Oseledets' splitting of standard-like maps.

For the class of differentiable maps of the plane and, in particular, for standard-like maps (McMillan form), a simple relation is shown between the directions of the local invariant manifolds of a generic point and its contribution to the finite-time Lyapunov exponents (FTLE) of the associated orbit. By computing also the point-wise curvature of the manifolds, we produce a comparative study between local Lyapunov exponent, manifold's curvature and splitting angle between stable/unstable manifolds. Interestingly, the analysis of the Chirikov-Taylor standard map suggests that the positive contributions to the FTLE average mostly come from points of the orbit where the structure of the manifolds is locally hyperbolic: where the manifolds are flat and transversal, the one-step exponent is predominantly positive and large; this behaviour is intended in a purely statistical sense, since it exhibits large deviations. Such phenomenon can be understood by analytic arguments which, as a by-product, also suggest an explicit way to point-wise approximate the splitting.

Therapeutic implications of novel mutations of the RFX6 gene associated with early-onset diabetes.

Identification of the genetic defect underlying early-onset diabetes is important for determining the specific diabetes subtype, which would then permit appropriate treatment and accurate assessment of recurrence risk in offspring. Given the extensive genetic and clinical heterogeneity of the disease, high-throughput sequencing might provide additional diagnostic potential when Sanger sequencing is ineffective. Our aim was to develop a targeted next-generation assay able to detect mutations in several genes involved in glucose metabolism. All 13 known MODY genes, genes identified from a genome-wide linkage study or genome-wide association studies as increasing the risk of type 2 diabetes and genes causing diabetes in animal models, were included in the custom panel. We selected a total of 102 genes by performing a targeting re-sequencing in 30 patients negative for mutations in the GCK, HNF1α, HNF4α, HNF1ß and IPF1 genes at the Sanger sequencing analysis. Previously unidentified variants in the RFX6 gene were found in three patients and in two of them we also detected rare variants in WFS1 and ABCC8 genes. All patients showed a good therapeutic response to dipeptidyl peptidase-4 (DPP4) inhibitors. Our study reveals that next-generation sequencing provides a highly sensitive method for identification of variants in new causative genes of diabetes. This approach may help in understanding the molecular etiology of diabetes and in providing more personalized treatment for each genetic subtype.

Novel FOXG1 mutations associated with the congenital variant of Rett syndrome.

BACKGROUND: Rett syndrome is a severe neurodevelopmental disorder representing one of the most common genetic causes of mental retardation in girls. The classic form is caused by MECP2 mutations. In two patients affected by the congenital variant of Rett we have recently identified mutations in the FOXG1 gene encoding a brain specific transcriptional repressor, essential for early development of the telencephalon. METHODS: 60 MECP2/CDKL5 mutation negative European Rett patients (classic and variants), 43 patients with encephalopathy with early onset seizures, and four atypical Rett patients were analysed for mutations in FOXG1. RESULTS AND CONCLUSIONS: Mutations have been identified in four patients, independently classified as congenital Rett variants from France, Spain and Latvia. Clinical data have been compared with the two previously reported patients with mutations in FOXG1. In all cases hypotonia, irresponsiveness and irritability were present in the neonatal period. At birth, head circumference was normal while a deceleration of growth was recognised soon afterwards, leading to severe microcephaly. Motor development was severely impaired and voluntary hand use was absent. In contrast with classic Rett, patients showed poor eye contact. Typical stereotypic hand movements with hand washing and hand mouthing activities were present continuously. Some patients showed abnormal movements of the tongue and jerky movements of the limbs. Brain magnetic resonance imaging showed corpus callosum hypoplasia in most cases, while epilepsy was a variable sign. Scoliosis was present and severe in the older patients. Neurovegetative symptoms typical of Rett were frequently present.

Early-onset seizure variant of Rett syndrome: definition of the clinical diagnostic criteria.

BACKGROUND: Rett syndrome is a severe neurodevelopmental disorder affecting almost exclusively females. Among Rett clinical variants, the early-onset seizure variant describes girls with early onset epilepsy and it is caused by mutations in CDKL5. METHODS: Four previously reported girls and five new cases with CDKL5 mutation, ranging from 14 months to 13 years, were evaluated by two clinical geneticists, classified using a severity score system based on the evaluation of 22 different clinical signs and compared with 128 classic Rett and 25 Zappella variant MECP2-mutated patients, evaluated by the same clinical geneticists. Clinical features were compared with previously described CDKL5 mutated patients. Both the statistical and the descriptive approach have been used to delineate clinical diagnostic criteria. RESULTS: All girls present epilepsy with onset varying from 10 days to 3 months. Patients may present different type of seizures both at onset and during the whole course of the disease; multiple seizure types may also occur in the same individual. After treatment with antiepileptic drugs patients may experience a short seizure-free period but epilepsy progressively relapses. Typical stereotypic hand movements severely affecting the ability to grasp are present. Psychomotor development is severely impaired. In the majority of cases head circumference is within the normal range both at birth and at the time of clinical examination. CONCLUSION: For the practical clinical approach we propose to use six necessary and eight supportive diagnostic criteria. Epilepsy with onset between the first week and 5 months of life, hand stereotypies, as well as severe hypotonia, are included among the necessary criteria.

