Loopsim: Enrichment Analysis of Chromosome Conformation Capture with Fast Empirical Distribution Simulation

Summary: Gene regulation is intricately influenced by the three-dimensional organization of the ge- nome. In particular, chromatin can exist in loop structures that enable long-range regulatory interac- tions. By utilizing chromosome conformation capture techniques such as Hi-C, valuable information regarding the organization of these loop structures in 3D space can be obtained. While functional/fea- ture enrichment has become a standard downstream analysis for different genomic data to provide biological context, tools that developed specifically for high throughput ass ays capturing chromo- some conformation are relatively limited. Here, we present Loopsim, a command-line application that performs enrichment analysis on Hi-C loop profiles against user-defined regions. Loopsim efficiently simulates a background distribution using a distinctive sampling approach that considers loop size, intervals, loop-loop distances, and structure; it then computes loop-level statistics based on the em- pirical null distribution. Availability: Loopsim is a Python package available via PyPI ( https://pypi.org/project/loopsim) and the source code is available on GitHub (https://github.com/CutaneousBioinf/Loopsim) under the MIT license. Contact: [email protected] 1 Introduction The organization of the genome plays a crucial role in regulating gene transcription, with chromatin loops connecting distant genomic sites to facilitate spatial proximity in three-dimensional space (Kadauke and Blobel, 2009). Chromosome conformation capture methods , such as Hi-C, can generate high-quality data for chromatin organization (Berkum, et al., 2010). Multiple high throughput chromosome confor- mation methods including promoter capture Hi -C, ChIA-PET, HiChIP, and PLAC-seq have been developed to identify loops associated with gene regulation (Durand, et al., 2016; Roayaei Ardakany, et al., 2020; Wolff, et al., 2022). These chromosome conformation capture methods have significant implications in uncovering the mechanisms of gene reg- ulation, including the interpretation of genetic signals, and revealing the structure of the regulatory complex as well as the gene target s of en- hancer regions (Sahlén, et al., 2021; Shi, et al., 2021) . Current down- stream analyses include chromatin loop and topologically associated do- main identifications, as well as differential loop analysis and chromatin compartment separations (Han and Wei, 2017). However, despite the present success in functional enrichment approaches developed for dif- ferent genomics and epigenomics platforms (Huang, et al., 2009), there are limited tools that integrate functional annotations to provide the bio- logical meanings of loops identified in Hi -C experiments. In this study, we present Loopsim, a tool designed to detect the sta- tistical significance of overlaps between identified chromatin loops and genomic regions of interest (e.g. GWAS signal; regulatory regions iden- tified in ChIP-seq or ATAC-seq). In contrast to existing tools (Table 1), Loopsim is packaged as a pipeline for enrichment analysis that includes Hi-C data validation, simulation, and visualization. It simulates the em- pirical null distribution of Hi-C loop profiles as background for enrich- ment analysis. The background simulation algorithm takes into consider- ation factors including loop size, intervals, loop-loop distances, and structural characteristics, while also implementing logic to avoid suc- cumbing to bias introduced as a result of particular characteristics of the inputted Hi-C loop profile. was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprint (whichthis version posted June 4, 2024. ; https://doi.org/10.1101/2024.06.03.595407doi: bioRxiv preprint Table 1. Comparison of Loopsim with existing chromosome conformation capture enrichment analysis tools Enrichment test Tool Input format Background Statistics Considering loop-associated variables Citation Loopsim BEDPE / BED Dataset matching simulated loops Empirical p-value ✓ HIPPIE BED Models the number of read pairs for each loop-facili- tated interaction with negative binomial distribution Negative binomial test ✗ (Hwang, et al., 2015) cLoops BEDPE Uses permuted local background of each loop as

