You changed the way the ∆Cts are calculated.
It would be helpful if you try to understand the meaning if such values.
---- PART 1 -----
Following from the exponential amplification with an E-fold amplificatipn per cycle (E is the amplification efficiency; E=2 means doubeling each cycle = ideal; E=1 means no amplification at all = the amount remains constant), the fluorescence signal F follows the function
F = p*N*E^C
where c is the cycle number, N is the initial concentration of the amplicon sequence and p is a proportionality factor translating product concentration to fluorescence intensity. This factor is some (usually unknown) constant for a given target/primer/reaction/instrument combination.
At the threshold value, F=Ft and c=Ct:
Ft = p*N*E^Ct
Solved for Ct:
Ft/p = N*E^Ct
log(Ft/p) = log(N*E^Ct) = log(N) + log(E^Ct) = log(N) + Ct*log(E)
Ct*log(E) = log(FT/p) - log(N)
Ct = log(FT/p)/log(E) - log(N)/log(E)
If we take the log to the base E the equation simplifies to
Ct = log(Ft/p) - log(N)
The part log(Ft/p) is just a reaction-specific constant, so we note that
Ct ∝ -log(N)
---- PART 2 -----
The initial amount (or concentration) of a gene of interest, N[goi], is normalized to a loading control, the initial amount of a reference gene, N[ref] by the ratio
q = N[goi] / N[ref]
The log-ratio is
log(q) = log(N[goi] / N[ref]) = log(N[goi]) - log(N[ref])
Now, as seen from part 1, log(N[goi]) ∝ -Ct[goi] and log(N[ref]) ∝ -Ct[ref]. Hence
log(q) = log(N[goi] / N[ref]) ∝ (-Ct[goi]) - (-Ct[ref]) = Ct[ref] - Ct[goi]
So when ∆Ct is calculated as Ct[ref] - Ct[goi], then
∆Ct ∝ log(N[goi] / N[ref]) = log(q)
---- PART 3 -----
The normalized amount of the goi in a treatment condition q[treat] should be compared to the normalized amount of the goi in a control condition q[ctrl] by
Q = q[treat] / q[ctrl]
Again, the log-ratio is
log(Q) = log(q[treat] / q[ctrl]) = log(q[treat]) - log(q[ctrl])
In part 2 you can see that log(q[treat]) = ∆Ct[treat] and log(q[ctrl]) = ∆Ct[ctrl], so we get
log(Q) ∝ ∆Ct[treat] - ∆Ct[ctrl]
For simplicity, I did not consider the proportionality factors that are different for goi and ref, but whatever they are, at this time they cancel out. Therefore, the proprotionality becomes an equality again:
log(Q) = ∆Ct[treat] - ∆Ct[ctrl]
Finally, if the ∆Cts are calculated as CT[ref] - CT[goi] and the ∆∆Ct is calculated as ∆Ct[treat] - ∆Ct[ctrl], then
∆∆Ct = log(Q)
and E^∆∆Ct = Q (since we used the log to the basis E).
---- REMARKS TO LOGARITHMS -----
No please think about this:
log(A/B) = log(A) - log(B)
log(B/A) = log(B) - log(A)
--->
log(A/B) = -log(B/A)
generally: log(x) = -log(1/x)
Further:
log( [A/B] / [C/D] ) = -log( [B/A] / [D/C] ) = -log( [C/D]/[A/B] ) = log( [D/C] / [B/A] )
Hi Sumreen
In a very simple sense .......if you subtract Ct (reference) gene from Ct (Gene of interest).
1) no change in ∆Ct means the level of gene of interest is similar to reference gene
2) +ve ∆Ct means gene is expressed at lower level than reference gene
3) -ve ∆Ct means gene is expressed at higher level than reference gene
4) undetermined Ct indicates that the instrument could not detect your gene under the assay conditions used....and there can be many reasons for that
however....you have to take care of many things before coming to final conclusions regarding levels of gene of interest
If you see some orignal articles on qPCR data analysis ...it will be clear to you..If you cannot find some basic papers on qPCR data analysis..please let me know I would send you some of them..
bye
Hey Sumreen,
I totally agree with Ajay's statement ... a precise and robust interpretation of gene epression levels is really complex and must be based on a good designed qRT-PCR experiment/study. If you are interested to get a better look on how to perform good qRT-PCR experiments, I would recommend to read the MIQE guidelines published by Bustin et al. in 2009.
