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Droplet volume variability and impact on digital PCR copy number concentration measurements Kerry R. Emslie, Jacob L. H. McLaughlin, Kate Griffiths, Michael Forbes-Smith, Leonardo B. Pinheiro, and Daniel Gerard Burke Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b05828 • Publication Date (Web): 18 Feb 2019 Downloaded from http://pubs.acs.org on February 19, 2019
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Analytical Chemistry
Droplet volume variability and impact on digital PCR copy number concentration measurements Kerry R. Emslie, Jacob L. H. McLaughlin, Kate Griffiths, Michael Forbes-Smith, Leonardo B. Pinheiro and Daniel G. Burke* National Measurement Institute, Lindfield, New South Wales, 2070, Australia. ABSTRACT: Digital polymerase chain reaction (dPCR) is increasingly being adopted by reference material producers and metrology institutes for value assignment, and for homogeneity and stability studies of nucleic acid reference materials. A reference method procedure should fulfil several requirements, and the uncertainty and biases should be completely understood. A bias in target concentration when inaccurate droplet volume is used in the droplet dPCR measurement equation has previously been documented. In this study, we characterize both intra-well and inter-well droplet volume variability using optical microscopy and determine the impact of these two sources of variability on target concentration estimates. A small optical distortion across the image was measured which, without correction, biased droplet volume measurements. Longitudinal monitoring of inter-well droplet volume over 39 weeks using several lots of mastermix demonstrated a mean droplet volume of 0.786 nL and intermediate precision of 1.7%. The frequency distribution of intra-well droplet volumes varied. Some wells displayed a skewed distribution which resulted in a small bias in estimated target concentration for a simulated dPCR with target concentrations of between 62 and 8 000 copies µL-1. The size and direction of this bias was influenced by the distribution pattern of the droplet volumes within the well. The proportion of mastermix in dPCR mix affected droplet volume. A pipetting error of 10% during mixing of the pre-mix and mastermix resulted in a 2.6% change in droplet volume and, consequently, a bias in concentration measurements highlighting the advantages of gravimetric preparation of dPCR mixes for high accuracy measurements.
Nucleic acid reference materials, when available, can be used in several steps of a measurement process, including method validation, calibration, quality control and proficiency programs. Extensive analysis using one or more reference methods is undertaken by reference material producers during production and certification of reference materials to provide a traceable link to the international system of units, Le Système International d'Unités (SI). The reference measurement procedure selected to characterize a reference material should be completely understood, have negligible systematic bias and should be described by a measurement equation containing relevant factors that can be expressed in SI units.1 The measurement uncertainty of the method should be sufficiently small to be applicable for the intended use of the reference material. The potential to utilize digital polymerase chain reaction (dPCR) as a reference method was recognized soon after the technology was commercialized.2,3 This technique relies on random distribution of dPCR mix containing target molecules throughout partitions of nominally equivalent volume prior to amplification such that some partitions contain no target molecules whilst the remaining partitions contain at least one target molecule. Following amplification, partitions are categorized and counted as either positive or negative based on their fluorescence intensity. The average number of targets per partition, λ, is then derived from the number of positive partitions, NP, and total partitions, NT, using Poisson statistics, where λ = - ln(1NP/NT).
Digital PCR possesses several key attributes that meet the requirements of a reference measurement procedure for nucleic acid quantification.4 Firstly, dPCR is fundamentally a counting technique, providing potential traceability to the SI. Secondly, a measurement equation (eq 1) for determination of copy (cp) number concentration, C, which combines λ with factors for partition volume, VP, and target volumetric dilution, D, both of which can be expressed in SI units is available.
