Contribution of 3D genome topological domains to genetic risk of cancers: a genome-wide computational study.

BACKGROUND: Genome-wide association studies have identified statistical associations between various diseases, including cancers, and a large number of single-nucleotide polymorphisms (SNPs). However, they provide no direct explanation of the mechanisms underlying the association. Based on the recent discovery that changes in three-dimensional genome organization may have functional consequences on gene regulation favoring diseases, we investigated systematically the genome-wide distribution of disease-associated SNPs with respect to a specific feature of 3D genome organization: topologically associating domains (TADs) and their borders. RESULTS: For each of 449 diseases, we tested whether the associated SNPs are present in TAD borders more often than observed by chance, where chance (i.e., the null model in statistical terms) corresponds to the same number of pointwise loci drawn at random either in the entire genome, or in the entire set of disease-associated SNPs listed in the GWAS catalog. Our analysis shows that a fraction of diseases displays such a preferential localization of their risk loci. Moreover, cancers are relatively more frequent among these diseases, and this predominance is generally enhanced when considering only intergenic SNPs. The structure of SNP-based diseasome networks confirms that localization of risk loci in TAD borders differs between cancers and non-cancer diseases. Furthermore, different TAD border enrichments are observed in embryonic stem cells and differentiated cells, consistent with changes in topological domains along embryogenesis and delineating their contribution to disease risk. CONCLUSIONS: Our results suggest that, for certain diseases, part of the genetic risk lies in a local genetic variation affecting the genome partitioning in topologically insulated domains. Investigating this possible contribution to genetic risk is particularly relevant in cancers. This study thus opens a way of interpreting genome-wide association studies, by distinguishing two types of disease-associated SNPs: one with an effect on an individual gene, the other acting in interplay with 3D genome organization.

High-salt-recovered sequences are associated with the active chromosomal compartment and with large ribonucleoprotein complexes including nuclear bodies.

The mammalian cell nucleus contains numerous discrete suborganelles named nuclear bodies. While recruitment of specific genomic regions into these large ribonucleoprotein (RNP) complexes critically contributes to higher-order functional chromatin organization, such regions remain ill-defined. We have developed the high-salt-recovered sequences-sequencing (HRS-seq) method, a straightforward genome-wide approach whereby we isolated and sequenced genomic regions associated with large high-salt insoluble RNP complexes. By using mouse embryonic stem cells (ESCs), we showed that these regions essentially correspond to the most highly expressed genes, and to cis-regulatory sequences like super-enhancers, that belong to the active A chromosomal compartment. They include both cell-type-specific genes, such as pluripotency genes in ESCs, and housekeeping genes associated with nuclear bodies, such as histone and snRNA genes that are central components of Histone Locus Bodies and Cajal bodies. We conclude that HRSs are associated with the active chromosomal compartment and with large RNP complexes including nuclear bodies. Association of such chromosomal regions with nuclear bodies is in agreement with the recently proposed phase separation model for transcription control and might thus play a central role in organizing the active chromosomal compartment in mammals.

Radius selection using kernel density estimation for the computation of nonlinear measures.

When nonlinear measures are estimated from sampled temporal signals with finite-length, a radius parameter must be carefully selected to avoid a poor estimation. These measures are generally derived from the correlation integral, which quantifies the probability of finding neighbors, i.e., pair of points spaced by less than the radius parameter. While each nonlinear measure comes with several specific empirical rules to select a radius value, we provide a systematic selection method. We show that the optimal radius for nonlinear measures can be approximated by the optimal bandwidth of a Kernel Density Estimator (KDE) related to the correlation sum. The KDE framework provides non-parametric tools to approximate a density function from finite samples (e.g., histograms) and optimal methods to select a smoothing parameter, the bandwidth (e.g., bin width in histograms). We use results from KDE to derive a closed-form expression for the optimal radius. The latter is used to compute the correlation dimension and to construct recurrence plots yielding an estimate of Kolmogorov-Sinai entropy. We assess our method through numerical experiments on signals generated by nonlinear systems and experimental electroencephalographic time series.

Kinetic Signature of Cooperativity in the Irreversible Collapse of a Polymer.

