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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. [ABSTRACT FROM AUTHOR]

Background: Understanding the mechanical properties of chromatin is an essential step towards deciphering the physical rules of gene regulation. In the past ten years, many single molecule experiments have been carried out, and high resolution measurements of the chromatin fiber stiffness are now available. Simulations have been used in order to link those measurements with structural cues, but so far no clear agreement among different groups has been reached. Results: We revisit here some of the most precise experimental results obtained with carefully reconstituted fibers. Conclusions: We show that the mechanical properties of the chromatin fiber can be quantitatively accounted for by the stiffness of the DNA molecule and the 3D structure of the chromatin fiber. [ABSTRACT FROM AUTHOR]

Genetic and epigenetic information in eukaryotic cells is carried on chromosomes, basically consisting of large compact supercoiled chromatin fibers. Micromanipulations have recently led to great advances in the knowledge of the complex mechanisms underlying the regulation of DNA transaction events by nucleosome and chromatin structural changes. Indeed, magnetic and optical tweezers have allowed opportunities to handle single nucleosomal particles or nucleosomal arrays and measure their response to forces and torques, mimicking the molecular constraints imposed in vivo by various molecular motors acting on the DNA. These challenging technical approaches provide us with deeper understanding of the way chromatin dynamically packages our genome and participates in the regulation of cellular metabolism. [ABSTRACT FROM AUTHOR]

Chromatin structure is a powerful tool to regulate eukaryotic transcription. Moreover, nucleosomes are constantly remodeled, disassembled, and reassembled in the body of transcribed genes. Here we propose a general model that explains, in quantitative terms, how transcription elongation affects nucleosome structure at a distance as a result of the positive torque the polymerases create as they translocate along DNA templates. [ABSTRACT FROM AUTHOR]

The biological functions played by the nucleus of eukaryotic cells and especially those involved in cellular differentiation not only depend on the genomic sequence but also on all the proteins which form the nucleo-protein complex named chromatin. The tridimensional organization of this huge polymer involves many structural levels, the most basic one being the nucleosome. Nucleosomes further organize into the so-called 30 nm fiber, which, according to recent works, is likely to be the main functional level of chromatin. We wish here to propose a plausible structure for the 30 nm chromatin fiber that could explain its functional role. In our model, silenced chromatin is locked by nucleosome stacking interactions. This is achieved by a conformational transition within the nucleosome core particle (NCP) which allows nucleosomes to stack along two helices without bending the DNA linkers. We used molecular modeling to check that this conformational transition was plausible. Then we proposed to modify the well-known two-angle model according to these atomic level results. The emerging picture is an allosteric behavior of the nucleosomes induced by their collective organization within the 30 nm chromatin fiber. [Copyright &y& Elsevier]

DNA condensation by multivalent cations plays a crucial role in genome packaging in viruses and sperm heads, and has been extensively studied using single-molecule experimental methods. In those experiments, the values of the critical condensation forces have been used to estimate the amplitude of the attractive DNA-DNA interactions. Here, to describe these experiments, we developed an analytical model and a rigid body Langevin dynamics assay to investigate the behavior of a polymer with self-interactions, in the presence of a traction force applied at its extremities. We model self-interactions using a pairwise attractive potential, thereby treating the counterions implicitly. The analytical model allows to accurately predict the equilibrium structures of toroidal and rod-like condensed structures, and the dependence of the critical condensation force on the DNA length. We find that the critical condensation force depends strongly on the length of the DNA, and finite-size effects are important for molecules of length up to 105 µm. Our Langevin dynamics simulations show that the force-extension behavior of the rod-like structures is very different from the toroidal ones, so that their presence in experiments should be easily detectable. In double-stranded DNA condensation experiments, the signature of the presence of rod-like structures was not unambiguously detected, suggesting that the polyamines used to condense DNA may protect it from bending sharply as needed in the rod-like structures. [ABSTRACT FROM AUTHOR]

We develop a new powerful method to reproduce in silico single-molecule manipulation experiments. We demonstrate that flexible polymers such as DNA can be simulated using rigid body dynamics thanks to an original implementation of Langevin dynamics in an open source library called Open Dynamics Engine. We moreover implement a global thermostat which accelerates the simulation sampling by two orders of magnitude. We reproduce force-extension as well as rotation-extension curves of reference experimental studies. Finally, we extend the model to simulations where the control parameter is no longer the torsional strain but instead the torque, and predict the expected behavior for this case which is particularly challenging theoretically and experimentally. [ABSTRACT FROM AUTHOR]

