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.

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.

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.

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.

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.

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.

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.

The 3D Genome Shapes the Regulatory Code of Developmental Genes.

We revisit the notion of gene regulatory code in embryonic development in the light of recent findings about genome spatial organization. By analogy with the genetic code, we posit that the concept of code can only be used if the corresponding adaptor can clearly be identified. An adaptor is here defined as an intermediary physical entity mediating the correspondence between codewords and objects in a gratuitous and evolvable way. In the context of the gene regulatory code, the encoded objects are the gene expression levels, while the concentrations of specific transcription factors in the cell nucleus provide the codewords. The notion of code is meaningful in the absence of direct physicochemical relationships between the objects and the codewords, when the mediation by an adaptor is required. We propose that a plausible adaptor for this code is the gene domain, that is, the genome segment delimited by topological insulators and comprising the gene and its enhancer regulatory sequences. We review recent evidences, based on genome-wide chromosome conformation capture experiments, showing that preferential contact domains found in metazoan genomes are the physical traces of gene domains. Accordingly, genome 3D folding plays a direct role in shaping the developmental gene regulatory code.

Exploring Mammalian Genome within Phase-Separated Nuclear Bodies: Experimental Methods and Implications for Gene Expression.

The importance of genome organization at the supranucleosomal scale in the control of gene expression is increasingly recognized today. In mammals, Topologically Associating Domains (TADs) and the active/inactive chromosomal compartments are two of the main nuclear structures that contribute to this organization level. However, recent works reviewed here indicate that, at specific loci, chromatin interactions with nuclear bodies could also be crucial to regulate genome functions, in particular transcription. They moreover suggest that these nuclear bodies are membrane-less organelles dynamically self-assembled and disassembled through mechanisms of phase separation. We have recently developed a novel genome-wide experimental method, High-salt Recovered Sequences sequencing (HRS-seq), which allows the identification of chromatin regions associated with large ribonucleoprotein (RNP) complexes and nuclear bodies. We argue that the physical nature of such RNP complexes and nuclear bodies appears to be central in their ability to promote efficient interactions between distant genomic regions. The development of novel experimental approaches, including our HRS-seq method, is opening new avenues to understand how self-assembly of phase-separated nuclear bodies possibly contributes to mammalian genome organization and gene expression.

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.

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.

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.

The Role of Supercoiling in the Motor Activity of RNA Polymerases.

RNA polymerase (RNAP) is, in its elongation phase, an emblematic example of a molecular motor whose activity is highly sensitive to DNA supercoiling. After a review of DNA supercoiling basic features, we discuss how supercoiling controls polymerase velocity, while being itself modified by polymerase activity. This coupling is supported by single-molecule measurements. Physical modeling allows us to describe quantitatively how supercoiling and torsional constraints mediate a mechanical coupling between adjacent polymerases. On this basis, we obtain a description that may explain the existence and functioning of RNAP convoys.

Quantifying the dynamics of emotional expressions in family therapy of patients with anorexia nervosa.

Emotional interactions have been considered dynamical processes involved in the affective life of humans and their disturbances may induce mental disorders. Most studies of emotional interactions have focused on dyadic behaviors or self-reports of emotional states but neglected the dynamical processes involved in family therapy. The main objective of this study is to quantify the dynamics of emotional expressions and their changes using the family therapy of patients with anorexia nervosa as an example. Nonlinear methods characterize the variability of the dynamics at the level of the whole therapeutic system and reciprocal influence between the participants during family therapy. Results show that the variability of the dynamics is higher at the end of the therapy than at the beginning. The reciprocal influences between therapist and each member of the family and between mother and patient decrease with the course of family therapy. Our results support the development of new interpersonal strategies of emotion regulation during family therapy. The quantification of emotional dynamics can help understanding the emotional processes underlying psychopathology and evaluating quantitatively the changes achieved by the therapeutic intervention.

Topological determinants of self-sustained activity in a simple model of excitable dynamics on graphs.

