There is a huge literature about that topic. What have you read so far? What is your specific problem?

Livak KJ, Schmittgen TD. Analysis of relative gene expression data using real-time quantitative PCR and the 2(-Delta Delta C(T)) Method. Methods. 2001 Dec;25(4):402-8.

Google for "Livak Schmittgen" to find a PDF.

Further resources on

http://www.ambion.com/techlib/basics/rtpcr/index.html

http://pathmicro.med.sc.edu/pcr/realtime-home.htm

From the practical view, how you are going to analyse your data without reference gene. the delta delta CT method base on the difference in CT values between your interest gene and the reference gene. As what @Jochen Wilhelm wrote before me,, there are huge literature about the topic.

Basically you calculate like the attached

I would also add this to your reading:

http://www.amazon.com/A-Z-Quantitative-PCR-IUL-Biotechnology/dp/0963681788

On a different note, the use of "Housekeeping genes" is somewhat controversial. You must choose your control gene carefully. See here:

http://www.ncbi.nlm.nih.gov/pubmed/15543203

You will note that not just any control gene should be chosen.

I forgot to say: the concept behind it (using a "housekeeping gene" - better: "reference gene"!) is to normalize the measured quantity of the target gene to the effective amount of starting material. That is, the reference gene simply serves as a loading control. If you can assure, by some other means and controls, that always the same effective amount of sample is used in each PCR that should be compared, you can skip normalization to a reference gene.

Hello, I guess qPCR can be very technical and complicated, but the basic principles are the same as for any quantification approach. As Jochen was saying, in order to measure the levels of your gene of interest in two conditions you have to be sure that in your samples you have the same amount of total material, and this is normally done using one or more reference genes (it's like when in Western Blotting you use actin or tubulin or GAPDH in order to calibrate your samples). Since years the most appreciated reference genes are the so-called housekeeping genes (GAPDH/LDH, ribosomal proteins, ribosomal RNA, general transcription factors, such as TBP, etc), genes that are abundantly expressed and are thought to be the most insensitive to any treatments of your sample. But as Mark was correctly pointing out, there is no gene virtually insensitive to any treatment, so the choice of a reference gene can be difficult and it would be best to choose at least 2 reference genes to calibrate your samples (but this will exclude the possibility to use the delta-delta-Ct method and get you into complicated mathematics). Since PCR works on cDNA, which does not exist in the cell, I would avoid not using any calibration gene, relying only on RNA quantification, because cDNA production will not depend only on the initial mRNA content, but also on the purity of the extracted mRNA.

The delta-delta Ct method is just like calibrating the gene of interest in every sample by the reference gene (delta-Ct) and then making the ratio between samples to find the fold change (the second delta). This is due to the properties of exponentials, in fact don't forget that the Ct is the exponential of the function that describes the cDNA quantity. A ratio between exponential functions with the same base can be solved by the base elevated to the difference (delta) between the exponentials.

And here is the problem of the delta-delta Ct method, the same base. The base is in fact the efficiency of the PCR reaction (the theoretical number is 2, which means that your amplicon duplicates at every cycle) and this is different for every PCR due to the thermodynamic and kinetic properties of primer annealing and the possible contaminants in you cDNA. Therefore the delta-delta Ct method lives on the approximation that all PCR reactions have equal efficiency (where you can choose the theoretical number 2 or you can try to evaluate the efficiency of you PCR reaction by serial dilutions of your cDNA and then use a different base, which might make the quantification more accurate... in most cases real PCR efficiency ranges between 1.8 and 1.9).

Keep in mind also using the Pfaffl method to quantify qPCR experiments, where you will use the real efficiency of PCR reaction for your gene of interest AND your calibration gene (Pfaffl,M.W. (2001) A new mathematical model for relative quantification in real-time RT–PCR. Nucleic Acids Res., 29, 2002–2007.)

I hope with this simplified notions you will be able to better understand the technical papers you will find in the literature (some of which were already suggested).

@Pietro, you write "that the Ct is the exponential of the function that describes the cDNA quantity" - maybe it is just a wording problem, but this is wrong as it was said. The Ct is a function of the negative logarithm of the initial cDNA quantity. It is not simply the log, but the log plus some unknown constant (coming from (i) the unknown proportionality between fluerescence intensity and amplicon concentration and (ii) the selected threshold). A dCt is a difference between the logarithms, plus the difference of the unknown constants for the two genes. So it is not simply a "log expression". In the ddCt, all the unknowns cancel out [given the amplification efficiencies are identical for target and reference gene!] and it remains a log expression ratio. The base of the logarithm depends on the ampification efficiency (often assumed to be 2).

Housekeeping genes are taken as normalizing control for amount of sample used in the procedure. Mostly their transcript level does not change significantly at variable conditions. In many cases there are multiple reference genes used for better and reliable quatitation.

Thank u

Dear Jochen, you are right, there was an extra c, I meant the DNA quantity, or the final amplicon quantity if this is more clear.

Pietro, you mean you wanted to say: "that the Ct is the exponential of the function that describes the cDNA quantity" ? - This is also wrong. Ct is not a function of the DNA-(PCR-product/final amplicon)quantity. At the Ct the PCR contains a given (fixed but unknown) amount of DNA (that is detected by the probe in use). The final amount of amplicon/PCR product is no at all related to the Ct.