Unfortunately qRT-PCR experiments are often designed and conducted insufficiently and the results are thereby mostly over-interpreted.
Greetz
I do NOT agree with Ajay's statement. The Ct depends on many things, and many of these are amplicon/sequence-specific. Thus, similar Cts of different genes do NOT(!!) indicate similar expression. Hence, the three conclusions are all wrong. The only way to compare the expression of *different* genes is via an external standardization.
The Ct value is proportional to -log(N), where N is the initial number of target molecules. The higher N, the lower is the Ct. As N goes to zero, -log(N) goes to infinity. Thus, the Ct value of a sample with zero target molecules would actually be infinity: the amplification curve will never rise (due to the specific amplification of the target sequence) and will thus never cross a threshold level. So theoretically you can substitute "Undetermined" by "Infinity". Practically, you can not know if target molecules were present and the actually performed number of amplification cycles was just not sufficient to reach the threshold, or if the reaction/detection just did not work. Therefore "Undetermined" is the better word here.
A negative ∆Ct just means that a higher Ct value was subtracted from a lower Ct value. That's all. There is no meaningful interpretation; this is just a mathematical fact.
Note: Since Ct ~ -log(N), ∆Ct = Ct[A]-Ct[B] ~ (-log(N[A]))-(-log(N[B])) = log(N[B])-log(N[A]) = log(N[B]/N[A]). The ∆Ct is proportional to a log-ratio of initial copy numbers. One of the genes (A or B) is typically used as "loading contol" (reference gene). If ∆Cts are determined for the same genes but under different conditions, the proportionality factors between conditions are still unknown but similar, so the ∆Cts can be compared over conditions.
@ Jochen Wilhelm: Based on your reply, I think I have to state my comment more precisely. Certainly you are right and the interpretation of the Cp isn't as simple as mentioned by Ajay, but I think he just tried to give an explanation how to understand Cp and qRT-PCR quantification in a very simple way.
For me the question pointed out that Sumreen may be new in the field of qRT-PCR and because of that I am not sure whether a very detailed and mathematical explanation is more helpful. That's the reason why a detailed study of primary literature concerning qRT-PCR would be recommendable at first. Nevertheless I agree with your annotations.
Concerning my confirmation of Ajay, I want to indicate that it was especially refered to his comment that there are many things you have to take care of before interpreting qRT-PCR experiments because of its complexicity.
Greetz
@ Jochen
I agree with the comments mentioned by you .....but as mentioned above by Athanassios....what I tried to explain above is a simple way to explain Ct values (definitely with a caution) to a person who seems to be new to the technique (mentioned by Athanassios above).....
A detailed explaination is definitely very important but may make the understanding the concept very difficut right in the begining.....one has to take one step at a time...carefully understanding each aspect of the technique very well.....before actually using for analysis of the results and inferring something out of it
bye
I agree: dont make things more complicated than neccessary, especially when starting a new topic.
But: I actually have faced this problem recently with colleagues; they wanted to compare Ct values exactly to state that two different genes are expressed on the same (or not the same) level. They ran into this misconception just because these "basics" of real-time PCR are often over-simplified.
Secondly, "...one has to take one step at a time...". Very good. And the first step in understanding real-time PCR is that the Ct is a measure that is proportional to -log(N), with a (usually) unknown, amplicon-specific proportionality factor. This is very, very fundamental (it is nothing else but the fact that the amplification process is exponential and the signal generation is somehow proportional to the amount of PCR product). If you skip this point then there is no fun in going further.
The psychological problem is further that people tend to take the first things they learn about a new topic very seriousely; they usually will base other information on this fixed mental fundament - and if this fundament is seriousely flawed or wrong (see example here), it leads to a series of misconceptions, misunderstandings and troubles.
Thank you very much all of you,I am new in qPCR field .I am working with some transfection experiments.It means, according to Jochen Wilhelm's comment If specific transcript of my gene would not be there,It will results in Undetermined / infinity hence no delta CT value.One more thing as delta Ct is a log ratio of initial copy number, if I got delta CT of one gene in two condition, 2 and 4.so delta Ct with value of 4 would be highly expressed in that condition .Am I right?
further I am attaching a graph,I need comments from all of you
If you calculate the delta-ct as ct[reference gene] minus ct[target gene], then a higher (towards positive direction) delta-ct corresponds to a higher expression. Very roughly, given an next-to-ideal amplification efficiency, a difference of 1 cylce in delta-cts correspond to a two-fold difference in initial copy numbers.