for that loop Consensus of hypergeometric, Poisson, and binomial tests ✗ (Cao, et al., 2020) HiC-DC BAM Fits read counts for each interaction to a hurdle nega- tive binomial model Binomial test ✗ (Carty, et al., 2017) HiCdat BAM Interaction frequencies of randomly selected regions of loops Empirical p-value ✗ (Schmid, et al., 2015) 2 Implementation and Features Loopsim is a command line program capable of working with Hi -C loop profiles, which are loop-calling results from standard Hi -C data pro- duced with tools such as HICCUPS (Rao, et al., 2014) or Mustache (Roayaei Ardakany, et al., 2020) . Loopsim provides a pipeline (Figure 1) that comprises input data preprocessing, identification of chromatin loops whose end regions overlap with genomic regions of interest, simu- lation of a background distribution of Hi -C loop profiles, and enrichment analysis of the original Hi-C loop profile against said background distri- bution. Furthermore, Loopsim is flexible concerning the data it can pro- cess, in that it can handle an arbitrary set of chromosomes and associated loci information. Validation. Prior to running the rest of the pipeline, Loopsim per- forms quality control on the input Hi -C loop profile, including validation checks to exclude chromatin loops that start and end on different chro- mosomes (Kadauke and Blobel, 2009) and filter out unrealistically long loops (e.g. ≥100 kb by default (Jackson, et al., 1990)); these values are user-configurable. Loopsim also checks and performs filtering for chro- matin loops with differently sized end regions and for overlapping end regions, both conditions potentially caused by data processing errors. After all checks are complete, Loopsim sorts the chromatin loops of the Hi-C loop profile by chromosome and the start locus of the loop. Next, Loopsim can be used to generate a simulated empirical back- ground distribution of Hi-C loop profiles against which to conduct en- richment analysis (Figure 1); alternatively, Loopsim can be used to per- form a cursory analysis of the inputted Hi -C loop profile. Cursory analysis of a Hi-C loop profile without simulated em- pirical background distribution. Loopsim calculates an “enrichment score” for the input Hi-C loop profile, denoting the proportion of chro- matin loops that overlap with genomic features of interest while also providing a list of the overlapping loops. Such information would inform a user, as a preliminary analysis step, whether their Hi -C data contains loops with potential for significant genomic interactions. Enrichment analysis of a Hi-C loop profile with a simulated empirical background distribution. Using the method described in Section 3, Loopsim generates a simulated empirical background distri- bution of Hi-C loop profiles to a user-specified size. Then, Loopsim per- forms a one-tailed difference of means test, comparing the average pro- portion of chromatin loops overlapping regions of interest in the empiri- cal null distribution with the proportion of overlapping loops in the input Hi-C loop profile. Loopsim employs this test to ascertain if the real Hi -C loop profile exhibits a significantly higher proportion of chromatin loops with ends overlapping genomic regions of interest compared to the back- ground distribution, and the result of this test is a measure of the Fig 1. Loopsim pipeline was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprint (whichthis version posted June 4, 2024. ; https://doi.org/10.1101/2024.06.03.595407doi: bioRxiv preprint Loopsim enrichment of the original Hi-C loop profile. Loopsim can also compute the enrichment statistic parametrically, and a normality test is provided. 3 Simulation Algorithm In order to generate a simulated background distribution of Hi -C loop profiles, Loopsim employs the following partially stochastic proce- dure (Figure 2) to simulate an individual Hi-C loop profile, and simply repeats it a user-specified number of times. To create one simulated Hi-C loop profile, Loopsim iterates loop by loop through the original Hi-C loop profile and generates corresponding loops for the simulated Hi -C loop profile. To generate each simulated chromatin loop, Loopsim uses one of two chromatin loop simulation methods , random simulation or nonrandom simulation. For Loopsim to perform nonrandom simulation, the distance between the real chromatin loop and the previous real chro- matin loop must be less than 1 Mb. This condition exists under the as- sumption that loci within 1 Mb of each other are more likely to interact with each other (Pennacchio, et al., 2013). As such, we want to retain such arrangements from the real chromatin loops when generating simu- lated chromatin loops. In nonrandom simulation, Loopsim first measures the distance between the first ends of the current and preceding real chro- matin loops. It then copies the previous simulated chromatin loop and positions this copy the same number of base pairs ahead of the previous simulated chromatin loop. In the opposite case that the distance between the real chromatin loop and the previous real chromatin loop is greater than or equal to 1 Mb, Loopsim performs random simulation, where it copies the previous real loop and positions the copy at a random locus within the same chromosome. 4 Results Figure 3A presents an example output from our Loopsim p rogram. To evaluate Loopsim's performance, we used a Hi -C loop profile gener- ated by deep sequencing Hi-C libraries (~1 billion reads/reaction). Then, using a contact map combining resolutions of 5Kb and 10Kb (resolution in this case meaning the length of the interval of either loop end), we identified Hi-C loops in each library using Mustache (Roayaei Ardakany, et al., 2020). The Hi-C loop profile was enriched for GWAS loci for psoriasis (Dand, et al., 2023). We ran Loopsim on this Hi-C loop profile and created simulated Hi-C background distributions of various sizes. Relative to the simulated background distribution, the experimen- tally derived Hi-C loop profile showed a higher degree of enrichment for psoriasis loci, as shown by the experimental data having a greater over- lapping proportion (Figure 3B). This observation underscores the accu- racy of Loopsim in simulating an appropriate background distribution. Furthermore, we observed that Loopsim has a runtime approximately lin- early proportional to the number of Hi-C loops in the dataset. We can also see that after approximately 2,000 simulations, Loopsim’s simulated

