The relevance of biological effects is typically on a relational scale, that is graphically best represented as logarithms.

Example: a two-fold up regulation should be assumed to be biologically as relevant as a 2-fold down regulation. Plotting the folds in a barchart will produce a bar of length 0.5 for the down regulation and a bar of length 2 for the up regulation. The ratio of the bar areas what is percepted by the reader's eye and brain indicates that there is a huge, important up up regulation, whereas the down regulation is relatively negligible. Even if a more appropriate dot-plot (or box plot or something like this) is used (with the reference line at y=1), the up regulation still looks much more strong and important than the down regulation. However, on the log-scale both effect look similar, only with different signs (to opposite directions; the reference line is now at y=0 -> log(1)=0).

Michael gave a compromise to plot negative folds as -1/fold, what makes the same regulation factor to either direction look of the same strength/importance. However, different strength of regulation still look distroted this way. A fold of 2 and a fold of 3 will have one unit difference in the plot. The same applies for the folds 7 and 8. However, the biological effect of the difference between a 2-fold and a 3-fold change is commonly considered much more relevant than a difference between a 7-fold and 8-fold change. On the log[2]-scale, the first difference is log[2](3/2) = 0.6, the second is log[2](8/7)=0.2, better reflecting the biological relevance.

So, clearly, only log-folds should be shown (and the whole analysis runs on the log-folds anyway). Using the base 2 (as Joseph pointed out) is convenient. Note that the axis labels could show the folds, so a reader may directly get the folds from the plot (although the axis is log-scaled).

I use two separate graphs- one upreg genes one downreg genes. All values relative to 1. Had the same worries you described.

Thanks Amanda. So your down regulated genes are plotted as negative fold change (e.g. -5 fold).

I think presenting them as + or - fold-change is the clearest way and symmetrical like you say. Negative fold-change can be calculated using the formula -1 / ratio. For example, a gene with 0.75 fold the expression level of control would be (-1) / 0.75 = -1.333...

With regard to the -1 fold-change, I see it as 1 or -1 being your baseline since the range is defined to be between +x and +1 for up genes, -1 and-x for down genes. So 1 or -1 is negligible with regard to relative expression in one sample compared to another.

One thing to be wary of that I have encountered with qPCR and fold-changes is to ensure the amplicon is reliably detected in all samples being compared. In my case I have had genes that are not expressed in some biological samples at all and result in very high Ct values with high variability. Because of this presenting a fold-change becomes problematic and unlikely to be a true reflection of the degree of change. Not stricly related to your question but it got me thinking about this issue.

No, they are plotted on scale 0-1. I like to see my down regulated genes bar being smaller than the control set at 1, so the graph image is psychologically making sense. But then I'm looking at small changes so I don't need to see the differences between e.g. 10 fold and 20 fold, which would be impossible to pick up on my graph being at 0.1 and 0.05. At the end of the day, it depends on the data set and which conclusions you want to be most visibly obvious from your results. You want the reader to get your take home message with a quick glance. So I choose the format that gets that across easiest.

I usually plot in log2. A log scale because I like the symmetry of magnitude for up and down regulated genes, and base 2 because it fits qPCR data nicely (each unit is essentially one cycle). But, I'll often add a second 'y-axis' or tick-marks on the right side of the plot and label them with the corresponding linear values (2,4,8,...) so that readers not accustomed to log2 can quickly grasp how large some of the fold changes might be. Best of both worlds.

The relevance of biological effects is typically on a relational scale, that is graphically best represented as logarithms.

Example: a two-fold up regulation should be assumed to be biologically as relevant as a 2-fold down regulation. Plotting the folds in a barchart will produce a bar of length 0.5 for the down regulation and a bar of length 2 for the up regulation. The ratio of the bar areas what is percepted by the reader's eye and brain indicates that there is a huge, important up up regulation, whereas the down regulation is relatively negligible. Even if a more appropriate dot-plot (or box plot or something like this) is used (with the reference line at y=1), the up regulation still looks much more strong and important than the down regulation. However, on the log-scale both effect look similar, only with different signs (to opposite directions; the reference line is now at y=0 -> log(1)=0).

