Approximation by multipoles of the multiple acoustic scattering by small obstacles and application to the Foldy theory of isotropic scattering.

50 (avec 1,5 interligne)International audienceThe asymptotic analysis, carried out in this paper, for the problem of a multiple scattering of a time-harmonic wave by obstacles whose size is small as compared with the wavelength establishes that the effect of the small bodies can be approximated at any order of accuracy by the field radiated by point sources. Among other issues, this asymptotic expansion of the wave furnishes a mathematical justification with optimal error estimates of Foldy's method that consists in approximating each small obstacle by a point isotropic scatterer. Finally, it is shown how this theory can be further improved by adequately locating the center of phase of the point scatterers and taking into account of self-interactions

A genetic basis for a postmeiotic X versus Y chromosome intragenomic conflict in the mouse.

Intragenomic conflicts arise when a genetic element favours its own transmission to the detriment of others. Conflicts over sex chromosome transmission are expected to have influenced genome structure, gene regulation, and speciation. In the mouse, the existence of an intragenomic conflict between X- and Y-linked multicopy genes has long been suggested but never demonstrated. The Y-encoded multicopy gene Sly has been shown to have a predominant role in the epigenetic repression of post meiotic sex chromatin (PMSC) and, as such, represses X and Y genes, among which are its X-linked homologs Slx and Slxl1. Here, we produced mice that are deficient for both Sly and Slx/Slxl1 and observed that Slx/Slxl1 has an opposite role to that of Sly, in that it stimulates XY gene expression in spermatids. Slx/Slxl1 deficiency rescues the sperm differentiation defects and near sterility caused by Sly deficiency and vice versa. Slx/Slxl1 deficiency also causes a sex ratio distortion towards the production of male offspring that is corrected by Sly deficiency. All in all, our data show that Slx/Slxl1 and Sly have antagonistic effects during sperm differentiation and are involved in a postmeiotic intragenomic conflict that causes segregation distortion and male sterility. This is undoubtedly what drove the massive gene amplification on the mouse X and Y chromosomes. It may also be at the basis of cases of F1 male hybrid sterility where the balance between Slx/Slxl1 and Sly copy number, and therefore expression, is disrupted. To the best of our knowledge, our work is the first demonstration of a competition occurring between X and Y related genes in mammals. It also provides a biological basis for the concept that intragenomic conflict is an important evolutionary force which impacts on gene expression, genome structure, and speciation

The multicopy gene Sly represses the sex chromosomes in the male mouse germline after meiosis.

Studies of mice with Y chromosome long arm deficiencies suggest that the male-specific region (MSYq) encodes information required for sperm differentiation and postmeiotic sex chromatin repression (PSCR). Several genes have been identified on MSYq, but because they are present in more than 40 copies each, their functions cannot be investigated using traditional gene targeting. Here, we generate transgenic mice producing small interfering RNAs that specifically target the transcripts of the MSYq-encoded multicopy gene Sly (Sycp3-like Y-linked). Microarray analyses performed on these Sly-deficient males and on MSYq-deficient males show a remarkable up-regulation of sex chromosome genes in spermatids. SLY protein colocalizes with the X and Y chromatin in spermatids of normal males, and Sly deficiency leads to defective repressive marks on the sex chromatin, such as reduced levels of the heterochromatin protein CBX1 and of histone H3 methylated at lysine 9. Sly-deficient mice, just like MSYq-deficient mice, have severe impairment of sperm differentiation and are near sterile. We propose that their spermiogenesis phenotype is a consequence of the change in spermatid gene expression following Sly deficiency. To our knowledge, this is the first successful targeted disruption of the function of a multicopy gene (or of any Y gene). It shows that SLY has a predominant role in PSCR, either via direct interaction with the spermatid sex chromatin or via interaction with sex chromatin protein partners. Sly deficiency is the major underlying cause of the spectrum of anomalies identified 17 y ago in MSYq-deficient males. Our results also suggest that the expansion of sex-linked spermatid-expressed genes in mouse is a consequence of the enhancement of PSCR that accompanies Sly amplification

Etude mathématique et numérique de modèles homogénéisés de métamatériaux

Dans la première partie des études des problèmes de propagation d'ondes en présence de métamatériaux homogénéisés tels que les équations de Maxwell, le systèmes de l'acoustique ou de l'élasticité linéaire. Nous établissons des résultats d'existence et d'unicité pour ces systèmes sous des hypothèses phénoménologiques sur le métamatériaux en accord avec certains modèles de la littérature. Nous abordons ensuite leurs approximations numériques. Nous présentons des résultats concernant les éléments finis pour l'approximation de l'équation de Helmholtz qui montrent que ce schéma peut ne pas converger en présence de métamatériaux. On propose alors un schéma Galerkin Discontinu dont on montre numériquement sa convergence sur des exemples de métamatériauxIn the first part, we investigate wave propagation problems with homogenized metamaterials for Maxwell's equations and acoustics or linear elasticity systems. We establish that each of these systems is well-posed under assumptions that are relevant for some models already designed in the literature. We next tackle their numerical approximation. We give results showing that the finite element method for the approximation of Helmholtz equation, when metatmaterials are involved, may not converges. We propose then a numerical scheme, the EF-AL schemen which can be with metamaterials and we prove that it converges as soon as the considered problem is well-posed. We finish studying the discontinuous galerkin scheme. We show numerically its convergence for some examples of metamaterials

Apparent non-canonical trans-splicing is generated by reverse transcriptase in vitro

Trans-splicing, the in vivo joining of two RNA molecules, is well characterized in several groups of simple organisms but was long thought absent from fungi, plants and mammals. However, recent bioinformatic analyses of expressed sequence tag (EST) databases suggested widespread trans-splicing in mammals^1-2^. Splicing, including the characterised trans-splicing systems, involves conserved sequences at the splice junctions. Our analysis of a yeast non-coding RNA revealed that around 30% of the products of reverse transcription lacked an internal region of 117 nt, suggesting that the RNA was spliced. The junction sequences lacked canonical splice-sites but were flanked by direct repeats, and further analyses indicated that the apparent splicing actually arose because reverse transcriptase can switch templates during transcription^3^. Many newly identified, apparently trans-spliced, RNAs lacked canonical splice sites but were flanked by short regions of homology, leading us to question their authenticity. Here we report that all reported categories of non-canonical splicing could be replicated using an in vitro reverse transcription system with highly purified RNA substrates. We observed the reproducible occurrence of ostensible trans-splicing, exon shuffling and sense-antisense fusions. The latter generate apparent antisense non-coding RNAs, which are also reported to be abundant in humans^4^. Different reverse transcriptases can generate different products of template switching, providing a simple diagnostic. Many reported examples of splicing in the absence of canonical splicing signals may be artefacts of cDNA preparation