Simple models of excitable dynamics on graphs are an efficient framework for studying the interplay between network topology and dynamics. This topic is of practical relevance to diverse fields, ranging from neuroscience to engineering. Here we analyze how a single excitation propagates through a random network as a function of the excitation threshold, that is, the relative amount of activity in the neighborhood required for the excitation of a node. We observe that two sharp transitions delineate a region of sustained activity. Using analytical considerations and numerical simulation, we show that these transitions originate from the presence of barriers to propagation and the excitation of topological cycles, respectively, and can be predicted from the network topology. Our findings are interpreted in the context of network reverberations and self-sustained activity in neural systems, which is a question of long-standing interest in computational neuroscience.

A single-molecule view of transcription reveals convoys of RNA polymerases and multi-scale bursting.

Live-cell imaging has revealed unexpected features of gene expression. Here using improved single-molecule RNA microscopy, we show that synthesis of HIV-1 RNA is achieved by groups of closely spaced polymerases, termed convoys, as opposed to single isolated enzymes. Convoys arise by a Mediator-dependent reinitiation mechanism, which generates a transient but rapid succession of polymerases initiating and escaping the promoter. During elongation, polymerases are spaced by few hundred nucleotides, and physical modelling suggests that DNA torsional stress may maintain polymerase spacing. We additionally observe that the HIV-1 promoter displays stochastic fluctuations on two time scales, which we refer to as multi-scale bursting. Each time scale is regulated independently: Mediator controls minute-scale fluctuation (convoys), while TBP-TATA-box interaction controls sub-hour fluctuations (long permissive/non-permissive periods). A cellular promoter also produces polymerase convoys and displays multi-scale bursting. We propose that slow, TBP-dependent fluctuations are important for phenotypic variability of single cells.

Network Modeling of Crohn's Disease Incidence.

BACKGROUND: Numerous genetic and environmental risk factors play a role in human complex genetic disorders (CGD). However, their complex interplay remains to be modelled and explained in terms of disease mechanisms. METHODS AND FINDINGS: Crohn's Disease (CD) was modeled as a modular network of patho-physiological functions, each summarizing multiple gene-gene and gene-environment interactions. The disease resulted from one or few specific combinations of module functional states. Network aging dynamics was able to reproduce age-specific CD incidence curves as well as their variations over the past century in Western countries. Within the model, we translated the odds ratios (OR) associated to at-risk alleles in terms of disease propensities of the functional modules. Finally, the model was successfully applied to other CGD including ulcerative colitis, ankylosing spondylitis, multiple sclerosis and schizophrenia. CONCLUSION: Modeling disease incidence may help to understand disease causative chains, to delineate the potential of personalized medicine, and to monitor epidemiological changes in CGD.

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.

Beyond ectomycorrhizal bipartite networks: projected networks demonstrate contrasted patterns between early- and late-successional plants in Corsica.

The ectomycorrhizal (ECM) symbiosis connects mutualistic plants and fungal species into bipartite networks. While links between one focal ECM plant and its fungal symbionts have been widely documented, systemic views of ECM networks are lacking, in particular, concerning the ability of fungal species to mediate indirect ecological interactions between ECM plant species (projected-ECM networks). We assembled a large dataset of plant-fungi associations at the species level and at the scale of Corsica using molecular data and unambiguously host-assigned records to: (i) examine the correlation between the number of fungal symbionts of a plant species and the average specialization of these fungal species, (ii) explore the structure of the plant-plant projected network and (iii) compare plant association patterns in regard to their position along the ecological succession. Our analysis reveals no trade-off between specialization of plants and specialization of their partners and a saturation of the plant projected network. Moreover, there is a significantly lower-than-expected sharing of partners between early- and late-successional plant species, with fewer fungal partners for early-successional ones and similar average specialization of symbionts of early- and late-successional plants. Our work paves the way for ecological readings of Mediterranean landscapes that include the astonishing diversity of below-ground interactions.