Michael gave a compromise to plot negative folds as -1/fold, what makes the same regulation factor to either direction look of the same strength/importance. However, different strength of regulation still look distroted this way. A fold of 2 and a fold of 3 will have one unit difference in the plot. The same applies for the folds 7 and 8. However, the biological effect of the difference between a 2-fold and a 3-fold change is commonly considered much more relevant than a difference between a 7-fold and 8-fold change. On the log[2]-scale, the first difference is log[2](3/2) = 0.6, the second is log[2](8/7)=0.2, better reflecting the biological relevance.

So, clearly, only log-folds should be shown (and the whole analysis runs on the log-folds anyway). Using the base 2 (as Joseph pointed out) is convenient. Note that the axis labels could show the folds, so a reader may directly get the folds from the plot (although the axis is log-scaled).

What i can do when im not able to detect ct value of a gene in some treatment. i calculate relative expression. but there is an issue when there is no ct value detected for a gene its relative fold change ultimately expressed very high as compare to other. i use 2^ -ddct method for calculating relative fold change

Praveen, if you are not able to measure a ct value, then you don't have a measurement (it is a s simple as this!). It is usually impossible to calculate "something" from "nothing". A missing ct typically indicates that the gene is not expressed.(*) In this scenario the question for any "fold-change" in completely insensible. Information about presence/absence of a transcript is lesser information than about the quantity of its abundance. You cannot calculate with information you do not have. So in this case (genes are sometimes not expressed/detecable), you have to face the fact that only relatively little useful information is provided from each measurement (i.e.: either it is detected or not), and this littel information has to be used appropriately. The type of the response changes from "metric" (ct, interval scaled) to "dichotomous" (absent/present, nominal scale with two categories). There are statistical tools to analyze dichotomous variables. You may consider using these tools. You may find that the required sample size will need to be much larger to confidently detect some effects, because the information provided from each measurement is lower.

(*) given the assay is well optimized and has an adequate performance. The gene may be expressed to such a low level that it cannot be detected/quantified. The limit of detection and the limit of quantification of the assay plays a role for interpretation here, but not for the statistical analysis per se.

I agree with most of the answers discussed here. As per the problem aroused by Mark, I agree that if fold change is represented as positive/ negative graph then it is contradictory to evaluate 1, 0 & -1 values. Rather, in such type of representation these three values (1,0 and -1) hold indifferent meaning. If there is no change in expression then it can be taken either as 1 or -1, both have same meaning. In my view, such type of plots should have a modified Y-axis where it can be plotted as 5, 4, 3, 2, 1, -2, -3, -4, -5.....and so on. In such modified Y-axis a meaningful representation can be made.

As suggested by other researchers, I too have same opinion that your representation depends upon the type of data you obtain. Logarithmic representation helps you intake far-off value within plottable area. If your data does not vary much from the normal, then you can plot fold change in simple linear one quadrant graph. If there is no expression at all as compared to control sample, then again it is a problem because you cannot state the fold difference.

Finally it depends upon the presenter how he/she can display the result in simplest possible way.

I'd agree with Atanu's "modified Y-axis", and would define the following:

2, 3, 4, 5 ... for activations/increases with "1" as reference 

-2, -3, -4, -5 ... for inactivations/decreases with "-1" as reference. 

They can plotted in the same figure.  The area of +1 and -1 is defined as a "dead zone" or "base".

Ct value *are* already on the log scale.

You just don't need to un-log the Ct-values.

dCt values are log-ratios (call it "log normalized expression"), ddCts are log-ratios of ratios (call it "log ratio of normalized expressions" or "log fold-changes").

Yes, you are right.

Note that log2(2^-ddCt) == -ddCt.

As you say you take 2^-ddCt as a fold change it seems that you follow the steps of Livak and Schmittgen. They made a mistake in the calculation of the dCt values. They wrote: dCt = Ct[goi] - Ct[ref], but is should have been dCt = (-Ct[goi]) - (-Ct[ref]) = Ct[ref] - Ct[goi]. As a consequence of this mistake the ddCt they calculated as the log of the resicprocal fold-change (FC). They corrected their mistake at the end when they gave the FC by switching the sign of the ddCt (instead of FC = 2^ddCt they wrote FC = 2^-ddCt).