distribution became approximately normal. We suggest that the user must specify at least appr oximately 2,000 simulations to gener- ate a statistically normal, realistic simulated background distribution (Figure 3C). 5 Conclusions We developed Loopsim to allow researchers to generate an accurate simulated empirical background distribution for Hi-C data analysis by considering loop size, intervals, distances, and structural characteristics. Applied to Hi-C data enriched for psoriasis, Loopsim successfully identified significant chromatin loops overlapping with GWAS loci, showcasing its potential for revealing meaningful genomic interactions. Loopsim’s user-friendly interface, comprehensive d ata validation, and robust end-to-end analysis pipeline make Loopsim an asset to genomic research. By enabling better enrichment a nalysis of Hi- C data, Loopsim can be used to enhance our understanding of 3D genome organization and gene regulation. Fig 2. Pseudocode for Loopsim simulation algorithm was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprint (whichthis version posted June 4, 2024. ; https://doi.org/10.1101/2024.06.03.595407doi: bioRxiv preprint G. Shaked et al.

Berkum, N.L.v., et al. Hi-C: A Method to Study the Three-dimensional Architecture of Genomes. JoVE (Journal of Visualized Experiments) 2010(39):e1869. Cao, Y. , et al. Accurate loop calling for 3D genomic data with cLoops. Bioinformatics 2020;36(3):666-675. Carty, M., et al. An integrated model for detecting significant chromatin interactions from high-resolution Hi-C data. Nature Communications 2017;8(1):15454. Dand, N., et al. GWAS meta-analysis of psoriasis identifies new susceptibility alleles impacting disease mechanisms and therapeutic targets. In.: medRxiv; 2023. Durand, N.C. , et al. Juicer Provides a One -Click System for Analyzing Loop - Resolution Hi-C Experiments. Cell Systems 2016;3(1):95-98. Han, Z. and Wei, G. Computational tools for Hi -C data analysis. Quantitative Biology 2017;5(3):215-225. Huang, D.W., Sherman, B.T. and Lempicki, R.A. Bioinformatics enrichment tools: paths toward the comprehensive functional analysis of large gene lists. Nucleic Acids Research 2009;37(1):1-13. Hwang, Y.-C., et al. HIPPIE: a high-throughput identification pipeline for promoter interacting enhancer elements. Bioinformatics 2015;31(8):1290-1292. Jackson, D.A., Dickinson, P. and Cook, P.R. The size of chromatin loops in HeLa cells. The EMBO Journal 1990;9(2):567-571. Kadauke, S. and Blobel, G.A. Chromatin loops in gene regulation. Biochimica et Biophysica Acta (BBA) - Gene Regulatory Mechanisms 2009;1789(1):17-25. Pennacchio, L.A. , et al. Enhancers: five essential questions. Nature Reviews Genetics 2013;14(4):288-295. Rao, S.S.P., et al. A 3D Map of the Human Genome at Kilobase Resolution Reveals Principles of Chromatin Looping. Cell 2014;159(7):1665-1680. Roayaei Ardakany, A. , et al. Mustache: multi -scale detection of chromatin loops from Hi -C and Micro -C maps using scale -space representation. Genome Biology 2020;21(1):256. Sahlén, P., et al. Chromatin interactions in differentiating keratinocytes reveal novel atopic dermatitis – and psoriasis -associated genes. Journal of Allergy and Clinical Immunology 2021;147(5):1742-1752. Schmid, M.W., Grob, S. and Grossniklaus, U. HiCdat: a fast and easy -to-use Hi-C data analysis tool. BMC Bioinformatics 2015;16(1):277. Shi, C., et al. Chromatin Looping Links Target Genes with Genetic Risk Loci for Dermatological Traits. Journal of Investigative Dermatology 2021;141(8):1975- 1984. Wolff, J., Backofen, R. and Grüning, B. Loop detection using Hi -C data with HiCExplorer. GigaScience 2022;11:giac061. Fig 3. (A): Simulated Hi-C background distributions of different sizes were generated with Loopsim. For each simulation in each distribution, the prop ortion of enriched chromatin loops (those overlapping genomic regions of interest) was calculated. The proportion of enriched chromatin loops was also calculated for the corresponding experimentally produced Hi -C loop profile. (B): A D’Agostino -Pearson test of normality was performed on varying sizes of randomly sampled Hi -C

distributions. A locally weight ed linear regression model was formed to indicate how the typical normality of Loopsim’s simulated Hi -C distributions varies with the number of simulated Hi -C loop profiles in the distribution. (C): Part of the output of the Loopsim analysis as demonstrated in Section 4. The first three columns from the left represent the first end of each chromatin loop, representing the chromosome, first loci, and last loci, respectively. The second three columns represent the last end of each chromatin loop in the same f ormat. The last column represents the regions of interest that each chromatin loop overlaps with. For example, the loop on the second row overlaps with regions 164, 165, 166, and 167, whose details are represented in a separate file. was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprint (whichthis version posted June 4, 2024. ; https://doi.org/10.1101/2024.06.03.595407doi: bioRxiv preprint