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. 2025 Oct 9;26:900. doi: 10.1186/s12864-025-11987-y

PB-DiffHiC: a statistical framework for detecting differential chromatin interactions from high resolution pseudo-bulk Hi-C data

Yan Zhou 1,#, Yaohua Hu 1,#, Liuting Tan 1, Jiadi Zhu 1, Yutong Fei 1, Ming Gu 2, Dechao Tian 2,✉
PMCID: PMC12512566  PMID: 41068581

Abstract

Single-cell Hi-C (scHi-C) data provide unprecedented opportunities for analyzing differential chromatin interactions, essential for understanding genome structure-function relationships across various biological conditions. However, biologically meaningful differential chromatin interaction analysis at high resolution (e.g., 10 Kb) remains challenging due to the inherent sparsity of scHi-C data. Existing approaches typically rely on single cell imputation, which is computationally intensive and lacks validation, or apply conventional bulk Hi-C tools to pseudo-bulk matrices aggregated from individual cells. The sparsity of high-resolution pseudo-bulk data limits the effectiveness of bulk-oriented methods. Here, we present PB-DiffHiC, an optimized parametric statistical framework that directly analyzes raw pseudo-bulk Hi-C data at 10 Kb resolution between conditions. PB-DiffHiC incorporates Gaussian convolution, the stability of short-range interactions, and Poisson modeling to jointly perform normalization and statistical testing. Benchmarking on cell-type-specific chromatin loops shows that PB-DiffHiC achieves higher precision than alternative methods. Application to pseudo-bulk and matched bulk Hi-C data demonstrates stronger concordance in identified differential interactions, reinforcing its reliability. In a case study, PB-DiffHiC successfully identifies Kcnq5-associated differential interactions that closely matching SnapHiC-D results, despite not relying on single-cell imputation. PB-DiffHiC is a statistically sound and robust method for high-resolution differential analysis of chromatin interactions using raw pseudo-bulk Hi-C data. The source code of PB-DiffHiC is publicly available at https://github.com/Tian-Dechao/PB-DiffHiC.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12864-025-11987-y.

Keywords: Pseudo-bulk , Hi-C single-cell, Hi-C Differential , Chromatin interactions, Differential analysis , 3D genome organization, Statistical modeling

Background

The development of high-throughput chromosome conformation capture (Hi-C) sequencing methods has provided critical insights into the three-dimensional (3D) chromatin architecture, revealing the hierarchical organization of mammalian genomes within the nucleus [1]. A fundamental organizational unit is chromatin interactions, which bring distal chromosomal loci into spatial proximity and play essential roles in transcriptional regulation and other biological functions. Chromatin interactions are highly dynamic and condition-specific, with condition-specific chromatin interactions associated with various biological states, including diseases [2–5]. Identifying differential chromatin interactions between conditions is crucial for understanding the genome structure-function relationships in health and disease.

The emergence of scHi-C techniques has enabled the study of chromatin interaction variability at single-cell level. However, high sparsity, low genome coverage, and substantial heterogeneity pose challenges for differential analysis between biological conditions [6], A common approach aggregates contact matrices from individual cells within the same condition into a pseudo-bulk Hi-C contact matrix, improving coverage and enabling the use of bulk Hi-C analysis tools [7, 8]. Yet, pseudo-bulk Hi-C contact matrices differ substantially from conventional bulk data. Their pronounced sparsity at high resolution (e.g., 10 Kb; see our own analysis later) presents a major challenge for reliably detecting differential chromatin interactions at a resolution that is essential for revealing biologically meaningful interactions between genes and distal regulatory elements, which are frequently missed at coarser resolutions.

The sparse nature of pseudo-bulk Hi-C data violates key assumptions underlying established bulk Hi-C differential analysis methods, including HOMER [9], HiBrowse [10], diffHiC [11], and multiHiCcompare [12]. These methods were developed within statistical frameworks such as edgeR and DESeq2, originally designed for bulk RNA-seq data, and rely on deeply sequenced input with multiple biological replicates. More recent approaches, including FIND [13], Selfish [14], and HiC-DC+ [15], incorporate spatial dependence among nearby chromatin interactions or distance-aware normalization. However, they remain optimized for bulk Hi-C datasets and do not adequately accommodating the sparse nature of pseudo-bulk Hi-C contact matrices at fine resolution.

Additional to pseudo-bulk Hi-C strategies, several methods have been specifically developed for scHi-C data to enable differential analysis on imputed single-cell contact matrices while preserving single-cell resolution. Pioneer methods such as SnapHiC-D [16] and scHiCDiff [17] conduct two-sample hypothesis testing directly on imputed single-cell Hi-C contact maps, while scHiCcompare applies imputation prior to pseudo-bulk aggregation and subsequent differential testing [18]. Although these approaches can enhance sensitivity, their performance depends heavily on the accuracy and reliability of imputation [19]. This dependency remain particularly challenging at high-resolutions (e.g., 10 Kb), where imputation methods are still evolving and lack rigorous validation [6, 20]. These challenges underscore the need for computational methods that bypass the reliance on imputation and instead directly analyze raw pseudo-bulk Hi-C data at high resolution.