You don't deed to repeat this mistake, and so you would not need to correct/switch the sign of the ddCt:

If you calculate dCt as Ct[ref] - Ct[goi], the dCt values will have the correct sign, i.e., samples with a higher goi expression (normalized to ref) will have higher dCt values.

If you then calculate ddCt as dCt[treat]-dCt[control], the sign of the ddCt value is also correct, i.e., positive ddCt indicate induction (up-regulation) and negative ddCt indicate repression (down-regulation).

Hi,

interesting answers. I would like to ask if there is possibility to get results like 1000-fold change (increase or decrease)?

The dynamic range for the Ct values is about 20 (from 10 to 30, roughly).

Therefore, the most extreme ddCt that is measurable is about 20, and 2^20 = 1048576.

Measuring a fold-change of 1000 would require a ddCt of log2(1000) = 10 cycles. This is well possible.

The qPCR has a large dynamic range, but a low precision. This makes this method very well suited to measure extremely large fold-changes, but it also makes it difficult to determine small fold-changes with sufficient precision.

So I use Ct (target gene) - Ct (gapdh) to calculate dCt and then dCt (target) - dCt (control) to calculate ddCt and use 2^-ddCt across ALL ddCT values too get fold change...I get >1 FC values to represent upregulation and 1 and

People often show their qPCR data in terms of relative gene abundance instead of fold change. Which one is a better method? And how do I plot relative gene abundance? 

If you want to show the differences in expression between many different conditions, showing dCt (or, if you want, "relative gene abundance") is easier, and the difference can be assessed visually by comparing whatever two conditions. If you have only few particular comparisons, it it better to show these differences (i,e, ddCt or "fold-changes") directly.

How to plot "relative gene abundance"?: The best way is to simply plot the dCt values, as a box-and-whisker plot (if the sample sizes are large enough (>10 or so) or as a (1D)-scatterplot (as a "beeswarm plot" showing each measurement or as a single dot for the mean and error bars indicating the confidence intervals).

Thanks a lot for your answer! I was trying to contact you directly but couldn't place your email id. In my case, I had 10 transgenic lines with down regulated target gene through RNAi. I had plotted fold change in my lines relative to untransformed control (which was obviously taken as 1) but I am now asked to plot relative gene expression (which otherwise means the same but I assume the reviewer wanted to say 'relative gene abundance'). So, I was in a fix how to plot that! Simple dCt values are of no use. Right? Then what else?

@Jochen Wilhelm 

If I did understand, did you mean that FC=dCT(treat)-dCT(control) if I used dCT=Ct[ref] - Ct[goi] is also correct to the FC=2^-ddCT and I should to obtain the same values?

Other question:  I have the FC values (qRTPCR) from triplicates, when I apply de log2 FC transformation in every sample and I plot I obtain a different mean when I obtain a mean from triplicates and apply the log2fc over these means....e.g:

                           S1       S2       S3       mean(S)      log2fc (mean(s))

FC                     3.14     6.24    0.82    3.41             1.77

log2FC             1.65     2.64     -0.25 

mean log2FC  1.35 

What is correct?

Not exactly.

The ddCt is the log2 FC, and the FC is the 2logFC = 2ddCt

Other question:

you should not average the FC but the logFC. So if you have

FC = (3.14, 6.24, 0.82)

then you have

log2FC = (1.651, 2.642, -0.286)

and the average log2FC is 1.335.

The average FC is then 21.335 = 2.52.

@Jochen Wilhelm

Ok!! Thank you... your explication was very helpful!

I'm understanding better now!! I need to relate RNAseq data with qRTPCR quantification and the methods to obtain the FC are a quite different!

Finally I get undertand the point exposed by @Jochen Wilhelm. Another fellow at the labb did the qRTPCR experiments she follow the Livack method... when I did the correlation of these data (using the ddCt calculated by her) I found a Proportionally inverse co-relation which does not make sense...when I did just the log2 (FC or 2^-DDCt) transformation data I get a logical correlation however these data have the opossite sign with ddCt obtained from her..... so, I should take in account that the log2FC is really a -(log2FC) which don't make sense or she should to review the method to obtain the ddCt and 2^-DDCt? I'm confused...

