On the bicomplex Gaussian Fibonacci and Gaussian Lucas numbers

We give the bicomplex Gaussian Fibonacci and the bicomplex Gaussian Lucas numbers and establish the generating functions and Binet’s formulas related to these numbers. Also, we present the summation formula, matrix representation and Honsberger identity and their relationship between these numbers. Finally, we show the relationships among the bicomplex Gaussian Fibonacci, the bicomplex Gaussian Lucas, Gaussian Fibonacci, Gaussian Lucas and Fibonacci numbers

Neural immunoglobulin superfamily interaction networks

The immunoglobulin superfamily (IgSF) encompasses hundreds of cell surface proteins containing multiple immunoglobulin-like (Ig) domains. Among these are neural IgCAMs, which are cell adhesion molecules that mediate interactions between cells in the nervous system. IgCAMs in some vertebrate IgSF subfamilies bind to each other homophilically and heterophilically, forming small interaction networks. In Drosophila, a global ‘interactome’ screen identified two larger networks in which proteins in one IgSF subfamily selectively interact with proteins in a different subfamily. One of these networks, the ‘Dpr-ome’, includes 30 IgSF proteins, each of which is expressed in a unique subset of neurons. Recent evidence shows that one interacting protein pair within the Dpr-ome network is required for development of the brain and neuromuscular system

Using the Web Sites of Kindergartens in Parenting Education and the Present Condition in Turkey

Family is the elementary school for children in the process of acquiring knowledge and skills. Qualities of family affect children directly. Supporting families in terms of children’s education and increasing their efficiencies will also positively affect children. Thus, schools should consider not only children, but also their families while providing education. The objective of this study is to offer a suggestion for using the web sites of kindergartens as an instrument in parenting education and examine the web sites of kindergartens in Turkey from this aspect. The study was conducted by using case study pattern, which is among qualitative research methods. The study group consisted of 81 official kindergartens from 81 different provinces and 20 private kindergartens from 20 different metropolitans. Schools in the study group were determined by using typical case sampling method, which is among purposeful sampling methods. The first official and private kindergartens that were reached in the internet search engine by writing the name of province and kindergarten (for example, Tokat kindergarten) were included in the study group. The study data were acquired by examining the web sites of kindergartens in the study group in terms of their content and the acquired data were analyzed via content analysis method. As a result of the study; it was seen that information contents were involved under titles like; Our School (f=81/ 100%), Connections (f=81/ 100%), Announcements (f=81/ 100%), Statistics (f=81/ 100%), News (f=80/ 98,4%), Classes (f=62/ 76,2%), Photo Gallery (f=60/ 73,8%) and Counseling (f=47/ 57,8%) in the web sites of official kindergartens. On the other hand, the contents were involved under titles like; Our School (f=20/ 100%), Communication (f=19/ 95%), Counseling (f=14/ 70%) and Announcements (f=9/ 45%) in the web sites of private kindergartens. It was seen that schools involved information about parenting education generally under the title of counseling. It was also seen that topic titles like parental attitudes, children’s developmental features, children’s nourishment and school adaptation were prominent regarding parenting education. Keywords: Preschool Period, Family, Parenting Education, Kindergarten, Web Site

Family of neural wiring receptors in bilaterians defined by phylogenetic, biochemical, and structural evidence

The evolution of complex nervous systems was accompanied by the expansion of numerous protein families, including cell-adhesion molecules, surface receptors, and their ligands. These proteins mediate axonal guidance, synapse targeting, and other neuronal wiring-related functions. Recently, 32 interacting cell surface proteins belonging to two newly defined families of the Ig superfamily (IgSF) in fruit flies were discovered to label different subsets of neurons in the brain and ventral nerve cord. They have been shown to be involved in synaptic targeting and morphogenesis, retrograde signaling, and neuronal survival. Here, we show that these proteins, Dprs and DIPs, are members of a widely distributed family of two- and three-Ig domain molecules with neuronal wiring functions, which we refer to as Wirins. Beginning from a single ancestral Wirin gene in the last common ancestor of Bilateria, numerous gene duplications produced the heterophilic Dprs and DIPs in protostomes, along with two other subfamilies that diversified independently across protostome phyla. In deuterostomes, the ancestral Wirin evolved into the IgLON subfamily of neuronal receptors. We show that IgLONs interact with each other and that their complexes can be broken by mutations designed using homology models based on Dpr and DIP structures. The nematode orthologs ZIG-8 and RIG-5 also form heterophilic and homophilic complexes, and crystal structures reveal numerous apparently ancestral features shared with Dpr-DIP complexes. The evolutionary, biochemical, and structural relationships we demonstrate here provide insights into neural development and the rise of the metazoan nervous system

