Fig 1.
Optimal Concentration Range for digital PCR Experiments.
Theoretical confidence intervals around λ across a variety of increasing available partitions. The dotted red line indicates the point of greatest achievable precision (independent of the number of available partitions) where approximately 20.3% of available partitions are negative.
Fig 2.
Dynamic Range dependence on Precision.
Fig. 2A shows the dynamic range associated with a level of precision of at least 10% for 20K partitions. Fig. 2B shows how the dynamic range varies as the required level of precision is relaxed (moved right along x-axis) or made more stringent (moved left along x-axis).
Fig 3.
Measurement Precision dependence on Available Partitions.
Measurement precision depends on the number of available partitions. Contour lines represent a specific level of precision and relate the number of partitions required to achieve the specified precision at various concentrations. The dotted red line (at approximately 20.3% negative partitions) highlights the concentration at which a minimal number of partitions are needed to achieve a particular level of precision.
Fig 4.
Lower Limit of Detection Dependence on Total Interrogated Volume.
Total interrogated volume influences the lower limit of detection for a given number of partitions. In the plot, precision curves for a given number of partitions (20,000) are shown where the difference is in the size of the partitions (1, 2, 10, 20, and 40 nanoliters). The larger the total interrogated volume increases (due to increase in partition size), the smaller the lower limit of detection. The colored dots represent the lower limit of detection for the various partition sizes at 10% precision.
Fig 5.
Effect of False Reaction Calls on Precision and Dynamic Range.
False positives effect precision curves differently from false negatives. False positive rates are represented in the plot via shapes (triangles = 0.0%, circles = 0.1%). False negative rates are represented by colors (red = 0.0%, green = 0.1%, blue = 0.2%). Note that false positives strongly impact precision at lower concentrations (where there are very few positives) and false negatives strongly impact precision at higher concentrations (where there are very few negatives)
Fig 6.
Target Load in Percent Negatives for Optimal Precision Under Non-zero False Call Rates.
Optimal load concentrations under the likely scenario of non-zero false reaction call rates will no longer target 20.3% negative partitions. For example, as the false negative rate increases (with a constant false positive rate), one should target a percentage of negatives > 20.3% in order to approach optimal precision.
Fig 7.
Lower Limit of Detection dependence on False Positive Rate.
Lower limit of detection is influenced most heavily by false positives. This dependence is due to limited effect false negatives have in counter balancing false positives due to the limited number of positives at lower concentrations. The plot demonstrates the effects of false reaction call rates on the lower limit of detection for 20,000 partitions at 20% precision. Using a baseline of 0% false positives and 0% false negatives, the lower limit of detection is measured at 0.006 copies/partition. Raising the false positive rate to 1% results in the raising of the lower limit of detection to 0.065 copies/partition, over an order of magnitude elevation.
Fig 8.
Effect of Volume Variation on Precision.
Volume variation affects precision significantly at higher concentrations. Volume variability is simulated by assuming a normal distribution of well volumes with the standard deviation taken as a percentage of the mean well volume. Volumes of 865pl for 10,000 partitions were used in the simulation. Note that concentration at peak precision moves toward lower concentrations (increasing negative percentage) as volume variability increases.
Fig 9.
Effect of Dilutions on the Ability to Detect Concentrations Near the Limit of Detection.
Diluting samples can bring samples with concentrations above the upper limit of detection into the support dynamic range of the digital PCR system. However, such dilutions can also move samples with concentrations close to the lower limit of detection outside of the supported dynamic range.
Fig 10.
Dilution Effects on Dynamic Range and Limits of Detection—Constant Available Partitioning.
Fig. shows the benefits and disadvantages of devoting a portion of available partitions to optimized dilution steps. Optimizing the dilution step is necessary to achieve a maximal increase in dynamic range while maintaining a continuous ability to detect concentrations throughout the dynamic range (i.e., without creating detection “gaps” between the steps). Fig. A demonstrates how a single dilution (using half of the available partitions) both raises the lower limit of detection on the undiluted sample and reduces the dynamic range of each individual step while increasing the overall dynamic range. Fig. B demonstrates the cumulative increase in overall dynamic range using 2 dilution steps (1: 2000) at various levels of precision.
Fig 11.
Gains in Dynamic Range via Increasing Number of Dilutions—Constant Available Partitioning.
Fig. shows the benefits to dynamic range spanned by increasing the number of dilution steps across available partitioning. X-axis depicts an increasing number of dilution steps spread across a constant (20,160) number of available partitions. Subsets are assumed to be equally sized. As partitions per subset decreases with increasing number of subsets, boxed dilution values represent optimized serial dilutions (# subsets—1 steps) ensuring maximum Dynamic Range gain while maintaining overlapping regions of detection. Benefits to Dynamic Range are slight at high levels of precision (e.g., 5%) and are even seen to occasionally decrease as subsets increase (e.g., 5% precision between 5 and 6 subsets). However, substantial improvement is also seen as precision requirements are relaxed.
Fig 12.
Reduced Sensitivity as the Number of Dilutions Increases—Constant Available Partitioning.
Fig. shows the deteriorating sensitivity for the lower limit of detect by increasing the number of dilution steps across available partitioning. Impacts to sensitivity are greatest at high levels of precision (e.g., 5%) but do substantially lessen as precision requirements are relaxed. X-axis depicts an increasing number of dilution steps spread across a constant number (20,160) of available partitions.
Fig 13.
Workflow to Select Dilution Factor For Paired Chip Strategy for Maximizing Dynamic Range.
Fig. shows how to select the dilution factor for the second chip in a pairing strategy to maximize the dynamic range.
Fig 14.
Trials with Two Dilution Factors to Select Optimal One For Use with Paired Dilution Strategy.
Fig. shows that the continuous detection criterion fails at the application of the 1:1000 dilution factor. The 1:200 dilution factor meets the continuous detection criterion at a 10% precision requirement.
Table 1.
Sample, Assay, Reaction Mix and Thermal Protocol Information.
Table 2.
Rules for Pruning Data in Paired Dilution Experiments for Quantification.
Fig 15.
Preferred Concentration Filtering: Two Chip Setup.
Fig. shows digital PCR results obtained on the two chip setup and filtered thru Rule 3 for each of 5 Unknown samples (diluted Samples D and E not run). Sample A original concentration chips excluded due to being outside the preferred concentration range (200–2000 copies/μl) while the diluted chips are within the preferred range.
Fig 16.
Quantification Results: Two Chip Setup.
Fig. shows computed quantification results for the 5 Unknown samples using the two chip strategy. For each Sample, at least one of the chips provided information useful for determining a quantity.
Fig 17.
Digital PCR Fold Change between Adjacent Samples.
Fig. shows the fold change between digital PCR computed quantities for all adjacent samples (e.g., between Sample A and Sample B). The values are seen to compare very well with the expected 6.8 fold difference between samples.
Fig 18.
Quantitative PCR CQ Results of Original Dilution Series.
Fig. shows computed CQ results for the 5 Unknown samples using the quantitative PCR. The CQ values correspond to a dynamic range of 3.393 logs between Samples A and Sample E and support the digital PCR results.