N D C ln 1 P NT VP
(1)
Thirdly, for homogeneity and stability studies, a measurement procedure with good precision and, depending on the stability study design, good intermediate precision is required and dPCR meets these criteria. To realize traceability to the SI, the influence of each component in the measurement equation (eq 1) on the measurement result needs to be understood. Several national measurement institutes, including ourselves, have developed optical microscopy methodologies for measuring partition volume in both microfluidic5,6 and droplet dPCR6-10 systems and have demonstrated a bias in estimated target concentration when an inaccurate partition volume, VP, is used in the dPCR measurement equation.7,10 However, the Poisson model-derived component, λ, can also be impacted by partition volume since this model assumes the partition population is monodisperse. Through
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dUTP) (100 µL) and TE0.1 buffer (100 µL) were gravimetrically prepared. Eight replicate wells of each dPCR mix were prepared and droplets generated using the AutoDG. Density Measurements. A mix of 2.5 mL ddPCR Supermix for Probes (No dUTP) and 2.5 mL TE0.1 buffer was gravimetrically prepared. Density was measured using a DMA 5000 M density meter (Anton Paar) at the controlled temperature of 20 ± 0.05 °C. Digital PCR. A QX200 Droplet Digital PCR system (Bio-Rad Laboratories Pty Ltd, Australia) was used for target DNA quantification. BRAFV600_1181 DNA present in the droplet emulsion was amplified using a C1000 Touch Thermal Cycler (BioRad Laboratories Pty Ltd, Australia). Thermal cycling conditions for the assay consisted of 10 min activation at 95 °C followed by 40 cycles of a two-step thermal profile of 30 s at 95 °C denaturation, 2.5 °C/s ramp rate to combined annealing – extension for 60 s at 60 °C and a final 10 min inactivation step at 98 °C. After thermal cycling, plates were transferred to a QX200 droplet reader (Bio-Rad Laboratories Pty Ltd, Australia). Read out of droplets with positive and negative signal was performed using auto fluorescence amplitude threshold setting with the combined wells option in QuantaSoft software (version 1.7.4.0917) (Bio-Rad Laboratories Pty Ltd, Australia). Wells containing less than 10 000 accepted droplets were excluded from subsequent data analysis. Target DNA concentration was calculated from the fraction of positive droplets (positive end-point reactions) and number of accepted droplets using Poisson statistics taking into account dilution factors and droplet volume as described previously.8 The measurement equation (eq 2) for calculating target DNA concentration was:
modeling and simulation studies, several groups have concluded that partition volume variability can cause a bias in cp number concentration estimates, particularly when the variability is relatively large.11-14 In this study, we characterized the variability of partition volume and its impact on the accuracy of target concentration measurements. We used a droplet dPCR platform to investigate inter-well droplet volume intermediate precision over time. Through analysis of between 1 000 and 3 000 droplets in individual wells, we assessed intra-well droplet volume variability and its impact on measurement accuracy. To determine whether small changes in the composition of the dPCR mix could affect partition volume, we measured the impact of mastermix concentration in the dPCR mix on droplet volume.
EXPERIMENTAL SECTION BRAFV600_1181 amplicon was produced by end point PCR from a template consisting of a linearized form of plasmid, BRAFV600, which contains a 1 188 base pair (bp) insert comprising exons 3 and 15 from human serine/threonine-protein kinase B-raf (BRAF) together with flanking intron sequences (Figure S-1). BRAFV600_1181 amplicon was then purified by high pressure liquid chromatography and fractionation and desalted by ultrafiltration (Supporting information S-1). Preparation of dPCR Mixes and Droplet Generation. For each experimental set-up, sufficient dPCR mix comprising ddPCR Supermix for Probes (No dUTP) (Bio-Rad Laboratories Pty Ltd, Australia) and dPCR pre-mix was prepared gravimetrically for the required number of dPCR and/or droplet volume replicate wells. Droplet generation was undertaken in accordance with manufacturer’s instructions using either a manual or AutoDG droplet generation system (Bio-Rad Laboratories Pty Ltd, Australia). Where feasible, replicates from a single dPCR mix were spread across the wells of the plate rather than being located in adjacent wells. For experiments requiring both droplet volume and cp number concentration, both measurements were completed on the same day using droplets generated from separate wells since completion of both measurements from a single well is not practical. To assess the impact of small changes in ddPCR Supermix for Probes (No dUTP) concentration in the dPCR mix on measured droplet volume and target DNA concentration, BRAFV600_1181 