Symmetries of differential-difference dynamical systems in a two-dimensional lattice

Classification of differential-difference equation of the form $\ddot{u}_{nm}=F_{nm}\big(t, \{u_{pq}\}|_{(p,q)\in \Gamma}\big)$ are considered according to their Lie point symmetry groups. The set $\Gamma$ represents the point $(n,m)$ and its six nearest neighbors in a two-dimensional triangular lattice. It is shown that the symmetry group can be at most 12-dimensional for abelian symmetry algebras and 13-dimensional for nonsolvable symmetry algebras.Comment: 24 pages, 1 figur

Multiple Organ System Defects and Transcriptional Dysregulation in the Nipbl+/− Mouse, a Model of Cornelia de Lange Syndrome

Cornelia de Lange Syndrome (CdLS) is a multi-organ system birth defects disorder linked, in at least half of cases, to heterozygous mutations in the NIPBL gene. In animals and fungi, orthologs of NIPBL regulate cohesin, a complex of proteins that is essential for chromosome cohesion and is also implicated in DNA repair and transcriptional regulation. Mice heterozygous for a gene-trap mutation in Nipbl were produced and exhibited defects characteristic of CdLS, including small size, craniofacial anomalies, microbrachycephaly, heart defects, hearing abnormalities, delayed bone maturation, reduced body fat, behavioral disturbances, and high mortality (75–80%) during the first weeks of life. These phenotypes arose despite a decrease in Nipbl transcript levels of only ∼30%, implying extreme sensitivity of development to small changes in Nipbl activity. Gene expression profiling demonstrated that Nipbl deficiency leads to modest but significant transcriptional dysregulation of many genes. Expression changes at the protocadherin beta (Pcdhb) locus, as well as at other loci, support the view that NIPBL influences long-range chromosomal regulatory interactions. In addition, evidence is presented that reduced expression of genes involved in adipogenic differentiation may underlie the low amounts of body fat observed both in Nipbl+/− mice and in individuals with CdLS

Alterations to Melanocortinergic, GABAergic and Cannabinoid Neurotransmission Associated with Olanzapine-Induced Weight Gain

Background/Aim: Second generation antipsychotics (SGAs) are used to treat schizophrenia but can cause serious metabolic side-effects, such as obesity and diabetes. This study examined the effects of low to high doses of olanzapine on appetite/ metabolic regulatory signals in the hypothalamus and brainstem to elucidate the mechanisms underlying olanzapineinduced obesity. Methodology/Results: Levels of pro-opiomelanocortin (POMC), neuropeptide Y (NPY) and glutamic acid decarboxylase (GAD65, enzyme for GABA synthesis) mRNA expression, and cannabinoid CB1 receptor (CB1R) binding density (using [ 3 H]SR-141716A) were examined in the arcuate nucleus (Arc) and dorsal vagal complex (DVC) of female Sprague Dawley rats following 0.25, 0.5, 1.0 or 2.0 mg/kg olanzapine or vehicle (36/day, 14-days). Consistent with its weight gain liability, olanzapine significantly decreased anorexigenic POMC and increased orexigenic NPY mRNA expression in a dose-sensitive manner in the Arc. GAD65 mRNA expression increased and CB1R binding density decreased in the Arc and DVC. Alterations to neurotransmission signals in the brain significantly correlated with body weight and adiposity. The minimum dosage threshold required to induce weight gain in the rat was 0.5 mg/kg olanzapine. Conclusions: Olanzapine-induced weight gain is associated with reduced appetite-inhibiting POMC and increased NPY. This study also supports a role for the CB1R and GABA in the mechanisms underlying weight gain side-effects, possibly b

Postnatal Changes in the Expression Pattern of the Imprinted Signalling Protein XLαs Underlie the Changing Phenotype of Deficient Mice

The alternatively spliced trimeric G-protein subunit XLαs, which is involved in cAMP signalling, is encoded by the Gnasxl transcript of the imprinted Gnas locus. XLαs deficient mice show neonatal feeding problems, leanness, inertia and a high mortality rate. Mutants that survive to weaning age develop into healthy and fertile adults, which remain lean despite elevated food intake. The adult metabolic phenotype can be attributed to increased energy expenditure, which appears to be caused by elevated sympathetic nervous system activity. To better understand the changing phenotype of Gnasxl deficient mice, we compared XLαs expression in neonatal versus adult tissues, analysed its co-localisation with neural markers and characterised changes in the nutrient-sensing mTOR1-S6K pathway in the hypothalamus. Using a newly generated conditional Gnasxl lacZ gene trap line and immunohistochemistry we identified various types of muscle, including smooth muscle cells of blood vessels, as the major peripheral sites of expression in neonates. Expression in all muscle tissues was silenced in adults. While Gnasxl expression in the central nervous system was also developmentally silenced in some midbrain nuclei, it was upregulated in the preoptic area, the medial amygdala, several hypothalamic nuclei (e.g. arcuate, dorsomedial, lateral and paraventricular nuclei) and the nucleus of the solitary tract. Furthermore, expression was detected in the ventral medulla as well as in motoneurons and a subset of sympathetic preganglionic neurons of the spinal cord. In the arcuate nucleus of Gnasxl-deficient mice we found reduced activity of the nutrient sensing mTOR1-S6K signalling pathway, which concurs with their metabolic status. The expression in these brain regions and the hypermetabolic phenotype of adult Gnasxl-deficient mice imply an inhibitory function of XLαs in energy expenditure and sympathetic outflow. By contrast, the neonatal phenotype of mutant mice appears to be due to a transient role of XLαs in muscle tissues