Extracting Labeled Topological Patterns from Samples of Networks

<div><p>An advanced graph theoretical approach is introduced that enables a higher level of functional interpretation of samples of directed networks with identical fixed pairwise different vertex labels that are drawn from a particular population. Compared to the analysis of single networks, their investigation promises to yield more detailed information about the represented system. Often patterns of directed edges in sample element networks are too intractable for a direct evaluation and interpretation. The new approach addresses the problem of simplifying topological information and characterizes such a sample of networks by finding its locatable characteristic topological patterns. These patterns, essentially sample-specific network motifs with vertex labeling, might represent the essence of the intricate topological information contained in all sample element networks and provides as well a means of differentiating network samples. Central to the accurateness of this approach is the null model and its properties, which is needed to assign significance to topological patterns. As a proof of principle the proposed approach has been applied to the analysis of networks that represent brain connectivity before and during painful stimulation in patients with major depression and in healthy subjects. The accomplished reduction of topological information enables a cautious functional interpretation of the altered neuronal processing of pain in both groups.</p></div

The location of the nine EEG electrodes selected for the connectivity analysis according to the extended International 10–20 System of Electrode Placement.

<p>The vertex labeling of the networks that represent significant interactions entails the information about these electrode locations.</p

Motifs of size 2 that were detected in the eight ECN samples.

<p>The occurrence of a 2-motif in an ECN sample is indicated by filled areas. These motifs represent important patterns of directed interactions that occur before and during the processing of painful electrical stimuli. The ECN samples stem from combinations of the group assignment and experimental conditions: MD–patients with major depression, HC–healthy control subjects, left and right–stimulated sides, pre and post–time windows with respect to the stimulus condition.</p

Results of the determination of the mixing parameter for which the edge-switching algorithm samples networks with prescribed in-degree and out-degree sequence uniformly.

<p>For every the resulting value of the performance index exceeds the corresponding -quantile of the test statistic distribution.</p

Examples of effective connectivity networks (ECNs).

<p>The upper row shows networks of a MD patient (#1) before (left network) and after (right network) left hand side stimulation. The lower row shows networks of a healthy control subject (#1) accordingly. These networks are representative for samples of equal sized networks with identical pairwise different vertex labels.</p

Six out of twelve motifs of size 3 that were detected in the eight ECN samples.

<p>The occurrence of a 3-motif in an ECN sample is indicated by filled areas. These motifs represent important directed interaction patterns of brain activity recorded at three different EEG electrodes that occur before and during the processing of painful electrical stimuli. The ECN samples stem from combinations of the group assignment and experimental conditions: MD–patients with major depression, HC–healthy control subjects, left and right–stimulated sides, pre and post–time windows with respect to the stimulus condition (The other 3-motifs are depicted in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0070497#pone-0070497-g005" target="_blank">Figure 5</a>.)</p

Six out of twelve motifs of size 3 that were detected in the eight ECN samples.

<p>The occurrence of a 3-motif in an ECN sample is indicated by filled areas. These motifs represent important directed interaction patterns of brain activity recorded at three different EEG electrodes that occur before and during the processing of painful electrical stimuli. The ECN samples stem from combinations of the group assignment and experimental conditions: MD–patients with major depression, HC–healthy control subjects, left and right–stimulated sides, pre and post–time windows with respect to the stimulus condition (The remaining 3-motifs are depicted in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0070497#pone-0070497-g006" target="_blank">Figure 6</a>.)</p

Loss of <i>RXFP2</i> and <i>INSL3</i> genes in Afrotheria shows that testicular descent is the ancestral condition in placental mammals