concentration in dPCR mix was measured by a hydrolysis probe dPCR assay targeting a unique sequence that is not found in nature. A bulk preparation of PCR pre-mix comprising BRAFV600_1181 (approximately 4 000 cp µL-1), 1 800 nM forward (BRAF_146543) and reverse (BRAR_149118) primers, 500 nM probe (BRAP_145227) (Table S-1) and 700 nM 5′-Cy5-T6-PO3-3′ (Integrated DNA Technologies, Inc. Australia) was prepared in 10 mM Tris.HCL, 0.1 mM EDTA, pH 8.0 (TE0.1) buffer. Five dPCR mixes (400 µL) comprising the following volumetric factors were gravimetrically prepared: 0.90×, 0.95×, 1.00×, 1.05×, 1.10× ddPCR Supermix for Probes (No dUTP) and 1.10×, 1.05×, 1.00×, 0.95×, 0.90× PCR premix, respectively. For dPCR and droplet volume measurements, two identical plate layouts containing eight replicate wells of each dPCR mix were prepared and droplets generated using the AutoDG. To assess intra-well droplet volume variability, three dPCR mixes (200 µL) comprising ddPCR Supermix for Probes (No
m N 103 m ρ C ln 1 P SM . N V m ρ T P dPCR mix
(2)
where C is BRAFV600_1181 concentration (cp µL-1) in the dPCR pre-mix, NP and NT are number of positive and accepted droplets, respectively, VP is partition (droplet) volume (nL), m and mSM are masses (mg) of dPCR pre-mix and ddPCR Supermix for Probes (No dUTP), respectively, and ρ and ρdPCR mix are densities (mg µL-1) of dPCR pre-mix and dPCR mix, respectively. Droplet Volume Measurements Using Optical Microscopy. Droplet volume was measured by optical microscopy of freshly prepared droplets. Droplets were not thermal cycled prior to volume measurement as the volume of droplets may change during the thermal cycling process and, if the resultant value for VP is used in eq 2, this would bias the estimated target DNA concentration. Following emulsion generation, droplets were transferred by pipette into 1 μ-Slide VI flat uncoated microscopy chambers (IBID Germany) that had been prefilled with Droplet Generation Oil for Probes using AutoDG (Bio-Rad Laboratories Pty Ltd, Australia). A calibrated optical microscope (Leica DM6000M) with digital CCD camera (DMC4500) was used to image droplets in the microscopy chambers as previously described 8 with the following changes. i) Images of 2 560 × 1 920 pixels (px) at 100× apparent magnification were recorded using a 3200 Objective N PLAN EPI 10x/0.25 BD, -/B, 16.1. ii) For some experiments, sixty digital images (4×15 tiled
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Analytical Chemistry images) were collected across the microscopy chamber automatically in a serpentine path. This enabled measurement of at least 1 000 droplets and removed potential operator bias in selection of the measurement field for image capture. To prevent duplication in droplet measurement, the serpentine pattern included an automatic overlap of 100 px between adjacent images in both the x-axis and y-axis which is slightly less than half of the average diameter of a droplet. A low-resolution composite of the 4×15 tiled images, assembled using Leica Application Software v3.5, provided a visual overview of all droplets in the measurement field. Optical system calibration, image processing and data analysis were undertaken as described in Supporting information S-2. The Type B droplet volume relative expanded uncertainty was determined from analysis of a single droplet image as previously described.8 Using this optical setup it was 2.3% (coverage factor of 2.01 to provide a level of confidence of 95%). The major component of the Type B uncertainty was the out-of-focus axis or spherical distortion. Intra-well Droplet Volume Evaluation. The multi-image approach was used to maximize the number of droplet volume measurements per well for 24 wells prepared as eight replicate wells from three independent dPCR mixes. For each well, the population of measured droplets was assumed to represent the accepted droplet population if analysed by dPCR. The experimentally determined droplet volume data was then used to evaluate the effect of intra-well droplet volume variability in a simulated dPCR with 15 000 accepted droplets and target concentrations in the dPCR mix ranging from 62 to 8 000 cp µL-1. An accepted droplet count of 15 000 was selected to approximate the typical number in an experimental droplet dPCR. Frequency Distribution of Droplet Volumes Within a Well. For each well, the frequency distribution of droplet volumes was determined by sorting droplet volume values into 36 bins of interval 0.02 nL with the mid-point of the middle bin being the well median droplet volume. A bin size of 0.02 nL was selected as it is approximately equal to the Type B expanded uncertainty for droplet volume using this optical setup. The percentage of droplets in each bin was calculated. dPCR Simulation with 15 000 Accepted Droplets. Copy number per droplet for bin i (λi) was estimated by multiplying the midpoint droplet volume for the bin, VDi, by target concentration in the PCR mix, C (eq 3).