Here, we introduce PB-DiffHiC (for Pseudo-Bulk Differential Hi-C), an optimized parametric statistical framework designed to identify differential chromatin interactions using raw pseudo-bulk Hi-C data at 10 Kb resolution. To mitigate sparsity, PB-DiffHiC applies a simple yet effective Gaussian convolution to raw pseudo-bulk Hi-C contact matrices, leveraging spatial dependencies among neighboring interactions. It then models interaction frequencies using an optimized Poisson-based hypothesis testing framework, with P-values computed via a conditional binomial distribution. To account for differences in sequencing depth, PB-DiffHiC estimates the normalization scaling factor by controlling the false discovery rate of short-range interactions that remain largely stable between conditions. This joint estimation strategy enables PB-DiffHiC to integrate normalization and hypothesis testing into a unified framework, unlike existing bulk Hi-C methods that handle them as separate steps. Benchmarking on cell-type-specific chromatin loops shows that PB-DiffHiC achieves higher precisions than alternative methods. PB-DiffHiC also exhibits stronger concordance between differential chromatin interactions identified in pseudo-bulk and matched bulk Hi-C data, reinforcing its reliability. In a case study, PB-DiffHiC successfully identifies differential chromatin interactions involving the Kcnq5 promoter, yielding results highly consistent with SnapHiC-D [16] despite not relying on single-cell imputation, demonstrating its robustness and effectiveness. Together, these results highlight PB-DiffHiC as a sound and robust method for high-resolution differential chromatin interaction analysis using raw pseudo-bulk Hi-C data.

Results

Overview of PB-DiffHiC

PB-DiffHiC is an optimized statistical framework designed to detect differential chromatin interactions using raw pseudo-bulk Hi-C contact matrices at 10 Kb resolution (Fig. 1). The framework provides a unified framework for the differential analysis of pseudo-bulk Hi-C data with two primary setups. The merged-replicate setup aggregates single-cell contact maps within a condition into a single pseudo-bulk Hi-C contact matrix. The two-replicate setup randomly divides single-cell contact maps within a condition into two groups, which are then aggregated into two pseudo-bulk Hi-C contact matrices representing biological replicates, enabling the incorporation of variability between replicates. In both setups, raw pseudo-bulk Hi-C contact matrices are binned at 10 Kb resolution. PB-DiffHiC consists of two key steps. The first step involves Gaussian convolution to enhance interaction signals in pseudo-bulk Hi-C data, by leveraging the strong dependencies among spatially proximal chromatin interactions. This simple yet effective approach bypasses complex single-cell imputation, offering a simpler alternative to complex imputation and enhancing interpretation. The second step is optimized parametric hypothesis testing framework, which combines the computation of P-values with the estimation of scaling factors for normalizing contact matrices between conditions. Scaling factors are estimated by controlling the false discovery rate of short-range chromatin interactions (spanning up to 5 bins) that are largely stable between conditions. The estimated scaling factors replace their corresponding terms to compute the P-value for each chromatin interaction. Together, PB-DiffHiC improves sensitivity and robustness in detecting differential chromatin interactions in raw pseudo-bulk Hi-C data.

Fig. 1.

Fig. 1

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Workflow of PB-DiffHiC with merged-replicate setup. The input consists of two pseudo-bulk Hi-C contact matrices, one from each condition, with resolution at 10 Kb. Example data shown here are pseudo-bulk Hi-C contact matrices from the Chr1:14.4-14.55 Mb region in mESC and NPC cells. Gaussian convolution smooths the Hi-C contact matrices by averaging nearby interaction frequencies based on spatial proximity. For a given interaction, its frequency in each condition follows a Poisson distribution. Conditional on the sum of interaction frequencies between the two conditions, the interaction follows a binomial distribution, with the probability parameter depending on the scaling factor s used to normalize the contact matrices. The scaling factor s is estimated by assuming that short-range interactions have a false discovery rate of 0.05. Based on the estimated scaling factor Inline graphic, the exact P-value is computed using the binomial distribution. Interactions with BH-adjusted p-values smaller than 0.05 are identified as differential chromatin interactions

Method benchmarking using cell-type-specific chromatin loops

To do this, we use a recent scHi-C dataset with high coverage [16]. The dataset has 94 mouse embryonic stem cells (mESCs) and 188 mouse neuron progenitor cells (NPCs), with median contact counts of 1.29 million and 0.95 million per cell, respectively. Aggregation of these single-cell data results in sparse pseudo-bulk Hi-C data at 10 Kb resolution. For example, 86.01% of chromatin interactions connecting regions within 20 kb to 2 Mb distance on Chromosome 1 are missing in the pseudo-bulk Hi-C data aggregated from 94 mESCs, and 71.75% are missing in the data from 188 NPCs.

For benchmarking, we designed two experimental setups: (1) two replicates per condition, where individual cells were randomly divided into two equal-sized groups to create two pseudo-bulk Hi-C contact matrices; and (2) merging all cells of each condition into one pseudo-bulk Hi-C contact matrix, mimicking merging replicates into one combined Hi-C data in the bulk scenario. The first setup is used for PB-DiffHiC (two-replicate setup), FIND, and HiC-DC+, while the second setup is used for PB-DiffHiC (merged-replicate setup) and Selfish. Due to lack of gold standard data for differential chromatin interactions, cell type-specific chromatin loops identified in matched bulk Hi-C data [21] are treated as positives (Inline graphic), while shared or overlapping loops between cell types are considered as negatives (Inline graphic). All methods use BH-adjusted P-values, with a threshold of 0.05 for statistical significant, except FIND, which uses a suggested stricter threshold of Inline graphic [13]. Precision, recall and F1 scores are calculated for performance comparison.

To isolate the contribution of Gaussian convolution, we conducted an ablation analysis comparing performance with and without this smoothing preprocessing. The results demonstrate that Gaussian convolution substantially improves detection accuracy, particularly for PB-DiffHiC (merged-replicate setup), FIND, and Selfish (Supplementary Table 1). Based on these findings, Gaussian convolution-smoothed pseudo-bulk Hi-C contact matrices were used as input for all methods in the benchmarking analysis to ensure a fair comparison.