We investigate the kinetics of a polymer collapse due to the formation of irreversible cross-links between its monomers. Using the contact probability P(s) as a scale-dependent order parameter depending on the chemical distance s, our simulations show the emergence of a cooperative pearling instability. Namely, the polymer undergoes a sharp conformational transition to a set of absorbing states characterized by a length scale ξ corresponding to the mean pearl size. This length and the transition time depend on the polymer equilibrium dynamics and the cross-linking rate. We confirm experimentally this transition using a DNA conformation capture experiment in yeast.

Probabilistic analysis of recurrence plots generated by fractional Gaussian noise.

Recurrence plots of time series generated by discrete fractional Gaussian noise (fGn) processes are analyzed. We compute the probabilities of occurrence of consecutive recurrence points forming diagonals and verticals in the recurrence plot constructed without embedding. We focus on two recurrence quantification analysis measures related to these lines, respectively, the percent determinism and the laminarity ( LAM ). The behavior of these two measures as a function of the fGn's Hurst exponent H is investigated. We show that the dependence of the laminarity with respect to H is monotonic in contrast to the percent determinism. We also show that the length of the diagonal and vertical lines involved in the computation of percent determinism and laminarity has an influence on their dependence on H . Statistical tests performed on the LAM measure support its utility to discriminate fGn processes with respect to their H values. These results demonstrate that recurrence plots are suitable for the extraction of quantitative information on the correlation structure of these widespread stochastic processes.

3D genome reconstruction from chromosomal contacts.

A computational challenge raised by chromosome conformation capture (3C) experiments is to reconstruct spatial distances and three-dimensional genome structures from observed contacts between genomic loci. We propose a two-step algorithm, ShRec3D, and assess its accuracy using both in silico data and human genome-wide 3C (Hi-C) data. This algorithm avoids convergence issues, accommodates sparse and noisy contact maps, and is orders of magnitude faster than existing methods.

Mathematical models of radiation action on living cells: From the target theory to the modern approaches. A historical and critical review.

Cell survival is conventionally defined as the capability of irradiated cells to produce colonies. It is quantified by the clonogenic assays that consist in determining the number of colonies resulting from a known number of irradiated cells. Several mathematical models were proposed to describe the survival curves, notably from the target theory. The Linear-Quadratic (LQ) model, which is to date the most frequently used model in radiobiology and radiotherapy, dominates all the other models by its robustness and simplicity. Its usefulness is particularly important because the ratio of the values of the adjustable parameters, α and ß, on which it is based, predicts the occurrence of post-irradiation tissue reactions. However, the biological interpretation of these parameters is still unknown. Throughout this review, we revisit and discuss historically, mathematically and biologically, the different models of the radiation action by providing clues for resolving the enigma of the LQ model.

Distinct polymer physics principles govern chromatin dynamics in mouse and Drosophila topological domains.

BACKGROUND: In higher eukaryotes, the genome is partitioned into large "Topologically Associating Domains" (TADs) in which the chromatin displays favoured long-range contacts. While a crumpled/fractal globule organization has received experimental supports at higher-order levels, the organization principles that govern chromatin dynamics within these TADs remain unclear. Using simple polymer models, we previously showed that, in mouse liver cells, gene-rich domains tend to adopt a statistical helix shape when no significant locus-specific interaction takes place. RESULTS: Here, we use data from diverse 3C-derived methods to explore chromatin dynamics within mouse and Drosophila TADs. In mouse Embryonic Stem Cells (mESC), that possess large TADs (median size of 840 kb), we show that the statistical helix model, but not globule models, is relevant not only in gene-rich TADs, but also in gene-poor and gene-desert TADs. Interestingly, this statistical helix organization is considerably relaxed in mESC compared to liver cells, indicating that the impact of the constraints responsible for this organization is weaker in pluripotent cells. Finally, depletion of histone H1 in mESC alters local chromatin flexibility but not the statistical helix organization. In Drosophila, which possesses TADs of smaller sizes (median size of 70 kb), we show that, while chromatin compaction and flexibility are finely tuned according to the epigenetic landscape, chromatin dynamics within TADs is generally compatible with an unconstrained polymer configuration. CONCLUSIONS: Models issued from polymer physics can accurately describe the organization principles governing chromatin dynamics in both mouse and Drosophila TADs. However, constraints applied on this dynamics within mammalian TADs have a peculiar impact resulting in a statistical helix organization.

