Extending digital PCR analysis by modelling quantification cycle data

Philip J. Wilson, Stephen L. R. Ellison

Digital PCR (dPCR) is a technique for estimating the concentration of a target nucleic acid by loading a sample into a large number of partitions, amplifying the target and using a fluorescent marker to identify which partitions contain the target. The standard analysis uses only the proportion of partitions containing target to estimate the concentration and depends on the assumption that the initial distribution of molecules in partitions is Poisson. In this paper we describe a way to extend such analysis using the quantification cycle (Cq) data that may also be available, but rather than assuming the Poisson distribution the more general Conway-Maxwell-Poisson distribution is used instead. A software package for the open source language R has been created for performing the analysis. This was used to validate the method by analysing Cq data from dPCR experiments involving 3 types of DNA (attenuated, virulent and plasmid) at 3 concentrations. Results indicate some deviation from the Poisson distribution, which is strongest for the virulent DNA sample. Theoretical calculations indicate that the deviation from the Poisson distribution results in a bias of around 5 % for the analysed data if the standard analysis is used, but that it could be larger for higher concentrations. Compared to the estimates of subsequent efficiency, the estimates of 1st cycle efficiency are much lower for the virulent DNA, moderately lower for the attenuated DNA and close for the plasmid DNA. Further method validation using simulated data gave results closer to the true values and with lower standard deviations than the standard method, for concentrations up to approximately 2.5 copies/partition. The Cq-based method is effective at estimating DNA concentration and is not seriously affected by data issues such as outliers and moderately non-linear trends. The data analysis suggests that the Poisson assumption of the standard approach does lead to a bias that is fairly small, though more research is needed. Estimates of the 1st cycle efficiency being lower than estimates of the subsequent efficiency may indicate samples that are mixtures of single-stranded and double-stranded DNA. The model can reduce or eliminate the resulting bias.