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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.

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.

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., Human Genomics, 16 (1), ISSN:1473-9542, ISSN:1479-7364

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 3-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.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 display such a preferential location 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 TAD border enrichment in risk loci differ between cancers and non-cancer diseases. Different TAD border enrichments are observed in embryonic stem cells and differentiated cells, which agrees with an evolution along embryogenesis of the 3D genome organization into topological domains.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 a direct effect on an individual gene, the other acting in interplay with 3D genome organization.Author summaryGenome-wide association studies comparing patients and healthy subjects have evidenced correlations between diseases and the presence of pointwise genetic variations known as single-nucleotide polymorphisms (SNPs). We exploit and extend this statistical analysis by investigating the location of risk loci, i.e. disease-associated SNPs, with respect to the 3D organization of the genome into spatially-insulated domains, the topologically-associating domains (TADs).We show that for certain diseases, mostly cancers, their associated risk loci are preferentially located in the borders of these topological domains. The predominance of cancers among these diseases is confirmed and even enhanced when considering only intergenic SNPs. A different enrichment behavior is observed in embryonic stem cells and derived cell lines at an early developmental stage, presumably due to the not fully mature TAD structure in these cells.Overall, our results show that genome variations in specific TAD borders may increase the risk of developing certain diseases, especially cancers. Our work underlines the importance of considering the genetic risk loci within their 3D genomic context, and suggests a role of 3D genome partitioning into topological domains in the genetic risk which differs between cancers and non-cancer diseases.

De nombreux scientifiques ont etudie l'apparition des formes vivantes a partir du mineral. Des notions fondamentales ont ainsi emerge, allant de la caracterisation des materiaux du vivant a leur auto-organisation par des processus actifs, consommant de l'energie pour produire des structures ordonnees. Dans un cheminement inverse, les artistes ceramistes ont explore les differentes facons de reproduire les formes vivantes dans la matiere minerale, pour depasser la dualite entre anime et inanime, entre vivant et inorganique. De nouveaux points de rencontre entre les formes vivantes et la ceramique se situent aujourd'hui dans les materiaux bio-inspires et les morphogeneses organiques.

accepted 2020-08-04; International audience; Recurrence quantification analysis (RQA) is an acknowledged method for the characterization of experimental time series. We propose a parametric version of RQA, pRQA, allowing a fast processing of spatial arrays of time series, once each is modeled by an autoregressive stochastic process. This method relies on the analytical derivation of asymptotic expressions for five current RQA measures as a function of the model parameters. By avoiding the construction of the recurrence plot of the time series, pRQA is computationally efficient. As a proof of principle, we apply pRQA to pattern recognition in multichannel electroencephalographic (EEG) data from a patient with a brain tumor.

International audience; When nonlinear measures are estimated from sampled temporal signals with finitelength, 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.

Motivation Genome-wide chromosomal contact maps are widely used to uncover the 3D organization of genomes. They rely on collecting millions of contacting pairs of genomic loci. Contacts at short range are usually well measured in experiments, while there is a lot of missing information about long-range contacts. Results We propose to use the sparse information contained in raw contact maps to infer high-confidence contact counts between all pairs of loci. Our algorithmic procedure, Boost-HiC, enables the detection of Hi-C patterns such as chromosomal compartments at a resolution that would be otherwise only attainable by sequencing a hundred times deeper the experimental Hi-C library. Boost-HiC can also be used to compare contact maps at an improved resolution. Availability and implementation Boost-HiC is available at https://github.com/LeopoldC/Boost-HiC. Supplementary information Supplementary data are available at Bioinformatics online.

La molécule d'ADN est le support physique de l'information génétique. Ce long polymère est compacté grâce à des protéines pour former les chromosomes. Ce repliement assure la régulation de l’expression des gènes au cours de la vie des cellules. La biochimie des chromosomes est un sujet d'intenses investigations, mais il apparait aujourd'hui que les propriétés physiques des chromosomes sont aussi au coeur de leur fonctionnement. Ces propriétés peuvent être décrites en combinant physique statistique et physique des polymères en solution. Dans cet article, nous présentons les méthodes multi-échelles que nous avons développées pour reconstruire et animer l'architecture fonctionnelle des chromosomes.