PB-DiffHiC exhibits superior performance in controlling false positives. Under the two-replicate setup, PB-DiffHiC achieves 1.5 time higher precision than the alternative methods, and under the merged-replicate setup, precision is 3 time higher (Fig. 2A). In contrast, FIND and Selfish achieve substantially higher recall and F1 scores, but at the expense of precision (Fig. 2A). For example, FIND achieves the highest recall (0.83), but its precision is close to random guessing (24.81%), indicating limited reliability in distinguishing positives from negatives. Closer inspection of the P-value distributions reveals limitations with the alternative methods. FIND over-estimated significance for the negative differential chromatin interactions, with the median P-value of Inline graphic and the 95th percentile of Inline graphic (Fig. 2D). Moreover, under the much strict significance threshold, adjusted P-values of Inline graphic, a larger proportion of negative differential chromatin interactions (91.61%) were deemed statistically significant compared to the positive differential chromatin interactions (83.35%). Similar patterns are found for Selfish (Fig. 2E). The observed high false positives of FIND and Selfish are consistent with a recent review study [22].

Fig. 2.

Fig. 2

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Method benchmarking using cell-type specific chromatin loops. A Performance comparison of PB-DiffHiC and alternative methods in terms of precision, recall, and F1 scores, ranked by decreasing precision. Methods include PB-DiffHiC (merged-replicate and two-replicate setups), Selfish, HiC-DC+, and FIND. Differential chromatin interactions are identified based on BH-adjusted P-values: Inline graphic for PB-DiffHiC, Selfish, and HiC-DC+, and Inline graphic for FIND. The dashed segment represents the expected precision by random guessing (24.81%). B-F Distribution of original P-values for positive and negative differential chromatin interactions, as computed by each method. G Comparison of PB-DiffHiC and HiC-DC+ based on original P-values, instead of BH-adjusted P-values. Significant level is 0.05 for PB-DiffHiC and 0.05 or 0.1 for HiC-DC+. Gold-standard differential chromatin interactions are defined using chromatin loops identified from matched bulk Hi-C data, with positives corresponding to cell type-specific loops and negatives to shared or overlapping loops between cell types

Unlike the aforementioned methods, HiC-DC+ under-estimates the significance of the positive differential chromatin interactions (Fig. 2F). No positive interactions have adjusted P-value below 0.05, and its smallest adjusted P-value is 0.67. Relaxing the significance threshold to the original P-values, HiC-DC+ has 478 P-values smaller than 0.05, yielding a precision of 0.14, recall of 0.04, and F1 score of 0.06. Further relaxing the significance threshold to 0.1 boosts the recall and F1 scores of HiC-DC+. HiC-DC+ has 1141 P-values smaller than 0.1, resulting in a precision of 0.15, recall of 0.09, and F1 score of 0.11 (Fig. 2G). However, in both scenarios, HiC-DC+ is outperformed by PB-DiffHiC, both with and without multiple-testing corrections (Fig. 2A, G).

To provide a more comprehensive evaluation, we assessed each method’s performance across a range of significance levels (0.001, 0.01, 0.05, 0.1). Precision-recall curves were generated, and the area under the Precision-recall curve (AUPRC) was computed to summarize overall performance (Supplementary Fig. 2). PB-DiffHiC (two-replicate setup) achieves the highest AUPRC (0.290), followed closely by the merged-replicate setup (0.279). Across significance levels Inline graphic, PB-DiffHiC consistently maintains high precision, with recall increasing as the significance threshold became more permissive. In contrast, FIND, Selfish, and HiC-DC+ exhibit relatively low precision across all thresholds, resulting in lower AUPRCs (0.198, 0.215, and 0.206, respectively). These results suggest that PB-DiffHiC achieves a more favorable balance between precision and recall across a range of significance levels.

Differing from the alternative methods, which are designed for bulk Hi-C data, PB-DiffHiC effectively accommodates the sparsity of pseudo-bulk Hi-C data derived from scHi-C studies. It offers flexibility with two settings: (1) two replicates per condition, which prioritizes higher recall and F1 scores, and (2) merged replicates, which achieves higher precision. This flexibility allows tailed analysis to specific research needs. Together, these results highlight the superior precision of PB-DiffHiC in controlling false positives, compared with alternative methods.

Agreements between differential chromatin interactions identified using pseudo-bulk and matched bulk Hi-C data

Single-cell Hi-C capture chromatin interactions in individual cells, while bulk Hi-C represent population-averaged chromatin interactions. Multiple algorithms have been developed for analyzing bulk Hi-C data, but few have been tested or optimized for sparse pseudo-bulk Hi-C data aggregated from scHi-C. A greater overlap between differential chromatin interactions identified using matched bulk and pseudo-bulk Hi-C data indicates that pseudo-bulk Hi-C methods effectively capture differential chromatin interactions consistent with bulk Hi-C data, ensuring cross-validation of findings. With the increasing availability of bulk and single-cell Hi-C datasets, evaluating this overlap is crucial, and methods with greater overlaps are desirable.

