A statistical contribution to the uncertainty of concentration measurements using digital PCR

Andreas Kummrow, 1, Annabell Plauth 1,*, Martin Hussels 1
1 Physikalisch-Technische Bundesanstalt, Germany; 

Measurement of the concentration of biological entities using quantitative PCR (qPCR) usually results in a large spread of results obtained in interlaboratory comparisons. As such, deviations in the range of ±0.6 on a logarithmic scale (base 10) are currently considered acceptable in the external quality assurance of quan- tification of viruses like HBV, HCV, and HIV-1 in Germany. Notably, a considerable contribution to this variance may originate from pre-analytical steps and variable efficacy of the assays utilized. Technical limitations of the instrument remain as a source of uncertainty of measurement, even if a perfect extraction and amplification is assumed. Digital PCR (dPCR) does neither require reference genes nor calibration material to quantify the concentra- tion in biological samples and thus might substantially improve the measurement uncertainty in concentration measurements com- pared to qPCR. An apparent physical limitation for concentration measurements using dPCR is the uncertainty of the reaction vol- ume. Recent studies quote an (unexpanded) uncertainty of around 2% using microscopic measurements of the average size of the respective reaction volume. In this study, we discuss the effect of the limited number of repeat reactions in dPCR on the uncertainty of concentration. It is generally accepted that a Poisson correc- tion must be applied to the concentration determined by dPCR, i.e. for an average of reactive DNA molecules in each reaction chamber, the probability of a positive reaction is p = (1 − exp(− )). Thus, for N reactions one expects A=pN positive reactions and B = (1 − p)N negative reactions. The statistical uncertainty for posi- tive (and negative) reactions does not follow a normal distribution. We show, that the uncertainty of finding positive reactions has to be calculated based on the standard deviation of the binomial distribution, which yields u = (AB/N)1/2 . This result is used to calcu- late the minimum number of reactions required for a given DNA concentration and targeted statistical uncertainty u of the con- centration. Additionally, the implications of this result on setting up dPCR experiments is discussed. We calculated the sweet spot for the fewest number of reactions around = 1.5, which falls to = 1 for large statistical uncertainties (>10%). Even in this case, at least 4000 reactions are required to reach a statistical uncertainty of 2%. To maintain this uncertainty for a dynamic range of 3 orders of mag- nitude requires using more than 300000 reactions. The research receives funding from the EMPIR project HLT-07 AntiMicroResist. The EMPIR programme is co-financed by the Participating States and the European Union’s Horizon 2020 research and innovation programme.

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