The structure and function of the human brain are highly stereotyped, implying a conserved molecular program responsible for its development, cellular structure, and function. We applied a correlation-based metric of “differential stability” (DS) to assess reproducibility of gene expression patterning across 132 structures in six individual brains, revealing meso-scale genetic organization. The highest DS genes are highly biologically relevant, with enrichment for brain-related biological annotations, disease associations, drug targets, and literature citations. Using high DS genes we identified 32 anatomically diverse and reproducible gene expression signatures, which represent distinct cell types, intracellular components, and/or associations with neurodevelopmental and neurodegenerative disorders. Genes in neuron-associated compared to non-neuronal networks showed higher preservation between human and mouse; however, many diversely-patterned genes displayed dramatic shifts in regulation between species. Finally, highly consistent transcriptional architecture in neocortex is correlated with resting state functional connectivity, suggesting a link between conserved gene expression and functionally relevant circuitry.

Spatial patterns of gene expression in the vertebrate brain are not independent, as pairs of genes can exhibit complex patterns of coexpression. Two genes may be similarly expressed in one region, but differentially expressed in other regions. These correlations have been studied quantitatively, particularly for the Allen Atlas of the adult mouse brain, but their biological meaning remains obscure. We propose a simple model of the coexpression patterns in terms of spatial distributions of underlying cell types and establish its plausibility using independently measured cell-typespecific transcriptomes. The model allows us to predict the spatial distribution of cell types in the mouse brain.neuroscience | bioinformatics | neuroanatomy B rain-wide and genome-wide maps of gene expression are now available (1, 2), due to the development of high-throughput neuroanatomical methods (3-6). This has enabled analysis of the spatial correlation structure of gene expression (7-12). In the Allen Brain Atlas (ABA) of the adult mouse, the brain is divided up into cubic voxels of size 200 μm. The expression energies of up to 20,000 genes in the adult C57BL/6J mouse are given by automatic processing of in situ hybridized (ISH) brain sections, coregistered to the Allen Reference Atlas (ARA) (13). Coexpression of two genes in a voxel may arise from two sources: ðiÞ both genes are expressed within the same cell type or ðiiÞ the two genes are expressed in two different cell types, both present in the voxel. These two possibilities cannot be disentangled solely on the basis of the ABA. Ideally, gene expression profiles should be experimentally obtained for each cell type in the brain, and indeed such transcriptome profiles are now available (14-21). This cell-based approach to the study of gene expression is complementary to the gene-based approach of the ABA. In ref. 22, the data of ref. 19 were used to extract neuron-specific genes, astrocyte-specific genes, and oligodendrocyte-specific genes, which resulted in three combinations of brain-wide maps from the ABA, whose clustering showed anatomical signatures of major brain subdivisions (see also ref. 23 for estimates of neuron-specific and oligodendrocyte-specific expression patterns, both in the mouse and in the human brain). The present paper goes beyond the broad classification of cell types into three classes and attempts to estimate density profiles of every cell type known by its transcriptome profile. To study the genes collectively we use a voxel-by-gene data matrix E, corresponding to V = 49;742 cubic voxels, and 3,041 genes, as in refs. 24-26. The entry Eðv; gÞ is the expression energy of the gene labeled g in the voxel labeled v [a measure representing the level of mRNA in situ hybridization (1, 10)]. We combine the ABA with cell-type-specific transcriptome profiles, to gain biological understanding of the coexpression patterns of the genes. Our model is based on G = 2;131 genes found in all these datasets and in the coronal ABA. The model proposed to estimate the brain-w...