We revisit the notion of gene regulatory code in embryonic development in the light of recent findings about genome spatial organisation. 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., Comment: Journal of Molecular Biology, Elsevier, 2019

International audience; 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.

International audience; Given a pattern on a network, i.e. a subset of nodes, can we assess, whether they are randomly distributed on the network or have been generated in a systematic fashion following the network architecture? This question is at the core of network-based data analyses across a range of disciplines-from incidents of infection in social networks to sets of differentially expressed genes in biological networks. Here we introduce generic 'pattern generators' based on an Eden growth model. We assess the capacity of different pattern measures like connectivity, edge density or various average distances, to infer the parameters of the generator from the observed patterns. Some measures perform consistently better than others in inferring the underlying pattern generator, while the best performing measures depend on the global topology of the underlying network. Moreover, we show that pattern generator inference remains possible in case of limited visibility of the patterns.

We investigate the kinetics of a polymer collapse due to the formation of irreversible crosslinks 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 $\xi$ corresponding to the mean pearl size. This length and the transition time depend on the polymer equilibrium dynamics and the crosslinking rate. We confirm experimentally this transition using a DNA conformation capture experiment in yeast., Comment: Article: 12 pages, 4 figures. Supplementary material: 22 pages, 7 supplementary figures

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.

As rock textures reflect the physical conditions and the mechanisms of formation of the rocks, new approaches are used for improving texture analyses, both qualitatively and quantitatively. Pioneer work has recently boosted interest in fractal analysis for quantifying and correlating patterns. Fractal-like patterns relate to a degree of multiscale organization, and fractal dimensions (FD) and their potential variations can be used to infer the physical conditions of rock formation at various scales of observation. Here, we characterize quantitatively the shape and distribution of orthopyroxene grains in ultramafic xenoliths in terms of FD and their relation with temperature of equilibration. Fractal analysis has been applied to several populations of mantle xenoliths: 7 xenoliths collected in the vicinity of Pico Santa Isabel on Bioko Island, an alkaline basaltic volcano in oceanic domain (Gulf of Guinea, Equatorial Atlantic), 9 samples from Sangilen, in the Agardag alkaline lamprophyre dyke (Russia), and 11 samples form Śnieznik (Lutynia, Poland), in the continental domain. Fractal analysis has been conducted to characterize the degree of complexity of the petrographic textures: it is indeed known that large values of FD are associated to more complex textures. The correlation here observed between the orthopyroxene fractal dimension and the temperature of equilibration suggests that FD captures a significant textural feature directly related to the temperature (i.e. generated by a temperature-controlled process). The significant difference in the FD–T correlation observed for the continental and oceanic mantle domains suggests that the mechanical and rheological behaviour is distinct in the oceanic and continental lithospheres. These first promising results should be confirmed by analysing other mantle suites of rocks in different geodynamic settings. Copyright © 2015 John Wiley & Sons, Ltd.

International audience; Plant leaves host species rich communities of foliar endophytic fungi (FEF). Compared to the other compartments of the plant microbiome, FEF diversity is poorly known. Here we document the communities of FEF associated with the endemic Corsican pine Pinus nigra subsp. laricio at three sites across its natural range and examine the effect of forest site, tree age and light exposure on FEF composition. Metabarcoding using next-generation sequencing provided 8,243,608 Ascomycota ITS2 sequences clustered into 642 FEF operational taxonomic units (OTUs). FEF communities did not differ in species richness across sites and tree cohorts, but differed in composition among forest patches and according to tree age. FEF community composition did not correlate with needle location (shade vs full light). Results are robust against the various options of the bioinformatic pipeline specifically developed. This study provides the first picture of FEF diversity in a Mediterranean island and underlines the complementarity of forest massifs for fungal conservation.