𝜆i = 𝐶 ∙ 𝑉Di
Estimating Target Concentration of Simulated dPCR. For each well, target concentration in the dPCR was estimated using eq 7, where n is number of bins, NT is 15 000 and VP is well median droplet volume.
𝐶 = −ln (1 −
𝐶=
(6)
(7)
∑𝑛1 𝑁i ⁄∑𝑛 𝑉 1 i
(8)
Figure 1. Length of px (lpx) on horizontal and vertical axes of 2 560 × 1 920 image. The number of px along calibrated 100 µm intervals on the stage micrometer x- and y-axes was measured when the stage micrometer was located at various positions within the measurement frame. Pixel length was determined by dividing the number of px along a measured interval by the calibrated interval length. Data points are the mean and standard deviation of between 5 and 16 images except for the data point at -1 250 which was from a single image. Coordinates of the centroid of each measured interval (Xrel and Yrel) were defined relative to the central px on each axis. Polynomial equations for x-scale and y-scale were lpx,x = 2.399×10-9Xrel2 + 7.950×10-7Xrel + 0.485 (r² = 0.97) and lpx,y = 3.052×10-9Yrel2 – 9.108×10-8Yrel + 0.485 (r² = 0.77), respectively.
To investigate whether the small variation in px length across the image would be reflected in droplet images, droplets were generated from a single well and transferred to a microscopy chamber. Sixty digital images were collected across the chamber providing a dataset of 2 301 droplets. For tightly packed droplets, a single 2 560 × 1 920 image contained approximately 80 droplets. The median values for the major and minor axes of the droplet elliptical fit were 236.2 px (5th, 95th percentiles: 235.1 px, 239.5 px) and 235.2 px (5th, 95th percentiles: 232.9 px,
Target cp number (Ni) and volume of accepted droplets (Vi), in bin i were determined using eq 5 and eq 6, respectively.
𝑉𝑖 = 𝑁Ti ∙ 𝑉Di
1 𝑉P
Validation of Droplet Imaging Process. With the calibrated micrometer centrally located in the 2 560 × 1 920 image, average px length across the x- and y- scales of the micrometer was 0.48445 µm with an expanded uncertainty of 0.00044 µm (coverage factor, k=2.0) (n=9 images collected over an 8-month period). Using data from images collected with the micrometer positioned at various locations around the 2 560 × 1 920 image, px length varied by 0.33% across the 2 560 px x-axis and 0.17% across the 1 920 px y-axis and was largest in the central region of the image (Figure 1).
(4)
(5)
)∙
RESULTS AND DISCUSSION
(3)
𝑁𝑖 = 𝑁Ti ∙ 𝜆i
𝑁T
For each well, target concentration in the dPCR was also estimated using eq 8, where n is number of bins.
For bin i, the number of accepted droplets (NTi) was calculated by multiplying the percentage of experimentally measured droplets in bin i by 15 000. The number of positive droplets in bin i (NPi) was estimated using eq 4, which is derived by rearranging the standard Poisson equation.
𝑁Pi = 𝑁Ti ∙ (1 − 𝑒 −𝜆i )
∑𝑛 1 𝑁Pi
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236.4 px), respectively. The difference between the number of px along the major and minor axes increased marginally towards the left and right hand side of the image (Figure 2A) indicating that the elliptical fit to the droplet outline was more elongated for droplets positioned at the left and right side of each image. In addition, towards the sides of the image, the angle between the major axis of the droplet elliptical fit and the xaxis approached either 0 or 180 degree (Figure 2B) showing that the major axis of the droplet elliptical fit was aligned most closely to the x-axis of the image.
