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

The three-dimensional data-driven Allen 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.