(peer-reviewed, accepted 2019-05-14); International audience; We present our use of analytical mean-field approaches in investigating how the interplay between graph topology and excitable dynamics produce spatio-temporal patterns. We first detail the derivation of mean-field equations for a few simple model situations, mainly 3-state discrete-time excitable dynamics with an absolute or a relative excita-tion threshold. Comparison with direct numerical simulation shows that their solution satisfactorily predicts the steady-state excitation density. In contrast, they often fail to capture more complex dynamical features, however we argue that the analysis of this failure is in itself insightful, by pinpointing the key role of mechanisms neglected in the mean-field approach. Moreover, we show how second-order mean-field approaches, in which a topological object (e.g. a cycle or a hub) is considered as embedded in a mean-field surrounding, allow us to go beyond the spatial homogenization currently associated with plain mean-field calculations. The confrontation between these refined analytical predictions and simulation quantitatively evidences the specific contribution of this topological object to the dynamics. Mathematics Subject Classification (2010). Primary 05C82; Secondary 92C42.

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.

International audience; The notion of disease-associated single-nucleotide polymorphisms (da-SNP), as determined in genome-wide association studies (GWAS), is relevant for many complex pathologies, including cancers. It appeared that da-SNPs are not only markers of causal genetic variation but may contribute to the disease development through an influence on gene expression levels. We argue that understanding this possible functional role of da-SNPs requires to consider their embedding in the tridimensional (3D) multi-scale organization of the human genome. We then focus on the potential impact of da-SNPs on chromatin loops and recently observed topologically associating domains (TADs). We show that for some diseases and cancer types, da-SNPs are over-represented in the borders of these topological domains, in a way that cannot be explained by an increased exon density. This analysis of the distribution of da-SNPs within the 3D genome organization suggests candidate loci for further experimental investigation of the mechanisms underlying genetic susceptibility to diseases, in particular cancer.

In this paper, the complexity in the spatial distribution of the lineaments was investigated from on remote sensing topographic (SRTM DEM) and multispectral (Landsat) data. Lineaments in equatorial Africa were chosen to apply the fractal analysis methodology. The good correlations of the obtained data with some geophysical data from the same area allow that the complexity in the spatial distribution of the lineaments can give qualitative information on the interior of the earth (or on other planets). This method can provide a bridge between classical geology and geophysics, and particularly powerful for studying large and inaccessible regions.

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., HIV-1 viral gene expression stochastically switches between active and inactive states. Here, using improved single molecule RNA microscopy, the authors show that HIV-1 RNA stochastic transcription is achieved by groups of closely spaced polymerases, and is regulated by Mediator and TBP at different time scales.

In higher organisms, all cells share the same genome, but every cell expresses only a limited and specific set of genes that defines the cell type. During cell division, not only the genome, but also the cell type is inherited by the daughter cells. This intriguing phenomenon is achieved by a variety of processes that have been collectively termed epigenetics: the stable and inheritable changes in gene expression patterns. This article reviews the extremely rich and exquisitely multi-scale physical mechanisms that govern the biological processes behind the initiation, spreading and inheritance of epigenetic states. These include not only the changes in the molecular properties associated with the chemical modifications of DNA and histone proteins, such as methylation and acetylation, but also less conventional ones, such as the physics that governs the three-dimensional organization of the genome in cell nuclei. Strikingly, to achieve stability and heritability of epigenetic states, cells take advantage of many different physical principles, such as the universal behavior of polymers and copolymers, the general features of non-equilibrium dynamical systems, and the electrostatic and mechanical properties related to chemical modifications of DNA and histones. By putting the complex biological literature under this new light, the emerging picture is that a limited set of general physical rules play a key role in initiating, shaping and transmitting this crucial "epigenetic landscape". This new perspective not only allows to rationalize the normal cellular functions, but also helps to understand the emergence of pathological states, in which the epigenetic landscape becomes dysfunctional., 34 pages, 13 figures

