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closederivation of the formula to correct aPCR data for amplification efficiencies
Posted by c-mnstr on 02 May 2013 at 02:34 GMT
This supplementary information was unfortunately omitted in the posted version of our paper.
Below we describe a simple transformation used in our paper that corrects raw qPCR data for the efficiency of amplification, allowing for direct application of linear model analysis. This transformation was previously introduced by Steibel et al (2009), although in a slightly different form.
The raw data of the RT-qPCR experiment come in the form of Cq (“quantification cycle”) values, corresponding to the number of PCR cycles required to detect a target. The amount of product accumulated during PCR at the quantification cycle Cq (N[Cq]) is given by the formula:
N[Cq] = N0 * E^Cq [1]
where N0 is the initial amount of target in the PCR reaction, and E is the amplification efficiency (the multiplication factor per PCR cycle, determined from amplification and linear regression analysis of dilution series, Pfaffl 2001).
Consequently,
N0 = N[Cq] * E ^(- Cq) [2]
Log2-transforming equation [2], we have
log2(N0) = log2(N[Cq]) + log2 (E – Cq) = log2(N[Cq]) - Cq * log2(E) [3]
For the purpose of relative quantification (comparing abundances of a particular gene across samples) any constant terms in the equation [3] can be ignored. Since for a given RT-qPCR assay and instrument NCq is assumed to be constant across all samples, we can drop the first term in the equation [3], resulting in the following transformation formula:
Ca = - Cq * log2(E) [4]
Applying formula [4] to the Cq values, therefore, transforms them into Ca (“absolute cycle”) values, directly proportional to the log2 of the original target amount. Note that, due to the use of 2 as the base of the logarithm, Ca = - Cq for qPCR with E = 2. Ca value can therefore be understood as a sign-inverted “ideal” Cq, the one that would have been observed for the same gene and sample if PCR was proceeding with perfect efficiency (E = 2).
For relative quantification, is is then convenient to center the data around the mean:
Ca[centered] = Ca - mean(Ca) [5]
This transformation, performed separately for each gene, represents the data as log2-transformed fold-differences relative to each gene's mean across samples. It makes the data more intuitive and all the genes comparable to each other on the same scale.
References
Steibel, J. P., R. Poletto, et al. (2009). "A powerful and flexible linear mixed model framework for the analysis of relative quantification RT-PCR data." Genomics 94(2): 146-152.
Pfaffl, M. W. (2001). "A new mathematical model for relative quantification in real-time RT-PCR." Nucleic Acids Research 29(9): e45.
Mikhail V. Matz, University of Texas at Austin, matz@utexas.edu