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Robust multiplexed clustering and denoising of digital PCR assays by data gridding Billy T. Lau, Christina Wood-Bouwens, and Hanlee P. Ji Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b02688 • Publication Date (Web): 30 Oct 2017 Downloaded from http://pubs.acs.org on October 31, 2017

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Robust multiplexed clustering and de-noising of digital PCR assays by data gridding Billy T. Lau1,†, Christina Wood-Bouwens2,†, Hanlee P. Ji2,* 1

Stanford Genome Technology Center, Stanford University, Palo Alto CA, 94304 Division of Oncology, Stanford School of Medicine, Stanford CA, 94305 *Corresponding author. Email: [email protected]. Phone: 650-721-1503. 2

ABSTRACT: Digital PCR (dPCR) relies on the analysis of individual partitions to accurately quantify nucleic acid species. The most widely used analysis method requires manual clustering through individual visual inspection. Some automated analysis methods have emerged, but do not robustly account for multiplexed targets, low target concentration, and assay noise. In this study, we describe an open source analysis software called Calico that uses “data gridding” to increase the sensitivity of clustering towards small clusters. Our workflow also generates quality score metrics in order to gauge and filter individual assay partitions by how well they were classified. We applied our analysis algorithm to multiplexed droplet-based digital PCR datasets in both EvaGreen and probes-based schemes, and targeted the oncogenic BRAF V600E and KRAS G12D mutations. We demonstrate an automated clustering sensitivity of down to 0.1% mutant fraction and filtering of artifactual assay partitions from low quality DNA samples. Overall, we demonstrate a vastly improved approach to analyzing ddPCR data that can be applied to clinical use, where automation and reproducibility are critical.

Digital PCR1,2 (dPCR), by virtue of massively parallel partitioning of bulk nucleic acid analytes, has emerged as one of the most sensitive methods for absolute quantification of specific nucleic acid molecules. When one uses a small number of analyte molecules, single molecule loading of the target template occurs over individual partitions, and specific nucleic species can be detected using a variety of molecular assays. Counting these partitions thus enables absolute quantification of the target template, or relative quantification with respect to other targets multiplexed in the same assay. Analyzing dPCR data involves the quantifying and classification of PCR amplification products across individual partitions. Amplification assays for specific target molecules are detected through nonspecific DNA dyes or 5’-nuclease “Taqman” probes that fluoresce upon degradation. In the commonly used droplet digital PCR (ddPCR) platform3, data is reported as partition-specific fluorescence intensities in two channels. Current methods of quantifying ddPCR data involve manual “gating” or “lassoing” of aggregated data similar to methods used in flow cytometry4,5. Manual analysis introduces variance from researcher bias. Furthermore, assay noise, such as the fluorescent variation in individual partitions, impedes the accuracy of manual analysis. Some approaches have been proposed to model or statistically account for amplification noise6,7, but have not been applied to multiplexed ddPCR datasets or ddPCR assays with unusual cluster patterns. While sophisticated statistical techniques using generalized linear models and multiple testing have been developed for analyzing digital PCR assays across experimental conditions8, clustering individual experiments remains an ongoing challenge. The ideal solution involves automated clustering of dPCR data. This approach reduces the numerous issues with manual inspection. For example, k-means clustering can be used to quickly define cluster locations. However, we observed that

the high proportion of negatively amplified partitions significantly degrades performance (Supporting Information, Figure S-1). Alternative algorithms, such as the modern DBSCAN algorithm9, can successfully cluster control dPCR data but only with significant optimization of parameters

Figure 1. Overview of data gridding and clustering workflow. (A) Mock multiplexed ddPCR data with two-channel fluorescence intensities is shown. Each point represents the end-point fluorescence of a reaction partition. (B) A grid is overlaid on top of the data, which divides reaction partitions into bins. Afterward, gridded data is converted to binary format corresponding to whether droplets are present at each grid coordinate position. (C) Data is transformed by a sliding window that takes the average of the number of droplet partitions found in each grid coordinate. A first round of k-means clustering then creates initialization coordinates. (D) Initialization coordinates from (C) generates robust clusters in the mock data by a second round of k-means clustering. (E) Estimated boundaries for each cluster region are generated. (F) To process ddPCR datasets with unknown template concentrations, partitions are classified by their distance to empirically derived cluster locations as determined in (E).