The difference of delta-ct-values between treatments (or treatment and control) is called delta-delta-ct value. This corresponst to the "log[2] fold-change" between the treatments. The basis of the log (2) is the efficiency of the amplification. It might be lower than 2 for your reactions.
Many thanks.One more thing if it is not two fold change,Is it better to show the results with only delta Ct?
To my opinion: yes, it is always better to show delta (or delta-delta) ct values.
3 Reasons:
1) it is what you measured.
2) they are on a log scale, error distributions are symmetrical.
3) the biological meaning of a "x-fold" induction/repression is as unknown as the biological meaning of a ddct of +/-x.
ad 3) many people *think* they understand the meaning of a "fold-change" (but not of "ddct"), and this hinders people to be aware of the fact that we actually have no idea what the biological relevance/meaning of a particular chage in expression *is*.
I found one mistake:
You calculate ∆Ct as Ct[REFERENCE]-Ct[TARGET]. That is ok. This way, a larger ∆Ct indicates a higher expression. [Note that Wittwer used the reciprocal value be subtractiong the reference gene Ct from the target gene Ct. This is not wrong, but counter-intuitive. Many people follow this blindly, just because is was once published this way; I do not advocate this. I find it much more intuitive and better to understand when the ∆Ct is calculated as ratios are typically calculated everywhere else, namely as "treated" versus "control", and due to the log-relationships of Ct and the copy number this translates to the subtraction of "treated"-Ct from the "control"-Ct]
Then you calculate ∆∆Ct as ∆Ct[CONTROL]-∆Ct[TREATED]. Using the ∆Ct values as you calculated them, this gives the log ratio of the expression in the control versus the treated condition, what might not be what you want. I suppose that you are actually interested in treated versus control, and this is ∆Ct[TREATED]-∆Ct[CONTROL].
You can follow your own results to understand:
your ∆Ct[CONTROL] is 1.5, your ∆Ct[TREATED] is -8.6. This tells you, that the gene of interest is expressed at a much *lower* level in "TREATED" than in "CONTROL": -8.6 is much lower (towards negative) than 1.5. You can alternatively say that the gene of interest is *higher* expressed in CONTROL than in TREATED.
If you want to see how the expression is changed (increased or decreased) by the treatment, you typically compare the expression in TREATED to the expression in CONTROL. Here is is obvious that the treatment seems to *decrease* (repress, lower) the expression. The corresponding ∆∆Ct value should thus be negative:
∆∆Ct = ∆Ct[TREATED]-∆Ct[CONTROL] = -8.6 - 1.5 = -10.1
A negative ∆∆Ct indicates down-regulation (a positive ∆∆Ct would indicate up-regulation). Given the amplification efficiency is 2, this means a regulation factor of 2^∆∆Ct = 0.0009; after the treatment, the gene is 0.0009-times as strong expressed as under control conditions.
The value you calculated is just the reciprocal 1/0.0009 = 1110. Both values are "correct", you only have to be clear about the interpretation. For instance, you can say that the treatment seemes to cause a 1000-fold *down*-regulation.
Thank you very much Jochen Wilhelm, It helped me alot, Please see another e.g.2 I am posting.I need your comments.Thanks
You changed the way the ∆Cts are calculated.
It would be helpful if you try to understand the meaning if such values.
---- PART 1 -----
Following from the exponential amplification with an E-fold amplificatipn per cycle (E is the amplification efficiency; E=2 means doubeling each cycle = ideal; E=1 means no amplification at all = the amount remains constant), the fluorescence signal F follows the function
F = p*N*E^C
where c is the cycle number, N is the initial concentration of the amplicon sequence and p is a proportionality factor translating product concentration to fluorescence intensity. This factor is some (usually unknown) constant for a given target/primer/reaction/instrument combination.
