Statistical Analysis of Nonuniform Volume Distributions for Droplet-Based Digital PCR Assays

Abstract

We present a method to determine the concentration of nucleic acids in a sample by partitioning it into droplets with a nonuniform volume distribution. This digital PCR method requires no special equipment for partitioning, unlike other methods that require nearly identical volumes. Droplets are generated by vortexing a sample in an immiscible oil to create an emulsion. PCR is performed, and droplets in the emulsion are imaged. Droplets with one or more copies of a nucleic acid are identified, and the nucleic acid concentration of the sample is determined. Numerical simulations of droplet distributions were used to estimate measurement error and dynamic range and to examine the effects of the total volume of droplets imaged and the shape of the droplet size distribution on measurement accuracy. The ability of the method to resolve 1.5- and 3-fold differences in concentration was assessed by using simulations of statistical power. The method was validated experimentally; droplet shrinkage and fusion during amplification were also assessed experimentally and showed negligible effects on measured concentration.

Figure 1.

A PCR/oil mixture (a) was vortexed (b) to create an emulsion of non-uniform volume distribution. (c) Emulsion aliquots underwent PCR in a thermal cycler. (d) Aliquots were transferred to a well-plate for imaging using scanning confocal microscopy. The red fluorescence image displays signal from the ROX dye (present in all droplets); the green image displays signal from the FAM dye (significant only in occupied droplets).

Figure 2.

(a) The cumulative number of occupied droplets for a simulation of 10,000 droplets and a concentration of 2.0×10⁻⁶ molecules/fL, ordered by droplet size. Other details were the same as in Table 1. (b) Clipped lognormal distribution used for simulations in Table 2.

Figure 3.

(a, b) Estimated power for a set of 10,000 droplets with a total volume of 9.5 μL. The green lines in each subplot are for a 1.5-fold resolution, and the blue lines are for a 3-fold resolution. The dotted line indicates a power of 0.95. (a) Simulated power with droplets from an even size distribution (4 to 190 μm diameter). Dashed lines are for measurement errors of size E₁, solid lines for measurement errors of size E₂. (b) Simulated power for set of droplets with a uniform diameter of 122 μm. Simulations assume droplet sizes are known exactly. (c, d) Estimated power for a set of 10,000 droplets with a total volume of 0.06 μL from a clipped lognormal distribution (c) and from a uniform size distribution with a diameter of 22.6 μm (d).

Figure 4.

(a) Best-fit concentration determined by emulsion PCR (ePCR) plotted against the concentration determined by measurement of absorbance at 260 nm. Samples were from a 10x serial dilution series (1×10⁷, 1×10⁶, 1×10⁵, and 1×10⁴ dilutions) of purified ERRB2 DNA. Triangles: replicate A (2.26×10¹⁰ copies/μL stock DNA concentration); Squares: replicate B (2.81×10¹⁰ copies/μL); Circles: replicate C (3.08×10¹⁰ copies/μL). For each replicate, two aliquots were collected at each dilution, denoted in the graph by either filled or open symbols. Best-fit concentrations were calculated from droplets with diameters in the range of 7–50 μm. The linear regression line through zero for all replicates is y=0.771x and R²=0.990. Measurement errors are not shown here, but can be seen in Figure 5. (b-d) DNA amplification was determined by FAM to ROX ratio histograms of amplified droplets containing (b1) 2.26×10³, (c1) 2.26×10⁶, and (d1) 2.26×10⁷ copies of double-stranded ERBB2 DNA per μL; bin size, 0.025. In the corresponding confocal imaged droplet insets (b2–d2), the ROX (red) and FAM signals (green) were colored and merged to depict droplet amplification (yellow). The inset scale bars are 50 μm.

Figure 5.

(a-c) The three serial dilutions described in Figure 4 (same symbols used). Error bars indicate ±2σ.