Male embryonic mice with mutations in the X-linked aristaless-related homeobox gene (Arx) developed with small brains due to suppressed proliferation and regional deficiencies in the forebrain. These mice also showed aberrant migration and differentiation of interneurons containing gamma-aminobutyric acid (GABAergic interneurons) in the ganglionic eminence and neocortex as well as abnormal testicular differentiation. These characteristics recapitulate some of the clinical features of X-linked lissencephaly with abnormal genitalia (XLAG) in humans. We found multiple loss-of-function mutations in ARX in individuals affected with XLAG and in some female relatives, and conclude that mutation of ARX causes XLAG. The present report is, to our knowledge, the first to use phenotypic analysis of a knockout mouse to identify a gene associated with an X-linked human brain malformation.

No abstract

We recently identified mutations of ARX in nine genotypic males with X-linked lissencephaly with abnormal genitalia (XLAG), and in several female relatives with isolated agenesis of the corpus callosum (ACC). We now report 13 novel and two recurrent mutations of ARX, and one nucleotide change of uncertain significance in 20 genotypic males from 16 families. Most had XLAG, but two had hydranencephaly and abnormal genitalia, and three males from one family had Proud syndrome or ACC with abnormal genitalia. We obtained detailed clinical information on all 29 affected males, including the nine previously reported subjects. Premature termination mutations consisting of large deletions, frameshifts, nonsense mutations, and splice site mutations in exons 1 to 4 caused XLAG or hydranencephaly with abnormal genitalia. Nonconservative missense mutations within the homeobox caused less severe XLAG, while conservative substitution in the homeodomain caused Proud syndrome. A nonconservative missense mutation near the C-terminal aristaless domain caused unusually severe XLAG with microcephaly and mild cerebellar hypoplasia. In addition, several less severe phenotypes without malformations have been reported, including mental retardation with cryptogenic infantile spasms (West syndrome), other seizure types, dystonia or autism, and nonsyndromic mental retardation. The ARX mutations associated with these phenotypes have included polyalanine expansions or duplications, missense mutations, and one deletion of exon 5. Together, the group of phenotypes associated with ARX mutations demonstrates remarkable pleiotropy, but also comprises a nearly continuous series of developmental disorders that begins with hydranencephaly, lissencephaly, and agenesis of the corpus callosum, and ends with a series of overlapping syndromes with apparently normal brain structure.

To fully extract cosmological information from nonlinear galaxy distribution in redshift space, it is essential to include higher-order statistics beyond the two-point correlation function. In this paper, we propose a new decomposition formalism for computing the anisotropic bispectrum in redshift space and for measuring it from galaxy samples. Our formalism uses tri-polar spherical harmonic decomposition with zero total angular momentum to compress the 3D modes distribution in the redshiftspace bispectrum. This approach preserves three fundamental properties of the Universe: statistical homogeneity, isotropy, and parity-symmetry, allowing us to efficiently separate the anisotropic signal induced by redshift-space distortions (RSDs) and the Alcock-Paczyński (AP) effect from the isotropic bispectrum. The relevant expansion coefficients in terms of the anisotropic signal are reduced to one multipole index L, and the L > 0 modes are induced only by the RSD or AP effects. Our formalism has two advantages: (1) we can make use of Fast Fourier Transforms (FFTs) to measure the bispectrum; (2) it gives a simple expression to correct for the survey geometry, i.e., the survey window function. As a demonstration, we measure the decomposed bispectrum from the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12, and, for the first time, present a 14σ detection of the anisotropic bispectrum in the L = 2 mode.