The interaction between two parallel charged plates in ionic solution is a general starting point for studying colloidal complexes. An intuitive expression of the pressure exerted on the plates is usually proposed, which includes an electrostatic plus an osmotic contribution. We present here an explicit and self-consistent derivation of this formula in the only framework of the Poisson-Boltzmann (PB) theory. We also show that, depending on external constraints, the correct thermodynamic potential can differ from the usual PB free energy. For asymmetric, oppositely charged plates, the resulting expression predicts a non-trivial equilibrium position with the plates separated by a finite distance. The depth of this energy minimum is decisive for the stability of the complex. It is therefore crucial to obtain its explicit dependence on the charge densities of the plates and on the ion concentration. Analytic expressions for the position and depth of the energy minimum were derived in 1975 by Ohshima [Colloid Polym. Sci. 253, 150 (1975)] but, surprisingly, these important results seem to have been overlooked. We retrieve these expressions in a simpler formalism, more familiar to the physics community, and give a physical interpretation of the observed behavior. [ABSTRACT FROM AUTHOR]

Ever since the discovery of the nucleosome in 1974, scientists have stumbled upon discrete particles in which DNA is wrapped around histone complexes of different stoichiometries: octasomes, hexasomes, tetrasomes, “split” half-nucleosomes, and, recently, bona fide hemisomes. Do all these particles exist in vivo? Under what conditions? What is their physiological significance in the complex DNA transactions in the eukaryotic nucleus? What are their dynamics? This review summarizes research spanning more than three decades and provides a new meaning to the term “nucleosome.” The nucleosome can no longer be viewed as a single static entity: rather, it is a family of particles differing in their structural and dynamic properties, leading to different functionalities. [Copyright &y& Elsevier]

Chromatin is a complex of DNA and specific proteins forming an intermediary level of organization of eukaryotic genomes, between double-stranded DNA and chromosome. Within a generic modeling of chromatin assembly, we investigate the interplay between the mechanical properties of the chromatin fiber and its biological functions. A quantitative step is to relate the mechanics at the DNA level and the mechanics described at the chromatin fiber level. It allows to calculate the complete set of chromatin elastic constants (twist and bend persistence lengths, stretch modulus and twist–stretch coupling constant), in terms of DNA elastic properties and geometric features of the fiber. These elastic constants are strongly sensitive to the local architecture of the fiber and we argue that this tunable elasticity might be a key feature in chromatin functions, for instance in the initiation and regulation of transcription. Moreover, this analysis provides a framework to interpret micromanipulation studies of chromatin fiber and suggests further experiments involving intercalators to scan the tunable elasticity of the fiber. [Copyright &y& Elsevier]