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(Supporting Information, Figure S-2). Assay variation across batches adversely the performance of these approaches. Importantly, these existing methods fail when attempting to analyze assays where the target template is in very low concentrations. In cancer, single nucleotide and copy number variants (SNVs and CNVs) reveal characteristics unique to a tumor, and inform treatment decisions in the “precision medicine” paradigm10. In this context, dPCR has emerged as a popular method for the sensitive detection of molecules with specific cancer mutations11,12. Some of the mutations have utility as drug resistance markers13. Moreover, analytes such as circulating tumor DNA can be tracked over time with extremely high sensitivity and enables longitudinal monitoring of disease progression14 and patient response to therapy15. These species of DNA molecules exist as a minor component of the overall DNA accessible in the blood. Thus, accurate classification of these nucleic acid molecules is critical for the analysis of genetic variation and thus motivates the need for the development of a robust analytical framework. We demonstrate robust clustering, classification, and denoising of dPCR data through a novel pipeline called “Calico” (Iterative clustering assisted by coarse-graining; available as open-source at https://github.com/billytcl/calico). With this algorithm we detect individual nucleic acid species with robust performance. It exploits three major innovations: coarse graining and smoothing of dPCR data, robust definition of control cluster locations, and definition of quality scores that are common in genomic datasets for data filtering (Figure 1). We apply this pipeline on multiplexed single-color dropletbased ddPCR assays with unusual cluster locations, as well as on standard probe-based ddPCR assays. To demonstrate Calico’s utility in assays with considerable assay noise, we demonstrate its performance on formalin-fixed paraffinembedded samples.

EXPERIMENTAL SECTION Data samples and processing. Cell line genomic DNA was obtained from the Coriell Institute (Camden NJ, NA18507 genomic DNA), ATCC (Manassas VA, LS411 cell line), and Sigma-Aldrich (St. Louis MO, GP2D). Circulating tumor DNA standards were purchased from Horizon Discovery (Cambridge UK). LS411 was purified on a Maxwell 16 instrument (Promega, Sunnyvale CA). BRAF V600E assays consisted of admixtures of NA18507 and LS411. KRAS G12D assays consisted of admixtures of NA18507 and GP2D, except for the KRAS G12D assays against circulating tumor DNA. Before input into each ddPCR assay, cell line genomic DNA was pre-digested with EcoRI (New England Biolabs, Ipswich MA) for 8h at 37C before heat inactivation at 65C. FFPE DNA containing known allelic fractions of BRAF V600E (Horizon Discovery, Cambridge UK) was purified with the Maxwell 16 instrument (Promega, Sunnyvale CA) and admixed together. All genomic DNA was quantified by dyebased fluorescence intensity on the Qubit instrument (Thermo Fisher Scientific, Sunnyvale CA) before performing ddPCR assays. ddPCR assay conditions. We performed probe-based 5’nuclease (Taqman) and multiplexed single color Evagreen ddPCR assays as previously described16,17. Briefly, noncomplementary primer “tails” of differing lengths corresponding to individual amplicons are used to manipulate droplet intensity and achieve multiplexing capability. Assembled reac-

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Figure 2. Characterizing the effects of data gridding. (A) Left: raw multiplexed ddPCR data assaying for BRAF V600E (c.1799 T>A) and wild-type allele. A 2D density heatmap is overlaid on top of the data, revealing that most of the data is contained in the left-most region. Right: k-means clustering with default parameters is applied (solving for three clusters), with each color representing a cluster call. (B) Left: gridded ddPCR data of the same dataset in (A). A 2D density heatmap is overlaid on top of the data, showing that data gridding changes the apparent density of data points. (B) Right: k-means clustering with default parameters is applied (solving for three clusters), with each color representing a cluster call. Data gridding enables the robust detection of three clusters concordant with visual inspection, whose coordinates can be used as initialization parameters for a second round of k-means clustering.

