Analyzing real-time PCR data by the comparative Ct method

Thomas D Schmittgen and Kenneth J Livak
Nature Protocols Vol. 3 No. 6 1101, 2008

Note: the procedures involved in preparing for and running the PCR are covered in the paper but will not be detailed in this post.

Real-time RT PCR is a method of analyzing gene expression.  The RT stands for reverse transcription; RNA is converted to DNA and then amplified by PCR.  Specific fluorescent probes allow for detection of the amount of the gene of interest present after each cycle.  The number of the cycle during which it reaches the threshold (the red line in the graph below; set at a value below which the noise is too great to give an accurate impression of the actual fluorescence due to DNA quantity), or Ct, depends on the amount of RNA for the target gene that was in the original sample.  The cycler will give out the exact Ct for each sample, along with a graph showing the fluorescence of the sample vs. the cycle number, to show how the fluorescence changes over time.  An example graph is shown below, with one sample being probed for two different genes.  Each gene is assayed in triplicate, so the graph shows six different curves (in two close groups of three).
 
A lower Ct means more RNA, which means more gene expression.  By comparing the Ct of the target gene (VGLUT2, in the above example) to the Ct of a reference gene (a gene that is always expressed in the same amount; HPRT, in the above example), we can come up with a ratio of expression of the target gene to expression of the reference green.  If this is done in many different samples, than we can compare those ratios to determine if the samples express the target gene in the same amounts.  This depends largely on two things: picking a good reference gene that is known to be equal in all samples and using a reliable mathematical approach to compare the samples.

Schmittgen and Livak spend a good deal of time on this second concern in their paper.  The most effective approach for comparing the treatment and control groups depends on what one is attempting to study, but the initial steps are the same.  First, average the triplicates; each sample is probed for each gene in triplicate to reduce the effect of pipetting error on the results.  If the triplicates are too different (if the standard deviation between the Ct values is more than 0.3), one or all three must be thrown out.  If they are within the acceptable range, then the average Ct will be used from here on out.

Secondly, calculate the deltaCt.  This is done by subtracting the Ct of the reference gene from the housekeeping gene (see equation below).  Do this for every sample.  After this, the next step depends on whether the goal is to compare individual samples to each other or to compare groups of samples to each other.  Now it becomes important to know the origin or importance of the samples, so I will refer to them as belonging to the treatment group or to the control group.

deltaCt = Ct(target gene) - Ct(reference gene)

If the goal is to compare each individual sample from the treatment group to a matched control, subtract the deltaCt of the control sample from the deltaCt of the treatment sample to get a deltadeltaCt (see first equation below).  Next raise 2 to the power of -deltadeltaCt to obtain a fold change (see second equation below).  For example, if deltadeltaCt is 2, the fold-change in gene expression will be 2^(-2), or 0.25.  This means that the target gene is expressed one-fourth as much in the treatment sample than in the control sample.  When this is calculated for each pair of treatment and control samples, the fold-change values can be averaged to obtain an average fold-change.  Note that when the fold change is less than one, it can be presented as 1/fold change; for example, a 0.25-fold change could be stated as a 4-fold reduction.

deltadeltaCt = deltaCt(treatment group) - deltaCt(control group)

Fold change = 2^(-deltadeltaCt)

If the goal is to compare a treatment group to a control group, average the deltaCt values within the groups and calculate the SDs.  After this, there will be one treatment deltaCt and SD, and one control deltaCt and SD.  The control group deltaCt can be subtracted from the treatment group deltaCt to obtain a deltadeltaCt.  This is used as above to obtain a fold-change.

The reason that the second situation requires averaging the Ct values and the first situation does not is that the samples in the second situation are not paired with controls.  If you have a clinical study in which you have matched your treatment subjects with controls based on age, weight, or other criteria, this is the first situation.  This is quite useful with small studies that have differences between their treatment individuals that could make lumping them together suppress the effects of the treatment (which would happen when averaging blood pressures, for example, when some patients are children and some are adults; matching each child to a control child and each adult to a control adult will control for difference within the group so that differences between the groups will be apparent).  However, many studies (especially larger ones) randomize their subjects and end up with two groups but no specific pairs.  In these cases, you could pair the subjects after the fact, but it would not be as necessary or as beneficial as it is in the first situation.  Therefore, averaging the deltaCts before calculating the deltadeltaCt is the better option.

Alternately, 2^-deltaCt can be calculated for each sample.  Those can be averaged for each group, and the fold-change would then be calculated by dividing the mean from the treatment group by the mean from the untreated group (see equation below).

Fold change = [2^(-deltaCt(treatment))]/[2^(-deltaCt(control))]

Now, all of this is only valid if the target and reference genes have similar amplification efficiencies, which are influenced by the primers and the PCR conditions.  Amplification efficiency is determined by running a PCR plate with different concentrations of the same sample and then plotting the Ct vs. log(concentration).  The data points should form a line, with the efficiency equal to 10^(-1/slope).  If the efficiencies are not within 10% of each other (and 10% of 2; an amplification efficiency of 2 shows that the DNA doubles each cycle), then the PCR conditions should be altered or new primers should be ordered.