Theoretical design and analysis of multivolume digital assays with wide dynamic range validated experimentally with microfluidic digital PCR

Abstract

This paper presents a protocol using theoretical methods and free software to design and analyze multivolume digital PCR (MV digital PCR) devices; the theory and software are also applicable to design and analysis of dilution series in digital PCR. MV digital PCR minimizes the total number of wells required for "digital" (single molecule) measurements while maintaining high dynamic range and high resolution. In some examples, multivolume designs with fewer than 200 total wells are predicted to provide dynamic range with 5-fold resolution similar to that of single-volume designs requiring 12,000 wells. Mathematical techniques were utilized and expanded to maximize the information obtained from each experiment and to quantify performance of devices and were experimentally validated using the SlipChip platform. MV digital PCR was demonstrated to perform reliably, and results from wells of different volumes agreed with one another. No artifacts due to different surface-to-volume ratios were observed, and single molecule amplification in volumes ranging from 1 to 125 nL was self-consistent. The device presented here was designed to meet the testing requirements for measuring clinically relevant levels of HIV viral load at the point-of-care (in plasma, <500 molecules/mL to >1,000,000 molecules/mL), and the predicted resolution and dynamic range was experimentally validated using a control sequence of DNA. This approach simplifies digital PCR experiments, saves space, and thus enables multiplexing using separate areas for each sample on one chip, and facilitates the development of new high-performance diagnostic tools for resource-limited applications. The theory and software presented here are general and are applicable to designing and analyzing other digital analytical platforms including digital immunoassays and digital bacterial analysis. It is not limited to SlipChip and could also be useful for the design of systems on platforms including valve-based and droplet-based platforms. In a separate publication by Shen et al. (J. Am. Chem. Soc., 2011, DOI: 10.1021/ja2060116), this approach is used to design and test digital RT-PCR devices for quantifying RNA.

Figure 1

a) General schematic of multivolume system used for digital PCR (MV digital PCR), with relationship between device features and performance abilities. Two hypothetical devices with identical dynamic range and with equal spacing (300 μm) between wells: b) a model MV digital PCR system (160 wells each at 125, 25, 5 and 1 nL) and c) a single volume digital PCR system (12,000 wells at 2.08 nL). With these design parameters the footprint of the MV wells is approximately 7 fold smaller than the single volume design. Note: Well sizes are based on assumption of cubic dimensions, and in the MV design the vertical spacing was kept constant from center of well to center of well, as would be required for proper slipping in a SlipChip platform, and is based on a 300 μm spacing between the largest wells.

Figure 2

Schematic for radial SlipChip to perform MV digital PCR. Design consists of 160 wells each at 125, 25, 5, and 1 nL. Sample is loaded from the center and after filling is rotationally slipped to isolate wells. After the reaction, wells containing template have enhanced signal and can be counted.

Figure 3

Experimental results for MV digital PCR on SlipChip using control DNA. Representative false color images (yellow represents positive wells that showed at least a 3-fold increase in intensity compared to negative wells) for solutions with input concentrations of (a) 1500 molecules/mL and (b) 600,000 molecules/mL (zoomed in on smaller wells). c, d) Graphical summary of all experiments comparing the input concentration, based on UV-V is measurements (black curve), and observed concentrations using MV digital PCR (× and +) over the entire dynamic range. Represented as (c) the actual concentration and (d) as a ratio to better show distribution of results. Stock samples were approximately 500, 1500, 8000, 20,000, 30,000, 100,000, 600,000 and 3,000,000 molecules/mL The confidence intervals (CI) for the combined system (solid gray curves) indicate where 95% of the experiments should fall. CI curves for the individual volumes (various dashed gray curves), are also provided to indicate over what range of concentration each volume contributes.

Figure 4

Separate analysis of 10 experimental results for different well volumes with input concentration of 30,000 molecules/mL shows the distribution of measured concentrations for each volume and overall agreement of results.

Figure 5

Relationship between the total number of wells in a single-volume system, and the minimum number of positive results required to meet the desired resolution at the LLQ-X. The symbols × correspond to the points listed in Table 3. The ULQ-X limit, not given here but identified in Table 3, is set by the ULQ definition above of having an average concentration corresponding to 3 negative wells in the total volume.

Figure 6

Plot of LLQ-X and ULQ-X as a function of VS at constant total well number and total volume. For each resolution level (X), the minimum (LLQ-X) and maximum (ULQ-X) concentrations that can achieve the desired power level (95%) are given for each design in Table 4. No concentration could be plotted if the resolution level (X) could not be achieved for a given VS.

Figure 7

Plot of LLQ-X and ULQ-X for the designs in Table S5 demonstrates impact of VS on resolution and total number of wells at constant total well number and dynamic range. For VS=10 the design consists of 36 wells each at 625, 62.5, 6.25 and 0.625 nL, for VS=8 the design consists of 58 wells each at 378.9, 47.36, 5.92 and 0.74 nL, for VS=5 the design consists of 160 wells each at 125, 25, 5 and 1 nL, for VS=2 the design consists of 1100 wells each at 12, 6, 3 and 1.5 nL and for VS=1 the design consists of 12,000 wells at 2.08 nL. For all designs the LDL is approximately 120 molecules/mL and the ULQ is approximately 4 million molecules/mL

Figure 8

Simulation results of plots generated from MVdPCR_RunPlot.m for (a) the design used in this paper, and (b) Design 1 from Table S5 (36 wells each at 625, 62.5, 6.25 and 0.625 nL), revealing approximate concentration ranges over which the desired resolution levels are achieved. The curves are for the lower of the two concentrations being resolved. LLQ-X corresponds to the concentration at which the curve rises above 0.95 (black line), and the ULQ-X corresponds to the concentration X times higher than the concentration at which the curve drops back below 0.95.