<div><p>Descent of testes from a position near the kidneys into the lower abdomen or into the scrotum is an important developmental process that occurs in all placental mammals, with the exception of five afrotherian lineages. Since soft-tissue structures like testes are not preserved in the fossil record and since key parts of the placental mammal phylogeny remain controversial, it has been debated whether testicular descent is the ancestral or derived condition in placental mammals. To resolve this debate, we used genomic data of 71 mammalian species and analyzed the evolution of two key genes (relaxin/insulin-like family peptide receptor 2 [<i>RXFP2</i>] and insulin-like 3 [<i>INSL3</i>]) that induce the development of the gubernaculum, the ligament that is crucial for testicular descent. We show that both <i>RXFP2</i> and <i>INSL3</i> are lost or nonfunctional exclusively in four afrotherians (tenrec, cape elephant shrew, cape golden mole, and manatee) that completely lack testicular descent. The presence of remnants of once functional orthologs of both genes in these afrotherian species shows that these gene losses happened after the split from the placental mammal ancestor. These “molecular vestiges” provide strong evidence that testicular descent is the ancestral condition, irrespective of persisting phylogenetic discrepancies. Furthermore, the absence of shared gene-inactivating mutations and our estimates that the loss of <i>RXFP2</i> happened at different time points strongly suggest that testicular descent was lost independently in Afrotheria. Our results provide a molecular mechanism that explains the loss of testicular descent in afrotherians and, more generally, highlight how molecular vestiges can provide insights into the evolution of soft-tissue characters.</p></div

New Rhinocerotidae from the Kisingiri localities (lower Miocene of western Kenya)

<p>We describe new material of Rhinocerotidae recently collected in western Kenya. A skull from Karungu is one of the best-preserved Miocene skulls in Africa. It differs substantially from that of <i>Rusingaceros leakeyi</i>, the only other relatively well-known rhino from this region and age, in its degree of brachycephaly, possession of a deep nasal notch, and long nasal bones that probably carried a horn of moderate size. Miocene African rhinos are still too poorly known to resolve their phylogenetic relationships, but we tentatively assign this skull to a new species of <i>Victoriaceros</i>, a genus whose type species comes from the younger site of Maboko, although the Karungu skull has a much smaller nasal horn. A parsimony analysis resolves them as sister species within the Elasmotheriini, close to the other African genera <i>Turkanatherium</i> and <i>Chilotheridium</i>, but we consider this result debatable, as <i>Victoriaceros</i> differs considerably from them. Still, they might all be descended from European forms. A partial skull from Gumba is assigned to the Aceratheriini, making it one of the earliest representatives of this group and suggesting that the origin of this tribe could be African.</p> <p>http://zoobank.org/urn:lsid:zoobank.org:pub:2B1E8135-CCD4-43EB-826B-6DF7176DC74E</p> <p>SUPPLEMENTAL DATA—Supplemental materials are available for this article for free at <a href="http://www.tandfonline.com/UJVP" target="_blank">www.tandfonline.com/UJVP</a></p> <p>Citation for this article: Geraads, D., T. Lehmann, D. J. Peppe, and K. P. McNulty. 2016. New Rhinocerotidae from the Kisingiri localities (lower Miocene of western Kenya). Journal of Vertebrate Paleontology. DOI: 10.1080/02724634.2016.1103247.</p

Gene-inactivating mutations in <i>RXFP2</i> in four afrotherian species.

<p>(A) The exon-intron structure of the coding region of the <i>RXFP2</i> gene is shown as boxes (exons, drawn to scale) and lines (introns, not drawn to scale). A vertical red line/arrowhead indicates a frameshifting deletion/insertion, with the number of deleted/inserted bases given above. Stop codon mutations are shown as a black vertical line. Splice site mutations are indicated by the mutated dinucleotide. A blue vertical line indicates a frame-preserving deletion. Red boxes are exons that are either deleted or accumulated numerous mutations that destroy any sequence similarity. All inactivating mutations were validated by unassembled genome sequencing reads stored in the SRA. Elephant, rock hyrax, and aardvark have an intact <i>RXFP2</i> gene and are not shown. A filled star indicates mutations that we confirmed by PCR and Sanger sequencing in the lesser hedgehog tenrec; the exon 17 frameshift was also found in the greater hedgehog tenrec (<a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.2005293#pbio.2005293.s005" target="_blank">S5A and S5B Fig</a>). An open star indicates mutations that we confirmed by PCR and sequencing in the dugong, the sister species of the manatee (<a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.2005293#pbio.2005293.s005" target="_blank">S5C and S5D Fig</a>). (B-I) Examples of inactivating mutations and their validation by unassembled SRA reads. <i>RXFP2</i>, relaxin/insulin-like family peptide receptor 2; SRA, Sequence Read Archive.</p