Precise regulation of the guidance receptor DMA-1 by KPC-1/Furin instructs dendritic branching decisions

Extracellular adhesion molecules and their neuronal receptors guide the growth and branching of axons and dendrites. Growth cones are attracted to intermediate targets, but they must switch their response upon arrival so that they can move away and complete the next stage of growth. Here, we show that KPC-1, a C. elegans Furin homolog, regulates the level of the branching receptor DMA-1 on dendrites by targeting it to late endosomes. In kpc-1 mutants, the level of DMA-1 is abnormally high on dendrites, resulting in trapping of dendrites at locations where a high level of the cognate ligand, the adhesion molecule SAX-7/L1, is present. The misregulation of DMA-1 also causes dendritic self-avoidance defects. Thus, precise regulation of guidance receptors creates flexibility of responses to guidance signals and is critical for neuronal morphogenesis

Precise regulation of the guidance receptor DMA-1 by KPC-1/furin instructs dendritic branching decisions

Extracellular adhesion molecules and their neuronal receptors guide the growth and branching of axons and dendrites. Growth cones are attracted to intermediate targets, but they must switch their response upon arrival so that they can move away and complete the next stage of growth. Here, we show that KPC-1, a C. elegans Furin homolog, regulates the level of the branching receptor DMA-1 on dendrites by targeting it to late endosomes. In kpc-1 mutants, the level of DMA-1 is abnormally high on dendrites, resulting in trapping of dendrites at locations where a high level of the cognate ligand, the adhesion molecule SAX-7/L1, is present. The misregulation of DMA-1 also causes dendritic self-avoidance defects. Thus, precise regulation of guidance receptors creates flexibility of responses to guidance signals and is critical for neuronal morphogenesis

Molecular basis of synaptic specificity by immunoglobulin superfamily receptors in drosophila

In stereotyped neuronal networks, synaptic connectivity is dictated by cell surface proteins, which assign unique identities to neurons, and physically mediate axon guidance and synapse targeting. We recently identified two groups of immunoglobulin superfamily proteins in Drosophila, Dprs and DIPs, as strong candidates for synapse targeting functions. Here, we uncover the molecular basis of specificity in Dpr–DIP mediated cellular adhesions and neuronal connectivity. First, we present five crystal structures of Dpr–DIP and DIP–DIP complexes, highlighting the evolutionary and structural origins of diversification in Dpr and DIP proteins and their interactions. We further show that structures can be used to rationally engineer receptors with novel specificities or modified affinities, which can be used to study specific circuits that require Dpr–DIP interactions to help establish connectivity. We investigate one pair, engineered Dpr10 and DIP-α, for function in the neuromuscular circuit in flies, and reveal roles for homophilic and heterophilic binding in wiring

An Extracellular Interactome of Immunoglobulin and LRR Proteins Reveals Receptor-Ligand Networks

Extracellular domains of cell surface receptors and ligands mediate cell-cell communication, adhesion, and initiation of signaling events, but most existing protein-protein “interactome” data sets lack information for extracellular interactions. We probed interactions between receptor extracellular domains, focusing on a set of 202 proteins composed of the Drosophila melanogaster immunoglobulin superfamily (IgSF), fibronectin type III (FnIII), and leucine-rich repeat (LRR) families, which are known to be important in neuronal and developmental functions. Out of 20,503 candidate protein pairs tested, we observed 106 interactions, 83 of which were previously unknown. We “deorphanized” the 20 member subfamily of defective-in-proboscis-response IgSF proteins, showing that they selectively interact with an 11 member subfamily of previously uncharacterized IgSF proteins. Both subfamilies interact with a single common “orphan” LRR protein. We also observed interactions between Hedgehog and EGFR pathway components. Several of these interactions could be visualized in live-dissected embryos, demonstrating that this approach can identify physiologically relevant receptor-ligand pairs