Various approaches to T-duality with NSNS three-form flux are reconciled. Non-commutative torus fibrations are shown to be the open-string version of T-folds. The non-geometric T-dual of a three-torus with uniform flux is embedded into a generalized complex six-torus, and the non-geometry is probed by D0-branes regarded as generalized complex submanifolds. The noncommutativity scale, which is present in these compactifications, is given by a holomorphic Poisson bivector that also encodes the variation of the dimension of the world-volume of D-branes under monodromy. This bivector is shown to exist in SU(3) × SU(3) structure compactifications, which have been proposed as mirrors to NSNS-flux backgrounds. The two SU(3)-invariant spinors are generically not parallel, thereby giving rise to a non-trivial Poisson bivector. Furthermore we show that for non-geometric T-duals, the Poisson bivector may not be decomposable into the tensor product of vectors. IntroductionCompactifications with H-flux are known to give rise to topology changes and even to nongeometric situations when T-duality is performed along directions which have non-trivial support of the NSNS H-flux [1,2,3,4,5,6,7,8]. Non-geometry occurs for example in the very simple situation of a three-torus endowed with an H-flux proportional to its volume form. Consider namely the three-torus as a trivial T 2 -fibration over a circle. Upon T-duality along the fibre, the metric picks up a factor that makes it shrink under monodromy around the base circle. The monodromy around the base is a non-trivial element of the O(2, 2; Z) group acting on the two-torus. This prevents a three-dimensional global Riemannian description from existing. Further T-dualizing along the base leads to more pathological situations, where points do not exist even in a local coordinate patch, and the fibres are conjectured to become non-associative [9,10]. We will restrict ourselves to the case of two T-dualities, and assume that local coordinate patches do exist. Progress in the description of non-associative T-duals was achieved in the recent paper [11], which also contains observations on the open-string metric and non-commutativity for two T-dualities that have some overlap with ours.Essentially three conjectures have been put forward for the description of the T-dual of a torus with H-flux: 1 (I) Field of non-commutative tori: Mathai and Rosenberg proposed that T-dualizing along a two-torus with non-zero H-flux yields a fibration by (or more precisely: field of) noncommutative tori. In particular, this fibration is encoded in a closed one-form, which is obtained by integrating the NSNS flux along the fibre directions [7,12,13].(II) T-folds: these are spaces where T-dualities can act as transition functions between local patches [8]. The T-dualized directions are doubled, and T-duality transformations may patch the doubled fibres together. A sigma model with a T-fold as its target space was proposed, and its boundary conditions were studied in [14,15,16,17,18].(III) G × G struc...

Autism spectrum disorder (ASD) is one of the most prevalent and highly heritable neurodevelopmental disorders in humans. There is significant evidence that the onset and severity of ASD is governed in part by complex genetic mechanisms affecting the normal development of the brain. To date, a number of genes have been associated with ASD. However, the temporal and spatial co-expression of these genes in the brain remain unclear. To address this issue, we examined the co-expression network of 26 autism genes from AutDB (http://mindspec.org/autdb.html), in the framework of 3,041 genes whose expression energies have the highest correlation between the coronal and sagittal images from the Allen Mouse Brain Atlas database (http://mouse.brain-map.org). These data were derived from in situ hybridization experiments conducted on male, 56-day old C57BL/6J mice co-registered to the Allen Reference Atlas, and were used to generate a normalized co-expression matrix indicating the cosine similarity between expression vectors of genes in this database. The network formed by the autism-associated genes showed a higher degree of co-expression connectivity than seen for the other genes in this dataset (Kolmogorov–Smirnov P = 5×10−28). Using Monte Carlo simulations, we identified two cliques of co-expressed genes that were significantly enriched with autism genes (A Bonferroni corrected P<0.05). Genes in both these cliques were significantly over-expressed in the cerebellar cortex (P = 1×10−5) suggesting possible implication of this brain region in autism. In conclusion, our study provides a detailed profiling of co-expression patterns of autism genes in the mouse brain, and suggests specific brain regions and new candidate genes that could be involved in autism etiology.

It has been argued recently that mirror symmetry exchanges two pure spinors characterizing a generic manifold with SU(3)-structure. We show how pure spinors are modified in the presence of topological D-branes, so that they are still exchanged by mirror symmetry. This exchange emerges from the fact that the modified pure spinors come out as moment maps for the symmetries of A and B-models. The modification by the gauge field is argued to ensure the inclusion into the mirror exchange of the A-model non-Lagrangian branes endowed with a non-flat connection. Treating the connection as a distribution on an ambient six-manifold, assumed to be T^3-fibered, the proposed mirror formula is established by fiberwise T-duality.Comment: 13 pages, LaTe