tions consisted of 20ul of 1X Probes or EvaGreen ddPCR Supermix (Bio-Rad Laboratories, Hercules CA) and primers with concentrations as listed in Table S-1 (Supporting Information). Each reaction was partitioned into ~15,000-20,000 droplets on a QX-200 droplet generator (Bio-Rad Laboratories, Hercules CA), transferred into 96 well plates (Eppendorf, Hamburg DE), thermocycled on a Veriti PCR instrument (Thermo Fisher Scientific, Sunnyvale CA), and read on the droplet reader (Bio-Rad Laboratories, Hercules CA). Minimum information for Publication of Quantitative Digital PCR Experiments (dMIQE)18 can be found in Table S-2 (Supporting Information). We performed a multiplexed EvaGreen ddPCR assay targeting BRAF V600E (c.1799 T>A) and the wild-type allele under the following conditions: 95C for 5 min; 95C for 30s, 58C for 1min (40 cycles); 4C for 5 min, 90C for 5min, 4C hold. The KRAS G12D assay was performed similar to the BRAF V600E assay, but with a 61C extension temperature. We also performed a BRAF V600E Taqman probe-based ddPCR assay under the following conditions: 95C for 1 min; 94C for 30s, 55C for 1min (40 cycles); 98C for 10min, 4C hold. The triplex BRAF V600E and Taqman RPP30 copy number ddPCR assay was performed under the following conditions: 95C for 5 min; 95C for 30s, 58C for 1min (40 cycles); 4C for 5 min, 90C for 5min, 4C hold. All ddPCR data was exported as a comma-separated text file using the QuantaSoft analysis suite (Bio-Rad Laboratories, Hercules CA). This data was used as input to the Calico pipe-

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line to generate reference cluster locations (for control datasets), or to automatically classify ddPCR partitions (for unknown samples). Full algorithmic details are available in Supporting Information.

RESULTS AND DISCUSSION Calico Overview. As noted, the high proportion of partitions without amplification products leads to poor clustering results. We found that the k-means algorithm was particularly susceptible to this issue. K-means clustering relies the minimization of the positional variance between classified data points to a potential cluster’s centroid locations. Because k-means clustering relies on random initialization of start points, we hypothesized that the large number of data points in the negative cluster leads to poor initialization results and centroid locations being trapped in local minima. To test this hypothesis, we used data from a control multiplexed BRAF V600E ddPCR assay. The assay uses a single color intercalator dye and provides results for both mutant and wild-type alleles16. We provided the k-means algorithm approximate centroid locations that were identified by visual inspection; the correct cluster locations were then identified (Supporting Information, Figure S-3). These results show that correct clustering with k-means relies on proper initialization. However, manual initialization cannot be scaled to large datasets. This type of dataset also cannot be automatically clustered by the commercially available software (e.g. BioRad QuantaSoft) and requires manual “gating” of data points. The visual inspection and manual clustering of ddPCR data were effective because of differences in the visual image den-

Figure 3. ddPCR clustering performance. (A) Gridded ddPCR data corresponding to a multiplexed BRAF V600E EvaGreen ddPCR assay can be clustered robustly. Centroids are used as initialization parameters on the raw dataset, which enables the robust determination of clusters and their boundaries. (B) Mutant detection performance. Admixtures of LS411 DNA into NA12878 control DNA is used as input into multiplexed BRAF V600E EvaGreen ddPCR assays. Clusters from a single well positive control (68%) is used to define cluster boundaries and classify droplet partitions as mutant or wild-type. Dashed line: linear model fit. Slope: 1.000 (p < 0.001), intercept: -0.002 (p < 0.72), R2=0.994.

