Novel StAR Gene Mutation Identified in a Moroccan Patient with Lipoid Congenital Adrenal Hyperplasia

Congenital Adrenal Hyperplasia (CAH) is an autosomal recessive condition  that results from the deficiency of one of the steroidogenesis enzymes responsible for cortisol biosynthesis. In the majority of cases, CAH is caused by   21-hydroxylase deficiency. More rarely, the deficiency concerns  11b-hydroxylase, 3b-hydroxysteroid dehydrogenase, 17hydroxylase, or exceptionally StAR and P450 oxydoreductase. Here, we report the case of a 3 year and 4 months old male child,  born from a consanguineous marriage who presented at 15 months old with the salt-loss syndrome. Physical examination found generalized melanoderma, micropenis and bilateral cryptorchidism. Biological assessment at the time of diagnosis revealed hyponatremia, hyperkalemia, functional renal failure, hypoglycemia, low blood cortisol level, and high blood level of ACTH,  suggesting primary adrenal insufficiency. The patient presented  also with the abnormality of sexual differentiation with a 46 XY karyotype, testosteronemia level was low at the baseline and after HCG stimulation, pelvic ultrasound and MRI showed bilateral testicular atrophy in the inguinal position. The genetic study revealed a likely pathogenic homozygous variant in the StAR (steroidogenic acute regulatory) gene. Therapeutically, our patient was hydrated by saline solution and treated with hydrocortisone and fludrocortisone, then benefited from a surgical testicular correction marked by a favorable evolution. Although mutations in StAR gene are rare, they can be responsible for the defect in the early stage of steroidogenesis and therefore cause a deficiency in adrenal and sexual hormones biosynthesis

Series and integral representations of the Taylor coefficients of the Weierstrass sigma-function

We provide two kinds of representations for the Taylor coefficients of the Weierstrass $\sigma$-function $\sigma(\cdot;\Gamma)$ associated to an arbitrary lattice $\Gamma$ in the complex plane $\mathbb{C}=\mathbb{R}^2$ - the first one in terms of the so-called Hermite-Gauss series over $\Gamma$ and the second one in terms of Hermite-Gauss integrals over $\mathbb{C}$.Comment: 12 page

Generalized second Bargmann transforms associated with the hyperbolic Landau levels on the Poincar\'e disk

We deal with a family of generalized coherent states associated to the hyperbolic Landau levels of the Schr\"odinger operator with uniform magnetic field on the Poincar\'e disk. Their associated coherent state transforms constitute a class of generalized second Bargmann transforms.Comment: 7 page

Spectral properties of the Cauchy transform on L2(C,e−|z|2λ(z))

AbstractLet hm,p(z), (m,p)∈Z+×Z+, be the Landau orthogonal basis of the Hilbert space on L2(C,e−|z|2dλ(z)) where λ(z) is the usual Lebesgue measure on the complex plane. In this paper we give some spectral properties of the Cauchy transform on the orthogonal complement of Bargmann space Λ0(C) in L2(C,e−|z|2dλ(z)). In particular for m fixed, we consider the orthogonal projection operator on the Hilbert subspace spanned by hm,p(z), p=0,1,2,…, and we give explicitly the sequence of singular values of its composition with the Cauchy transform in L2(C,e−|z|2dλ(z)). As application of these of the Cauchy transform we get some identities for special functions which could be of independent interest