Cortical fast-spiking parvalbumin interneurons enwrapped in the perineuronal net express the metallopeptidases Adamts8, Adamts15 and Neprilysin.

The in situ hybridization Allen Mouse Brain Atlas was mined for proteases expressed in the somatosensory cerebral cortex. Among the 480 genes coding for protease/peptidases, only four were found enriched in cortical interneurons: Reln coding for reelin; Adamts8 and Adamts15 belonging to the class of metzincin proteases involved in reshaping the perineuronal net (PNN) and Mme encoding for Neprilysin, the enzyme degrading amyloid ß-peptides. The pattern of expression of metalloproteases (MPs) was analyzed by single-cell reverse transcriptase multiplex PCR after patch clamp and was compared with the expression of 10 canonical interneurons markers and 12 additional genes from the Allen Atlas. Clustering of these genes by K-means algorithm displays five distinct clusters. Among these five clusters, two fast-spiking interneuron clusters expressing the calcium-binding protein Pvalb were identified, one co-expressing Pvalb with Sst (PV-Sst) and another co-expressing Pvalb with three metallopeptidases Adamts8, Adamts15 and Mme (PV-MP). By using Wisteria floribunda agglutinin, a specific marker for PNN, PV-MP interneurons were found surrounded by PNN, whereas the ones expressing Sst, PV-Sst, were not.

Interoperable atlases of the human brain.

The last two decades have seen an unprecedented development of human brain mapping approaches at various spatial and temporal scales. Together, these have provided a large fundus of information on many different aspects of the human brain including micro- and macrostructural segregation, regional specialization of function, connectivity, and temporal dynamics. Atlases are central in order to integrate such diverse information in a topographically meaningful way. It is noteworthy, that the brain mapping field has been developed along several major lines such as structure vs. function, postmortem vs. in vivo, individual features of the brain vs. population-based aspects, or slow vs. fast dynamics. In order to understand human brain organization, however, it seems inevitable that these different lines are integrated and combined into a multimodal human brain model. To this aim, we held a workshop to determine the constraints of a multi-modal human brain model that are needed to enable (i) an integration of different spatial and temporal scales and data modalities into a common reference system, and (ii) efficient data exchange and analysis. As detailed in this report, to arrive at fully interoperable atlases of the human brain will still require much work at the frontiers of data acquisition, analysis, and representation. Among them, the latter may provide the most challenging task, in particular when it comes to representing features of vastly different scales of space, time and abstraction. The potential benefits of such endeavor, however, clearly outweigh the problems, as only such kind of multi-modal human brain atlas may provide a starting point from which the complex relationships between structure, function, and connectivity may be explored.

Altered gene expression in the dorsolateral prefrontal cortex of individuals with schizophrenia.

The underlying pathology of schizophrenia (SZ) is likely as heterogeneous as its symptomatology. A variety of cortical and subcortical regions, including the prefrontal cortex, have been implicated in its pathology, and a number of genes have been identified as risk factors for disease development. We used in situ hybridization (ISH) to examine the expression of 58 genes in the dorsolateral prefrontal cortex (DLPFC, comprised of Brodmann areas 9 and 46) from 19 individuals with a premorbid diagnosis of SZ and 33 control individuals. Genes were selected based on: (1) previous identification as risk factors for SZ; (2) cell type markers or (3) laminar markers. Cell density and staining intensity were compared in the DLPFC, as well as separately in Brodmann areas 9 and 46. The expression patterns of a variety of genes, many of which are associated with the GABAergic system, were altered in SZ when compared with controls. Additional genes, including C8orf79 and NR4A2, showed alterations in cell density or staining intensity between the groups, highlighting the need for additional studies. Alterations were, with only a few exceptions, limited to Brodmann area 9, suggesting regional specificity of pathology in the DLPFC. Our results agree with previous studies on the GABAergic involvement in SZ, and suggest that areas 9 and 46 may be differentially affected in the disease. This study also highlights additional genes that may be altered in SZ, and indicates that these potentially interesting genes can be identified by ISH and high-throughput image analysis techniques.

Dimension independence in exterior algebra.

The identities between homogeneous expressions in rank 1 vectors and rank n - 1 covectors in a Grassmann-Cayley algebra of rank n, in which one set occurs multilinearly, are shown to represent a set of dimension-independent identities. The theorem yields an infinite set of nontrivial geometric identities from a given identity.

A geometric identity for Pappus' theorem.

An expression in the exterior algebra of a Peano space yielding Pappus' theorem was originally given by Doubilet, Rota, and Stein [Doubilet, P., Rota, G.-C. & Stein, J. (1974) Stud. Appl. Math. 8, 185-216]. Motivated by an identity of Rota, I give an identity in a Grassmann-Cayley algebra of step 3, involving joins and meets alone, which expresses the theorem of Pappus.