Background: Localized functional domains within chromosomes, known as topologically associating domains (TADs), have been recently highlighted. In Drosophila, TADs are biochemically defined by epigenetic marks, this suggesting that the 3D arrangement may be the "missing link" between epigenetics and gene activity. Recent observations (Boettiger et al. in Nature 529(7586):418–422, 2016) provide access to structural features of these domains with unprecedented resolution thanks to super-resolution experiments. In particular, they give access to the distribution of the radii of gyration for domains of different linear length and associated with different transcriptional activity states: active, inactive or repressed. Intriguingly, the observed scaling laws lack consistent interpretation in polymer physics. Results: We develop a new methodology conceived to extract the best information from such super-resolution data by exploiting the whole distribution of gyration radii, and to place these experimental results on a theoretical framework. We show that the experimental data are compatible with the finite-size behavior of a self-attracting polymer. The same generic polymer model leads to quantitative differences between active, inactive and repressed domains. Active domains behave as pure polymer coils, while inactive and repressed domains both lie at the coil–globule crossover. For the first time, the "color-specificity" of both the persistence length and the mean interaction energy are estimated, leading to important differences between epigenetic states. Conclusion: These results point toward a crucial role of criticality to enhance the system responsivity, resulting in both energy transitions and structural rearrangements. We get strong indications that epigenetically induced changes in nucleosome–nucleosome interaction can cause chromatin to shift between different activity states. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The hallmark of sickle cell disease (SCD) is vasoocclusive crisis (VOC). The sickle red blood cells (SS-RBCs) present enhanced adhesion to activated endothelial cells (ECs) as compared to normal RBCs (AA-RBCs) and believed to contribute to VOC. Hydroxycarbamide (HC), the sole drug thus far proven as efficacious at reducing VOC frequency, alters the expression of adhesion proteins both on RBCs and ECs. We investigated the functional effect of HC on the adhesive properties of ECs from the micro- or the macrocirculation (TrHBMEC, HPMEC, and HUVEC). Using a flow chamber, we analyzed RBC dynamics on the treated or untreated EC bed and firm adhesion in basal and inflammatory conditions. Most significant effects were obtained with ECs from the pulmonary microcirculation (HPMEC). HC treatment of ECs affects both transient interactions and firm adhesion of SS-RBCs to the EC bed. Indeed, first, HC-treatment of ECs decreases the number of firmly adherent SS-RBCs to the adhesion level of AA-RBCs in a VCAM-1 independent manner. Second, HC significantly increases the mean velocity of SS-RBCs and reduces the population of SS-RBCs in contact with the EC bed. These data provide additional evidence that modulation of SS-RBCs/ECs interactions by HC represents an important aspect of its mechanism of action. [ABSTRACT FROM AUTHOR]

Using a simple geometric model, we propose a general method for computing the linking number of the DNA embedded in chromatin fibers. The relevance of the method is reviewed through the single molecule experiments that have been performed in vitro with magnetic tweezers. We compute the linking number of the DNA in the manifold conformational states of the nucleosome which have been evidenced in these experiments and discuss the functional dynamics of chromosomes in the light of these manifold states. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

Thecontrol over DNA elongation in nanofluidic devices holds great potentialfor large-scale genomic analysis. So far, the manipulation of DNAin nanochannels has been mostly carried out with electrophoresis andseldom with hydrodynamics, although the physics of soft matter innanoscale flows has raised considerable interest over the past decade.In this report the migration of DNA is studied in nanochannels oflateral dimension spanning 100 to 500 nm using both actuation principles.We show that the relaxation kinetics are 3-fold slowed down and theextension increases up to 3-fold using hydrodynamics. We propose amodel to account for the onset in elongation with the flow, whichassumes that DNA response is determined by the shear-driven lift forcesmediated by the proximity of the channels’ walls. Overall,we suggest that hydrodynamic actuation allows for an improved manipulationof DNA in nanochannels. [ABSTRACT FROM AUTHOR]

Complex diseases involve both a genetic component and a response to environmental factors or lifestyle changes. Recently, genome-wide association studies (GWAS) have succeeded in identifying hundreds of polymorphisms that are statistically associated with complex diseases. However, the association is usually weak and none of the associated allelic forms is either necessary or sufficient for the disease occurrence. We argue that this promotes a network view, centred on functional redundancy. We adapted reliability theory to the concerned sub-network, modelled as a parallel array of functional modules. In our model, as long as one module remains active, the function correlated with the respective disease is ensured and disease does not occur. Genetic factors reduce the initial number of available modules while environment, contingent surroundings, personal history, epigenetics, and some intrinsic stochasticity influence their persistence time. This model reproduces age-specific incidence curves and explains the influence of environmental changes. It offers a new paradigm, according to which disease occurs due to a lack of functional elements, depending on many idiosyncratic factors. Genetic risk assessed from GWAS is only a statistical notion with no direct interpretation at the individual level. However, genomic profiling could be useful at population level in devising models to guide decisions in heakh care policy. [ABSTRACT FROM AUTHOR]

Summary: Using magnetic tweezers to investigate the mechanical response of single chromatin fibers, we show that fibers submitted to large positive torsion transiently trap positive turns at a rate of one turn per nucleosome. A comparison with the response of fibers of tetrasomes (the [H3-H4]2 tetramer bound with ∼50 bp of DNA) obtained by depletion of H2A-H2B dimers suggests that the trapping reflects a nucleosome chiral transition to a metastable form built on the previously documented right-handed tetrasome. In view of its low energy, <8 kT, we propose that this transition is physiologically relevant and serves to break the docking of the dimers on the tetramer that in the absence of other factors exerts a strong block against elongation of transcription by the main RNA polymerase. [Copyright &y& Elsevier]

