Why is the PCR amplification efficiency still ignored?

Although this situation gives the impression that delta delta Ct needs no explanation for the users of qPCR, the opposite is true. Seemingly the presence of asterisks (to denote statistical significance) in the graphs satisfies the reviewer and the reader and thus abolishes the need for further understanding; the results are significant whatever they are. Without knowing, the reader has assumed that the amplification efficiencies of both target of interest and reference gene were all equal to 2, which means a doubling per PCR cycle or a 100% efficient assay. However, from the onset of qPCR, the authors in the field have highlighted that dCt and ddCt cannot be applied when there is a difference in amplification efficiency of the target and reference genes being compared.

The $2^{-\Delta\Delta C_t}$ equation for relative quantification that is referred to in most publications was originally accompanied by a procedure to check that the amplification efficiencies of the target and reference genes were sufficiently similar (Livak and Schmittgen, 2001). However, within a few years of qPCR it was clear that the implicit assumption of this equation that all PCR assays were 100% efficient was wrong and an alternative equation for efficiency corrected relative quantification was published (Pfaffl, 2001). The required PCR efficiency could be derived from a dilution series, yet the qPCR efficiency calculation is rarely carried through to the final results. When such dilution series are dutifully performed, the linearity of the Ct against log(input) is checked and, if confirmed, the resulting PCR efficiencies are quietly forgotten. Indeed, my experience is that in qPCR courses, less than 50% of the participants is aware of the role of the amplification efficiency in PCR.

As the MIQE guidelines (Bustin et al., Clinical Chemistry, 2009) propose to use quantification cycle ($C_q$) over threshold cycle ($C_t$) and other terms referring to the same value from the real-time instrument, I will be using $C_q$ for the remainder of this post.

Whereas the original paper on efficiency corrected relative quantification in qPCR (Pfaffl, 2001) attempted to stay close to the original $\Delta\Delta C_q$ equation, the realization that multiple reference genes were required (Vandesompele et al., 2002) necessitated the developers of qPCR analysis software to go back to the original kinetic equation of the PCR reaction ($N_C = N_0 \cdot E^C$). The target quantity $N_0$ can be directly derived from inversion of this equation and the definition of $C_q$. Because $C_q$ is the number of cycles needed to reach a threshold $N_q$, the inversion of the kinetic equation shows that $N_0 = N_q / E^{C_q}$ (Ruijter et al., 2009).

When the $C_q$ is derived for a target gene (with efficiency $E_T$) and for a reference gene ($E_R$), for control and treated conditions, the relative gene expression (target/reference for treated/control) can be calculated as:

With the assumption that both efficiencies are 2 and a rearrangement of the $C_q$ values in the exponent, this equation simplifies to the full write-out of the $2^{-\Delta\Delta C_q}$ equation:

The effect of this simplifying assumption is illustrated with four target genes and a reference gene in an experiment with three treatments and a control condition. The target genes all have the same expression level but show a three-fold increase between the control and each of the treatments; the expression level of the reference gene is constant in all conditions. Note that each target is amplified with another efficiency.

Target 1, amplified with an efficiency of 2, shows the correct fold change in each of the treatments, regardless whether [Eq. 1] or [Eq. 2] is used for the calculation. For treatment 1, with only a 3-fold difference compared to the control, the use of [Eq. 2] results in only slightly deviating values, even when the efficiency value of the target is far below 2. However, with increasing effect of the treatment and decreasing PCR efficiency of the targets the bias caused by [Eq. 2] becomes increasingly clear.

Given the sensitivity of qPCR, with enough biological replicates the use of the $\Delta\Delta C_q$ equation will lead to the conclusion that the targets are differentially expressed in treatments 2 and 3. This obviously wrong conclusion illustrates why the actual PCR efficiencies have to be included in the calculation of qPCR results.

But what is the reason that PCR efficiencies of the targets and references are often ignored and implicitly considered to be 2? Probably because most researchers, reviewers and readers think that in relative quantification the efficiency differences disappear from the calculation. The example shows that is not the case. It shows what can happen to the published results when PCR assays are not 100% efficient.