Bayesian Inference of Spatial Organizations of Chromosomes

Knowledge of spatial chromosomal organizations is critical for the study of transcriptional regulation and other nuclear processes in the cell. Recently, chromosome conformation capture (3C) based technologies, such as Hi-C and TCC, have been developed to provide a genome-wide, three-dimensional (3D) view of chromatin organization. Appropriate methods for analyzing these data and fully characterizing the 3D chromosomal structure and its structural variations are still under development. Here we describe a novel Bayesian probabilistic approach, denoted as “Bayesian 3D constructor for Hi-C data” (BACH), to infer the consensus 3D chromosomal structure. In addition, we describe a variant algorithm BACH-MIX to study the structural variations of chromatin in a cell population. Applying BACH and BACH-MIX to a high resolution Hi-C dataset generated from mouse embryonic stem cells, we found that most local genomic regions exhibit homogeneous 3D chromosomal structures. We further constructed a model for the spatial arrangement of chromatin, which reveals structural properties associated with euchromatic and heterochromatic regions in the genome. We observed strong associations between structural properties and several genomic and epigenetic features of the chromosome. Using BACH-MIX, we further found that the structural variations of chromatin are correlated with these genomic and epigenetic features. Our results demonstrate that BACH and BACH-MIX have the potential to provide new insights into the chromosomal architecture of mammalian cells.Statistic

Inferring Diploid 3D Chromatin Structures from Hi-C Data

The 3D organization of the genome plays a key role in many cellular processes, such as gene regulation, differentiation, and replication. Assays like Hi-C measure DNA-DNA contacts in a high-throughput fashion, and inferring accurate 3D models of chromosomes can yield insights hidden in the raw data. For example, structural inference can account for noise in the data, disambiguate the distinct structures of homologous chromosomes, orient genomic regions relative to nuclear landmarks, and serve as a framework for integrating other data types. Although many methods exist to infer the 3D structure of haploid genomes, inferring a diploid structure from Hi-C data is still an open problem. Indeed, the diploid case is very challenging, because Hi-C data typically does not distinguish between homologous chromosomes. We propose a method to infer 3D diploid genomes from Hi-C data. We demonstrate the accuracy of the method on simulated data, and we also use the method to infer 3D structures for mouse chromosome X, confirming that the active homolog exhibits a bipartite structure, whereas the active homolog does not

EM algorithm for reconstructing 3D structures of human chromosomes from chromosomal contact data

Recent research suggested that chromosomes have preferred spatial conformations to facilitate necessary long-range interactions and regulations within a nucleus. So that, getting the 3D shape of chromosomes of a genome is very important for understanding how the genome folds and how the genome interact, which can know more about the secrete of life. The introduction of the chromosome conformation capture (3C) based techniques has risen the development of construct the 3D structure of chromosome model. Several works have been done to build the 3D model, among which can be divided into two groups one is consensus methods in early work, the other is ensemble method. In this paper I proposed an ensemble method for reconstructing the 3D structure of chromosome structure. First step is to process Hi-C data, and then do normalization. After that I applied the Bayesian inference model to get an objective function. Finally I used EM based algorithm along with using gradient descent method which is applied in expectation step. I applied the objective function and the optimization method to all 23 Hi-C chromosomal data at a resolution of 1MB

Inferring Single-Cell 3D Chromosomal Structures Based On the Lennard-Jones Potential

Reconstructing three‐dimensional (3D) chromosomal structures based on single‐cell Hi‐C data is a challenging scientific problem due to the extreme sparseness of the single‐cell Hi‐C data. In this research, we used the Lennard‐Jones potential to reconstruct both 500 kb and high‐resolution 50 kb chromosomal structures based on single‐cell Hi‐C data. A chromosome was represented by a string of 500 kb or 50 kb DNA beads and put into a 3D cubic lattice for simulations. A 2D Gaussian function was used to impute the sparse single‐cell Hi‐C contact matrices. We designed a novel loss function based on the Lennard‐Jones potential, in which the ε value, i.e., the well depth, was used to indicate how stable the binding of every pair of beads is. For the bead pairs that have single‐cell Hi‐C contacts and their neighboring bead pairs, the loss function assigns them stronger binding stability. The Metropolis–Hastings algorithm was used to try different locations for the DNA beads, and simulated annealing was used to optimize the loss function. We proved the correctness and validness of the reconstructed 3D structures by evaluating the models according to multiple criteria and comparing the models with 3D‐FISH data

Integrative modelling of cellular assemblies

A wide variety of experimental techniques can be used for understanding the precise molecular mechanisms underlying the activities of cellular assemblies. The inherent limitations of a single experimental technique often requires integration of data from complementary approaches to gain sufficient insights into the assembly structure and function. Here, we review popular computational approaches for integrative modelling of cellular assemblies, including protein complexes and genomic assemblies. We provide recent examples of integrative models generated for such assemblies by different experimental techniques, especially including data from 3D electron microscopy (3D-EM) and chromosome conformation capture experiments, respectively. We highlight general concepts in integrative modelling and discuss the need for careful formulation and merging of different types of information

SCL: A Lattice-Based Approach To Infer 3D Chromosome Structures From Single-Cell Hi-C Data

