On the dynamics of Extrasolar Planetary Systems under dissipation. Migration of planets

We study the dynamics of planetary systems with two planets moving in the same plane, when frictional forces act on the two planets, in addition to the gravitational forces. The model of the general three-body problem is used. Different laws of friction are considered. The topology of the phase space is essential in understanding the evolution of the system. The topology is determined by the families of stable and unstable periodic orbits, both symmetric and non symmetric. It is along the stable families, or close to them, that the planets migrate when dissipative forces act. At the critical points where the stability along the family changes, there is a bifurcation of a new family of stable periodic orbits and the migration process changes route and follows the new stable family up to large eccentricities or to a chaotic region. We consider both resonant and non resonant planetary systems. The 2/1, 3/1 and 3/2 resonances are studied. The migration to larger or smaller eccentricities depends on the particular law of friction. Also, in some cases the semimajor axes increase and in other cases they are stabilized. For particular laws of friction and for special values of the parameters of the frictional forces, it is possible to have partially stationary solutions, where the eccentricities and the semimajor axes are fixed.Comment: Accepted in Celestial Mechanics and Dynamical Astronom

Manipulation of the follicular phase: Uterodomes and pregnancy - is there a correlation?

BACKGROUND: Manipulation of the follicular phase uterine epithelium in women undergoing infertility treatment, has not generally shown differing morphological effects on uterine epithelial characteristics using Scanning Electron Microscopy (SEM) and resultant pregnancy rates have remained suboptimal utilising these manipulations. The present study observed manipulation of the proliferative epithelium, with either 7 or 14 days of sequential oestrogen (E) therapy followed by progesterone (P) and assessed the appearance of pinopods (now called uterodomes) for their usefulness as potential implantation markers in seven women who subsequently became pregnant. Three endometrial biopsies per patient were taken during consecutive cycles: day 19 of a natural cycle - (group 1), days 11/12 of a second cycle after 7 days E then P - (group 2), and days 19/22 of a third cycle after 14 days E then P - (group 3). Embryo transfer (ET) was performed in a subsequent long treatment cycle (as per Group 3). RESULTS: Seven pregnancies resulted in seven viable births including one twins and one miscarriage. Analysis of the individual regimes showed 5 days of P treatment to have a higher correlation for uterodomes in all 3 cycles observed individually. It was also observed that all 7 women demonstrated the appearance of uterodomes in at least one of their cycles. CONCLUSIONS: We conclude that manipulation of the follicular phase by shortening the period of E exposure to 7 days, does not compromise uterine epithelial morphology and we add weight to the conclusion that uterodomes indicate a receptive endometrium for implantation

The role of chick Ebf genes in the mediolateral patterning of the somites

This study was conducted to check whether the three chick Early B-cell Factor (Ebf) genes, particularly cEbf1, would be targets for Shh and Bmp signals during somites mediolateral (ML) patterning. Tissue manipulations and gain and loss of function experiments for Shh and Bmp4 were performed and the results revealed that cEbf1 expression was initiated in the cranial presomitic mesoderm by low dose of Bmp4 from the lateral mesoderm and maintained in the ventromedial part of the epithelial somite and the medial sclerotome by Shh from the notochord; while cEbf2/3 expression was induced and maintained by Bmp4 and inhibited by high dose of Shh. To determine whether Ebf1 plays a role in somite patterning, transfection of a dominant-negative construct was carried out; this showed suppression of cPax1 expression in the medial sclerotome and upregulation and medial expansion of cEbf3 and cPax3 expression in sclerotome and dermomyotome, respectively, suggesting that Ebf1 is important for ML patterning. Thus, it is possible that low doses of Bmp4 set up Ebf1 expression which, together with Shh from the notochord, leads to establishment of the medial sclerotome and suppression of lateral identities. These data also conclude that Bmp4 is required in both the medial and lateral domain of the somitic mesoderm to keep the ML identity of the sclerotome through maintenance of cEbf gene expression. These striking findings are novel and give a new insight on the role of Bmp4 on mediolateral patterning of somites

Coordination of Cell Differentiation and Migration in Mathematical Models of Caudal Embryonic Axis Extension

Vertebrate embryos display a predominant head-to-tail body axis whose formation is associated with the progressive development of post-cranial structures from a pool of caudal undifferentiated cells. This involves the maintenance of active FGF signaling in this caudal region as a consequence of the restricted production of the secreted factor FGF8. FGF8 is transcribed specifically in the caudal precursor region and is down-regulated as cells differentiate and the embryo extends caudally. We are interested in understanding the progressive down-regulation of FGF8 and its coordination with the caudal movement of cells which is also known to be FGF-signaling dependent. Our study is performed using mathematical modeling and computer simulations. We use an individual-based hybrid model as well as a caricature continuous model for the simulation of experimental observations (ours and those known from the literature) in order to examine possible mechanisms that drive differentiation and cell movement during the axis elongation. Using these models we have identified a possible gene regulatory network involving self-repression of a caudal morphogen coupled to directional domain movement that may account for progressive down-regulation of FGF8 and conservation of the FGF8 domain of expression. Furthermore, we have shown that chemotaxis driven by molecules, such as FGF8 secreted in the stem zone, could underlie the migration of the caudal precursor zone and, therefore, embryonic axis extension. These mechanisms may also be at play in other developmental processes displaying a similar mode of axis extension coupled to cell differentiation