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and minor (lpx,mn) axis for each droplet outline was then determined (eq 9 and eq 10, respectively), where A is the angle between the major axis of the droplet elliptical fit and the x-axis.
𝑙px,mj = (|
𝐴 90
𝑙px,mn = (|
𝐴 90
− 1|) ∙ 𝑙px,x + (1 − |1 −
𝐴 90
− 1|) ∙ 𝑙px,y + (1 − |1 −
|) ∙ 𝑙px,y
𝐴 90
|) ∙ 𝑙px,x
(9) (10)
Well median droplet volume calculated using px length at the droplet centroid location differed by less than 0.3% than the value determined using average px length of 0.48445 µm. However, variability in droplet volume was smaller (median, 0.777 nl; 5th, 95th percentiles: 0.771 nL, 0.788 nL) (Error! Reference source not found.B). Whilst the impact of this observation on concentration estimates is minimal (less than 0.3%), the bias in measured droplet volume observed using average px length could be misinterpreted as increased polydispersity in intra-well droplet volume.
Figure 2. Metrics for 2 301 droplets generated from a single well. (A) Number of px along major and minor axes of elliptical fit of droplet outline Note: Not all major axis data points are visible since they overlap with some minor data points. (B) Angle between the major axis of an imaged droplet and the x-axis are plotted as a function of distance from central px on x-axis.
Using an average px length of 0.48445 µm to convert the major and minor axes values to µm, the measured well median droplet volume for the 2 301 imaged droplets was 0.779 nL (5th, 95th percentiles: 0.770 nL, 0.794 nL). Measured droplet volume was smallest in the central region of each image and increased towards the edges of the image with a more pronounced effect on the longer horizontal axis (Figure 3A). Hence, use of average px length (0.48445 µm) to convert the axes to µm overestimated the volume of droplets at the image edge and underestimated the volume of droplets in the image central region. To account for this observed bias, px length along the x-axis (lpx,x) and y-axis (lpx,y) at the centroid of each droplet outline was determined using polynomial equations derived from measurements of the stage micrometer at various locations across the measurement frame (Figure 1). Pixel length of the major (lpx,mj)
Figure 3. Measured volume of 2 301 droplets generated from one well plotted as a function of distance of droplet centroid to central px on the image x-axis. Median droplet volume (grey line) calculated using px length (A) of 0.48445 µm and (B) based on droplet centroid location was 0.779 nL (5th, 95th percentiles: 0.770 nL, 0.794 nL) and 0.777 nL (5th, 95th percentiles: 0.771 nL, 0.788 L), respectively.
Longitudinal Monitoring of Inter-Well Droplet Volume. To characterize a candidate nucleic acid reference material using dPCR, we measure droplet volume using the same reagents and lot numbers as used to assign the reference value. This provided a longitudinal data set of droplets generated from 71 wells over a period of 39 weeks, using five lots of ddPCR Supermix for
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Analytical Chemistry the central bin thus falling within the Type B standard uncertainty for analysis of a single droplet image using the optical setup defined for this study. Some wells displayed a relatively symmetrical droplet volume population whilst others displayed either a positive (Wells 11, 13, 15 to 24) or negative (Well 1) skewed distribution (Figure 5). Theoretically, a droplet with a volume that is higher than the median droplet volume will have a higher probability of being positive in a dPCR. The converse applies to droplets with lower than the median droplet volume. Applying Poisson statistics to a non-uniform population of droplets could thus result in a bias in estimated target concentration. Target Concentration in Simulated dPCR. Assuming the measured droplets were representative of the entire well, we estimated number of positive droplets in each bin for simulated dPCRs with 62 to 8 000 cp µL-1 target DNA (example shown in Table S-2). We have previously demonstrated that a linear response is obtained over this concentration range using the BioRad dPCR system.8 Target concentration was estimated using eq 7 and the well median droplet volume. A positively skewed well droplet volume distribution generally resulted in a small positive bias (