At the threshold value, F=Ft and c=Ct:
Ft = p*N*E^Ct
Solved for Ct:
Ft/p = N*E^Ct
log(Ft/p) = log(N*E^Ct) = log(N) + log(E^Ct) = log(N) + Ct*log(E)
Ct*log(E) = log(FT/p) - log(N)
Ct = log(FT/p)/log(E) - log(N)/log(E)
If we take the log to the base E the equation simplifies to
Ct = log(Ft/p) - log(N)
The part log(Ft/p) is just a reaction-specific constant, so we note that
Ct ∝ -log(N)
---- PART 2 -----
The initial amount (or concentration) of a gene of interest, N[goi], is normalized to a loading control, the initial amount of a reference gene, N[ref] by the ratio
q = N[goi] / N[ref]
The log-ratio is
log(q) = log(N[goi] / N[ref]) = log(N[goi]) - log(N[ref])
Now, as seen from part 1, log(N[goi]) ∝ -Ct[goi] and log(N[ref]) ∝ -Ct[ref]. Hence
log(q) = log(N[goi] / N[ref]) ∝ (-Ct[goi]) - (-Ct[ref]) = Ct[ref] - Ct[goi]
So when ∆Ct is calculated as Ct[ref] - Ct[goi], then
∆Ct ∝ log(N[goi] / N[ref]) = log(q)
---- PART 3 -----
The normalized amount of the goi in a treatment condition q[treat] should be compared to the normalized amount of the goi in a control condition q[ctrl] by
Q = q[treat] / q[ctrl]
Again, the log-ratio is
log(Q) = log(q[treat] / q[ctrl]) = log(q[treat]) - log(q[ctrl])
In part 2 you can see that log(q[treat]) = ∆Ct[treat] and log(q[ctrl]) = ∆Ct[ctrl], so we get
log(Q) ∝ ∆Ct[treat] - ∆Ct[ctrl]
For simplicity, I did not consider the proportionality factors that are different for goi and ref, but whatever they are, at this time they cancel out. Therefore, the proprotionality becomes an equality again:
log(Q) = ∆Ct[treat] - ∆Ct[ctrl]
Finally, if the ∆Cts are calculated as CT[ref] - CT[goi] and the ∆∆Ct is calculated as ∆Ct[treat] - ∆Ct[ctrl], then
∆∆Ct = log(Q)
and E^∆∆Ct = Q (since we used the log to the basis E).
---- REMARKS TO LOGARITHMS -----
No please think about this:
log(A/B) = log(A) - log(B)
log(B/A) = log(B) - log(A)
--->
log(A/B) = -log(B/A)
generally: log(x) = -log(1/x)
Further:
log( [A/B] / [C/D] ) = -log( [B/A] / [D/C] ) = -log( [C/D]/[A/B] ) = log( [D/C] / [B/A] )
Jochen Wilhelm
Hi Jochen, I have been following your replies to different posts regarding Rt-PCR and the possible ways to present the data. Many things have become clear to me based upon your suggestions.
I am also having the same problem as mentioned in this question (although it was posted 5 years ago). I am working on mice neutrophils and have 4 different groups (wild type v/s knockout strains and further: uninfected and infected). I have multiple genes to test for (baseline expression in both mice strains and then the expression in the infected samples compared to the baseline). I have tried both deltadeltaCt method and the fold expression method (2 exponential -deltadelta Ct). The fold expression values gives data which is all over the chart. I am thinking of showing data in terms of deltadelta Ct. I was reading carefully what you have suggested. I am attaching my sample excel sheet for your suggestion (if I have understood it correctly). I have followed two methods to calculate deltadeltaCt (keeping GAPDH as house keeping gene in first and then without it). I am not sure if the later is a goo way to present data.
Also, can you please suggest a possible way to present this data and how should I apply stats (there are two variables; the type of mice itself and then the infection parameter)? Besides, if I am plotting my deltadelta Ct values in prism, do I first convert to log and then present? I am keeping my wild type (B6) uninfected (-) mice as calibrator sample. With deltadeltaCt value for this as 0, what I need to show on the graph. Sorry if the question seems very trivial or stupid but I would really appreciate your help.
Regards
Manmeet
It is good to look at a few links below.
https://www.researchgate.net/post/qpcr_statistical_analysis
https://bitesizebio.com/24894/4-easy-steps-to-analyze-your-qpcr-data-using-double-delta-ct-analysis/
https://toptipbio.com/delta-delta-ct-pcr/
@Manmeet Bhalla,
there is only a single sample/mouse per condition. How will you do statistics there?
Jochen Wilhelm
So the attached sheet shows only one set (obtained from one wild type and one knockout mice with infected and un-infected conditions, in-vitro). I have >4 independent data sets which I want to combine in the end. The attached sheet was just for your reference to confirm the calculation part.
Thanks
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