Large-Scale Clonal Analysis Reveals Unexpected Complexity in Surface Ectoderm Morphogenesis

Background: Understanding the series of morphogenetic processes that underlie the making of embryo structures is a highly topical issue in developmental biology, essential for interpreting the massive molecular data currently available. In mouse embryo, long-term in vivo analysis of cell behaviours and movements is difficult because of the development in utero and the impossibility of long-term culture. Methodology/Principal Findings: We improved and combined two genetic methods of clonal analysis that together make practicable large-scale production of labelled clones. Using these methods we performed a clonal analysis of surface ectoderm (SE), a poorly understood structure, for a period that includes gastrulation and the establishment of the body plan. We show that SE formation starts with the definition at early gastrulation of a pool of founder cells that is already dorso-ventrally organized. This pool is then regionalized antero-posteriorly into three pools giving rise to head, trunk and tail. Each pool uses its own combination of cell rearrangements and mode of proliferation for elongation, despite a common clonal strategy that consists in disposing along the antero-posterior axis precursors of dorso-ventrally-oriented stripes of cells. Conclusions/Significance: We propose that these series of morphogenetic processes are organized temporally and spatially in a posterior zone of the embryo crucial for elongation. The variety of cell behaviours used by SE precursor cells indicates that these precursors are not equivalent, regardless of a common clonal origin and a common clonal strategy. Anothe

A resonant-term-based model including a nascent disk, precession, and oblateness: application to GJ 876

Investigations of two resonant planets orbiting a star or two resonant satellites orbiting a planet often rely on a few resonant and secular terms in order to obtain a representative quantitative description of the system's dynamical evolution. We present a semianalytic model which traces the orbital evolution of any two resonant bodies in a first- through fourth-order eccentricity or inclination-based resonance dominated by the resonant and secular arguments of the user's choosing. By considering the variation of libration width with different orbital parameters, we identify regions of phase space which give rise to different resonant ''depths,'' and propose methods to model libration profiles. We apply the model to the GJ 876 extrasolar planetary system, quantify the relative importance of the relevant resonant and secular contributions, and thereby assess the goodness of the common approximation of representing the system by just the presumably dominant terms. We highlight the danger in using ''order'' as the metric for accuracy in the orbital solution by revealing the unnatural libration centers produced by the second-order, but not first-order, solution, and by demonstrating that the true orbital solution lies somewhere ''in-between'' the third- and fourth-order solutions. We also present formulas used to incorporate perturbations from central-body oblateness and precession, and a protoplanetary or protosatellite thin disk with gaps, into a resonant system. We quantify these contributions to the GJ 876 system, and thereby highlight the conditions which must exist for multi-planet exosystems to be significantly influenced by such factors. We find that massive enough disks may convert resonant libration into circulation; such disk-induced signatures may provide constraints for future studies of exoplanet systems.Comment: 39 pages of body text, 21 figures, 5 tables, 1 appendix, accepted for publication in Celestial Mechanics and Dynamical Astronom

Dynamic 3D Cell Rearrangements Guided by a Fibronectin Matrix Underlie Somitogenesis

Somites are transient segments formed in a rostro-caudal progression during vertebrate development. In chick embryos, segmentation of a new pair of somites occurs every 90 minutes and involves a mesenchyme-to-epithelium transition of cells from the presomitic mesoderm. Little is known about the cellular rearrangements involved, and, although it is known that the fibronectin extracellular matrix is required, its actual role remains elusive. Using 3D and 4D imaging of somite formation we discovered that somitogenesis consists of a complex choreography of individual cell movements. Epithelialization starts medially with the formation of a transient epithelium of cuboidal cells, followed by cell elongation and reorganization into a pseudostratified epithelium of spindle-shaped epitheloid cells. Mesenchymal cells are then recruited to this medial epithelium through accretion, a phenomenon that spreads to all sides, except the lateral side of the forming somite, which epithelializes by cell elongation and intercalation. Surprisingly, an important contribution to the somite epithelium also comes from the continuous egression of mesenchymal cells from the core into the epithelium via its apical side. Inhibition of fibronectin matrix assembly first slows down the rate, and then halts somite formation, without affecting pseudopodial activity or cell body movements. Rather, cell elongation, centripetal alignment, N-cadherin polarization and egression are impaired, showing that the fibronectin matrix plays a role in polarizing and guiding the exploratory behavior of somitic cells. To our knowledge, this is the first 4D in vivo recording of a full mesenchyme-to-epithelium transition. This approach brought new insights into this event and highlighted the importance of the extracellular matrix as a guiding cue during morphogenesis