Complementing Hi-C information for 3D chromatin reconstruction by ChromStruct

A multiscale method proposed elsewhere for reconstructing plausible 3D configurations of the chromatin in cell nuclei is recalled, based on the integration of contact data from Hi-C experiments and additional information coming from ChIP-seq, RNA-seq and ChIA-PET experiments. Provided that the additional data come from independent experiments, this kind of approach is supposed to leverage them to complement possibly noisy, biased or missing Hi-C records. When the different data sources are mutually concurrent, the resulting solutions are corroborated; otherwise, their validity would be weakened. Here, a problem of reliability arises, entailing an appropriate choice of the relative weights to be assigned to the different informational contributions. A series of experiments is presented that help to quantify the advantages and the limitations offered by this strategy. Whereas the advantages in accuracy are not always significant, the case of missing Hi-C data demonstrates the effectiveness of additional information in reconstructing the highly packed segments of the structure

Development of New Computational Tools for Analyzing Hi-C Data and Predicting Three-Dimensional Genome Organization

Background: The development of Hi-C (and related methods) has allowed for unprecedented sequence-level investigations into the structure-function relationship of the genome. There has been extensive effort in developing new tools to analyze this data in order to better understand the relationship between 3D genomic structure and function. While useful, the existing tools are far from maturity and (in some cases) lack the generalizability that would be required for application in a diverse set of organisms. This is problematic since the research community has proposed many cross-species "hallmarks" of 3D genome organization without confirming their existence in a variety of organisms. Research Objective: Develop new, generalizable computational tools for Hi-C analysis and 3D genome prediction. Results: Three new computational tools were developed for Hi-C analysis or 3D genome prediction: GrapHi-C (visualization), GeneRHi-C (3D prediction) and StoHi-C (3D prediction). Each tool has the potential to be used for 3D genome analysis in both model and non-model organisms since the underlying algorithms do not rely on any organism-specific constraints. A brief description of each tool follows. GrapHi-C is a graph-based visualization of Hi-C data. Unlike existing visualization methods, GrapHi-C allows for a more intuitive structural visualization of the underlying data. GeneRHi-C and StoHi-C are tools that can be used to predict 3D genome organizations from Hi-C data (the 3D-genome reconstruction problem). GeneRHi-C uses a combination of mixed integer programming and network layout algorithms to generate 3D coordinates from a ploidy-dependent subset of the Hi-C data. Alternatively, StoHi-C uses t-stochastic neighbour embedding with the complete set of Hi-C data to generate 3D coordinates of the genome. Each tool was applied to multiple, independent existing Hi-C datasets from fission yeast to demonstrate their utility. This is the first time 3D genome prediction has been successfully applied to these datasets. Overall, the tools developed here more clearly recapitulated documented features of fission yeast genomic organization when compared to existing techniques. Future work will focus on extending and applying these tools to analyze Hi-C datasets from other organisms. Additional Information: This thesis contains a collection of papers pertaining to the development of new tools for analyzing Hi-C data and predicting 3D genome organization. Each paper's publication status (as of January 2020) has been provided at the beginning of the corresponding chapter. For published papers, reprint permission was obtained and is available in the appendix

Unravelling higher order chromatin organisation through statistical analysis

Recent technological advances underpinned by high throughput sequencing have given new insights into the three-dimensional structure of mammalian genomes. Chromatin conformation assays have been the critical development in this area, particularly the Hi-C method which ascertains genome-wide patterns of intra and inter-chromosomal contacts. However many open questions remain concerning the functional relevance of such higher order structure, the extent to which it varies, and how it relates to other features of the genomic and epigenomic landscape. Current knowledge of nuclear architecture describes a hierarchical organisation ranging from small loops between individual loci, to megabase-sized self-interacting topological domains (TADs), encompassed within large multimegabase chromosome compartments. In parallel with the discovery of these strata, the ENCODE project has generated vast amounts of data through ChIP-seq, RNA-seq and other assays applied to a wide variety of cell types, forming a comprehensive bioinformatics resource. In this work we combine Hi-C datasets describing physical genomic contacts with a large and diverse array of chromatin features derived at a much finer scale in the same mammalian cell types. These features include levels of bound transcription factors, histone modifications and expression data. These data are then integrated in a statistically rigorous way, through a predictive modelling framework from the machine learning field. These studies were extended, within a collaborative project, to encompass a dataset of matched Hi-C and expression data collected over a murine neural differentiation timecourse. We compare higher order chromatin organisation across a variety of human cell types and find pervasive conservation of chromatin organisation at multiple scales. We also identify structurally variable regions between cell types, that are rich in active enhancers and contain loci of known cell-type specific function. We show that broad aspects of higher order chromatin organisation, such as nuclear compartment domains, can be accurately predicted in a variety of human cell types, using models based upon underlying chromatin features. We dissect these quantitative models and find them to be generalisable to novel cell types, presumably reflecting fundamental biological rules linking compartments with key activating and repressive signals. These models describe the strong interconnectedness between locus-level patterns of local histone modifications and bound factors, on the order of hundreds or thousands of basepairs, with much broader compartmentalisation of large, multi-megabase chromosomal regions. Finally, boundary regions are investigated in terms of chromatin features and co-localisation with other known nuclear structures, such as association with the nuclear lamina. We find boundary complexity to vary between cell types and link TAD aggregations to previously described lamina-associated domains, as well as exploring the concept of meta-boundaries that span multiple levels of organisation. Together these analyses lend quantitative evidence to a model of higher order genome organisation that is largely stable between cell types, but can selectively vary locally, based on the activation or repression of key loci

Modeling and Simulation in Engineering

This book provides an open platform to establish and share knowledge developed by scholars, scientists, and engineers from all over the world, about various applications of the modeling and simulation in the design process of products, in various engineering fields. The book consists of 12 chapters arranged in two sections (3D Modeling and Virtual Prototyping), reflecting the multidimensionality of applications related to modeling and simulation. Some of the most recent modeling and simulation techniques, as well as some of the most accurate and sophisticated software in treating complex systems, are applied. All the original contributions in this book are jointed by the basic principle of a successful modeling and simulation process: as complex as necessary, and as simple as possible. The idea is to manipulate the simplifying assumptions in a way that reduces the complexity of the model (in order to make a real-time simulation), but without altering the precision of the results

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described