Maintaining extensivity in evolutionary multiplex networks

In this paper, we explore the role of network topology on maintaining the extensive property of entropy. We study analytically and numerically how the topology contributes to maintaining extensivity of entropy in multiplex networks, i.e. networks of subnetworks (layers), by means of the sum of the positive Lyapunov exponents, HKS, a quantity related to entropy. We show that extensivity relies not only on the interplay between the coupling strengths of the dynamics associated to the intra (short-range) and inter (long-range) interactions, but also on the sum of the intra-degrees of the nodes of the layers. For the analytically treated networks of size N, among several other results, we show that if the sum of the intra-degrees (and the sum of inter-degrees) scales as N?+1, ? > 0, extensivity can be maintained if the intra-coupling (and the inter-coupling) strength scales as N??, when evolution is driven by the maximisation of HKS. We then verify our analytical results by performing numerical simulations in multiplex networks formed by electrically and chemically coupled neurons

BMP signaling components in embryonic transcriptomes of the hover fly Episyrphus balteatus (Syrphidae)

<p>Abstract</p> <p>Background</p> <p>In animals, signaling of Bone Morphogenetic Proteins (BMPs) is essential for dorsoventral (DV) patterning of the embryo, but how BMP signaling evolved with changes in embryonic DV differentiation is largely unclear. Based on the extensive knowledge of BMP signaling in <it>Drosophila melanogaster</it>, the morphological diversity of extraembryonic tissues in different fly species provides a comparative system to address this question. The closest relatives of <it>D. melanogaster </it>with clearly distinct DV differentiation are hover flies (Diptera: Syrphidae). The syrphid <it>Episyrphus balteatus </it>is a commercial bio-agent against aphids and has been established as a model organism for developmental studies and chemical ecology. The dorsal blastoderm of <it>E. balteatus </it>gives rise to two extraembryonic tissues (serosa and amnion), whereas in <it>D. melanogaster</it>, the dorsal blastoderm differentiates into a single extraembryonic epithelium (amnioserosa). Recent studies indicate that several BMP signaling components of <it>D. melanogaster</it>, including the BMP ligand Screw (Scw) and other extracellular regulators, evolved in the dipteran lineage through gene duplication and functional divergence. These findings raise the question of whether the complement of BMP signaling components changed with the origin of the amnioserosa.</p> <p>Results</p> <p>To search for BMP signaling components in <it>E. balteatus</it>, we generated and analyzed transcriptomes of freshly laid eggs (0-30 minutes) and late blastoderm to early germband extension stages (3-6 hours) using Roche/454 sequencing. We identified putative <it>E. balteatus </it>orthologues of 43% of all annotated <it>D. melanogaster </it>genes, including the genes of all BMP ligands and other BMP signaling components.</p> <p>Conclusion</p> <p>The diversification of several BMP signaling components in the dipteran linage of <it>D. melanogaster </it>preceded the origin of the amnioserosa.</p> <p>[Transcriptome sequence data from this study have been deposited at the NCBI Sequence Read Archive (SRP005289); individually assembled sequences have been deposited at GenBank (<ext-link ext-link-id="JN006969" ext-link-type="gen">JN006969</ext-link>-<ext-link ext-link-id="JN006986" ext-link-type="gen">JN006986</ext-link>).]</p