In [Brandman et al., 2005] it was proposed that interlinked fast and slow positive feedback loops are a frequent motif in biological signaling, because such a device can allow for a rapid response to an external stimulus (sensitivity) along with a certain noise-buffering capacity (robustness), as soon as the two loops operate on different time scales. Here we explore the properties of the nonlinear system responsible for this behavior. We argue that (a) the noise buffering is not linked to the stochastic nature of the stimulus, but only to the time scale of the stimulus variation compared to the intrinsic time scales of the system, and (b) this buffering of stimulus variations follows from the stabilization of a region of the state space away from the equilibrium branches of the system. Our analysis is based on a slow-fast decomposition of the dynamics. We analyze the strength of this buffering as a function of the time scales involved and the Boolean logic of the coupling between dynamic variables, as well as of the amplitude of the stimulus variations. We underline that such a nonequilibrium regime is universal as soon as the stimulus time scale is smaller than the larger time scale of the system, preventing the prediction of the behavior from the features of the bifurcation diagram or using a linear analysis.

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. Contact: arndt@ihes.fr

Chaque forme est une interrogation. Les mathematiques y repondent en termes de structures et de symetries, et elles nous offrent un dictionnaire de formes ideales avec lequel decrire notre perception. La physique nous apprend qu'une forme naturelle revele tout autant les forces et processus qui l'ont engendree que les proprietes de la matiere dans laquelle elle s'incarne. Le vivant ajoute une dimension evolutive et adaptative pour produire des formes fonctionnelles et des organismes autonomes. Chaque forme est une interrogation. Elle renvoie a une question ancestrale: qu'est-ce que c'est? Est-ce dangereux? L'homme a du savoir distinguer la forme d'un lion ou celle d'une biche dans une tache beige lointaine. En effet, c'est d'abord et surtout par leur forme que nous identifions les objets qui nous environnent. Celle presentee Figure~1 interpelle ainsi l'observateur, si on ne l'accompagne pas d'explications. Une premiere reponse a la question de l'identification d'une forme est apportee par les mathematiques. Les objets mathematiques fournissent un repertoire de formes ideales avec lequel decrire les formes reelles de facon plus ou moins approchee. Par exemple, un cercle et son interieur, le disque, resument les proprietes geometriques communes a tous les ronds: roue, couronne de pain, rond de serviette, globule rouge. Les formes mathematiques les plus typiques, par exemple le cercle ou le carre, sont associees a des symetries remarquables. La formulation operatoire de la symetrie d'une forme est son invariance par un ensemble de transformations: le cercle est invariant par toute rotation autour de son centre, alors qu'un carre est seulement invariant par rotation d'un ou plusieurs quarts de tour autour de son point central, ou bien par reflexion par rapport a un axe median. Des symetries plus complexes peuvent egalement se rencontrer, comme par exemple la symetrie helicoidale d'une double helice (forme mathematique de la molecule d'ADN) ou l'autosimilarite d'une structure fractale (forme mathematique d'un relief cotier ou d'un flocon de neige, invariante sous l'action iteree d'un zoom local). En general une forme mathematique peut aussi s'exprimer par une equation. Les formes mathematiques presentent ainsi un aspect geometrique (les symetries qu'elles possedent). Un cercle peut ainsi etre defini par l'equation 'rayon = constante', et il est caracterise (avec le disque et la couronne) par son invariance par toute rotation autour de son centre. Ces formes mathematiques nous permettent de classifier les formes reelles, de percevoir et de decrire les points communs de leur geometrie, en les associant a des archetypes. Ce sont ces formes mathematiques qui sous-tendent l'esquisse d'un objet reel, lorsqu'on se concentre sur sa forme. Elles reduisent la diversite des formes naturelles a un nombre plus restreint de formes abstraites et ideales. En ce sens les formes naturelles apparaissent comme les avatars multiples des formes ideales rencontrees en mathematiques.

International audience; 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.

This paper introduces an extension of recurrence analysis to symbolic sequences. Heuristic arguments based on Shannon–McMillan–Breiman theorem suggest several relations between the statistical features of "symbolic" recurrence plots and the entropy per unit time of the dynamics; their practical efficiency for experimental sequences of finite length is checked numerically on two paradigmatic models, namely discretized logistic map trajectories and Markov chains, and also on experimental behavioral sequences. Specific advantages of RP analysis are presented, among which is the detection of nonstationary features.

