Overview

SEBULA implements a semi-parametric probabilistic model for multiplet detection in snATAC-seq data (Fig 1). Following a preprocessing strategy similar to AMULET, we generate a binary matrix of multi-read sites, where rows correspond to genomic loci with more than two overlapping reads in at least one cell (i.e., high-coverage loci), and columns represent individual nuclei. From this matrix, we compute the high-coverage locus count (HCLC) for each cell, which serves as input to SEBULA. Intuitively, cells with unusually high HCLC values are more likely to be multiplets.

Download:

• PNG
  larger image
• TIFF
  original image

Fig 1. Overview of the SEBULA framework.

(A) Formation of multiplets. In droplet-based platforms, individual cells or nuclei are encapsulated together with barcoded beads in oil droplets. Ideally, each droplet contains a single cell (singlet), but some droplets capture multiple cells (multiplets) or remain empty. Multiplets generate hybrid molecular profiles that can confound downstream analyses. Modern single-cell assays, including single-cell RNA sequencing, single-nucleus ATAC sequencing, CITE-seq, and multimodal platforms such as DOGMA-seq, measure complementary molecular layers, including the transcriptome, chromatin accessibility, and surface protein abundance (Created in BioRender. Tsoi, A. L. (2026) https://BioRender.com/xrpr281). (B) Computational workflow. SEBULA operates in three stages. In Stage 1 (preprocessing), fragment-level chromatin accessibility data are used to compute the high-coverage locus count (HCLC). Cells with very low HCLC values are truncated to stabilize estimation, and a Box-Cox transformation is applied to the remaining HCLC data. In Stage 2, the transformed HCLC distribution is modeled using a nonparametric empirical Bayes framework to estimate the singlet distribution and derive a posterior probability of multiplet status based on ATAC-seq evidence. In Stage 3, when evidence from additional data features and modalities is available, SEBULA integrates feature-specific probabilistic evidence and yields a combined posterior probability of multiplet status given all available measurements.

https://doi.org/10.1371/journal.pcbi.1013653.g001

The key innovation of SEBULA lies in its semi-parametric procedure for directly estimating the distributions of HCLC in singlets and multiplets from observed data. Real snATAC-seq datasets with ground-truth multiplet annotations suggest that commonly used parametric families for count data, such as the Poisson (used by AMULET) and negative binomial distributions, fit the empirical HCLC data poorly (Fig 2). Informed by these empirical observations, we reason that effective multiplet detection should prioritize distinguishing multiplets from singlets with moderate to high HCLC values, since cells with extremely low HCLC values are most likely singlets and therefore provide limited information for multiplet detection. To achieve this, we adopt a strategy analogous to the zero assumption in non-parametric empirical Bayes (NPEB) inference [23], focusing on accurate characterization of the right-tail behavior of the singlet distribution. Specifically, cells with very low HCLC values (defined by a user-specified threshold) are excluded, and the remaining counts are transformed to a continuous domain using a Box-Cox transformation. The empirical density of the transformed values, denoted by f(x), is then estimated and modeled as a mixture of singlet and multiplet distributions:

where x denotes the transformed count, and and represent the proportions of singlets and multiplets, respectively.

Download:

• PNG
  larger image
• TIFF
  original image

Fig 2. Commonly-used parametric models fit poorly to singlet HCLC data.

Plotting data are from a DOGMA-seq dataset, with ground-truth singlet and multiplet labels obtained via cell hashing. (A) Quantile–quantile (Q–Q) plots comparing the observed singlet distribution with the quantiles of fitted values under Poisson and negative binomial models. Neither parametric model adequately fits the data. (B) Histograms of values for singlet (light blue) and doublet (red) nuclei in a DOGMA-seq dataset (PB-3), stratified by ground-truth labels. Kernel density estimates are overlaid. The figure shows that singlets and doublets become separable after transformation; however, no simple parametric model adequately captures the empirical distributions.

