Mark Robert Segal

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.

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.

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 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. Illustration makes recourse to comparisons between four different cell types.

Summary: 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.

SUMMARY: Traumatic spinal cord injury (SCI) produces a complex syndrome that is expressed across multiple endpoints ranging from molecular and cellular changes to functional behavioral deficits. Effective therapeutic strategies for CNS injury are therefore likely to manifest multi-factorial effects across a broad range of biological and functional outcome measures. Thus, multivariate analytic approaches are needed to capture the linkage between biological and neurobehavioral outcomes. Injury-induced neuroinflammation (NI) presents a particularly challenging therapeutic target, since NI is involved in both degeneration and repair ^1,2 . Here, we used big-data integration and large-scale analytics to examine a large dataset of preclinical efficacy tests combining 5 different blinded, fully counter-balanced treatment trials for different acute anti-inflammatory treatments for cervical spinal cord injury in rats. Multi-dimensional discovery, using topological data analysis ³ (TDA) and principal components analysis (PCA) revealed that only one showed consistent multidimensional syndromic benefit: intrathecal application of recombinant soluble TNFα receptor 1 (sTNFR1), which showed an inverse-U dose response efficacy. Using the optimal acute dose, we showed that clinically-relevant 90 min delayed treatment profoundly affected multiple biological indices of NI in the first 48 hrs after injury, including reduction in pro-inflammatory cytokines and gene expression of a coherent complex of acute inflammatory mediators and receptors. Further, a 90 min delayed bolus dose of sTNFR1 reduced the expression of NI markers in the chronic perilesional spinal cord, and consistently improved neurological function over 6 weeks post SCI. These results provide validation of a novel strategy for precision preclinical drug discovery that is likely to improve translation in the difficult landscape of CNS trauma, and confirm the importance of TNFα signaling as a therapeutic target.

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 d hyperrefata 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.

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 ofknearest neighbors (kNNs). More generally, we anticipate a monotone decreasing relationship between StatDn values andkNN 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 donotprovide 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.

Background Three dimensional (3D) genome spatial organization is critical for numerous cellular functions, including transcription. Genome architecture had been difficult to elucidate but the suite of chromatin conformation capture assays, notably Hi-C transformed understanding of chromatin organization, yielding numerous insights, many deriving from 3D reconstructions. In part, these benefits derive from the ability to superpose genomic features on the reconstruction. However, the advantages of 3D structure-based analyses are clearly conditional on the accuracy of the corresponding reconstruction, which is difficult to assess due to an absence of gold standards. Proponents of competing reconstruction algorithms have evaluated their accuracy by recourse to simulation of toy structures and limited FISH imaging that 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 remains 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, 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 ( k NNs). More generally, we anticipate a monotone decreasing relationship between StatDn values and k NN distances. After initially evaluating the reproducibility of StatDns across replicate Hi-C data sets, we use this implied StatDn - k NN 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.

Three dimensional (3D) genome spatial organization is critical for numerous cellular functions, including transcription, while certain conformation-driven structural alterations are frequently oncogenic. Genome conformation had been difficult to elucidate but the advent chromatin conformation capture assays, notably Hi-C, has transformed understanding of chromatin architecture and yielded numerous biological insights. Although most of these findings have flowed from analysis of proximity data produced by these assays, added value in generating 3D reconstructions has been demonstrated, deriving, in part, from superposing genomic features on the reconstruction. However, advantages of 3D structure-based analyses are clearly conditional on the accuracy of the attendant reconstructions, which is difficult to assess. Proponents of competing reconstruction algorithms have evaluated their accuracy by recourse to simulation of toy structures and/or limited fluorescence in situ hybridization (FISH) imaging that features a handful of low resolution probes. Accordingly, new methods of reconstruction accuracy assessment are needed. Here we utilize two recently devised assays to develop methodology for assessing 3D reconstruction accuracy. Multiplex FISH increases the number of probes by an order of magnitude and hence the number of inter-probe distances by two orders, providing sufficient information for structure-level evaluation via mean-squared deviations (MSD). Crucially, underscoring multiplex FISH applications are large numbers of coordinate-system aligned replicates that provide the basis for a referent distribution for MSD statistics. Using this system we show that reconstructions based on Hi-C data for IMR90 cells are accurate for some chromosomes but not others. The second new assay, genome architecture mapping, utilizes large numbers of thin cryosections to obtain a measure of proximity. We exploit the planarity of the cryosections – not used in inferring proximity – to obtain measures of reconstruction accuracy, with referents provided via resampling. Application to mouse embryonic stem cells shows reconstruction accuracies that vary by chromosome. We have developed methods for assessing the accuracy of 3D genome reconstructions that exploit features of recently advanced multiplex FISH and genome architecture mapping assays. These approaches can help overcome the absence of gold standards for making such assessments which are important in view of the considerable uncertainties surrounding 3D genome reconstruction.

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.