On the convergence of the no response test

The no response test is a new scheme in inverse problems for partial differential equations which was recently proposed in [D. R. Luke and R. Potthast, SIAM J. Appl. Math., 63 (2003), pp. 1292–1312] in the framework of inverse acoustic scattering problems. The main idea of the scheme is to construct special probing waves which are small on some test domain. Then the response for these waves is constructed. If the response is small, the unknown object is assumed to be a subset of the test domain. The response is constructed from one, several, or many particular solutions of the problem under consideration. In this paper, we investigate the convergence of the no response test for the reconstruction information about inclusions D from the Cauchy values of solutions to the Helmholtz equation on an outer surface $\partial\Omega$ with $\overline{D} \subset \Omega$. We show that the one‐wave no response test provides a criterion to test the analytic extensibility of a field. In particular, we investigate the construction of approximations for the set of singular points $N(u)$ of the total fields u from one given pair of Cauchy data. Thus, the no response test solves a particular version of the classical Cauchy problem. Also, if an infinite number of fields is given, we prove that a multifield version of the no response test reconstructs the unknown inclusion D. This is the first convergence analysis which could be achieved for the no response test.

Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test

In this article, we use the no-response test idea, introduced in Luke and Potthast (2003) and Potthast (Preprint) and the inverse obstacle problem, to identify the interface of the discontinuity of the coefficient gamma of the equation del (.) gamma(x)del + c(x) with piecewise regular gamma and bounded function c(x). We use infinitely many Cauchy data as measurement and give a reconstructive method to localize the interface. We will base this multiwave version of the no-response test on two different proofs. The first one contains a pointwise estimate as used by the singular sources method. The second one is built on an energy (or an integral) estimate which is the basis of the probe method. As a conclusion of this, the probe and the singular sources methods are equivalent regarding their convergence and the no-response test can be seen as a unified framework for these methods. As a further contribution, we provide a formula to reconstruct the values of the jump of gamma(x), x is an element of partial derivative D at the boundary. A second consequence of this formula is that the blow-up rate of the indicator functions of the probe and singular sources methods at the interface is given by the order of the singularity of the fundamental solution.

Interfacial structure of wild-type and mutant forms of puroindoline-b bound to DPPG monolayers

The interaction of wild-type puroindoline-b (Pin-b+) and two mutant forms having single residue substitutions (G46S or W44R) with L-alpha-dipalmitoylphosphatidyl-dl-glycerol (DPPG) as a Langmuir monolayer at the air/water interface was investigated by neutron reflectivity (NR) and Brewster angle microscopy (BAM). NR profiles were fitted using a three-layer model to enable differences in penetration of protein between the lipid headgroup and acyl regions to be determined. The data showed similar surface excesses for each of the three proteins at the interface; however, it was revealed that the depth of penetration of protein into the lipid region differed for each protein with Pin-b+ penetrating further into the acyl region of the lipid compared to the mutant forms of the protein that interacted with the headgroup region only. BAM images revealed that the domain structure of the DPPG monolayers was disrupted when Pin-b+ adsorption had reached equilibrium, suggesting protein penetration had led to compression of the lipid region. In contrast, the domain structure was unaffected by the W44R mutant, suggesting no change in compression of the lipid region and hence little or no penetration of protein into the lipid layer.

Genesis and expansion of metazoan transcription factor gene classes

We know little about the genomic events that led to the advent of a multicellular grade of organization in animals, one of the most dramatic transitions in evolution. Metazoan multicellularity is correlated with the evolution of embryogenesis, which presumably was underpinned by a gene regulatory network reliant on the differential activation of signaling pathways and transcription factors. Many transcription factor genes that play critical roles in bilaterian development largely appear to have evolved before the divergence of cnidarian and bilaterian lineages. In contrast, sponges seem to have a more limited suite of transcription factors, suggesting that the developmental regulatory gene repertoire changed markedly during early metazoan evolution. Using whole- genome information from the sponge Amphimedon queenslandica, a range of eumetazoans, and the choanoflagellate Monosiga brevicollis, we investigate the genesis and expansion of homeobox, Sox, T- box, and Fox transcription factor genes. Comparative analyses reveal that novel transcription factor domains ( such as Paired, POU, and T- box) arose very early in metazoan evolution, prior to the separation of extant metazoan phyla but after the divergence of choanoflagellate and metazoan lineages. Phylogenetic analyses indicate that transcription factor classes then gradually expanded at the base of Metazoa before the bilaterian radiation, with each class following a different evolutionary trajectory. Based on the limited number of transcription factors in the Amphimedon genome, we infer that the genome of the metazoan last common ancestor included fewer gene members in each class than are present in extant eumetazoans. Transcription factor orthologues present in sponge, cnidarian, and bilaterian genomes may represent part of the core metazoan regulatory network underlying the origin of animal development and multicellularity.

