Reconstruction of Inclusions for the Inverse Boundary Value Problem of Non-stationary Heat Equation

An inverse problem for identifying an inclusion inside an isotropic, homogeneous heat conductive medium is considered. The shape of inclusion can change depending on time. For the one space dimensional case, we developed an analogue of the probe method known for inverse boundary value problems for elliptic equations and gave the reconstruction procedure for identifying the inclusion from the Neumann to Dirichlet map

Reconstruction of Inclusions for the Inverse Boundary Value Problem of Non-stationary Heat Equation

An inverse problem for identifying an inclusion inside an isotropic, homogeneous heat conductive medium is considered. The shape of inclusion can change depending on time. For the one space dimensional case, we developed an analogue of the probe method known for inverse boundary value problems for elliptic equations and gave the reconstruction procedure for identifying the inclusion from the Neumann to Dirichlet map

A conserved non-reproductive GnRH system in chordates.

Gonadotropin-releasing hormone (GnRH) is a neuroendocrine peptide that plays a central role in the vertebrate hypothalamo-pituitary axis. The roles of GnRH in the control of vertebrate reproductive functions have been established, while its non-reproductive function has been suggested but less well understood. Here we show that the tunicate Ciona intestinalis has in its non-reproductive larval stage a prominent GnRH system spanning the entire length of the nervous system. Tunicate GnRH receptors are phylogenetically closest to vertebrate GnRH receptors, yet functional analysis of the receptors revealed that these simple chordates have evolved a unique GnRH system with multiple ligands and receptor heterodimerization enabling complex regulation. One of the gnrh genes is conspicuously expressed in the motor ganglion and nerve cord, which are homologous structures to the hindbrain and spinal cord of vertebrates. Correspondingly, GnRH receptor genes were found to be expressed in the tail muscle and notochord of embryos, both of which are phylotypic axial structures along the nerve cord. Our findings suggest a novel non-reproductive role of GnRH in tunicates. Furthermore, we present evidence that GnRH-producing cells are present in the hindbrain and spinal cord of the medaka, Oryzias latipes, thereby suggesting the deep evolutionary origin of a non-reproductive GnRH system in chordates

EC₅₀ values (nM) of tGnRHs for intracellular calcium ion mobilization in HEK293-MSR cells expressing only Ci-GnRHR1 or co-expressing Ci-GnRHR1 and 4.

<p>The EC₅₀ values of tGnRH-6 are underlined to emphasize the dramatic increase in the potency on the cells co-transfected with Ci-GnRHR1 and 4.</p

EC₅₀ values (nM) of t-GnRHs for cAMP production in HEK293-MSR cells expressing only Ci-GnRHR1, 2, 3 or co-expressing Ci-GnRHR1 and 4, or Ci-GnRHR3 and 4.

<p>No markedly altered effects of co-expression with Ci-GnRHR4 on activities of tGnRHs were detected.</p

The <i>C. intestinalis</i> GnRH receptors (GnRHRs) and spatial expression patterns of <i>gnrhr</i> genes in the larva.

<p>(A) Genomic organization of the <i>C. intestinalis</i> GnRHRs. Three GnRHRs (Ci-GnRHR1, Ci-GnRHR2, and Ci-GnRHR3) are encoded by a gene cluster located on Scaffold 93 while the gene encoding another GnRHR (Ci-GnRHR4) is located in Scaffold 198. Arrows indicate the location and orientation of the genes. Gene model IDs in the JGI version 1.0 genome database are indicated below the arrows. (B-E) Whole larvae showing localization of transcripts of <i>Ci-GnRHR1</i> (B), <i>Ci-GnRHR2</i> (C), <i>Ci-GnRHR3</i> (D), or <i>Ci-GnRHR4</i> (E). (F1–F3) A middle part of the tail of the same individual with different focal planes showing muscle cells and caudal epidermal neurons (cen) expressing <i>Ci-GnRHR2</i>. (G-I) GFP reporter expression in the tail muscle (mu) or notochord (no) under the control of the regulatory region of <i>Ci-GnRHR1</i> (G), <i>Ci-GnRHR2</i> (H), or <i>Ci-GnRHR3</i> (I). <b>cen</b>, caudal epidermal neuron; <b>mu</b>, muscle; <b>no</b>, notochord. Scale bars: 100 µm in (B), 50 µm in (F1) and (G).</p