sity of data points versus the actual density. Put differently, one’s perception of the image with its lack of resolution for data granularity, enables one to consider images more generally. In the BRAF V600E ddPCR assay, the vast majority of data points occurred within the negative amplification cluster. This bias prevented effective clustering of positively amplified populations corresponding to the two possible alleles (Figure 2a). To computationally reproduce such an effect, we coarse grained and smoothed dPCR data into lower resolution grids. Full algorithmic details are described in Supporting Information. This method is commonly referred to as “rastering”, “coarse graining”, “data gridding”, and “tessellation”. It is used in fields such as geographic information systems (GIS) and computer graphics. We then applied conventional k-means clustering to the coarse-grained datasets to achieve approximate centroid locations for each cluster (Figure 2b). These locations are then applied to the unprocessed dataset for a second iterative round of k-means clustering. This approach effectively reduced the apparent density of data points in a ddPCR dataset. As a result, the initialization points within the cluster centroid locations matched those identified by visual inspection (Figure 3a). Definition of cluster-specific regions. To classify ddPCR reaction partitions in unknown samples, we utilized a control sample to generate an empirical model of cluster centroid locations and cluster bounding regions. Using this information, partitions in any ddPCR dataset can be classified as belonging to clusters based on their relative distance to other clusters as defined by the empirical model. This relies on the repeatable positioning of clustering locations across multiple ddPCR assay replicates. Namely, we observed low variance in wellto-well fluctuations for determining cluster locations (Supporting Information, Figure S-4).

Figure 4. ddPCR droplet filtering. Droplets outside of boundaries determined by control datasets can be filtered out. Quality scores are assigned to the cluster classification of each droplet based on its relative distance to the cluster called versus those of other clusters. Droplets that do not exceed a cutoff score can be optionally omitted from the data. A multiplexed BRAF V600E EvaGreen ddPCR assay is shown with (A) no filtering, (B) q = 1 cutoff, (C) q = 2, and (D) q = 3 cutoff. Droplets that are filtered out of the analysis are shown as gray droplets and marked with a red asterisk.

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To assess the performance of this clustering approach, we performed a serial dilution of LS411 cell line DNA into NA18507 control DNA. We tested this DNA mixture with a multiplexed BRAF V600E assay using a single color Evagreen fluorescent dye. We observed good correlation in the number of detected mutant and wild-type target molecules with the amount of input DNA (Figure 3b). We noted that low concentrations of target analytes are difficult to cluster when processed through standard k-means clustering, but can be robustly identified when an empirical model is generated beforehand with Calico. We also confirmed that Quantasoft is unable to cluster these datasets and generates nonsensical results (Supporting Information, Figure S-5). ddPCR partition filtering. An empirical model for classifying ddPCR assays of unknown samples enables the generation of general “quality scores” for filtering. Such quality scores are commonly used in the genomics and DNA sequencing fields to filter out low-quality nucleotides for variant detection and assay quality. In our pipeline, we generated a quality score reflecting the quality of each droplet’s cluster classification. This value is based on the normalized Euclidean distance (Mahalanobis distance) of any partition’s amplitude across two fluorescence channels to the centroid of each empirically-derived cluster location. The inter-partition variance around the centroid locations from a control dataset defines the density of a specific cluster and is used to calculate an overall confidence score (Full details in Supporting Information). Lower quality scores reflect low-confidence classification of assay partitions which are systematically filtered out of downstream assays. To demonstrate this novel filtering scheme, we apply quality score-based filtering on a control BRAF V600E dataset derived from FFPE DNA displaying a heterozygous mutant as before (Figure 4a-d). Evidently, the number of partitions outside the boundaries defined by the control datasets drops as the quality score threshold is raised. As a result, the mutant to wild-type allelic fraction is less affected by droplet partitions outside of empirically-derived boundaries. We also confirmed Calico’s performance on FFPE DNA through a standard curve analysis (Supporting Information, Figure S-6). The use of partition filtering is also useful for clustering ddPCR data with high amounts of input DNA, as shown by multiplexed KRAS G12D Evagreen ddPCR assays of GP2D