A single formula to describe radiation-induced protein relocalization: towards a mathematical definition of individual radiosensitivity.

Immunofluorescence with antibodies against DNA damage repair and signaling protein is revolutionarising the estimation of the genotoxic risk. Indeed, a number of stress response proteins relocalize in nucleus as identifiable foci whose number, pattern and appearance/disappearance rate depend on several parameters such as the stress nature, dose, time and individual factor. Few authors proposed biomathematical tools to describe them in a unified formula that would be relevant for all the relocalizable proteins. Based on our two previous reports in this Journal (Foray et al., 2005; Gastaldo et al., 2008), we considered that foci response to stress is composed of a recognition and a repair phase, both described by an inverse power function provided from a Euler's Gamma distribution. The resulting unified formula called "Bodgi's function" is able to describe appearance/disappearance kinetics of nuclear foci after any condition of genotoxic stress. By applying the Bodgi's formula to DNA damage repair data from 45 patients treated with radiotherapy, we deduced a classification of human radiosensitivity based on objective molecular criteria, notably like the number of unrepaired DNA double-strand breaks and the radiation-induced nucleo-shuttling of the ATM kinase.

Multiscale analysis of biological systems.

It is argued that multiscale approaches are necessary for an explanatory modeling of biological systems. A first step, besides common to the multiscale modeling of physical and living systems, is a bottom-up integration based on the notions of effective parameters and minimal models. Top-down effects can be accounted for in terms of effective constraints and inputs. Biological systems are essentially characterized by an entanglement of bottom-up and top-down influences following from their evolutionary history. A self-consistent multiscale scheme is proposed to capture the ensuing circular causality. Its differences with standard mean-field self-consistent equations and slow-fast decompositions are discussed. As such, this scheme offers a way to unravel the multilevel architecture of living systems and their regulation. Two examples, genome functions and biofilms, are detailed.

Predicting attractors from spectral properties of stylized gene regulatory networks.

How the architecture of gene regulatory networks shapes gene expression patterns is an open question, which has been approached from a multitude of angles. The dominant strategy has been to identify nonrandom features in these networks and then argue for the function of these features using mechanistic modeling. Here we establish the foundation of an alternative approach by studying the correlation of network eigenvectors with synthetic gene expression data simulated with a basic and popular model of gene expression dynamics: Boolean threshold dynamics in signed directed graphs. We show that eigenvectors of the network adjacency matrix can predict collective states (attractors). However, the overall predictive power depends on details of the network architecture, namely the fraction of positive 3-cycles, in a predictable fashion. Our results are a set of statistical observations, providing a systematic step towards a further theoretical understanding of the role of network eigenvectors in dynamics on graphs.

Improving the efficiency of multidimensional scaling in the analysis of high-dimensional data using singular value decomposition.

MOTIVATION: Multidimensional scaling (MDS) is a well-known multivariate statistical analysis method used for dimensionality reduction and visualization of similarities and dissimilarities in multidimensional data. The advantage of MDS with respect to singular value decomposition (SVD) based methods such as principal component analysis is its superior fidelity in representing the distance between different instances specially for high-dimensional geometric objects. Here, we investigate the importance of the choice of initial conditions for MDS, and show that SVD is the best choice to initiate MDS. Furthermore, we demonstrate that the use of the first principal components of SVD to initiate the MDS algorithm is more efficient than an iteration through all the principal components. Adding stochasticity to the molecular dynamics simulations typically used for MDS of large datasets, contrary to previous suggestions, likewise does not increase accuracy. Finally, we introduce a k nearest neighbor method to analyze the local structure of the geometric objects and use it to control the quality of the dimensionality reduction. RESULTS: We demonstrate here the, to our knowledge, most efficient and accurate initialization strategy for MDS algorithms, reducing considerably computational load. SVD-based initialization renders MDS methodology much more useful in the analysis of high-dimensional data such as functional genomics datasets.

The condensed chromatin fiber: an allosteric chemo-mechanical machine for signal transduction and genome processing.