Magnetic tweezers were used to study the mechanical response under torsion of single nucleosome arrays reconstituted on tandem repeats of 5S positioning sequences. Regular arrays are extremely resilient and can reversibly accommodate a large amount of supercoiling without much change in length. This behavior is quantitatively described by a molecular model of the chromatin three-dimensional architecture. In this model, we assume the existence of a dynamic equilibrium between three conformations of the nucleosome, corresponding to different crossing statuses of the entry/exit DNAs (positive, null or negative, respectively). Torsional strain displaces that equilibrium, leading to an extensive reorganization of the fiber's architecture. The model explains a number of long-standing topological questions regarding DNA in chromatin and may provide the basis to better understand the dynamic binding of chromatin-associated proteins.Note: In the supplementary information initially published online to accompany this article, Supplementary Figure 2 was mistakenly replaced by Supplementary Equation 2. The error has been corrected online. [ABSTRACT FROM AUTHOR]

Abstract: During the eukaryotic cell cycle, chromatin undergoes several conformational changes, which are believed to play key roles in gene expression regulation during interphase, and in genome replication and division during mitosis. In this paper, we propose a scenario for chromatin structural reorganization during mitosis, which bridges all the different scales involved in chromatin architecture, from nucleosomes to chromatin loops. We build a model for chromatin, based on available data, taking into account both physical and topological constraints DNA has to deal with. Our results suggest that the mitotic chromosome condensation/decondensation process is induced by a structural change at the level of the nucleosome itself. [Copyright &y& Elsevier]

Crohn's disease (CD) is a complex genetic disorder for which aetiology is unknown. Recently, genetic factors for susceptibility have been described. Several genetic loci have been mapped and partially explain the familial aggregations of the disease. However, environmental factors may also contribute to these aggregations. We considered that if the role of non-genetic factors was negligible, CD patients would be randomly distributed in sibships with multiple affected siblings. On the other hand if there was a significant environmental contribution, the siblings would be affected non-randomly over exposure status. In order to test this hypothesis, we studied 102 sibships with two or more affected siblings. A statistical test, named Cluster of Affected Sibling Test or CAST, was developed, based on the exact calculation of the probability of observing a given number of clusters of affected siblings in multiplex families. The null hypothesis of a random distribution of affected siblings was rejected (P=0,005). The observed excess of affected sibling clusters indicates that birth order influences the disease status. Considering that an adjacent order of birth is a global estimate of environmental sharing, this observation strongly suggests that environmental factors contribute to the observed familial aggregations of the disease. This observation provides evidence that familial CD is a relevant tool for further studies of environmental factors and gene-environment interaction. More generally, the CAST statistics may be widely applicable to estimate the involvement of environmental factors in the aetiology of other binary traits which may be observed in multiple members of the same sibship. [ABSTRACT FROM AUTHOR]

Chromosome dynamics are recognized to be intimately linked to genomic transactions, yet the physical principles governing spatial fluctuations of chromatin are still a matter of debate. Using high-throughput single-particle tracking, we recorded the movements of nine fluorescently labeled chromosome loci located on chromosomes III, IV, XII, and XIV of Saccharomyces cerevisiae over an extended temporal range spanning more than four orders of magnitude (10 (-2)10 (3) sec). Spatial fluctuations appear to be characterized by an anomalous diffusive behavior, which is homogeneous in the time domain, for all sites analyzed. We show that this response is consistent with the Rouse polymer model, and we confirm the relevance of the model with Brownian dynamics simulations and the analysis of the statistical properties of the trajectories. Moreover, the analysis of the amplitude of fluctuations by the Rouse model shows that yeast chromatin is highly flexible, its persistence length being qualitatively estimated to <30 nm. Finally, we show that the Rouse model is also relevant to analyze chromosome motion in mutant cells depleted of proteins that bind to or assemble chromatin, and suggest that it provides a consistent framework to study chromatin dynamics. We discuss the implications of our findings for yeast genome architecture and for target search mechanisms in the nucleus. [ABSTRACT FROM AUTHOR]