Invariant higher-order variational problems II

Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as Riemannian cubics on object manifolds that are endowed with normal metrics. The prime examples of such object manifolds are the symmetric spaces. We characterize the class of cubics on object manifolds that can be lifted horizontally to cubics on the group of transformations. Conversely, we show that certain types of non-horizontal geodesics on the group of transformations project to cubics. Finally, we apply second-order Lagrange--Poincar\'e reduction to the problem of Riemannian cubics on the group of transformations. This leads to a reduced form of the equations that reveals the obstruction for the projection of a cubic on a transformation group to again be a cubic on its object manifold.Comment: 40 pages, 1 figure. First version -- comments welcome

Evolutionary origins of the estrogen signaling system : insights from amphioxus

Author Posting. © The Author(s), 2011. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Journal of Steroid Biochemistry and Molecular Biology 127 (2011): 176–188, doi:10.1016/j.jsbmb.2011.03.022.Classically, the estrogen signaling system has two core components: cytochrome P450 aromatase (CYP19), the enzyme complex that catalyzes the rate limiting step in estrogen biosynthesis; and estrogen receptors (ERs), ligand activated transcription factors that interact with the regulatory region of target genes to mediate the biological effects of estrogen. While the importance of estrogens for regulation of reproduction, development and physiology has been well-documented in gnathostome vertebrates, the evolutionary origins of estrogen as a hormone are still unclear. As invertebrates within the phylum Chordata, cephalochordates (e.g. the amphioxus of the genus Branchiostoma) are among the closest invertebrate relatives of the vertebrates and can provide critical insight into the evolution of vertebrate-specific molecules and pathways. To address this question, this paper briefly reviews relevant earlier studies that help to illuminate the history of the aromatase and ER genes, with a particular emphasis on insights from amphioxus and other invertebrates. We then present new analyses of amphioxus aromatase and ER sequence and function, including an in silico model of the amphioxus aromatase protein, and CYP19 gene analysis. CYP19 shares a conserved gene structure with vertebrates (9 coding exons) and moderate sequence conservation (40% amino acid identity with human CYP19). Modeling of the amphioxus aromatase substrate binding site and simulated docking of androstenedione in comparison to the human aromatase shows that the substrate binding site is conserved and predicts that androstenedione could be a substrate for amphioxus CYP19. The amphioxus ER is structurally similar to vertebrate ERs, but differs in sequence and key residues of the ligand binding domain. Consistent with results from other laboratories, amphioxus ER did not bind radiolabeled estradiol, nor did it modulate gene expression on an estrogen-responsive element (ERE) in the presence 59 of estradiol, 4-hydroxytamoxifen, diethylstilbestrol, bisphenol A or genistein. Interestingly, it has been shown that a related gene, the amphioxus “steroid receptor” (SR), can be activated by estrogens and that amphioxus ER can repress this activation. CYP19, ER and SR are all primarily expressed in gonadal tissue, suggesting an ancient paracrine/autocrinesignaling role, but it is not yet known how their expression is regulated and, if estrogen is actually synthesized in amphioxus, whether it has a role in mediating any biological effects . Functional studies are clearly needed to link emerging bioinformatics and in vitro molecular biology results with organismal physiology to develop an understanding of the evolution of estrogen signaling.Supported by grants from the NIEHS P42 ES07381 (GVC, SV) and EPA (STAR-RD831301) (GVC), a Ruth L Kirschstein National Research Service Award (AT, F32 ES013092-01), an NIH traineeship (SS, SG), a NATO Fellowship (AN) and the Boston University Undergraduate Research Program (LC)

Distribution of lymphocytes and adhesion molecules in human cervix and vagina

Knowledge of the histological distribution of leucocytes and adhesion molecules in the human genital tract is scarce although local immunity in this region is important. Using immunohistochemical methods, we here describe the organization of CD3+, CD8+ and CD4+ T cells, CD19+ B cells, CD38+ plasma cells, major histocompatibility complex (MHC) class II+ antigen-presenting cells and CD14+ monocytes, as well as the expression of endothelial addressins in normal human ecto-cervical and vaginal mucosa. T cells were clustered in a distinct band beneath the epithelium and were also dispersed in the epithelium and the lamina propria, whereas CD38+ plasma cells were present only in the lamina propria. MHC class II+ cells were numerous in the lamina propria and in the epithelium, where they morphologically resembled dendritic cells. Lymphoid aggregates containing CD19+ and CD20+B cells as well as CD3+, CD4+ and CD8+ cells were also found in the cervix. The mucosal addressin cell adhesion molecule-1 (MAdCAM-1) was not expressed on the vascular endothelium in the cervical or vaginal mucosa. In contrast, intercellular adhesion molecule-1 (ICAM-1), vascular adhesion protein-1 (VAP-1) and P-selectin were expressed in all tissue samples, and vascular cell adhesion molecule-1 (VCAM-1) and E-selectin were found in four of seven samples. We conclude that the distribution of leucocytes and adhesion molecules is very similar in the ecto-cervical and the vaginal mucosa and that the regulation of lymphocyte homing to the genital tract is different from that seen in the intestine. Our results also clearly suggest that the leucocytes are not randomly scattered in the tissue but organized in a distinct pattern