Allostery is a key concept of molecular biology which refers to the control of an enzyme activity by an effector molecule binding the enzyme at another site rather than the active site (allos = other in Greek). We revisit here allostery in the context of chromatin and argue that allosteric principles underlie and explain the functional architecture required for spacetime coordination of gene expression at all scales from DNA to the whole chromosome. We further suggest that this functional architecture is provided by the chromatin fiber itself. The structural, mechanical and topological features of the chromatin fiber endow chromosomes with a tunable signal transduction from specific (or nonspecific) effectors to specific (or nonspecific) active sites. Mechanical constraints can travel along the fiber all the better since the fiber is more compact and regular, which speaks in favor of the actual existence of the (so-called 30 nm) chromatin fiber. Chromatin fiber allostery reconciles both the physical and biochemical approaches of chromatin. We illustrate this view with two supporting specific examples. Moreover, from a methodological point of view, we suggest that the notion of chromatin fiber allostery is particularly relevant for systemic approaches. Finally we discuss the evolutionary power of allostery in the context of chromatin and its relation to modularity.

SAGA interacting factors confine sub-diffusion of transcribed genes to the nuclear envelope.

Changes in the transcriptional state of genes have been correlated with their repositioning within the nuclear space. Tethering reporter genes to the nuclear envelope alone can impose repression and recent reports have shown that, after activation, certain genes can also be found closer to the nuclear periphery. The molecular mechanisms underlying these phenomena have remained elusive. Here, with the use of dynamic three-dimensional tracking of a single locus in live yeast (Saccharomyces cerevisiae) cells, we show that the activation of GAL genes (GAL7, GAL10 and GAL1) leads to a confinement in dynamic motility. We demonstrate that the GAL locus is subject to sub-diffusive movement, which after activation can become constrained to a two-dimensional sliding motion along the nuclear envelope. RNA-fluorescence in situ hybridization analysis after activation reveals a higher transcriptional activity for the peripherally constrained GAL genes than for loci remaining intranuclear. This confinement was mediated by Sus1 and Ada2, members of the SAGA histone acetyltransferase complex, and Sac3, a messenger RNA export factor, physically linking the activated GAL genes to the nuclear-pore-complex component Nup1. Deleting ADA2 or NUP1 abrogates perinuclear GAL confinement without affecting GAL1 transcription. Accordingly, transcriptional activation is necessary but not sufficient for the confinement of GAL genes at the nuclear periphery. The observed real-time dynamic mooring of active GAL genes to the inner side of the nuclear pore complex is in accordance with the 'gene gating' hypothesis.

Predictable topological sensitivity of Turing patterns on graphs.

Reaction-diffusion systems implemented as dynamical processes on networks have recently renewed the interest in their self-organized collective patterns known as Turing patterns. We investigate the influence of network topology on the emerging patterns and their diversity, defined as the variety of stationary states observed with random initial conditions and the same dynamics. We show that a seemingly minor change, the removal or rewiring of a single link, can prompt dramatic changes in pattern diversity. The determinants of such critical occurrences are explored through an extensive and systematic set of numerical experiments. We identify situations where the topological sensitivity of the attractor landscape can be predicted without a full simulation of the dynamical equations, from the spectrum of the graph Laplacian and the linearized dynamics. Unexpectedly, the main determinant appears to be the degeneracy of the eigenvalues or the growth rate and not the number of unstable modes.

The 3D Organization of Chromatin Colors in Mammalian Nuclei.

While many computational methods have been proposed for 3D chromosome reconstruction from chromosomal contact maps, these methods are rarely used for the interpretation of such experimental data, in particular Hi-C data. We posit that this is due to the lack of an easy-to-use implementation of the proposed algorithms, as well as to the important computational cost of most methods. We here give a detailed implementation of the fast ShRec3D algorithm. We provide a tutorial that will enable the reader to reconstruct 3D consensus structures for human chromosomes and to decorate these structures with chromatin epigenetic states. We use this methodology to show that the bivalent chromatin, including Polycomb-rich domains, is spatially segregated and located in between the active and the quiescent chromatin compartments.