To quantify this overlap, the same single-cell Hi-C data used in the previous section is used here as well. Matched bulk Hi-C data from mESC and NPC are downloaded under accession number GSE94452 [23]. Due to the vast number of genome-wide chromatin interactions at 10 Kb resolution, the analysis focuses on mouse chromosome 1, which contains 19,548 10-Kb chromosomal bins and 1,930,203 chromatin interactions spanning distances between 20 Kb and 1 Mb, representative of genome-wide chromatin interactions within this range. To assess consistency across dataset, two sets of NPC bulk Hi-C data are used: control condition at day 4 (GSM4386026, GSM4386027) and auxin washout condition at day 4 (GSM4386030, GSM4386031). The results are consistent across both datasets (Fig. 3, Supplementary Fig. 3), with findings primarily reported using the auxin washout condition.

Fig. 3.

Fig. 3

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Agreement between differential chromatin interactions identified using pseudo-bulk and matched bulk Hi-C data. A Hexbin plot showing the correlations between P-values from bulk and pseudo-bulk Hi-C data. Dashed lines represent the statistical significance threshold of 0.05. The analysis includes 1,930,203 interactions between 10-Kb chromosomal bins spanning distances from 20 Kb to 1 Mb on Chromosome 1. B Venn diagram showing the number of shared significant differential chromatin interactions between bulk and pseudo-bulk Hi-C data. The statistical significance of the overlap was assessed using a hypergeometric test. C Line plot showing the number of shared interactions between the top K differential chromatin interactions from the pseudo-bulk Hi-C data and the top 100,000 differential chromatin interactions from the bulk Hi-C data. D Line plot showing the proportion (number/K) of shared interactions between the same sets of interactions. Consistent results are observed using a different set of bulk NPC Hi-C data (Supplementary Fig. 3)

First, the associations between P-values computed using the bulk and pseudo-bulk Hi-C data are investigated. PB-DiffHiC (two-replicate setup) achieves the strongest association, followed by Selfish, PB-DiffHiC (merged-replicate setup), and HiC-DC+ (Fig. 3A). However, no method achieves a strong association, with the highest Spearman’s Inline graphic reaching only 0.23, suggesting limited concordance between bulk and pseudo-bulk differential interactions, likely due to differences in data sparsity. Visual inspection shows that pseudo-bulk Hi-C produces substantially fewer P-values below 0.05 than bulk Hi-C across all methods except Selfish (Fig. 3A), suggesting that the increased sparsity in pseudo-bulk Hi-C reduces statistical power and weakens the detection of significant differential interactions, as expected.

Thus, to ensure comparability, original P-values are used to call differential chromatin interactions using pseudo-bulk Hi-C data across all methods, while bulk Hi-C data follows a mixed approach: adjusted P-values are used for PB-DiffHiC and Selfish, whereas HiC-DC+ uses original P-values due to its limited number of detected differential interactions at an adjusted P-value threshold of 0.05. The significance level is set at 0.05.

Across the tested 1,930,203 chromatin interactions, PB-DiffHiC (two-replicate setup) detects the highest proportion of statistically significant differential chromatin interactions using bulk Hi-C data (41.41%), followed by PB-DiffHiC (merged-replicate setup, 23.40%), Selfish (1.09%), and HiC-DC+ (1.39%). When the same methods are applied to the pseudo-bulk Hi-C data, the proportions are substantially lower (2.18%, 1.47%, 9.18%, and 0.05%, respectively). Examining the agreement between differential chromatin interactions identified using bulk Hi-C and pseudo-bulk Hi-C data reveals substantial variation across methods. PB-DiffHiC achieves the strongest agreement, with the highest proportion of differential interactions identified in pseudo-bulk Hi-C data that are shared with those from bulk Hi-C data (merged-replicate setup, 41.98%; two-replicate setup, 78.09%). In contrast, the next-best method, Selfish, has a proportion of 4.73%, more than 8 times lower than PB-DiffHiC (Fig. 3B).

Because each method identifies a different number of significant differential chromatin interactions, we further investigate how the statistical significance threshold affects overlap. To this end, the top 100,000 differential chromatin interactions with the strongest statistical significance from both pseudo-bulk and bulk Hi-C data are extracted. These interactions account for 5.18% of all tested chromatin interactions and exceed the number of differential chromatin interactions identified in both bulk and pseudo-bulk Hi-C data for all methods, except PB-DiffHiC with bulk Hi-C and Selfish. Fixing the top 100,000 differential chromatin interactions from the bulk Hi-C data, the number of shared interactions with the top K, Inline graphic, from the pseudo-bulk Hi-C data varies by method. The number of shared interactions increases as K increases across all methods, but the rate of increase differs (Fig. 3C), indicating method-specific prioritization of significant interactions. Beyond the absolute number of shared interactions, the proportion of top K differential chromatin interactions from the pseudo-bulk Hi-C data that overlap with those from bulk Hi-C data reveals substantial variation across methods (Fig. 3D). PB-DiffHiC (two-replicate setup) consistently achieves the highest proportion of shared interaction(Inline graphic20%), followed by Selfish (Inline graphic13%) and PB-DiffHiC (merged-replicate setup, Inline graphic10%). HiC-DC+ consistently achieves the lowest overlap (<4%), suggesting the weakest concordance between its differential chromatin interactions in pseudo-bulk and bulk Hi-C data. Additionally, only PB-DiffHiC (both setups) achieve a relatively stable proportion of shared interactions, with the overlap stabilizing between Inline graphic20,000 and 100,000 (Fig. 3D). This stability highlights the robustness of PB-DiffHiC across different significance thresholds.

These results demonstrate that PB-DiffHiC provides stronger concordance between P-value distributions in pseudo-bulk and bulk Hi-C data and achieves a higher and more stable overlap of identified differential chromatin interactions, making it a preferred method for analyzing differential chromatin interactions using pseudo-bulk Hi-C data.

