DeltaCt is quite a difficult concept for people who aren't used to looking at qPCR data because the lower numbers equate to higher concentrations of DNA - this is counter-intuitive.

40-DeltaCt is a simple transformation of the results which doesn't affect the validity of the statistics but it does make the results more intuitive (ie bigger numbers are higher concentrations)

I have used this for presenting data to growers and industry reps and I would be quite happy publishing papers with this harmless transformation.

The number 40 has no meaning. You can substitute it by any arbitary other value without changing the interpretation.

The interpretation is not wrong, but the way is unfortunate, and - to my opinion - rather silly.

I think that, as Edward already pointed out, the dct is calculated as ct[target gene] - ct[reference gene]. This is in fact a counter-intuitive way to calculate a log ratio, since this way actually the expression-signal of the reference gene is normalized to the expression.signal of the target gene. Students are blamed for less stupid things.

When the dct is calculated this (unfortunate or silly) way, then higher dct values indicate a lower normalized target gene expression.Some authors try to put this right by presenting -dct as a measure or a log normalized expression value. This is fine, but would be unnneccesary if right from the start the expression of the traget gene would have been normalized to the expression of the reference gene (i.e. dct = ct[ref] - ct[target]).

It makes no difference for the interpretation if I give just -dt, 40-dct, oor x-dct with x being any arbitrary value. dt-values are relative measures. They have no meaning on their own, but they can be compared between groups (e.g. treated vs. control). The comparison is typically (and sensibly) done by calculating the difference of dct values, called the ddct value(what is a log fold-change or log ratio of the normalized expressions in the groups). You see that whatever value x is, it will anyway cancel out.

To my opinion, calculating dct as ct[target]-ct[reference] is un-natural, counter-intuitive, and misleading. Although it is not wrong (as long as it is not interpreted wrongly), this clearly is a bad scientific practice and should be avoided.

The reason for calculating it this way are:

1) people do not understand where this formula comes from and

2) people just repeat the unfortunate mistake of Livak et al. who first reported the use of dct and ddct values for quantification (instead of recognizing the mistake and to make it better).

There is no harm in stating in the methods section how the dct is calculated. When there is written that dct = ct[ref] - ct[target] and that ddct = dct[treated] - dct[control], everything is clear and noone needs to be confused about signs and directions.

People doing real-time PCR should know and understand that

Ft = p * N0 * E^ct

where:

Ft : Fluorescence at the threshold

p:  (unknown) proportionality factor (depending on the assay)

N0: (unknown) starting amount of the amplicon sequence

E: amplification efficiency (may be assumed to be 2.0)*

ct: the (measured) ct-value

* for the ddct-method it is only required that E is identical for all assays.

This is the fundamental equation for real-time PCR. I am very sad that only very few people working with real-time PCR know this and are able to understand this.

What does a ct-value mean then?

take the logarithm (to the base E): log(Ft) = log(p) + log(N0) + ct

solve for ct: ct = log(Ft) - log(p) - log(N0)

You can see that the ct-value is proportional to minus log(N0). The lower the ct, the larger is N0.

The dct for two genes/assays A and B is

dct = ct[A] - ct[B]

dct =( log(Ft[A]) - log(p[A]) - log(N0[A]) ) - ( log(Ft[B]) - log(p[B]) - log(N0[B]) )

dct =( log(Ft[A]) - log(Ft[B]) - log(p[A]) + log(p[B]) ) + ( log(N0[B]) - log(N0[A]) )

dct = Z + log(N0[B] / N0[A])

So the dct is a log ratio of B/A. This means, the values of B is normalized to the value of A. So A serves as "reference".

This log ratio is shifted by a constant Z. The value of Z is unknown, but it is constant for the combination of assays and it will cancel out in the calculation of ddct values. This unkwon part of the dct value makes it a "relative" measure. We do not know relative to what it is. So a dct just remains a number. But different dct-values from the same combi of assays are comparable, because they are relative to the same (still unknown) thing.

This means: knwing that a dct value is, say, -6.3 does not tell my anything. And I do not get any more information from 40-6.3, or from -5-6.3. But if I have two dct-values, one for treated and another for controls, then I can well ineterpret the difference between these dct values.

ddct = dct[trt] - dct[ctl]

ddct = ( Z + log(N0[B,trt] / N0[A,trt]) ) - ( Z + log(N0[B,ctl] / N0[A,ctl]) ) 

ddct = log(N0[B,trt] / N0[A,trt]) - log(N0[B,ctl] / N0[A,ctl])

Z cancelled out!

ddct = log( (N0[B,trt] / N0[A,trt]) / (N0[B,ctl] / N0[A,ctl]) )

Here you see that ddct is the log-ratio the normalized amounts of B, normalized to the amounts of A. It makes perfect sense when A is a reference gene and B is a target gene. Therefore I say that the dct and ddct should be calculated as

dc = ct[reference gene] - ct[target gene]

ddct = dct[treated] - dct[control]

I agree with both Jochen and Edward. 

