s> Ct of X against REF of both conditions. (dCt = X-REF)</p>
</li>
<li><p>The delta delta CT (<code>ddCt</code>) would then correspond the the difference of the dCt of the experiment condition minus the dCt of the control condition.</p>
</li>
</ol>
<p>=&gt; If ddCT &gt; 0 then the gene of interest is <s>upregulated</s> downregulated (Ct is antiproportional to gene expression). (the difference of the dCt in the experiment condition is larger than in the control condition)</p>
<p>But now: the ratio <code>R = 2ˆ(–delta delta CT)</code> would then correspond to a value smaller than 1 (because of the minus).</p>
<p>I read sentences like</p>
<blockquote>
<p>&quot;We see a 10% decrease of expression (R=0.9)...&quot;</p>
</blockquote>
<p><s>But actually the raw data clearly shows a upregulation</s>... This is confusing since only the ratio R decreases by 10% but the this would correspond to an increase of raw expression...</p>
<p><s>I could interprete R as the ratio of the control against the gene of interest. But why not the other way around?</s></p>
<p><strong>Edit: Ct is antiproportional to gene expression =&gt; dCt does not directly reflect the gene expression.</strong></p>
<blockquote>
<p>Sources:</p>
<p><a href="https://bmcbioinformatics.biomedcentral.com/articles/10.1186/s12859-020-03696-y" rel="nofollow noreferrer">https://bmcbioinformatics.biomedcentral.com/articles/10.1186/s12859-020-03696-y</a></p>
<p>&quot;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% (̂ =0.73) lower than that of plants with average hormone concentration&quot; (just
below equation 8)</p>
<p>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)</p>
</blockquote>

CC BY-SA 4.0
2020-11-25T02:55:04.487Z
Perhaps this pdf of the ddCt package helps: https://bioconductor.org/packages/release/bioc/vignettes/ddCt/inst/doc/rtPCR.pdf . See equations 6, 7 and 8.
Peter
CC BY-SA 4.0
2020-11-26T14:29:19.503Z
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
<normalization><qpcr>
Why is there a minus in the 2ˆ(–delta delta CT) method (qPCR)
# Why is there a minus in the 2ˆ(–delta delta CT) method (qPCR)

(Asked by: username_0 on 2020-11-09)

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).

I read sentences like

> "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% (̂ =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)

**Tags:** normalization, qpcr
> **Comments:**
> **username_1**: Perhaps this pdf of the ddCt package helps: https://bioconductor.org/packages/release/bioc/vignettes/ddCt/inst/doc/rtPCR.pdf . See equations 6, 7 and 8.  
> **username_0**: 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  

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## 0 answers