Case-study: Validating PB-DiffHiC on Kcnq5-associated chromatin interactions

SnapHiC-D utilizes a two-sample t-test on imputed and normalized individual contact maps to detect differential chromatin interactions. Its performance is showcased in an analysis of Kcnq5 promoter interactions, comparing hippocampal CA1 pyramidal neurons (CA1) and dentate gyrus (DG) cells [16]. To further evaluate PB-DiffHiC on raw pseudo-bulk Hi-C data, we reanalyzed this case-study dataset. PB-DiffHiC includes cells with over 150,000 contacts, resulting in 408 CA1 cells and 1040 DG cells [24], similar to SnapHiC-D. PB-DiffHiC is run in a merged-replicate setup with pseudo-bulk Hi-C at 10 Kb resolution. Unlike SnapHiC-D, PB-DiffHiC does not impute individual contact maps, but instead aggregates them into pseudo-bulk Hi-C, testing its effectiveness under sparse conditions. Given the sparsity of pseudo-bulk data, significant is defined by a raw P-value less than 0.05 instead of adjusted P-values used elsewhere.

The differential chromatin interactions identified by PB-DiffHiC are largely consistent with those detected by SnapHiC-D (Fig. 4). SnapHiC-D identified 11 differential chromatin interactions, all with higher chromatin interaction frequencies in CA1 than in DG. Similarly, PB-DiffHiC identifies 20 differential chromatin interactions, all showing higher chromatin interaction frequencies in CA1 after normalization. Both sets of differential chromatin interactions consistently connect the Kcnq5 promoter with its upstream gene body region and gene Gsta3, as well as a downstream putative enhancer region, marked by elevated H3K27ac signals in CA1 (Fig. 4). While largely overlap, the two sets of differential chromatin interactions have subtle differences. For example, PB-DiffHiC identifies a few differential interactions approximately 60 Kb upstream of those detected by SnapHiC-D. The subset of differential chromatin interactions are associated with higher H3K27ac and H3K4me1 marks in CA1, suggesting their biological relevance. This difference suggests that PB-DiffHiC may detect additional distal regulatory interactions, potentially indicating unrecognized enhancer-promoter interactions relevant to Kcnq5 transcriptional regulation.

Fig. 4.

Fig. 4

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Case study focused on the Kcnq5 promoter region using raw scHi-C data at 10 Kb resolution. From top to bottom: differential chromatin interactions identified by PB-DiffHiC and SnapHiC-D; RNA-seq data from CA1 (pink track) and DG (blue track); H3K27ac and H3K4me1 histone marks indicating active promoter and enhancer regions; and Refseq gene annotations. Solid boxes highlight consistent differential chromatin interactions (teal) and unique differential interactions identified by PB-DiffHiC and SnapHiC-D (orange and blue, respectively). All differential chromatin interactions have higher interaction frequencies in CA1 compared to DG. Data are downloaded from [24]. Visualization is performed using the pyGenomeTracks package [25]

Using pseudo-bulk Hi-C data aggregated from raw scHi-C data (analyzed as a single sample in PB-DiffHiC) instead of imputed scHi-C data across individual cells (analyzed as multiple samples in SnapHiC-D) may inherently reduce the detection power. However, PB-DiffHiC still yields results closely aligned with SnapHiC-D, highlighting its effectiveness in analyzing raw pseudo-bulk Hi-C data.

Conclusion

In this study, we introduce PB-DiffHiC, a statistically principled method for detecting differential chromatin interactions in raw pseudo-bulk Hi-C data at 10 Kb resolution. Unlike existing methods that rely on bulk Hi-C frameworks or imputation-based approaches, PB-DiffHiC directly analyzes raw pseudo-bulk Hi-C data, mitigating sparsity through Gaussian convolution smoothing and leveraging spatial dependencies to enhance signal detection. Additionally, it estimates scaling factors for cross-condition and cross-replicate normalization by controlling the false discovery rate of short-range chromatin interactions, which are expected to remain stable between conditions.

These results highlight PB-DiffHiC’s effectiveness in detecting differential chromatin interactions while addressing the unique challenges of pseudo-bulk Hi-C data at high resolution. In this paper, we extensively evaluated PB-DiffHiC’s performance at 10 kKb resolution as a representative case. We anticipate that PB-DiffHiC can be effectively applied to high-coverage scHi-C datasets at finer resolutions, such as 5 Kb, similar to how SnapHiC2 is used to detect 5 Kb chromatin loops from scHi-C data [26]. As scHi-C technologies continue to advance, PB-DiffHiC provides a robust computational framework for analyzing differential chromatin interactions at high resolution, facilitating deeper insights into 3D genome organization and their biological functions across different biological conditions.

Beyond its application to high resolution pseudo-bulk Hi-C data, PB-DiffHiC is also applicable to conventional bulk Hi-C data, as demonstrated by our analysis showing consistent identification of differential chromatin interactions between bulk and pseudo-bulk Hi-C data. Its unified framework supports both merged-replicate and two-sample setups, making it adaptable to various types of Hi-C experiments. Although our benchmarking focused on mouse pseudo-bulk Hi-C data, the design of PB-DiffHiC does not rely on species-specific assumptions. Therefore, it is in principle applicable to Hi-C datasets from other organisms, such as human, plant, or invertebrate genomes, provided that sufficient sequencing depth and resolution are available to construct reliable pseudo-bulk contact matrices.