https://doi.org/10.1371/journal.pcbi.1013653.g002

Following the principle of the zero assumption, we make two key assumptions: (i) singlets are substantially more abundant than multiplets (), and (ii) cells near the mode of the empirical distribution are predominantly singlets. Leveraging these assumptions, we apply non-parametric density estimation around the mode of f(x) to infer the singlet distribution f₀(x) and estimate its mixing proportion (Methods). The multiplet distribution f₁(x) and its mixing proportion are subsequently induced. With these distributional estimates, the posterior probability that a cell is a multiplet is computed via Bayes’ rule:

(1)

These estimates also enable a principled framework for local and Bayesian FDR control procedures in multiplet detection. Specifically, under a decision rule that classifies all cells with HCLC ≥t as multiplets, the corresponding estimated false discovery rate (FDR) is given by

(2)

The detailed procedures for FDR and lfdr computation are provided in Section 2 of S1 Text.

Quantifying multiplet evidence from the HCLC on a probabilistic scale allows seamless integration with other probabilistic signals, whether derived from additional features in snATAC-seq data, or from complementary modalities such as scRNA-seq. Consequently, SEBULA can be combined with other multiplet detection tools that generate probabilistic outputs, including scDblFinder and COMPOSITE, to further enhance sensitivity and specificity.

This integration follows the principle of Bayesian sequential updating [24]. Specifically, the Bayes factor for the HCLC data, , can be obtained directly from the posterior probability (1) given the snATAC-seq HCLC data . By treating the posterior probability derived from additional feature data y, , as a feature-informed prior, we construct a naïve Bayes classifier that integrates evidence across both sources. This yields the updated classification posterior:

(3)

The integration step operates on modality-specific scores and does not require joint modeling of high-dimensional feature spaces. Additionally, this procedure above can be modified to integrate evidence in the form of p-values or z-scores. The details are provided in the Methods section and Section 3 of S1 Text.

Evaluation using simulated artificial doublets

We generated synthetic snATAC-seq data to examine the performance of SEBULA and AMULET using only HCLC-derived information. Starting from a real DOGMA-seq dataset from Xu et al. [16], we extracted the scATAC-seq modality and removed all annotated multiplets. Artificial doublets were then created by randomly pairing the remaining 15,788 singlet cells. To assess performance across a range of practical scenarios, we constructed multiple datasets with artificial doublet proportions ranging from 5% to 25%. For each simulated dataset, the processed HCLC values were provided as input to both SEBULA and AMULET.

We evaluated the sensitivity and specificity of each method using receiver operating characteristic (ROC) curves and F1 scores across all simulated datasets. SEBULA consistently outperformed AMULET by a wide margin under all conditions (Figs 3 and S1). Notably, the performance of AMULET declined as the proportion of doublets increased, likely due to its reliance on a global mean estimate to approximate the singlet distribution. In contrast, SEBULA exhibited robust performance across varying doublet proportions, reflected by consistently higher AUC values (S1 Fig).

Download:

• PNG
  larger image
• TIFF
  original image

Fig 3. Performance evaluation of SEBULA and AMULET using simulated doublet datasets.

In all panels, boxplots are stratified by the proportion of doublets in simulated datasets (5%–25%). Each boxplot summarizes results from 20 replicate simulations per condition. (A) Optimal F1 scores. (B) F1 scores evaluated at an FDR control level of 0.2. (C) Estimated singlet proportions ().

https://doi.org/10.1371/journal.pcbi.1013653.g003

Both SEBULA and AMULET can estimate the false discovery rate (FDR) to determine a multiplet classification threshold, using Eqn. (2) and the built-in q-value method, respectively. At the 20% FDR control level, Fig 3B shows that SEBULA achieves substantially better classification performance than AMULET, as measured by the F1 score. Furthermore, SEBULA provides reasonably accurate estimates of multiplet proportions across all datasets (Fig 3C), suggesting that the probabilities derived from SEBULA’s semi-parametric model exhibit good calibration properties. These multiplet proportion estimates can also serve as a useful quality control (QC) indicator for snATAC-seq data.

