Pascal Grange

Canonical genetic signatures of the adult human brain

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 called differential stability to assess reproducibility of gene expression patterning across 132 structures in six individual brains, revealing mesoscale genetic organization. The genes with the highest differential stability are highly biologically relevant, with enrichment for brain-related annotations, disease associations, drug targets and literature citations. Using genes with high differential stability, 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 marked 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.

Cell-type–based model explaining coexpression patterns of genes in the brain

Significance Neuroanatomy is experiencing a renaissance due to the study of gene-expression data covering the entire mouse brain and the entire genome that have been recently released (the Allen Atlas). On the other hand, some cell types extracted from the mouse brain have been characterized by their genetic activity. However, given a cell type, it is not known in which brain regions it can be found. We propose a computational model using the Allen Atlas to solve this problem, thus estimating previously unidentified cell-type–specific maps of the mouse brain. The model can be used to define brain regions through genetic data. 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-type–specific transcriptomes. The model allows us to predict the spatial distribution of cell types in the mouse brain.

T-duality with H-flux: Non-commutativity, T-folds and G x G structure

Abstract 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 non-commutativity 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.

Co-expression Profiling of Autism Genes in the Mouse Brain

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.

Modified pure spinors and mirror symmetry

Abstract It has been argued recently that mirror symmetry exchanges two pure spinors characterizing a generic manifold with SU ( 3 ) structure. We show that quantities involved in stability conditions for topological D-branes, and containing gauge fields in their expressions, are exchanged by mirror symmetry. This exchange can be considered as an open-string version of the mirror symmetry between pure spinors. It 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.

Towards mirror symmetry a la SYZ for generalized Calabi-Yau manifolds

Fibrations of flux backgrounds by supersymmetric cycles are investigated. For an internal six-manifold M with static SU(2) structure and mirror hat M, it is argued that the product M × hat M is doubly fibered by supersymmetric three-tori, with both sets of fibers transverse to M and hat M. The mirror map is then realized by T-dualizing the fibers. Mirror-symmetric properties of the fluxes, both geometric and non-geometric, are shown to agree with previous conjectures based on the requirement of mirror symmetry for Killing prepotentials. The fibers are conjectured to be destabilized by fluxes on generic SU(3) × SU(3) backgrounds, though they may survive at type-jumping points. T-dualizing the surviving fibers ensures the exchange of pure spinors under mirror symmetry.

Computational neuroanatomy and gene expression: Optimal sets of marker genes for brain regions

The three-dimensional data-driven Anatomic Gene Expression Atlas of the adult mouse brain consists of numerized in situ hybridization data for thousands of genes, co-registered to the Allen Reference Atlas. We propose quantitative criteria to rank genes as markers of a brain region, based on the localization of the gene expression and on its functional fitting to the shape of the region. These criteria lead to natural generalizations to sets of genes. We find sets of genes weighted with coefficients of both signs with almost perfect localization in all major regions of the left hemisphere of the brain, except the pallidum. Generalization of the fitting criterion with positivity constraint provides a lesser improvement of the markers, but requires sparser sets of genes.

Tachyon condensation and D-branes in generalized geometries

In generalized complex geometry, D-branes can be seen as maximally isotropic spaces and are thus in one-to-one correspondence with pure spinors. When considered on the sum of the tangent and cotangent bundles to the ambient space, all the branes are of the same dimension and the transverse scalars enter on par with the gauge fields; the split between the longitudinal and transverse directions is done in accordance with the type of the pure spinor corresponding to the given D-brane. We elaborate on the relation of this picture to the T-duality transformations and stability of D-branes. A discussion of tachyon condensation in the context of the generalized complex geometry is given, linking the description of D-branes as generalized complex submanifolds to their K-theoretic classification.

Computational neuroanatomy and co-expression of genes in the adult mouse brain, analysis tools for the Allen Brain Atlas

We review quantitative methods and software developed to analyze genome-scale, brain-wide spatially-mapped gene-expression data. We expose new methods based on the underlying high-dimensional geometry of voxel space and gene space, and on simulations of the distribution of co-expression networks of a given size. We apply them to the Allen Atlas of the adult mouse brain, and to the coexpression network of a set of genes related to nicotine addiction retrieved from the NicSNP database. The computational methods are implemented in BrainGeneExpressionAnalysis (BGEA), a Matlab toolbox available for download.

Deformation of p-adic string amplitudes in a magnetic field

A new term in the p-adic world-sheet action is proposed, which couples a constant B-field to the boundary of the world-sheet at disk level. The induced deformation of tachyon scattering amplitudes by star-products is derived. This is in agreement with the deformation of effective action postulated in recent investigations of non-commutative solitons in p-adic string theory.