PCR amplification ensures sufficient input material in RNA-Seq sequencing. However, efficiency variations in PCR also introduce bias in subsequent gene and isoform quantification. Unique molecular identifiers (UMIs) can identify PCR duplicates. Hence, the number of pre-PCR fragment copies is often estimated as the number of distinct UMIs (UMI counting).
Here, we investigate computational methods for estimating pre-PCR fragment copies if the numbers of UMIs is too small for UMI counting or if UMIs are not uniformly distributed. We study two types of methods. The first is a correction to UMI counting, the second can be summarized as duplication model estimates (DME). For DMEs the post-PCR counts for each UMI are modelled by distributions parameterized by the number of pre-PCR copies and the duplication efficiency. Parameters are estimated simultaneously for all UMIs by maximum likelihood optimization. For duplication models with Poisson and binomial process we give closed form solutions.
We perform experiments on synthetic data from duplication models with Poisson, binomial and branching process and efficiencies between 0.5 and 0.9. Data were generated for 64 and 256 UMIs with even and biased distribution, pre-PCR fragment numbers range from 10 to 10k. Simple UMI counting fails in most cases. Corrected UMI counting leads to improved results but fails to converge once most UMIs have been seen. DMEs, in contrast, yield bias free results for all pre-PCR abundances with variance in most cases significantly smaller than that of the other methods. For Poisson or binomial duplication models the closed form solutions provide a fast algorithm. For duplication models with branching process DMEs with multi-component mixtures for the post-PCR UMI counts give the best performance amongst all duplication models and methods. Since a branching process is the most accurate description of PCR amplification we expect DMEs to perform well on real RNA-Seq data.