For comparison, we also implemented and evaluated an alternative negative binomial mixture model (NBMM), in which the HCLC distribution of singlets is explicitly modeled by a negative binomial distribution (Section 1 of S1 Text). However, when applied to the simulated artificial doublet datasets, the NBMM produced poorly calibrated classification probabilities: both the estimated singlet proportions and individual posterior probabilities for the vast majority of cells were heavily concentrated near 1 (i.e., indicating singlets with near certainty) across all simulation settings (S2 Fig). We interpret this as evidence that the negative binomial assumption is inadequate for modeling singlet distributions in real data. While the negative binomial distribution addresses some limitations of the Poisson model used by AMULET (such as the inability to accommodate overdispersion or zero inflation), it appears overly permissive for large HCLC values and thus fails to effectively separate multiplets from singlets. From another perspective, this experiment further highlights SEBULA’s key advantage in accurately modeling the singlet and multiplet distributions in real data.

Multiplet detection in trimodal single-cell data

We applied SEBULA to seven trimodal single-cell datasets generated by DOGMA-seq experiments and benchmarked its performance against state-of-the-art multiplet detection methods. DOGMA-seq simultaneously profiles the transcriptome (scRNA-seq), chromatin accessibility (scATAC-seq), and cell surface protein expression (via antibody-derived tags, or ADTs) in single cells. We collected seven benchmarking datasets generated from human peripheral blood T cell experiments, including one dataset from Xu et al. [16] (GSE200417) and six from Hu et al. [14]. In all cases, high-confidence binary labels for multiplet classification were obtained using cell hashing [7] and were treated as ground truth for evaluation.

Among the methods that rely solely on the scATAC-seq modality, SEBULA consistently outperformed AMULET and ArchR in terms of F1 score and performed comparably to scDblFinder (Fig 4). Notably, both ArchR and scDblFinder classify multiplets using in silico doublet generation and leverage multiple features from scATAC-seq data, excluding HCLC. The performance gap between SEBULA and AMULET corroborates the findings from our synthetic data simulations. We further hypothesize that the benchmarking datasets are enriched for homotypic multiplets, a setting in which the HCLC statistic is particularly informative. This likely explains SEBULA’s advantage over ArchR and, in some cases, over scDblFinder.

Download:

• PNG
  larger image
• TIFF
  original image

Fig 4. Benchmarking SEBULA against existing multiplet detection methods using seven DOGMA-seq datasets.

Boxplots show F1 scores for each multiplet detection method evaluated across seven DOGMA-seq datasets. Multiplet labels in all datasets are derived from cell hashing. SEBULA-MI denotes SEBULA’s results from multiomic integration. AMULET(ATAC), ArchR(ATAC), SEBULA(ATAC), and scDblFinder(ATAC) denote methods applied using only ATAC-seq data, whereas scDblFinder(RNA) denotes scDblFinder applied using only RNA-seq data. SEBULA-MI(ATAC)^* denotes SEBULA integrating its ATAC-seq analysis with evidence from scDblFinder’s ATAC-seq analysis. COMPOSITE(RNA+ATAC)^* denotes COMPOSITE applied to both RNA-seq and ATAC-seq data. SEBULA(RNA+ATAC)^* denotes SEBULA integrating its ATAC-seq analysis with evidence from scDblFinder’s RNA-seq analysis. Each point represents the result for a single dataset; boxes span the interquartile range with the median marked by a horizontal line, and whiskers extend to 1.5× the interquartile range.

https://doi.org/10.1371/journal.pcbi.1013653.g004

Next, we applied the scheme in Eqn. (3) to integrate the classification probabilities derived from scDblFinder and SEBULA within the ATAC-seq modality, effectively combining the evidence from ATAC-seq features leveraged by scDblFinder with that from the HCLC statistic. This evidence ensemble achieved the best overall performance in the ATAC-seq modality across all benchmarking datasets (Fig 4).