Expression and regulation of Nkd-1, an intracellular component of Wnt signalling pathway in the chick embryo

The Wnt family of secreted signalling molecules control a wide range of developmental processes in all metazoans. The intracellular response to Wnt signalling depends on the choice of signalling cascade activated in the responding cell. Cells can activate either the canonical pathway that modulates gene expression to control cellular differentiation and proliferation, or the non-canonical pathway that controls cell polarity and movement. Recent work has identified the protein Naked Cuticle to act as an intracellular switch to promote the non-canonical pathway at the expense of the canonical pathway. We have cloned chick Naked Cuticle-1 (cNkd-1) and show that it is expressed in a dynamic manner during early embryogenesis. We show that it is expressed in the somites and in particular regions where cells are undergoing movement. Lastly, we show that the expression of cNkd-1 is regulated by Wnt expression originating from the neural tube. This study provides evidence that non-canonical Wnt signalling plays a part in somite development.

Expression of AmphiCoe, an amphioxus COE/EBF gene, in the developing central nervous system and epidermal sensory neurons

The COE/EBF gene family marks a subset of prospective neurons in the vertebrate central and peripheral. nervous system; including neurons deriving from some ectodermal placodes. Since placodes are often considered unique to vertebrates, we have characterised an amphioxus COE/EBF gene with the aim of using it as a marker to examine the timing and location of peripheral neuron differentiation. A single COE/EBF family member, AmphiCoe, was isolated from the amphioxus Branchiostoma floridae: AmphiCoe lies basal to the vertebrate COE/EBF genes in molecular phylogenetic analysis, suggesting that the duplications that formed the vertebrate COE/EBF family were specific to the vertebrate lineage. AmphiCoe is expressed in the central nervous system and in a small number of scattered ectodermal cells on the flanks of neurulae stage embryos. These cells become at least largely recessed beneath the ectoderm. Scanning electron microscopy was used to examine embryos in which the ectoderm had been partially peeled away. This revealed that these cells have neuronal morphology, and we infer that they are the precursors of epidermal primary sensory neurons. These characters lead us to suggest that differentiation of some ectodermal cells into sensory neurons with a tendency to sink beneath the embryonic surface represents a primitive feature that has become incorporated into placodes during vertebrate evolution. (C) 2004 Wiley-Liss, Inc.

Dispersal of NK homeobox gene clusters in amphioxus and humans

The Drosophila melanogaster genome has six physically clustered NK-related homeobox genes in just 180 kb. Here we show that the NK homeobox gene cluster was an ancient feature of bilaterian animal genomes, but has been secondarily split in chordate ancestry. The NK homeobox gene clusters of amphioxus and vertebrates are each split and dispersed at two equivalent intergenic positions. From the ancestral NK gene cluster, only the Tlx-Lbx and NK3-NK4 linkages have been retained in chordates. This evolutionary pattern is in marked contrast to the Hox and ParaHox gene clusters, which are compact in amphioxus and vertebrates, but have been disrupted in Drosophila.

Pitch range and vowel duration in the speech of children with Williams syndrome

This paper reports the pitch range and vowel duration data from a group of children with Williams syndrome (WS) in comparison with a group of typically developing children matched for chronological age (CA) and a group matched for receptive language abilities (LA). It is found that the speech of the WS group has a greater pitch range and that vowels tend to be longer in duration than in the speech of the typically developing children. These findings are in line with the impressionistic results reported by Reilly, Klima and Bellugi [17].

Cellular and molecular investigations into the development of the pectoral girdle

The forelimbs of higher vertebrates are composed of two portions: the appendicular region (stylopod, zeugopod and autopod) and the less prominent proximal girdle elements (scapula and clavicle) that brace the limb to the main trunk axis. We show that the formation of the muscles of the proximal limb occurs through two distinct mechanisms. The more superficial girdle muscles (pectoral and latissimus dorsi) develop by the “In–Out” mechanism whereby migration of myogenic cells from the somites into the limb bud is followed by their extension from the proximal limb bud out onto the thorax. In contrast, the deeper girdle muscles (e.g. rhomboideus profundus and serratus anterior) are induced by the forelimb field which promotes myotomal extension directly from the somites. Tbx5 inactivation demonstrated its requirement for the development of all forelimb elements which include the skeletal elements, proximal and distal muscles as well as the sternum in mammals and the cleithrum of fish. Intriguingly, the formation of the diaphragm musculature is also dependent on the Tbx5 programme. These observations challenge our classical views of the boundary between limb and trunk tissues. We suggest that significant structures located in the body should be considered as components of the forelimb.

