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Three-dimensional (3D) genome architecture is critical for numerous cellular processes, including transcription, while certain conformation-driven structural alterations are frequently oncogenic. Inferring 3D chromatin configurations has been advanced by the emergence of chromatin conformation capture assays, notably Hi-C, and attendant 3D reconstruction algorithms. These have enhanced understanding of chromatin spatial organization and afforded numerous downstream biological insights. Until recently, comparisons of 3D reconstructions between conditions and/or cell types were limited to prescribed structural features. However, multiMDS, a pioneering approach developed by Rieber and Mahony (2019). that performs joint reconstruction and alignment, enables quantification of all locus-specific differences between paired Hi-C data sets. By subsequently mapping these differences to the linear (1D) genome the identification of relocalization regions is facilitated through the use of peak calling in conjunction with continuous wavelet transformation. Here, we seek to refine this approach by performing the search for significant relocalization regions in terms of the 3D structures themselves, thereby retaining the benefits of 3D reconstruction and avoiding limitations associated with the 1D perspective. The search for (extreme) relocalization regions is conducted using the patient rule induction method (PRIM). Considerations surrounding orienting structures with respect to compartmental and principal component axes are discussed, as are approaches to inference and reconstruction accuracy assessment. The illustration makes recourse to comparisons between four different cell types., (© The Author 2021. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Background: Methods for inferring the three-dimensional (3D) configuration of chromatin from conformation capture assays that provide strictly pairwise interactions, notably Hi-C, utilize the attendant contact matrix as input. More recent assays, in particular split-pool recognition of interactions by tag extension (SPRITE), capture multi-way interactions instead of solely pairwise contacts. These assays yield contacts that straddle appreciably greater genomic distances than Hi-C, in addition to instances of exceptionally high-order chromatin interaction. Such attributes are anticipated to be consequential with respect to 3D genome reconstruction, a task yet to be undertaken with multi-way contact data. However, performing such 3D reconstruction using distance-based reconstruction techniques requires framing multi-way contacts as (pairwise) distances. Comparing approaches for so doing, and assessing the resultant impact of long-range and multi-way contacts, are the objectives of this study., Results: We obtained 3D reconstructions via multi-dimensional scaling under a variety of weighting schemes for mapping SPRITE multi-way contacts to pairwise distances. Resultant configurations were compared following Procrustes alignment and relationships were assessed between associated Procrustes root mean square errors and key features such as the extent of multi-way and/or long-range contacts. We found that these features had surprisingly limited influence on 3D reconstruction, a finding we attribute to their influence being diminished by the preponderance of pairwise contacts., Conclusion: Distance-based 3D genome reconstruction using SPRITE multi-way contact data is not appreciably affected by the weighting scheme used to convert multi-way interactions to pairwise distances., (© 2023. The Author(s).)

Three-dimensional (3D) genome spatial organization is critical for numerous cellular processes, including transcription, while certain conformation-driven structural alterations are frequently oncogenic. Genome architecture had been notoriously difficult to elucidate, but the advent of the suite of chromatin conformation capture assays, notably Hi-C, has transformed understanding of chromatin structure and provided downstream biological insights. Although many findings have flowed from direct analysis of the pairwise proximity data produced by these assays, there is added value in generating corresponding 3D reconstructions deriving from superposing genomic features on the reconstruction. Accordingly, many methods for inferring 3D architecture from proximity data have been advanced. However, none of these approaches exploit the fact that single chromosome solutions constitute a one-dimensional (1D) curve in 3D. Rather, this aspect has either been addressed by imposition of constraints, which is both computationally burdensome and cell type specific, or ignored with contiguity imposed after the fact. Here, we target finding a 1D curve by extending principal curve methodology to the metric scaling problem. We illustrate how this approach yields a sequence of candidate solutions, indexed by an underlying smoothness or degrees-of-freedom parameter, and propose methods for selection from this sequence. We apply the methodology to Hi-C data obtained on IMR90 cells and so are positioned to evaluate reconstruction accuracy by referencing orthogonal imaging data. The results indicate the utility and reproducibility of our principal curve approach in the face of underlying structural variation., (© The Author 2020. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Background: The spatial configuration of chromosomes is essential to various cellular processes, notably gene regulation, while architecture related alterations, such as translocations and gene fusions, are often cancer drivers. Thus, eliciting chromatin conformation is important, yet challenging due to compaction, dynamics and scale. However, a variety of recent assays, in particular Hi-C, have generated new details of chromatin structure, spawning a number of novel biological findings. Many findings have resulted from analyses on the level of native contact data as generated by the assays. Alternatively, reconstruction based approaches often proceed by first converting contact frequencies into distances, then generating a three dimensional (3D) chromatin configuration that best recapitulates these distances. Subsequent analyses can enrich contact level analyses via superposition of genomic attributes on the reconstruction. But, such advantages depend on the accuracy of the reconstruction which, absent gold standards, is inherently difficult to assess. Attempts at accuracy evaluation have relied on simulation and/or FISH imaging that typically features a handful of low resolution probes. While newly advanced multiplexed FISH imaging offers possibilities for refined 3D reconstruction accuracy evaluation, availability of such data is limited due to assay complexity and the resolution thereof is appreciably lower than the reconstructions being assessed. Accordingly, there is demand for new methods of reconstruction accuracy appraisal., Results: Here we explore the potential of recently proposed stationary distributions, hereafter StatDns, derived from Hi-C contact matrices, to serve as a basis for reconstruction accuracy assessment. Current usage of such StatDns has focussed on the identification of highly interactive regions (HIRs): computationally defined regions of the genome purportedly involved in numerous long-range intra-chromosomal contacts. Consistent identification of HIRs would be informative with respect to inferred 3D architecture since the corresponding regions of the reconstruction would have an elevated number of k nearest neighbors (kNNs). More generally, we anticipate a monotone decreasing relationship between StatDn values and kNN distances. After initially evaluating the reproducibility of StatDns across replicate Hi-C data sets, we use this implied StatDn - kNN relationship to gauge the utility of StatDns for reconstruction validation, making recourse to both real and simulated examples., Conclusions: Our analyses demonstrate that, as constructed, StatDns do not provide a suitable measure for assessing the accuracy of 3D genome reconstructions. Whether this is attributable to specific choices surrounding normalization in defining StatDns or to the logic underlying their very formulation remains to be determined.