We subsequently extended the evidence integration across data modalities by combining scRNA-seq-based inference from scDblFinder with ATAC-seq-based inference from SEBULA, again using Eqn. (3) to compute per-cell classification probabilities. Notably, scRNA-seq-based inference alone achieved higher sensitivity and specificity for multiplet detection than scATAC-seq-based inference. Nevertheless, integrating evidence from both modalities led to substantial improvements over either modality alone, underscoring the complementary value of multimodal data. Remarkably, the ensemble classifier’s performance was on par with (and in some cases slightly better than) COMPOSITE, a state-of-the-art method specifically designed for cross-modality multiplet detection.

Finally, we evaluated the computational efficiency of SEBULA relative to ArchR and scDblFinder (ATAC) across representative benchmark datasets (Section 4 of S1 Text). SEBULA required substantially shorter runtime and lower memory usage for multiplet detection (S3 Fig). Given the HCLC data, mixture model fitting and posterior computation in SEBULA are computationally lightweight. These results demonstrate that SEBULA provides an efficient alternative to simulation-based approaches for large-scale single-cell datasets.

Pre-processing and HCLC generation

To generate the high-coverage locus count (HCLC) statistics required for SEBULA, we largely follow the preprocessing procedures established in AMULET, which consist of two main stages.

In the first stage, we process fragment files containing all read alignments along with a set of confidently called cell barcodes. For each autosomal chromosome in each cell, we retain fragments with insert sizes less than 900 base pairs. We then identify and record high-coverage loci (defined as genomic intervals overlapped by more than two fragments within a single cell) using a sweep-line algorithm.

In the second stage, we aggregate the high-coverage loci identified across all cells to create a non-redundant set of genomic intervals for each chromosome. This is achieved using a greedy interval-merging algorithm. Based on these merged loci, we construct a binary matrix in which each row corresponds to a high-coverage locus and each column corresponds to a cell. An entry in the matrix is set to 1 if the cell contains a fragment overlapping the corresponding locus, and 0 otherwise. The HCLC for each cell is then computed as the sum of entries in the corresponding column.

Semi-parametric modeling of HCLC

Let denote the HCLC values for N cell barcodes in an experiment. We first exclude cells with HCLC strictly below a predefined threshold , assuming that such cells are predominantly singlets. In the Method part, we provide a computational procedure for selecting an optimal value of based on the overall goodness-of-fit of the SEBULA model. However, we find that SEBULA’s results are generally robust when , where Q₁ denotes the 25th percentile. We denote the set of filtered HCLC values by and the number of retained cells by N_T. For each , we apply a variance-stabilizing and Box-Cox transformation [28],

where the parameter is determined by maximizing the Box-Cox log-likelihood. SEBULA models the Box-Cox transformed HCLC data, , using a two-component mixture distribution:

where f₀ is assumed to be a normal density with (unknown) mean, , and variance, .

Mixture density estimation via poisson spline smoothing.

We estimate the mixture density f(z) using a smoothed histogram of the truncated variable , partitioned into K equally spaced bins (default K = 120). For , let y_i denote the observed count in the ith bin and c_i the center of the bin.

Following Efron [23,29,30], we treat y_i as independent Poisson observations and fit a generalized linear model (GLM) with natural spline basis of degree 7. Specifically, we assume

where denotes the kth basis function of the natural spline. This yields a smooth estimate of the mixture density. The fitted values at bin centers, , are normalized to produce a discrete approximation of the density:

A smooth estimate of the cumulative distribution function (CDF), , is subsequently obtained by linearly interpolating the bin centers c_i against the cumulative sums of .

Singlet density estimation by central matching.

We apply Efron’s central matching method [23] to estimate the singlet density f₀(z) and the singlet proportion in the transformed HCLC data. The key assumption here is that the vast majority of the transformed HCLC values within a predefined central window correspond to singlet cells. (By default, we specify the central window spanning the 20th to 60th percentiles of the empirical distribution of .) By isolating data within this range, we fit a quadratic model to the log of the sub-density as follows:

(4)

where is the center of the histogram bin where the estimated mixture density attains its maximum.