An important direction for future work is the development of data-adaptive strategies for selecting the smoothing parameter Inline graphic in Gaussian convolution. Different datasets—and even distinct genomic regions within the same contact map—may require varying degrees of smoothing depending on factors such as sequencing depth, resolution, and local interaction density. A context-aware choice of Inline graphic could enhance PB-DiffHiC’s robustness and generalizability, and would likewise benefit other computational frameworks that incorporate Gaussian convolution in Hi-C data analysis. In parallel, future work would explore its applicability to single-cell Hi-C data at the true single-cell level, enabling even more precise insights into chromatin interactions in individual cells.

Methods

Merging raw scHi-C contact maps into pseudo-bulk Hi-C contact maps

PB-DiffHiC supports two setups for merging raw scHi-C data into pseudo-bulk Hi-C data at 10 Kb resolution.

The first setup merges all single-cell Hi-C contact maps within the same condition into a single pseudo-bulk Hi-C matrix. This approach facilitates integration with other scHi-C data analysis pipelines, such as those examining topologically associating domains (TADs) and A/B compartments.

The second setup randomly divides the single-cell Hi-C contact maps within the same condition into two groups, aggregates contacts within each group to construct two pseudo-bulk Hi-C matrices. The two-replicate setup accounts for variability in sequencing depth between pseudo-bulk Hi-C matrices, ensuring a more reliable comparison between conditions. By estimating replicate-specific scaling factors, this approach effectively adjusts for differences in total contact counts while leveraging within-condition variation.

For simplicity, the first setup is referred to as the merged-replicate setup, and the second setup as the two-replicate setup.

PB-DiffHiC (merged-replicate setup): Gaussian convolution to handle spatial dependency and sparsity in raw pseudo-bulk Hi-C data

Gaussian convolution smooths Hi-C contact matrices by applying a Gaussian kernel, which assigns weights based on spatial proximity to average nearby interactions. This enhances signal resolution by leveraging the strong dependency among spatially proximal chromatin interactions, a property successfully utilized by FIND [13] and Selfish [14]. In PB-DiffHiC, this operation is applied once to each raw pseudo-bulk Hi-C contact matrix, enhancing signal resolution and implicitly imputing missing entries [17]. In contrast to conventional single-cell imputation methods—which operate on individual cells using complex, often learning-based models—this convolution step is deterministic, efficient, and avoids the computational and methodological burdens associated with cell-level imputation [20].

To implement Gaussian convolution in Hi-C data preprocessing, an Inline graphic kernel is applied to the contact matrix, where k defines the local neighborhood over which interactions are averaged. The kernel assigns weights to each interaction based on a Gaussian function, ensuring that closer interactions contribute more than distant ones. Specifically, the weight function follows the form

graphic file with name d33e776.gif

where i, j represent the relative positions within the kernel, and Inline graphic controls the degree of smoothing. A smaller Inline graphic places most of the weight on immediately adjacent interactions, preserving fine-scale structure, whereas a larger Inline graphic distributes the weight more broadly across distant neighbors, resulting in stronger smoothing. For simplicity and consistency across datasets, we fixed Inline graphic in this study.

Because pseudo-bulk Hi-C data typically exhibit low interaction frequencies, it is important to scale up the interaction frequencies while ensuring that the original interaction frequency dominates the averaged interaction frequency. To achieve this, the weights w(i, j) are normalized as w(i, j)/w(0, 0), where w(0, 0) is the weight at the center of the Gaussian convolution kernel. Applying systematically across the Hi-C contact matrix, Gaussian convolution enhances interactions frequencies while preserving biologically meaningful patterns.

PB-DiffHiC (merged-replicate setup): optimized parametric hypothesis testing

PB-DiffHiC models Hi-C contact frequencies using the Poisson distribution, which naturally scales with total interaction frequencies and remains robust in datasets with limited replicates, as is common in Hi-C experiments. While methods such as HiC-DC+ and FIND also use Poisson-based models for detecting differential chromatin interactions in bulk Hi-C data, they require at least two biological replicates per condition to estimate variability. PB-DiffHiC extends this framework by employing a conditional probability-based strategy to support both individual and merged replicates per condition. Normalization is essential for comparing Hi-C contact matrices between conditions. Unlike existing methods that estimate scaling factors separately from hypothesis testing, PB-DiffHiC integrates these steps by leveraging P-values from stable short-range interactions. This approach enhances normalization accuracy while maintaining a unified statistical framework. Its flexibility allows PB-DiffHiC to be applied to a broad range of single-cell and bulk Hi-C studies.

First, we introduce the mathematical notations. Let Inline graphic denote the biological condition. Let Inline graphic represent the Hi-C contact matrix under condition c, obtained by merging replicates and applying Gaussian convolution, Let Inline graphic be the random variable representing the contact frequency between chromosomal bin i and chromosomal bin j under condition c. Let Inline graphic denote the observed contact frequency, which corresponds to the ij-th element of Inline graphic and is a realization of the random variable Inline graphic. Assume that Inline graphic is an unknown parameter proportional to the expected value of Inline graphic and is not affected by sequencing depth.

