The Theoretical Basis of qPCR and ddPCR Copy Number Estimates: A Critical Review and Exposition

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The polymerase chain reaction (PCR) is a molecular biology tool with diverse applications in the aquatic sciences. Classical PCR is a nonquantitative method that can be used to detect target DNA sequences that are characteristic of particular microbial taxa but cannot determine their concentrations in water samples. Various quantitative forms of PCR have been developed to remove this limitation. Of these, the two that currently are used most widely are real-time quantitative PCR (qPCR) and droplet digital PCR (ddPCR). Several outlines of the mathematical and statistical basis of these methods for estimating target sequence concentrations are available in the literature, but we are aware of no thorough and rigorous derivation of the theoretical underpinnings of either. The purpose of this review is to provide such derivations, and to identify and compare the main strengths and weaknesses of the two methods. We find that both estimation methods are sound, provided careful attention is paid to specific details that differ between the two. With qPCR, it is especially important to reduce any significant PCR inhibition by sample constituents and to properly fit the standard curve to heteroskedastic calibration data. With ddPCR, it is important to ensure that the value of the mean droplet volume used in calculating concentrations is correct for the particular combination of droplet generator and master mix used. The advantages of qPCR include lower instrument and per-sample costs, a shorter turnaround time for obtaining results, a higher upper limit of quantification, and a wider dynamic range. The advantages of ddPCR include freedom from dependence on a standard curve, an inherently lower sensitivity to PCR inhibitors, a lower limit of quantification, a simpler theoretical basis, and simpler data analysis. We suggest qPCR often will be preferable in laboratory studies where investigators have significant control over the range of target sequence concentrations in samples, concentrations are sufficiently high so proper calibration does not require standards with concentrations low enough to exhibit exaggerated variability in the threshold cycle, and no significant inhibition is present, or more generally, in studies where funding levels do not permit the higher cost of instrumentation and supplies required by ddPCR or where the shorter turnaround time for qPCR is essential. If sufficient funds are available, ddPCR often will be preferable when the ability to quantify low concentrations is important, especially if inhibitors are likely to be present at concentrations that are problematic for qPCR.