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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]

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]

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]

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]