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.

Ionic currents across neuron and glial cells membranes lie at the origin of the entire brain electrophysiology. They are the common root of functional brain dynamics and mesoscopic or macroscopic phenomena such as extracellular fields. In particular, they provide the relevant basis to relate cellular electrophysiology and macroscopic dipole models. In order to derive robust features and to envision the multi-scale approaches required to connect the different levels of observation, an essential prerequisite is to have minimal model of elementary ionic motions. In this paper, we propose a general cellular automata framework allowing to investigate the distribution of ionic currents in heterogeneous media interspersed with membranes, from which follows the local electromagnetic field.

Face a la complexite gigantesque des systemes biologiques, un des problemes auxquels sont confrontes les scientifiques est d’expliquer pourquoi elle est tellement superieure a celle des objets inanimes, alors qu’il est aujourd’hui etabli que leurs ingredients elementaires — les atomes, ions et electrons — sont exactement les memes et qu’ils sont regis par les memes lois physico-chimiques. Cette complexite a ete recemment invoquee comme un argument en faveur d’un “dessein intelligent” a l’œuvre dans la creation du monde, selon lequel le monde vivant serait trop complexe pour n’etre que le resultat de processus materiels aveugles. Nous allons ici developper l’idee inverse, a savoir que cette complexite peut tout a fait s’expliquer a partir des lois du monde physique, si l’on se place dans le cadre de la theorie de l’evolution par selection naturelle et des processus d’adaptation associes. Il apparait ainsi qu’un point essentiel pour comprendre le monde vivant actuel est de prendre en compte sa nature historique. La biosphere evolue, allant jusqu’a modifier radicalement les conditions physico-chimiques environnantes (la composition de l’atmosphere, par exemple), les especes en presence, et leurs interactions cooperatives ou competitives. Decrire la diversite actuelle du vivant et la complexite des organismes vivants observes aujourd’hui amene naturellement a la question de l’apparition de cette complexite, et donc a s’interesser aussi a des situations intermediaires, plus archaiques, de complexite tres inferieure. Nous devons cependant souligner ici que notre hypothese de travail, squelette des raisonnements et continuellement soumise a l’epreuve des faits, est que la vie est nee spontanement du monde physique, et que l’histoire a expliquer est bien une complexification et une diversification des formes et processus biologiques.

International audience; 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 robust- ness and simplicity. Its usefulness is particularly important because the ratio of the values of the adjustable parameters, α and β, 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.

International audience; 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.

Ce texte discute les enjeux des approches interdisciplinaires, par opposition a une specialisation accrue, face aux grandes questions de la biologie actuelle et aux defis que posent l'analyse et l'interpretation de donnees experimentales de plus en plus riches et extensives. Pour favoriser l'etablissement de collaborations interdisciplinaires efficaces et durables, nous organisons depuis 2002 une ecole-chercheurs annuelle, dans l'ile de Berder (Morbihan), soutenue par les formations permanentes du CNRS et de l'Inra. Nous decrivons les specificites de cette ecole et comment elle repond aux attentes de formation et d'echanges de ses participants : un grand nombre d'orateurs, un equilibre entre les differentes disciplines, des exposes synthetiques et pedagogiques, une grande place laissee aux questions, debats, interactions et animations de terrain, pendant une semaine intense et coupee des preoccupations immediates.

International audience; Recent investigations on 3D chromatin folding revealed that the eukaryote genomes are both highly compartmentalized and extremely dynamic. This review presents the most recent advances in topological domains' organization of the eukaryote genomes and discusses the relationship to chromatin loop formation. CTCF protein appears as a central factor of these two organization levels having either a strong insulating role at TAD borders, or a weaker architectural role in chromatin loop formation. TAD borders directly impact on chromatin dynamics by restricting contacts within specific genomic portions thus confining chromatin loop formation within TADs. We discuss how sub-TAD chromatin dynamics, constrained into a recently described statistical helix conformation, can produce functional interactions by contact stabilization.

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.