Endogenous Retroviral Sequences Behave as Putative Enhancers Controlling Gene Expression through HP1-Regulated Long-Range Chromatin Interactions.

About half of the mammalian genome is constituted of repeated elements, among which endogenous retroviruses (ERVs) are known to influence gene expression and cancer development. The HP1 (Heterochromatin Protein 1) proteins are known to be essential for heterochromatin establishment and function and its loss in hepatocytes leads to the reactivation of specific ERVs and to liver tumorigenesis. Here, by studying two ERVs located upstream of genes upregulated upon loss of HP1, Mbd1 and Trim24, we show that these HP1-dependent ERVs behave as either alternative promoters or as putative enhancers forming a loop with promoters of endogenous genes depending on the genomic context and HP1 expression level. These ERVs are characterised by a specific HP1-independent enrichment in heterochromatin-associated marks H3K9me3 and H4K20me3 as well as in the enhancer-specific mark H3K4me1, a combination that might represent a bookmark of putative ERV-derived enhancers. These ERVs are further enriched in a HP1-dependent manner in H3K27me3, suggesting a critical role of this mark together with HP1 in the silencing of the ERVs, as well as for the repression of the associated genes. Altogether, these results lead to the identification of a new regulatory hub involving the HP1-dependent formation of a physical loop between specific ERVs and endogenous genes.

The economy of chromosomal distances in bacterial gene regulation.

In the transcriptional regulatory network (TRN) of a bacterium, the nodes are genes and a directed edge represents the action of a transcription factor (TF), encoded by the source gene, on the target gene. It is a condensed representation of a large number of biological observations and facts. Nonrandom features of the network are structural evidence of requirements for a reliable systemic function. For the bacterium Escherichia coli we here investigate the (Euclidean) distances covered by the edges in the TRN when its nodes are embedded in the real space of the circular chromosome. Our work is motivated by 'wiring economy' research in Computational Neuroscience and starts from two contradictory hypotheses: (1) TFs are predominantly employed for long-distance regulation, while local regulation is exerted by chromosomal structure, locally coordinated by the action of structural proteins. Hence long distances should often occur. (2) A large distance between the regulator gene and its target requires a higher expression level of the regulator gene due to longer reaching times and ensuing increased degradation (proteolysis) of the TF and hence will be evolutionarily reduced. Our analysis supports the latter hypothesis.

Coupling Between Production of Ribosomal RNA and Maturation: Just at the Beginning.

Ribosomal RNA (rRNA) production represents the most active transcription in the cell. Synthesis of the large rRNA precursors (35S/47S in yeast/human) is achieved by up to hundreds of RNA polymerase I (Pol I) enzymes simultaneously transcribing a single rRNA gene. In this review, we present recent advances in understanding the coupling between rRNA production and nascent rRNA folding. Mapping of the distribution of Pol I along ribosomal DNA at nucleotide resolution, using either native elongating transcript sequencing (NET-Seq) or crosslinking and analysis of cDNAs (CRAC), revealed frequent Pol I pausing, and CRAC results revealed a direct coupling between pausing and nascent RNA folding. High density of Pol I per gene imposes topological constraints that establish a defined pattern of polymerase distribution along the gene, with a persistent spacing between transcribing enzymes. RNA folding during transcription directly acts as an anti-pausing mechanism, implying that proper folding of the nascent rRNA favors elongation in vivo. Defects in co-transcriptional folding of rRNA are likely to induce Pol I pausing. We propose that premature termination of transcription, at defined positions, can control rRNA production in vivo.

Transcription within condensed chromatin: Steric hindrance facilitates elongation.

During eukaryotic transcription, RNA-polymerase activity generates torsional stress in DNA, having a negative impact on the elongation process. Using our previous studies of chromatin fiber structure and conformational transitions, we suggest that this torsional stress can be alleviated, thanks to a tradeoff between the fiber twist and nucleosome conformational transitions into an activated state named "reversome". Our model enlightens the origin of polymerase pauses, and leads to the counterintuitive conclusion that chromatin-organized compaction might facilitate polymerase progression. Indeed, in a compact and well-structured chromatin loop, steric hindrance between nucleosomes enforces sequential transitions, thus ensuring that the polymerase always meets a permissive nucleosomal state.