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, 3 (8), e2876

Mathematical Analysis of Copy Number Variation in a DNA Sample Using Digital PCR on a Nanofluidic Device


Mathematical Analysis of Copy Number Variation in a DNA Sample Using Digital PCR on a Nanofluidic Device

Simant Dube et al. PLoS One.


Copy Number Variations (CNVs) of regions of the human genome have been associated with multiple diseases. We present an algorithm which is mathematically sound and computationally efficient to accurately analyze CNV in a DNA sample utilizing a nanofluidic device, known as the digital array. This numerical algorithm is utilized to compute copy number variation and the associated statistical confidence interval and is based on results from probability theory and statistics. We also provide formulas which can be used as close approximations.

Conflict of interest statement

Competing Interests: The authors are employees of Fludigim Corporation and for this research project they used a technology platform which is being commercialized by Fluidigm.


Figure 1
Figure 1. A digital array has 12 panels of 765 reaction chambers each.
PCR mixes are loaded into each panel and single DNA molecules are randomly partitioned into the chambers. The digital array can be thermocycled, imaged on a BioMark instrument, and the data analyzed using the Digital PCR Analysis software.
Figure 2
Figure 2. Human genomic DNA NA10860 (left 5 panels) and the RPP30 synthetic construct (right 5 panels) were quantitated using the RPP30 (FAM) assay on this digital array.
The two bottom panels are NTC (no template control). Digital PCR Analysis software can count the number of positive chambers in each panel. When two assays with two fluorescent dyes are used in a multiplex digital PCR reaction, two genes can be independently quantitated. This is the basis of the CNV study using the digital array.
Figure 3
Figure 3. Consider an infinite universe of chambers.
A digital array panel is a finite sampling of this universe. The goal is to determine λ, the mean number of the target molecules per chamber in the DNA sample. The number of positive chambers, which have hits of one or more molecules, shown as filled green squares in the panel with C( = 765) chambers is H.
Figure 4
Figure 4. From the sampling distribution of estimation of p, one can obtain the sampling distribution of estimation of λ.
Figure 5
Figure 5. Histogram of number of positive chambers H = P×C obtained by choosing M = 400 as the mean number of molecules per panel over 70 thousand panels and running a simulation using a random number generator.
The green curve is the sampling distribution predicted by the theory.
Figure 6
Figure 6. Geometric interpretation of Fieller's Theorem to compute confidence interval of ratio of two normally distributed random variables and in which confidence ellipse of the joint sampling distribution is projected on a vertical line.
Figure 7
Figure 7. Illustration of a numerical projection algorithm to compute the sampling distribution of ratio of two random variables with arbitrary probability distributions by slicing the 2-D space into thin wedges and accumulating the joint probabilities in the wedges.
Most of the contribution would come from the confidence ellipse region.
Figure 8
Figure 8. Results of actual CNV experiments on the digital array with varying number of copies of the target gene.
In total, 6 different known ratios were estimated by running the experiments for varying number of panels. The graphs for different numbers of copies are slightly staggered to allow visual comparison of overlap of the 95% confidence intervals.

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