The identification of whether chromatin interaction (i, j) is differential between conditions is formulated as a hypothesis testing problem:

graphic file with name d33e922.gif

Denote the total number of observed contact frequencies in condition c as Inline graphic Assuming that the total observed contact frequencies are distributed among interactions with probability proportional to Inline graphic, the expectation of the random variable Inline graphic is

graphic file with name d33e950.gif

The hypothesis test can be rewritten in terms of the expectation of Inline graphic:

graphic file with name d33e963.gif

Define Inline graphic as the unknown scaling factor for condition 2 relative to condition 1. Assuming that the random variable Inline graphic follows a Poisson distribution,

graphic file with name d33e982.gif

The hypothesis testing can be further reformulated as

graphic file with name d33e989.gif

Under the null hypothesis, given that the sum of Inline graphic and Inline graphic is fixed at Inline graphic, the random variable Inline graphic follows a binomial distribution with probability mass function

graphic file with name d33e1020.gif

where Inline graphic, the probability parameter Inline graphic is a function of the unknown scaling factor s, given by

graphic file with name d33e1042.gif

Conceptually, greater differences in absolute value between Inline graphic and Inline graphic than the observed difference provide evidence against the null hypothesis. Under the null hypothesis, this can be reformulated as comparing the deviation between normalization-adjusted Inline graphic from its expectation under the conditional binomial distribution with the observed deviation. A two-sided P-value is computed as

graphic file with name d33e1070.gif

In this formula, Inline graphic is the deviation of random variable Inline graphic from the expected value under null hypothesis, while Inline graphic represents the observed deviation. Both terms are normalized using scaling factor s. P-value is computed using the conditional binomial distribution.

Next section explains how to estimate the unknown scaling factor s and compute the exact P-value Inline graphic. After computing P-value for every chromatin interaction, P-values are adjusted for multiple comparisons using the Benjamini-Hochberg (BH) method.

PB-DiffHiC (merged-replicate setup): estimating the scaling factor s using Inline graphic of short-range chromatin interactions

To account for differences in sequencing depth and experimental variability, motivated by Zhou et al. [27], PB-DiffHiC estimates the scaling factor s by leveraging short-range interactions, defined as interactions spanning up to five chromosomal bins in this paper. Unlike alternative methods that apply global scaling or per-distance normalization, PB-DiffHiC estimates the scaling factor by ensuring that the false discovery rate of these interactions aligns with the nominal level under the null hypothesis. Since short-range interactions reflect self-ligation events rather than spatial chromatin interactions at 10 Kb resolution, they are expected to remain stable between conditions. Median contact frequency differences at short genomic distances are comparable to those at longer distances (Supplementary Fig. 1), reinforcing the use of short-range interactions as a reliable reference for estimating s and improving the accuracy of differential chromatin interaction detection.

Under the null hypothesis, P-values Inline graphic, for short-range interactions, where Inline graphic, are expected to follow a uniform distribution on (0,1). Given a significance level Inline graphic, the false discovery rate for these interactions should be close to the nominal level Inline graphic if s is correctly specified. Thus, s is estimated by minimizing the following objective function:

graphic file with name d33e1184.gif

where m is the total number of short-range interactions satisfying Inline graphic. A grid search is performed over a range of possible values for s, and the value that minimizes the objective function is chosen as the estimate Inline graphic. Note that the theoretical value of s does not depend on Inline graphic.

Once Inline graphic is determined, the exact P-values for all interactions are computed by substituting Inline graphic and BH-adjusted to identify significant differential chromatin interactions.

PB-DiffHiC (merged-replicate setup): determining the condition with higher interaction frequencies

To determine which condition exhibits higher chromatin interaction frequency for each significant differential interaction connecting bin i and bin j, we compare the normalized expectations under the assumption of Poisson distributions. Specifically, under the null hypothesis Inline graphic, we assume that their expected values satisfying

graphic file with name d33e1251.gif

Here, the ratio between unknown expected values Inline graphic and Inline graphic are replaced with the ratio between the corresponding observed interaction frequencies Inline graphic and Inline graphic, which is its point estimate. The unknown scaling factor s is substituted with its estimate Inline graphic. Then Inline graphic is compared with Inline graphic If Inline graphic is greater than Inline graphic, the interaction is considered to have a higher frequency in condition 1. Otherwise, the higher interaction frequency is in condition 2.

PB-DiffHiC (two-replicate setup)

The two-replicate setup accounts for within-condition variability by incorporating two independent Hi-C contact maps per condition. To integrate this setup into PB-DiffHiC, it is transformed into a merged-replicate setup using a weighted summation approach. The first contact map is treated as the reference, while the remaining three are iteratively compared against it to estimate replicate-specific scaling factors Inline graphic, Inline graphic, and Inline graphic, which adjust for differences in sequencing depth and technical variability.

Given the Hi-C contact matrix Inline graphic for condition c and replicate r, the observed contact frequency Inline graphic is a realization of the Poisson-distributed random variable Inline graphic with expected frequency Inline graphic. The first contact matrix Inline graphic is treated as the reference matrix representing condition 1, while the remaining three contact matrices, Inline graphic, and Inline graphic, are iteratively treated as condition 2. In the merged-replicate framework of PB-DiffHiC, the scaling factors Inline graphic, Inline graphic, and Inline graphic are estimated respectively.

The sum of the two replicates in condition 1, given by Inline graphic, follows a Poisson distribution with mean proportional to Inline graphic, where Inline graphic. Similarly, the sum of the two replicates in condition 2, given by Inline graphic, follows a Poisson distribution with mean proportional to Inline graphic. The transformed random variables Inline graphic and Inline graphic are treated as the corresponding variables in the merged-replicate setup.

Under the null hypothesis, conditional on the sum of Inline graphic and Inline graphic being fixed at Inline graphic, the random variable Inline graphic follows a binomial distribution with probability parameter

graphic file with name d33e1479.gif

The P-value is computed accordingly as in the merged-replicate setup.

While this section highlights the case of two replicates per condition, PB-DiffHiC can be extended to datasets with more than two replicates by following the same approach.