We investigate the evolution of a system composed of N non-interacting point particles of mass m in a container divided into two chambers by a movable adiabatic piston of mass M≫m. Using a two-time-scale perturbation approach in terms of the small parameter α=2m/(M+m), we show that the evolution towards thermal equilibrium proceeds in two stages. The first stage is a fast, deterministic, adiabatic relaxation towards mechanical equilibrium. The second stage, which takes place at times $$\mathcal{O}$$ (M), is a slow fluctuation-driven, diathermic relaxation towards thermal equilibrium. A very simple equation is derived which shows that in the second stage, the position of the piston is given by X M (t)= L[1/2−ξ(αt)] where the function ξ is independent of M. Numerical simulations support the assumptions underlying our analytical derivations and illustrate the large mass range in which the picture holds.

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. Electronic supplementary material The online version of this article (doi:10.1186/s12864-015-1786-8) contains supplementary material, which is available to authorized users.

International audience; The notion of allostery introduced for proteins about fifty years ago has been extended since then to DNA allostery, where a locally triggered DNA structural transition remotely controls other DNA-binding events. We further extend this notion and propose that chromatin fiber allosteric transitions, induced by histone-tail covalent modifications, may play a key role in transcriptional regulation. We present an integrated scenario articulating allosteric mechanisms at different scales: allosteric transitions of the condensed chromatin fiber induced by histone-tail acetylation modify the mechanical constraints experienced by the embedded DNA, thus possibly controlling DNA-binding of allosteric transcription factors or further allosteric mechanisms at the linker DNA level. At a higher scale, different epigenetic constraints delineate different statistically dominant subsets of accessible chromatin fiber conformations, which each favors the assembly of dedicated regulatory complexes, as detailed on the emblematic example of the mouse Igf2-H19 gene locus and its parental imprinting. This physical view offers a mechanistic and spatially structured explanation of the observed correlation between transcriptional activity and histone modifications. The evolutionary origin of allosteric control supports to speak of an 'epigenetic code', by which events involved in transcriptional regulation are encoded in histone modifications in a context-dependent way.

International audience; We identify three different visions of complexity with the aim to clarify the research field on complex systems. We use Laplace’s demon as a reference for formulating these visions. Vision 1 breaks Laplace’s dream by exhibiting fundamental difficulties in mathematics, physics and computer sciences hampering to derive systemic properties from the knowledge of components characteristics and their interactions rules. Vision 2 reactivates Laplace’s dream, with new demons based on increased computation power and big data availability, yet subject to the limitation identified by vision 1. Finally, vision 3 challenges Laplace’s demon to simulate subjectivity, counterfactuals, empathy and their cascading collective effects.; Nous distinguons trois visions de la complexité afin de clarifier les contours de la recherche dans ce domaine. Nous utilisons le démon de Laplace comme référence pour présenter ces visions. La vision 1 brise le rêve du démon de Laplace en identifiant des systèmes particuliers qui lui résistent en mathématiques, physique et informatique. La vision 2 propose une nouvelle version du rêve de Laplace fondée sur la disponibilité récente de grandes quantités de données et de nouvelles technologies de programmation, de stockage et de calcul. La vision 3 met le démon face au défi de simuler la subjectivité et ses effets collectifs.

We consider the evolution of a system composed of N non-interacting point particles of mass m in a cylindrical container divided into two regions by a movable adiabatic wall (the adiabatic piston). We study the thermodynamic limit for the piston where the area A of the cross-section, the mass M of the piston, and the number N of particles go to infinity keeping A/M and N/M fixed. The length of the container is a fixed parameter which can be either finite or infinite. In this thermodynamic limit we show that the motion of the piston is deterministic and the evolution is adiabatic. Moreover if the length of the container is infinite, we show that the piston evolves toward a stationary state with velocity approximately proportional to the pressure difference. If the length of the container is finite, introducing a simplifying assumption we show that the system evolves with either weak or strong damping toward a well-defined state of mechanical equilibrium where the pressures are the same, but the temperatures different. Numerical simulations are presented to illustrate possible evolutions and to check the validity of the assumption.