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and NA18507 DNA mixtures with up to 2000 genome equivalents of input DNA (Supporting Information, Figure S-7). We also successfully used ddPCR partition filtering to assay the oncogenic KRAS G12D mutation from circulating tumor reference DNA (Supporting Information, Figure S-8). Circulating tumor DNA is particularly hard to analyze because of low input amounts in addition to the degraded and fragmented nature of the analyte. Calico enabled the filtering of assay noise and identification of small droplet clusters. Clustering of probe-based assays. Our clustering and classification approach is agnostic to the type of molecular assay. Thus, one can extrapolate the shape and specific locations of each ddPCR cluster regardless of the experimental method. As a demonstration, we characterized Calico’s performance on a Taqman-based ddPCR dataset. We performed a series of multiplexed BRAF V600E Taqman ddPCR assays following a serial dilution. After analysis with Calico, we observed that our clustering algorithm robustly detected the four clusters corresponding to negative and positively loaded droplets. Delineating the wild-type and mutant alleles was made difficult by the presence of double-positives where both types of molecules are present in the same droplet. Analyzing this type of dataset required manually setting the number of clusters to four. This dataset was additionally filtered using a quality threshold of q=1 (Supporting Information, Figure S-9). With this dataset, we observed robust droplet classification sensitivity down to 0.1% mutant fraction (Figure 5). The QuantaSoft analysis software was anomalously unable to automatically cluster droplets in some reactions but Calico was capable of handling automated clustering properly across all reactions (Supporting Information, Figure S-10). Manual thresholding was required to recover clustering performance in QuantaSoft. Higher level multiplexing. We sought to determine whether Calico can be applied to ddPCR assays utilizing higher level multiplexing. Successful application would then be conducive towards Calico’s wider usage in the community for specialized assays. Although difficult to experimentally implement and optimize, as a proof-of-concept we successfully performed a triplex ddPCR assay combining Taqman and EvaGreen assay chemistries in a single reaction. We showed that Calico is able to successfully cluster this type of data (Supporting Information, Figure S-11), which was otherwise unsuccessfully processed with both QuantaSoft and classical k-means algorithms. QuantaSoft and standard k-means algorithms unsuccessfully clustered this dataset due to extensive assay noise and extremely small separation distance between some droplet clusters.

CONCLUSION

Figure 5. Mutant detection performance of multiplexed Taqman ddPCR assays. Multiplexed Taqman ddPCR assays targeting wild-type and mutant BRAF V600E were performed at several admixture ratios. Clusters from a single positive control (69%) is used to define an empirical model to classify droplet partitions as mutant or wild-type. Dashed-line: linear model fit. Slope: 1.052 (p < 0.001), intercept: 0.008 (p < 0.76), R2=0.9995. Inset: zoomed plot showing 0.1% and 1% mutant fractions.

In conclusion, we described an analytical workflow called Calico to robustly classify partitions in ddPCR datasets by using an iterative clustering approach. It takes advantage of data gridding to increase the sensitivity of k-means clustering and to generate a set of initialization coordinates for a second iterative round of k-means clustering. Calico also generates soft boundaries for the generation of quality scores that are correlated with how well an unknown droplet partition can be classified. Compared to other clustering methods (Supporting Information, Table S-3), Calico enables a flexible workflow for automated clustering. We successfully demonstrated the use of Calico on both EvaGreen and probes-based ddPCR datasets. Calico is compatible with any digital PCR system that can export partition data as a plain two column text file,

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with each row representing a single partition and each column representing a fluorescence channel. We envision that this open source tool to be widely used, and that future revisions will be performed to accommodate for more types of ddPCR assays.

ASSOCIATED CONTENT Supporting Information Figures S-1-5, Table S-1-3 and detailed methods of the implementation of Calico is detailed in Supporting Information as a PDF. The Supporting Information is available free of charge on the ACS Publications website.

AUTHOR INFORMATION Corresponding Author * Corresponding author. Email: [email protected]. Phone: 650-721-1503.

Author Contributions † B.T.L. and C.W.B. contributed equally to this work. B.T.L. wrote the analysis software package “Calico”. C.W.B performed the experiments. B.T.L., C.W.B., and H.P.J. designed the experiments. B.T.L., C.W.B., and H.P.J., wrote the manuscript. All authors have given approval to the final version of the manuscript.

ACKNOWLEDGMENT This work was supported by US National Institutes of Health grants NHGRI P01HG000205 (to B.T.L., C.M.W., and H.P.J.), NCI R33CA174575 (to H.P.J.) and NHGRI R01HG006137 (to H.P.J.). The American Cancer Society provided additional support to H.P.J. (Research Scholar grant, s). H.P.J. also received support from the Doris Duke Charitable Foundation, the Clayville Foundation, the Seiler Foundation and the Howard Hughes Medical Institute.

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