The spatial organization of the genome influences cellular function, notably gene regulation. Recent studies have assessed the three-dimensional (3D) co-localization of functional annotations (e.g. centromeres, long terminal repeats) using 3D genome reconstructions from Hi-C (genome-wide chromosome conformation capture) data; however, corresponding assessments for continuous functional genomic data (e.g. chromatin immunoprecipitation-sequencing (ChIP-seq) peak height) are lacking. Here, we demonstrate that applying bump hunting via the patient rule induction method (PRIM) to ChIP-seq data superposed on a Saccharomyces cerevisiae 3D genome reconstruction can discover 'functional 3D hotspots', regions in 3-space for which the mean ChIP-seq peak height is significantly elevated. For the transcription factor Swi6, the top hotspot by P-value contains MSB2 and ERG11 - known Swi6 target genes on different chromosomes. We verify this finding in a number of ways. First, this top hotspot is relatively stable under PRIM across parameter settings. Second, this hotspot is among the top hotspots by mean outcome identified by an alternative algorithm, k-Nearest Neighbor (k-NN) regression. Third, the distance between MSB2 and ERG11 is smaller than expected (by resampling) in two other 3D reconstructions generated via different normalization and reconstruction algorithms. This analytic approach can discover functional 3D hotspots and potentially reveal novel regulatory interactions., (© The Author(s) 2016. Published by Oxford University Press on behalf of Nucleic Acids Research.)

Background: The three-dimensional (3D) configuration of chromosomes within the eukaryote nucleus is an important factor for several cellular functions, including gene expression regulation, and has also been linked with cancer-causing translocation events. While visualization of such architecture remains limited to low resolutions, the ability to infer structures at increasing resolutions has been enabled by recently-devised chromosome conformation capture techniques. In particular, when coupled with next generation sequencing, such methods yield an inventory of genome-wide chromatin contacts or interactions. Various algorithms have been advanced to operate on such contact data to produce reconstructed 3D configurations. Studies have shown that these reconstructions can provide added value over raw interaction data with respect to downstream biological insights. However, only limited, low-resolution reconstructions have been realized for mammals due to computational bottlenecks., Results: Here we propose a two-stage algorithm to partially overcome these computational barriers. The central idea is to initially utilize existing reconstruction techniques on an individual chromosome basis, using intra-chromosomal contacts, and then to relatively position these chromosome-level reconstructions using inter-chromosomal contacts. This two-stage strategy represents a natural approach in view of the within- versus between- chromosome distribution of contacts. It can increase resolution ≈ 20 fold for mouse and human. After describing the algorithm we present 3D architectures for mouse embryonic stem cells and human lymphoblastoid cells. We evaluate the impact of several factors on reconstruction reproducibility and explore a variety of sampling schemes. We further analyze replicate data at differing resolutions obtained from recently devised in situ Hi-C assays. In all instances we demonstrate insensitivity of the whole-genome 3D reconstruction obtained by the two-stage algorithm to the sampling strategy used., Conclusions: Our two-stage algorithm has the potential to significantly increase the resolution of 3D genome reconstructions. The improvements are such that we can progress from 1 Mb resolution to 100 kb resolution, notable since this latter value has been identified as critical to inferring topological domains in analyses performed on the contact (rather than 3D) level.

It is widely recognized that the three-dimensional (3D) architecture of eukaryotic chromatin plays an important role in processes such as gene regulation and cancer-driving gene fusions. Observing or inferring this 3D structure at even modest resolutions had been problematic, since genomes are highly condensed and traditional assays are coarse. However, recently devised high-throughput molecular techniques have changed this situation. Notably, the development of a suite of chromatin conformation capture (CCC) assays has enabled elicitation of contacts-spatially close chromosomal loci-which have provided insights into chromatin architecture. Most analysis of CCC data has focused on the contact level, with less effort directed toward obtaining 3D reconstructions and evaluating the accuracy and reproducibility thereof. While questions of accuracy must be addressed experimentally, questions of reproducibility can be addressed statistically-the purpose of this paper. We use a constrained optimization technique to reconstruct chromatin configurations for a number of closely related yeast datasets and assess reproducibility using four metrics that measure the distance between 3D configurations. The first of these, Procrustes fitting, measures configuration closeness after applying reflection, rotation, translation, and scaling-based alignment of the structures. The others base comparisons on the within-configuration inter-point distance matrix. Inferential results for these metrics rely on suitable permutation approaches. Results indicate that distance matrix-based approaches are preferable to Procrustes analysis, not because of the metrics per se but rather on account of the ability to customize permutation schemes to handle within-chromosome contiguity. It has recently been emphasized that the use of constrained optimization approaches to 3D architecture reconstruction are prone to being trapped in local minima. Our methods of reproducibility assessment provide a means for comparing 3D reconstruction solutions so that we can discern between local and global optima by contrasting solutions under perturbed inputs., (© The Author 2014. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)