Motivation: In contrast to population-based Hi-C data, single-cell Hi-C data are zero-inflated and do not indicate the frequency of proximate DNA segments. There are a limited number of computational tools that can model the 3D structures of chromosomes based on single-cell Hi-C data. Results: We developed single-cell lattice (SCL), a computational method to reconstruct 3D structures of chromosomes based on single-cell Hi-C data. We designed a loss function and a 2 D Gaussian function specifically for the characteristics of single-cell Hi-C data. A chromosome is represented as beads-on-a-string and stored in a 3 D cubic lattice. Metropolis–Hastings simulation and simulated annealing are used to simulate the structure and minimize the loss function. We evaluated the SCL-inferred 3 D structures (at both 500 and 50 kb resolutions) using multiple criteria and compared them with the ones generated by another modeling software program. The results indicate that the 3 D structures generated by SCL closely fit single-cell Hi-C data. We also found similar patterns of trans-chromosomal contact beads, Lamin-B1 enriched topologically associating domains (TADs), and H3K4me3 enriched TADs by mapping data from previous studies onto the SCL-inferred 3 D structures. Availability and Implementation: The C++ source code of SCL is freely available at http://dna.cs.miami.edu/SCL/

FastHiC: a fast and accurate algorithm to detect long-range chromosomal interactions from Hi-C data

Motivation: How chromatin folds in three-dimensional (3D) space is closely related to transcription regulation. As powerful tools to study such 3D chromatin conformation, the recently developed Hi-C technologies enable a genome-wide measurement of pair-wise chromatin interaction. However, methods for the detection of biologically meaningful chromatin interactions, i.e. peak calling, from Hi-C data, are still under development. In our previous work, we have developed a novel hidden Markov random field (HMRF) based Bayesian method, which through explicitly modeling the non-negligible spatial dependency among adjacent pairs of loci manifesting in high resolution Hi-C data, achieves substantially improved robustness and enhanced statistical power in peak calling. Superior to peak callers that ignore spatial dependency both methodologically and in performance, our previous Bayesian framework suffers from heavy computational costs due to intensive computation incurred by modeling the correlated peak status of neighboring loci pairs and the inference of hidden dependency structure

Deciphering hierarchical organization of topologically associated domains through change-point testing.

BACKGROUND: The nucleus of eukaryotic cells spatially packages chromosomes into a hierarchical and distinct segregation that plays critical roles in maintaining transcription regulation. High-throughput methods of chromosome conformation capture, such as Hi-C, have revealed topologically associating domains (TADs) that are defined by biased chromatin interactions within them. RESULTS: We introduce a novel method, HiCKey, to decipher hierarchical TAD structures in Hi-C data and compare them across samples. We first derive a generalized likelihood-ratio (GLR) test for detecting change-points in an interaction matrix that follows a negative binomial distribution or general mixture distribution. We then employ several optimal search strategies to decipher hierarchical TADs with p values calculated by the GLR test. Large-scale validations of simulation data show that HiCKey has good precision in recalling known TADs and is robust against random collisions of chromatin interactions. By applying HiCKey to Hi-C data of seven human cell lines, we identified multiple layers of TAD organization among them, but the vast majority had no more than four layers. In particular, we found that TAD boundaries are significantly enriched in active chromosomal regions compared to repressed regions. CONCLUSIONS: HiCKey is optimized for processing large matrices constructed from high-resolution Hi-C experiments. The method and theoretical result of the GLR test provide a general framework for significance testing of similar experimental chromatin interaction data that may not fully follow negative binomial distributions but rather more general mixture distributions

Routes for breaching and protecting genetic privacy

We are entering the era of ubiquitous genetic information for research, clinical care, and personal curiosity. Sharing these datasets is vital for rapid progress in understanding the genetic basis of human diseases. However, one growing concern is the ability to protect the genetic privacy of the data originators. Here, we technically map threats to genetic privacy and discuss potential mitigation strategies for privacy-preserving dissemination of genetic data.Comment: Draft for comment

Data mining and machine learning methods for chromosome conformation data analysis

Sixteen years after the sequencing of the human genome, the Human Genome Project (HGP), and 17 years after the introduction of Chromosome Conformation Capture (3C) technologies, three-dimensional (3-D) inference and big data remains problematic in the field of genomics, and specifically, in the field of 3C data analysis. Three-dimensional inference involves the reconstruction of a genome's 3D structure or, in some cases, ensemble of structures from contact interaction frequencies extracted from a variant of the 3C technology called the Hi-C technology. Further questions remain about chromosome topology and structure; enhancer-promoter interactions; location of genes, gene clusters, and transcription factors; the relationship between gene expression and epigenetics; and chromosome visualization at a higher scale, among others. In this dissertation, four major contributions are described, first, 3DMax, a tool for chromosome and genome 3-D structure prediction from H-C data using optimization algorithm, second, GSDB, a comprehensive and common repository that contains 3D structures for Hi-C datasets from novel 3D structure reconstruction tools developed over the years, third, ClusterTAD, a method for topological associated domains (TAD) extraction from Hi-C data using unsupervised learning algorithm. Finally, we introduce a tool called, GenomeFlow, a comprehensive graphical tool to facilitate the entire process of modeling and analysis of 3D genome organization. It is worth noting that GenomeFlow and GSDB are the first of their kind in the 3D chromosome and genome research field. All the methods are available as software tools that are freely available to the scientific community.Includes bibliographical reference