Hi all,

I have struggled a lot during my PhD to find the most appropriate way to analyze and display qPCR data. I was quite astonished to realize that in the enormous majority of the publications qPCR data is not well analyzed nor well graphically presented. In case it is useful for anyone, below is how I deal with and plot qPCR data.

I analyze qPCR data using LinReg software, which determines the PCR efficiency for each set of primers based on each sample amplification curve (without the need so assume that it is 100% like in the delta delta ct method, nor making dilution curves). With the efficiency, the threshold and corresponding CT value, the software returns the N0 value for each well, which represents the starting amount of DNA, derived from the exponential formula of PCR: threshold = N0 * Eff ^ Ct . The software allows to export the data to an excel spreadsheet, where I do most of the following calculations.

For normalization, I use at least two housekeeping genes. First, I average the N0s of the technical replicates for all the samples (GOIs and housekeepings). Then, I calculate the geometrical mean of the averaged N0s for the housekeepings for each condition. I always plot the N0s of the housekeepings and the GeoMean and make sure that when put on a log scale, the curves for the housekeepings are parallel between conditions (that is, that both housekeepings trully reflect the differences in initial DNA mass in the same way, see image attached). I use the GeoMean to normalize the averaged N0s for the GOIs.

Since we are very bad at getting insight from tables, making informative graphs is one of the most important parts of qPCR data analysis. I normally start by plotting the normalized N0s for each condition for every GOI. qPCR data should always be presented in log2 scale, since we are generally interested in proportions. Lineal scale can be very misleading, not only because it treats down and upregulated genes in a different way (graphically speaking), but it can also obscure interpretation due to scaling. I believe this to be one of the major in the great majority of the publications that present qPCR data. For this, one can either transform the data to log2 and plot it, or plot it directly but setting the graph y scale to log2.

Finally, for an experiment to be statistically valid, it should contain at least 3 biological replicates. After having performed the specific statistics (wich I am skipping, but show be performed with the normalized data)... how do we merge all the biological replicates in a single graph? Generally speaking, it is common practice to relativize the normalized N0s for a GOI to a control condition (a specific treatment, or day 0, etc). Here comes a step where many mistakes are often made:

Some people relativize independently each biological replicate to its control condition. For instance:

DAY: 0 1 2

Rep1: 1 3 12

Rep2: 1 4 11

Rep3: 1 7 15

Then they take the mean and SEM of each condition and present that. However, in this way they are trimming the variability of the control condition. Most importantly, if for any reason only the value of the control condition of one replicate is off (e.g. an outlier), this would make a big bias on the rest of the data of the other conditions for that replicate (For these reasons, statistical analysis should never be performed with data relativized in this way, but rather, with the original normalized data).

For relativizing in a way that does not change the distribution of the data, first of all, normalized data should be log2 transformed. Only then one can take the arithmetic mean of the transformed data for the control condition, and then divide each normalized N0s of each condition of every replicate to that mean

(if not transforming the data, the geometrical mean should be used instead).

If one has only three replicates, it is always better to show the actual data as a scatter plot for each condition (not bars!!!!). If more replicates are used, then a bloxplot might be better. If for any reason one prefers to reduce the replicates to one value (to use bars, timelines, etc), this should be thearithmetic ('regular') mean of the log transformed values for each condition (control will be 0, etc). Regarding the error bars, SEM can be calculated also using the log transformed data [note: if data is log transformed independently, then the scaling of the plot should not be set to log!!].

I am aware that many people are not comfortable with the Y axis displaying log2 exponents instead of the original data (0,1,2,3 instead of 1,2,4,8, etc). This can be solved by transforming back the data - i.e. calculating 2^transformed data and setting the axis to log2. This is the only way to go that I can think of if one wants to display results only as mean +- SEM. Direct calculation of the mean log value could be done by taking the geomatrical mean of the original values, but for calculation of SEM one must compulsory use the log transformed data.

I know this probably sounded like a lot, but once you've learned how to do it it can be performed in 5 minutes in an excel spreadsheet. Hope this was useful!!

Best,

Ariel