The XLMR gene ACSL4 plays a role in dendritic spine architecture.

ACSL4 is a gene involved in non-syndromic X-linked mental retardation. It encodes for a ubiquitous protein that adds coenzyme A to long-chain fatty acids, with a high substrate preference for arachidonic acid. It presents also a brain-specific isoform deriving from an alternative splicing and containing 41 additional N-terminal amino acids. To start to unravelling the link between ACSL4 and mental retardation, we have performed molecular and cell biological studies. By retro-transcription polymerase chain reaction analyses we identified a new transcript with a shorter 5'-UTR region. By immunofluorescence microscopy in embryonic rat hippocampal neurons we report that ACSL4 is associated preferentially to endoplasmic reticulum tubules. ACSL4 knockdown by siRNAs in hippocampal neurons indicated that this protein is largely dispensable for these cells' gross architectural features (i.e. axonal and dendritic formation and final length) yet it is required for the presence of normal spines. In fact, reduced levels of ACSL4 led to a significant reduction in dendritic spine density and an alteration in spine/filopodia distribution. The possible mechanisms behind this phenotype are discussed.

The Italian XLMR bank: a clinical and molecular database.

Mental retardation (MR) is a nonprogressive condition characterized by a significant impairment of intellectual capabilities with deficit of cognitive and adaptive functioning and onset before 18 years. Mental retardation occurs in about 2 to 3% of the general population and it is estimated that 25 to 35% of the cases may be due to genetic causes. Among these "genetic" MR, 25 to 30% are probably due to mutations in a gene on the X chromosome (X-linked mental retardation, XLMR). Given the genetic heterogeneity of XLMR, the availability of a considerable number of patients with accurate phenotypic classification is a crucial factor for research. The X-linked Mental Retardation Italian Network, which has been active since 2003, has collected detailed clinical information and biological samples from a vast number of MR patients. Collected samples and clinical information are inserted within the XLMR bank, a comprehensive molecular and clinical web-based database available at the address http://xlmr.unisi.it. The database is organized in three distinct parts. Part I and II contain several electronic schedules to register information on the family, the phenotypic description, the photographs, and a 20 sec movie of the patient. Part III allows the registration of molecular analyses performed on each case; samples and clinical data are usable via password-restricted access. Clinical and molecular centers interested in joining the network may request a password by simply contacting the Medical Genetics of the University of Siena. The XLMR bank is an innovative biological database that allows the collection of molecular and clinical data, combines descriptive and iconographic resources, and represents a fundamental tool for researchers in the field of mental retardation.

2q24-q31 deletion: report of a case and review of the literature.

We report a patient with a de novo interstitial deletion of the long arm of chromosome 2 involving bands 2q24.3-q31.1. The patient shows postnatal growth retardation, microcephaly, ptosis, down-slanting palpebral fissures, long eyelashes and micrognathia. Halluces are long, broad and medially deviated, while the other toes are laterally deviated and remarkably short with hypoplastic phalanges. She also showed developmental delay, seizures, lack of eye contact, stereotypic and repetitive hand movements and sleep disturbances with breath holding. Prenatal and three independent postnatal karyotypes were normal. Array-CGH analysis allowed us to identify and characterize a "de novo" 2q interstitial deletion of about 10.4Mb, involving segment between cytogenetic bands 2q24.3 and 2q31.1. The deletion was confirmed by quantitative PCR. About 30 children with 2q interstitial deletion have been reported. The deletion described here is overlapping with 15 of these cases. We have attempted to compare the clinical features of our patient with 15 overlapping cases. The emerging phenotypes include low birth weight, postnatal growth retardation, mental retardation and developmental delay, microcephaly, and peculiar facial dysmorphisms. Peculiar long and broad halluces with an increased distance between the first and the second toe are ("sandal gap" sign) present in most of the described patients. The gene content analysis of the deleted region revealed the presence of some genes that may be indicated as good candidates in generating both neurological and dysmorphic phenotype in the patient. In particular, a cluster of SCNA genes is located within the deleted region and it is known that loss of function mutations in SCNA1 gene cause a severe form of epilepsy.

Asymptotic quantum behavior of classically anomalous maps.

In the framework of quantum chaos, the theory of dynamical localization plays an outstanding role, both for its conceptual relevance and physical import. Theoretical arguments, confirmed by a large amount of numerical simulations, have shown in the case of complete classical chaos, that the localization length is related to the classical diffusion constant and the effective Planck's constant Planck's over 2 pi. We investigate the quantum behavior when classical dynamics exhibits anomalous diffusion (so that the diffusion constant is not defined): we show that dynamical localization still takes place, and that the scaling with the quantum parameter is the same as the classically diffusive case.