Jochen, I guess we don't understand each other... The Ct is the exponential of the function that describes the DNA quantity does nor mean that the Ct is function of the DNA amount, means that it is the exponential in the function that describes the DNA amount.

Ok let's try in this way, classical mathematics of a PCR reaction: DNA quantity at cycle n q(n) depends on the initial template amount q(0) and the number of amplification cycles that have occurred, which is written this way:

q(n) = q(0) x 2EXP(n)

(Assuming theoretical efficiency of 2).

When you choose your Ct then it is:

q(Ct) = q(0) x 2EXP(Ct)

That's all. Ct is the exponential of the function that describes the DNA amount in your PCR reaction at the cycle n=Ct (Threshold cycle), but obviously it is not a function of anything. But this is the base for all calculations during calibration of your samples. Infact, when you calibrate, you make a ratio between the amount of your gene of interest and the amount of a reference gene, which means you divide two exponentials with same base that mathematically can be written as the base elevated to the difference between the exponentials (delta Ct):

q(CtA)/q(Ct)R = q(0A)/q(0R) x 2EXP(CtA-CtR)

When you make the ratio between two conditions (treatment and control) you obtain the second delta.

But you can work with logarithms as well, no problem. They are just the inverse function of exponentials and benefit of the same properties in their arguments.

I hope now we understand each other.

Yes, ok, I see what you mean. However, since I misunderstood what you meant, I consider it likely that some others might also misunderstand it, so I think is was worth it to go through this.

In you last post, however, I not another mistake, that often leads to some confusion:

q(n) = q(0) x 2^n)

is correct, but you do not measure the the quantity q but the fluorescence F, where F = p x q (p being some assay-specific proportionality factor:

F(n) = p x q(0) x 2^n

At the threshold *fluorescence* (not quantity!), it is

Ft = p x q(0) x 2^Ct

Ct = log2 (FT/p/q(0)) = log2 (FT/p) - log2(q(0))

Note that the part log2 (FT/p) is array- (and, thus, gene-)specific. Now you measure Ct values for reference gene (R) and gene of interest (A) (and not neccesarily at the same threhold!), you have

CtR = log2 (FTR/pR) - log2(q(0R))

CtA = log2 (FTA/pA) - log2(q(0A))

and

dCt = CtR - CtA

= log2 (FTR/pR) - log2(q(0R)) - [log2 (FTA/pA) - log2(q(0A))]

= log2 (FTR/pR) - log2 (FTA/pA) + log2(q(0A)) - log2(q(0R))

= log2 (FTR/FTA x pA/pR) + log2(q(0A)/q(0R))

The last term is the log-ratio of the initial quantities, but the dCt value is not simply this log-ratio, it is offset by some assay-specific constants (that are typically unknown)!

I stress this point because I often see that people argue that a dCt of 0 would mean that the two genes are expressed to a similar level (what would *only* be the case if FTR/pR = FTA/pA, or that a value of 0 would have some other "special" meaning (therfore, for instance, showing dCt values as barcharts is nonsense).

I know that this "mistake" is not relevant to our previous discussion and to the point you made. It is a different topic. I just wanted to mention it.

And I totally agree with you, in fact I always consider the delta-delta Ct method like subtracting apples from pears, it is functional in a certain approximated way, but it is quite nonsense if you look at it properly. That's also the reason why I suggested the Pfaffl method, where several points are corrected, such as the thresholding problem, that you very correctly mention, and the specific PCR reaction efficiency, besides the possibility to use multiple reference genes (although the relationship between fluorescence and quantity in practice will always remain an approximation, hopefully small enough) and you still keep the analysis simple enough...

But, you know, it seems that this question was posed by a person at the very initial stage in qPCR and probably all this interesting discussion will anyway mean little to him for the moment. I only tried to give him some means to understand the publications that all the people here suggested, using possibly simple words.

Anyway, it was a pleasure discussing, even if your wording can sometimes be a bit tough... ;-)

Sorry for my wording! English is not mother tongue, so some things may not sound as intended or are expressed in an unneccessary complicated way...

Simple wording, simple examples, analogies etc. are absolutely ok and recommended. But, however, simplification should not lead to faulty concepts.

The discussion may "mean little to him [Revathi] for the moment", but he will so see that qPCR needs a little more thinking than initially thought. When he is willing to learn the method properly, he will (later) surely find it helpful and useful.

Thank you too for the discussion!

btw: ddCt is the difference between two similar dCt-values. So This is actually subtracting apples from apples (so that's ok), only that we do not have a precise understanding of what an "apple" (dCt) here actually is. However, the delta-apple (ddCt) is a log fold-change :)

Hahaha... I see you really need to have the last word. Fine, fine, I'll just make one more comment and then you can feed in your last thoughts!!

The ddCt is fine, the problem is the first dCt... that's not just an apple, as you very well explained in words and mathematics, it is the subtraction between two values determined in different (and kind of arbitrary) ways, dependent from different factors, referring to different DNA sequences, and that relate to the initial cDNA template in a different way... that's what I mean by subtracting apples from pears.

Possibly I'm wrong or excessive... but that's my impression... :-)

But I highly appreciated the discussion, overall it made me think at quite a few additional points, and I completely agree that although our poor friend Revathi must be totally scared now, he's been warned: qPCR is a serious and complicated story, he'll need to study quite a bit what's behind, and then come back and read again all this thread and realize why we got into this very fruitful discussion! Good reading to everybody!