3D genome structures are important because they help us understand spatial gene regulation, transcription efficiency, genome interpretation, function implication (ENCODE), disease diagnosis, treatments and drug design. Recent study suggests that the spatial arrangement of chromosomes helps chromosomes to interact with themselves. This phenomenon convinced many researchers of the value of understanding the 3D genome structure, drawing interest to the field of genome modeling. Here we constructed 3D conformations of genomes using chromosomal contact data acquired by using the Hi-C technique. This technique is designed to determine both intra- and inter-chromosomal contacts in an unbiased manner at the whole genome scale. To construct 3D structures of any chromosome we only consider intrachromosomal contacts or interactions. We can think of a chromosome as a necklace with beads threaded together on a string. Now in our case, we can cut the whole chromosome into chunks that are one megabase (1Mb) in size, which gives us loci that we can treat as beads. Using our approach we can construct 3D structures of genomes at 1Mb scale by plotting the 3D coordinates of each 1Mb region and then connecting them. In a 3D modeling problem, it is crucial to initialize the starting model before using any optimization technique. So at first we try to initialize the coordinates using growth step which provides a probabilistic approach in determining their location. Chromatin that is not compressed into the dense chromosome form still resides in a globular shaped nucleus, suggesting a spherical model as a starting model for the smaller chromosomes. For larger chromosomes, former initialization is used as they have more regions for a specific resolution (i.e. 1Mb). After initialization, we apply two widely known optimization techniques, simulated annealing and genetic algorithms. Our novel scoring function allows optimization procedures to satisfy more intra-chromosomal contacts and non-contacts as well as some additional constraints. To perturb the position of the regions, as is mandatory for modeling optimization algorithms, the adaptation technique is used. This technique tries to fix the position of each region with high contact or noncontact satisfaction. This approach is inspired by similar work for proteins and can generate an ensemble of structures very quickly. The models generated are then compared with the published results of the MCMC5C method. It is found that in all cases our method produces models that are superior to the MCMC5C models. We present some visualization techniques to show how many contacts/non-contacts are satisfied/unsatisfied and also derive some simple yet powerful scoring measurements to evaluate widely known long range contacts. The robustness of the method is measured by convergence testing and recovering capability. Finally, we examine our final model for compartment features that Lieberman et al. suggested exist in chromosomes 14 and 22. We found those features to exist in our models as well, which validates our method.

This book provides a timely summary of physical modeling approaches applied to biological datasets that describe conformational properties of chromosomes in the cell nucleus. Chapters explain how to convert raw experimental data into 3D conformations, and how to use models to better understand biophysical mechanisms that control chromosome conformation. The coverage ranges from introductory chapters to modeling aspects related to polymer physics, and data-driven models for genomic domains, the entire human genome, epigenome folding, chromosome structure and dynamics, and predicting 3D genome structure.