Assuming , the log sub-density expands as

(5)

The least squares estimates, , from the fit of (4) induce the estimates of and for the normal density of the singlet distribution:

An unnormalized estimate of the singlet count in each histogram bin i is then computed by

where denotes the fitted count from the Poisson spline model at the ith bin center, c_i.

Finally, the singlet proportion is estimated by normalizing the total fitted singlet density:

Note that represents the proportion of singlets among the cells after initial filtering. To report the estimate of the singlet proportion in the entire original library, we use

Optimizing truncation point.

In practice, we find that filtering out zero and low HCLC values can substantially improve the efficiency of mixture distribution estimation. Although the final results for multiplet classification are generally robust to the specific choice of the threshold , provided that , we propose a simple computational procedure to aid in selecting an value to optimize the performance of SEBULA.

The proposed procedure evaluates the goodness-of-fit between the transformed HCLC values within a specific range and the estimated normal distribution using cross-entropy loss. Specifically, after filtering the data and fitting the mixture model, we define

and compute the cross-entropy for the corresponding as

The cross-entropy measures the discrepancy between the fitted normal distribution and the empirical distribution of the data; lower values indicate a better fit. Therefore, selecting an that minimizes the cross-entropy supports the validity of the central matching assumption.

Because the mixture fitting procedure is computationally efficient, SEBULA can quickly evaluate cross-entropy values over a range of settings. To balance improved goodness-of-fit with retaining sufficient data for stable estimation of the mixture model, SEBULA constructs a trace plot of and selects the elbow point as the optimal threshold (S4 Fig).

To further assess SEBULA’s robustness to the choice of truncation threshold, we conducted a sensitivity analysis by varying over a broad range. Classification performance metrics, including F1 score, AUROC, and AUPRC, as well as the called multiplet rate, remained stable over practical threshold choices (S5 Fig). These results indicate that SEBULA is not highly sensitive to moderate variations in and that the proposed cross-entropy-based selection procedure provides a reasonable and stable operating point.

Multiplet classification

Based on the overall procedure, we compute the posterior probability that cell j is a multiplet as

Thresholding the p_j values is a standard classification approach in machine learning practice. By default, we classify cells with p_j > 0.8 as multiplets, corresponding to a local false discovery rate threshold of 20%.

Alternatively, we also implement a classification procedure that controls the overall false discovery rate (FDR), primarily for comparison with AMULET. Note that the estimated densities and induce corresponding cumulative distribution functions and . For a decision rule that classifies all cells with Box-Cox transformed values z ≥ t as multiplets, the estimated FDR at threshold t is given by

This approach allows users to pre-specify a target FDR level (e.g., 20%) and then identify the corresponding z cutoff directly from the data.

Probabilistic evidence integration

To integrate probabilistic evidence from HCLC with evidence derived from other data features and/or modalities, we adopt a general Bayesian framework for sequentially updating posterior multiplet probabilities.

We regard the existing posterior probability for a target cell, , as the new prior for re-analyzing the HCLC data. We then recover the HCLC likelihood for each cell from the earlier HCLC-only analysis. Specifically, we compute the marginal likelihood of the HCLC data, i.e., the Bayes factor, for cell j as

where p_j is the posterior multiplet probability based on HCLC alone, and is the estimated proportion of singlets in the original library.

Assuming conditional independence between and , i.e.,

(6)

The updated posterior probability incorporating HCLC evidence is given by the Bayes rule:

(7)

Note that the conditional independence assumption in (6) is the naïve independence assumption used in the naïve Bayes classifier. While this assumption may not hold exactly in practice, empirical evidence suggests that it is approximately valid (Section 5 of S1 Text), particularly when integrating data across distinct modalities. Additionally, the same naïve Bayes procedure can be applied to integrate evidence in the form of p-values or z-scores (see Section 3 of S1 Text).