Manipulations of germ-cell populations in the gonad of the fowl

1. Embryos of the domestic fowl have been partially sterilised by injecting the drug busulphan into 24-h incubated eggs. 2. Some of these embryos were injected with primordial germ cells (PGCs) after 55 h of incubation to attempt to repopulate the gonads. 3. Primordial germ cells transfected with a defective retrovirus containing the reporter gene lac Z were shown to settle in these sterilised gonads. 4. Quantitative histology of 6-d embryos showed that busulphan produced 75% sterilisation but that PGCs could repopulate these gonads. 5. The technique of producing such germ line chimaeras is of value in studying cell kinetics, gonad differentiation and the production of transgenics.

Amphioxus type I keratin cDNA and the evolution of intermediate filament genes

We report the cloning of an intermediate filament (IF) cDNA from the cephalochordate amphioxus that encodes a protein assignable to the type I keratin group. This is the first type I keratin reported from an invertebrate. Molecular phylogenetic analyses reveal that amphioxus also possesses a type II keratin, and that the genes encoding short-rod IF proteins underwent different patterns of duplication in vertebrates and their closest relatives, the cephalochordates. Extensive IF gene duplication and divergence may have facilitated the origin of new specialised cell types in vertebrates.

Identification and characterisation of five novel miniature inverted-repeat transposable elements (MITEs) in amphioxus (Branchiostoma floridae)

As the sister group to vertebrates, amphioxus is consistently used as a model of genome evolution for understanding the invertebrate/vertebrate transition. The amphioxus genome has not undergone massive duplications like those in the vertebrates or disruptive rearrangements like in the genome of Ciona, a urochordate, making it an ideal evolutionary model. Transposable elements have been linked to many genomic evolutionary changes including increased genome size, modified gene expression, massive gene rearrangements, and possibly intron evolution. Despite their importance in genome evolution, few previous examples of transposable elements have been identified in amphioxus. We report five novel Miniature Inverted-repeat Transposable Elements (MITEs) identified by an analysis of amphioxus DNA sequence, which we have named LanceleTn-1, LanceleTn-2, LanceleTn-3a, LanceleTn-3b and LanceleTn-4. Several of the LanceleTn elements were identified in the amphioxus ParaHox cluster, and we suggest these have had important implications for the evolution of this highly conserved gene cluster. The estimated high copy numbers of these elements implies that MITEs are probably the most abundant type of mobile element in amphioxus, and are thus likely to have been of fundamental importance in shaping the evolution of the amphioxus genome.

Complex history of a chromosomal paralogy region: insights from amphioxus aromatic amino acid hydroxylase genes and insulin-related genes

Aromatic amino acid hydroxylase (AAAH) genes and insulin-like genes form part of an extensive paralogy region shared by human chromosomes 11 and 12, thought to have arisen by tetraploidy in early vertebrate evolution. Cloning of a complementary DNA (cDNA) for an amphioxus (Branchiostoma floridae) hydroxylase gene (AmphiPAH) allowed us to investigate the ancestry of the human chromosome 11/12 paralogy region. Molecular phylogenetic evidence reveals that AmphiPAH is orthologous to vertebrate phenylalanine (PAH) genes; the implication is that all three vertebrate AAAH genes arose early in metazoan evolution, predating vertebrates. In contrast, our phylogenetic analysis of amphioxus and vertebrate insulin-related gene sequences is consistent with duplication of these genes during early chordate ancestry. The conclusion is that two tightly linked gene families on human chromosomes 11 and 12 were not duplicated coincidentally. We rationalize this paradox by invoking gene loss in the AAAH gene family and conclude that paralogous genes shared by paralogous chromosomes need not have identical evolutionary histories.

Clustered Fox genes in lophotrochozoans and the evolution of the bilaterian Fox gene cluster

FoxC, FoxF, FoxL1 and FoxQ1 genes have been shown to be clustered in some animal genomes, with mesendodermal expression hypothesised as a selective force maintaining cluster integrity. Hypotheses are, however, constrained by a lack of data from the Lophotrochozoa. Here we characterise members of the FoxC, FoxF, FoxL1 and FoxQ1 families from the annelid Capitella teleta and the molluscs Lottia gigantea and Patella vulgata. We cloned FoxC, FoxF, FoxL1 and FoxQ1 genes from C. teleta, and FoxC, FoxF and FoxL1 genes from P. vulgata, and established their expression during development. We also examined their genomic organisation in C. teleta and L. gigantea, and investigated local syntenic relationships. Our results show mesodermal and anterior gut expression is a common feature of these genes in lophotrochozoans. In L. gigantea FoxC, FoxF and FoxL1 are closely linked, while in C. teleta Ct-foxC and Ct-foxL1 are closely linked, with Ct-foxF and Ct-foxQ1 on different scaffolds. Adjacent to these genes there is limited evidence of local synteny. This demonstrates conservation of genomic organisation and expression of these genes can be traced in all three bilaterian Superphyla. These data are evaluated against competing theories for the long-term maintenance of gene clusters.