Method benchmarking

To evaluate the performance of PB-DiffHiC in detecting differential chromatin interactions in pseudo-bulk Hi-C data, we benchmarked against three widely used Hi-C differential analysis methods: FIND, Selfish, and HiC-DC+. These methods represent different statistical and computational approaches to identifying differential chromatin interactions. We first briefly describe each method, followed by tailored experimental design for a fair comparison on the hypothesis testing for differential chromatin interaction detection.

FIND is among the first methods to explicitly incorporate spatial dependencies among neighboring chromatin interactions [13]. It assumes that a true differential chromatin interaction exhibit consistent changes in both its own interaction frequency and its neighboring interactions. However, FIND requires Hi-C replicates, limiting its applicability to pseudo-bulk Hi-C data. Selfish adopts a different approach by directly comparing merged Hi-C data from each condition rather than analyzing replicates separately [14]. It applies Gaussian convolution to smooth contact maps and captures changes in both interaction frequencies and their surrounding regions. FIND is included in the benchmark analysis using cell-type-specific chromatin loops but excluded in the analysis assessing the agreement between differential chromatin interactions detected using pseudo-bulk and bulk Hi-C data due to high computational-demands in both time and CPU memory. Selfish bypasses explicit normalization by using z-score transformations of interaction frequencies, making it robust to differences in sequencing depth. HiC-DC+ extends earlier RNA-seq-based approaches by incorporating distance-dependent scaling [15], improving normalization over methods like HiC-DC. However, it assumes that interactions are independent, ignoring the spatial dependencies among neighboring interactions, which are fundamental to 3D chromatin architecture. Like FIND, HiC-DC+ requires biological replicates.

For a fair comparison, alternative methods are modified as follows. First, Gaussian convolution is a simple yet effective technique for enhancing the signal-to-noise ratio in sparse pseudo-bulk Hi-C data. While alternative methods are originally designed for bulk Hi-C data, which typically do not require signal enhancement, pseudo-bulk Hi-C data smoothed by Gaussian convolution is used as input for all methods. This eliminate any potential advantages PB-DiffHiC may gain from Gaussian convolution smoothing, ensuring a consistent preprocessing step across methods. To assess the specific contribution of Gaussian convolution, we also conducted an ablation analysis for all methods, comparing performance with and without this smoothing preprocessing (Supplementary Table 1). Second, each method applies specific filtering criteria to select interactions for hypothesis testing, leading to variations in the number of tested chromatin interactions. To standardize the set of chromatin interactions tested, non-filtered interactions are used as the reference list, and missing P-values are imputed as 1. Third, HiC-DC+ follows a two-step framework: first, identifying significant chromatin interactions within each condition, and second, testing the union of significant chromatin interactions across conditions for differential chromatin interactions. The first step substantially narrows the search space for differential chromatin interactions, which is disadvantages in method benchmarking. To address this, all interactions are considered significant interactions within each condition in the first step, ensuring that the full set of interactions is tested for differential chromatin interactions between conditions.

Supplementary Information

Supplementary Material 1. (796.4KB, pdf)

Acknowledgements

We thank the anonymous reviewers for their constructive comments and valuable suggestions, which helped improve the clarity and quality of this manuscript.

Authors'contributions

Yan Zhou and Dechao Tian conceived the study, developed the methodology, supervised the research, and acquired funding. Liuting Tan and Jiadi Zhu implemented the software. Formal analysis was performed by Liuting Tan, Yaohua Hu, Yutong Fei, and Ming Gu. The original manuscript was drafted by Liuting Tan, Jiadi Zhu, Yan Zhou, Yaohua Hu, and Dechao Tian. Dechao Tian reviewed and edited the manuscript. All authors read and approved the final version of the manuscript.

Funding

This work was supported by the National Natural Science Foundation of China [12271536] to D.T.; National Natural Science Foundation of China [12222112] and Shenzhen Science and Technology Program [RCJC20221008092753082] to Y.H.; Natural Science Foundation of Guangdong Province of China [2023A1515011399, 2024A1515012037] to Y.Z.

Data availability

The source code of PB-DiffHiC is publicly available at https://github.com/Tian-Dechao/PB-DiffHiC and a reproducible computational capsule is provided via Code Ocean at https://codeocean.com/capsule/5307439/tree. All datasets used in this study are publicly accessible. The scHi-C data for 94 mouse embryonic stem cells (mESCs) and 188 mouse neuron progenitor cells (NPCs) are downloaded from the Gene Expression Omnibus (GEO) under accession number GSE210585 [16]. The matched bulk Hi-C data for mESC and NPC are downloaded from GEO under accession number GSE94452 [23]. Additionally, scHi-C data for hippocampal CA1 pyramidal neurons (CA1) and dentate gyrus (DG) cells are downloaded under accession number GSE156683 [24].

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.

Footnotes

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Yan Zhou and Yaohua Hu contributed equally to this work.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supplementary Material 1. (796.4KB, pdf)

Data Availability Statement

The source code of PB-DiffHiC is publicly available at https://github.com/Tian-Dechao/PB-DiffHiC and a reproducible computational capsule is provided via Code Ocean at https://codeocean.com/capsule/5307439/tree. All datasets used in this study are publicly accessible. The scHi-C data for 94 mouse embryonic stem cells (mESCs) and 188 mouse neuron progenitor cells (NPCs) are downloaded from the Gene Expression Omnibus (GEO) under accession number GSE210585 [16]. The matched bulk Hi-C data for mESC and NPC are downloaded from GEO under accession number GSE94452 [23]. Additionally, scHi-C data for hippocampal CA1 pyramidal neurons (CA1) and dentate gyrus (DG) cells are downloaded under accession number GSE156683 [24].

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