This dissertation summarizes my graduate work on the structure and organization of mouse genome during preimplantation development. My research is divided into three different areas, which I will discuss in turn. To begin, I will discuss my collaborative work on parental-to-embryo switch of chromosome organization during critical stages of early development. Notably, both paternal and maternal epigenomes undergo significant modifications following fertilization. Recent epigenomic studies have revealed the extraordinary chromatin landscapes found in oocytes, sperm, and early preimplantation embryos, including atypical histone modification patterns and differences in chromosome organization and accessibility. However, these studies reached polar opposite conclusions: the global absence of local topological-associated domains (TADs) in gametes and their appearance in the embryo versus the zygote's pre-existence of TADs and loops. The issues of whether parental structures can be inherited in the newly formed embryo and how these structures may be related to allele-specific gene regulation remain unresolved. To address this question, we use an optimized single cell high-throughput chromosome conformation capture (HiC) protocol to map genomic interactions for each parental genome (including the X chromosome) during mouse preimplantation. We integrate chromosome organization with allelic expression states and chromatin marks and demonstrate that after fertilization, higher-order chromatin structure is associated with an allele specific enrichment of histone H3 lysine 27 methylation. These early parental-specific domains are associated with gene repression and contribute to parentally biased gene expression-including newly described transiently imprinted loci. Additionally, we observe that these domains emerge in a non-parental-specific manner during the second wave of genome assembly. Finally, we discover that these domains are lost as genes are silenced on the paternal X chromosome but persist in regions that are not inactivated by the X chromosome. These findings highlight the complexities of three-dimensional genome organization and gene expression dynamics during early development. Second, I will discuss my work on some common and cell type-specific themes of higher order chromatin arrangements during mouse preimplantation development. Mapping the spatial organization of the genome is critical for comprehending its regulatory function in health, disease, and development. Our findings demonstrate an extraordinary amount of parent-specific chromosome choreography during the concatenation of two genomes. After fertilization, we observe an abrupt emergence of a Rabl-like configuration and a high head-to-head and tail-to-tail alignment of the chromosomes, which are gradually lost by the 64-cell stage. Additionally, the characteristics and marks of active and inactive chromatin exhibit a distinct radial profile across developmental stages and the genome. Finally, in addition to the well-known hallmarks of genome organization, we observe a preferential organization of chromosome territories - which call the "Territome". We were able to distinguish cell types based on the radial and relative positioning of the chromosomes in the 3D reconstructions. This suggest that interchromosomal interactions are just as critical for defining chromatin architecture and cellular identity as intrachromosomal interactions. Our findings establish a novel criterion for classifying cells when other hallmarks are difficult to quantify or when transcriptomics data is unavailable, thus paving a whole new way of looking at cells and learning how they function. Finally, with advances in experimental and theoretical approaches for generating single cell chromatin conformation capture assays, elucidating the genome's structure-function relationship has become a highly active area of research. Numerous computational methods have been developed to infer the genome's three-dimensional organization using Hi-C data from single cells. This is referred to as the three-dimensional genome reconstruction problem in formal terms (3D-GRP). While numerous methods exist for predicting the three-dimensional structure of a single genomic region, chromosome, or genome, the reconstructed models do not satisfy all of the input constraints. To address this, we present CUT & GROW, a method for improving the accuracy of three-dimensional chromosome structure inference using an iterative importance sampling strategy. CUT & GROW refines the structure of a three-dimensional chromosome (or genome) model by regrowing fragments of varying sizes locally, satisfying the majority of input constraints and providing a more precise view of the structure-function relationship

This thesis is organized as follows. In the first chapter, we introduce a computational model to simulate chromatin structure and dynamics. The model defines chromatin states by taking one-dimensional genomics and epigenomics data as input and quantitatively learns interacting patterns between these states using experimental contact data. Once learned, the model is able to make de novo predictions of 3D chromatin structures at five-kilo-base resolution across different cell types. The manuscript associated with this study is published in PLoS Computational Biology, 15.6, e1007024 (2019).

Encyclopedia of Bioinformatics and Computational Biology: ABC of Bioinformatics, Three Volume Set combines elements of computer science, information technology, mathematics, statistics and biotechnology, providing the methodology and in silico solutions to mine biological data and processes. The book covers Theory, Topics and Applications, with a special focus on Integrative –omics and Systems Biology. The theoretical, methodological underpinnings of BCB, including phylogeny are covered, as are more current areas of focus, such as translational bioinformatics, cheminformatics, and environmental informatics. Finally, Applications provide guidance for commonly asked questions. This major reference work spans basic and cutting-edge methodologies authored by leaders in the field, providing an invaluable resource for students, scientists, professionals in research institutes, and a broad swath of researchers in biotechnology and the biomedical and pharmaceutical industries. Brings together information from computer science, information technology, mathematics, statistics and biotechnology Written and reviewed by leading experts in the field, providing a unique and authoritative resource Focuses on the main theoretical and methodological concepts before expanding on specific topics and applications Includes interactive images, multimedia tools and crosslinking to further resources and databases

To approach the still largely unknown sequential and three-dimensional organization of the human cell nucleus, the structural-, scaling- and dynamic properties of interphase chromosomes and cell nuclei were simulated on the 30 nm chromatin fiber level with Monte Carlo, Brownian Dynamics and parallel computing methods. Differences between used models explain various experimental conditions, favouring a Multi-Loop-Subcompartment model with 63-126 kbp loops aggregated to possibly rosettes connected by 63-126 kbp linkers, and predict correctly the transport of molecules by moderately obstructed diffusion excluding the Interchromosomal Domain hypothesis. Correlation analyses of completely sequenced Archaea, Bacteria and Eucaria chromosomes revealed fine-structured positive long-range correlations due to codon, nucleosomal or block organization of the genomes, allowing classification and tree construction. By construction and expression of fusionproteins from the histones H1, H2A, H2B, H3, H4 and mH2A1.2 with the autofluorescent proteins CFP, GFP, YFP, DsRed-1 and DsRed-2 the chromatin morphology could be investigated in vivo during interphase, mitosis or apoptosis and revealed different interphase morphologies for cell lines quantifiable by scaling analyses. Finally, construct conversions in simultaneous co-transfections due to recombination/repair/replication were discovered in 25 % of cells and led to a variety of new applications.