Although Jochen is correct, it is often difficult to convince reviewers that something should be done in a way that is non-standard. The method proposed works if one can pair samples well. If one is dealing with specimens from experiments where such pairing is not easily performed, the ddCt method is more difficult to apply. Additionally the dCt values are frequently graphed to illustrate the distributions and although the scale is arbitrary it has the log2 relationship, every n unit increase is 2^n more expression.

The essence of Constant - Ct is easy to comprehend as a scaling transformation. In addition it maintains the data on the original log2 scale. The exponential transformation (2^Ct) results in data that have to be transformed again for most statistical tests to be valid.

The value 40 for the constant, although arbitrary, has some intuitive sense in that experiments rarely exceed 40 cycles (which is amplification somewhere in the range of 1e-9 to 1e-12 times). 

Gerard, I think you are wrong here:

"The method proposed works if one can pair samples well. If one is dealing with specimens from experiments where such pairing is not easily performed, the ddCt method is more difficult to apply."

The "pairing" is only between the genes (target and reference) within the same biological sample/specimen. This is natural, since the ct of the reference gene serves as loading control to normalize the ct of the target gene of the very same sample/specimen. You always measure these pairs of genes (target and reference) in each sample/specimen. So you nesseralily always do have paired ct-values, from which you calculate dct values.

There is no need than the dct values are paired*. You have two groups of dct values, one group for the "controls" and one group for the "treated" samples. You can calculate the mean difference for such dct values (=ddct) and the standard error and confidence interval of this estimate; you can also test any hypothesis about it.

*well, they may be, depending on the experimental design - but often they are not

I completely agree with the emptiness of "40-Ct" transformation. Some of my experiments only run for 30 cycles (abundant snRNAs) or 45 cycles (pre-amp + amp of rare miRNAs).

In general, I'd be very very cautious in applying ANY of the above Ct-based calculations, as they assume that the amplification of both genes (reference and interest) is of equal efficiency. This is rarely the case, and over a large number of cycles, differences creep up. We include a standard curve for each gene and convert Ct values to relative input, which can then be normalised in any way you see fit. Also include a titration of RNA input into the reverse transcription. You'd be surprised how many commercial kits are saturating their reactions, which affects abundant and rare transcripts in different ways!

We also stopped using a single reference gene, but use a geometric mean of 3-4. This cannot easily be done with ddct, unless you accept averaging Ct as geo-averaging input etc. When dealing with a perturbation experiment in cell lines, it does not matter. But when dealing with heterogeneous samples (e.g. patient material), it is a much more robust measure.

Lastly, I would urge everyone to consider the MiQE guidelines championed by S.A. Bustin. 

A.

Thanks everybody for the answers. They’ve been really helpful.

I’m having some trouble in representing qPCR data. We just want to demonstrate that a low-expression transcript is present in wt animals, and we cannot perform absolute quantification (which would be the best way to do it) since we do not have any plasmid to generate a standard curve, and we are in a bit of a hurry to present the results.

I understand that using a ct of 40 as the reference sample for the ddct method is arbitrary and as Anna Git says, quiet an empty transformation. However, when you do not have a reference/calibrator sample (any wt compared to tg animals, any non-treated group compared to treated group) in your experiment and you are just trying to demonstrate presence of a transcript in a homogenous population, what could you use as a reference?

I thought about presenting the data as the exponential transformation (2^Ct) of dct for each sample calculated with the endogenous control (without comparing them to any reference group), though in that way you would be just showing how is the target transcript expressed relative to the endongenous control in each sample and not normalizing for the cDNA quantity, right?

I would appreciate some opinions on this topic.

Thanks a lot.

Dear Nuria,

"We just want to demonstrate that a low-expression transcript is present in wt animals" - this is a "simple" task and does not require any quantification. Just show that you get a clear positive PCR in at least one of your wt samples and also demonstrate that at the same time, all negative controls (water, -RT) are negative.

"I thought about presenting the data as the exponential transformation (2^Ct) of dct for each sample calculated with the endogenous control"

Firstly, you don't need any endogenous control. You could use it to show that the sample did in fact contain amplifiable cDNA - but this control would be important only when you wanted to show the absence of the target gene transcript (not its [occasional] presence). In no case there is a need for calibration, as it is sufficient to show that the specific sequence is amplified. Secondly, any transformation of your (d)Ct values is nonsense. If you use sequence-specific detection (hydrolysis probes, hybridization probes, beacons, whatever...) the fact that the amplification curve raises at some time during the first 35 cycles is sufficient to show that there was (at least one molecule of the) traget sequence present in the sample. If you use a dsDNA dye like SYBR Green, you should in any case make a subsequent gel (idally 4-6% PAGE, but agarose may also work) to demonstrate that the correct sequence was amplified.

Norbert Nass Hello Sir,

Can you provide me the link to the paper using 40-DeltaCt method for calculating relative gene expression?

Thank you

Please Can you provide me the link to the paper using 40-DeltaCt method for calculating relative gene expression?

Thank you