Linear and nonlinear parity-time-symmetric oligomers: a dynamical systems analysis

In the present work, we focus on the cases of two-site (dimer) and three-site (trimer) configurations, i.e. oligomers, respecting the parity-time (PT) symmetry, i.e. with a spatially odd gain-loss profile. We examine different types of solutions of such configurations with linear and nonlinear gain/loss profiles. Solutions beyond the linear PT-symmetry critical point as well as solutions with asymmetric linearization eigenvalues are found in both the nonlinear dimer and trimer. The latter feature is absent in linear PT-symmetric trimers, while both of them are absent in linear PT-symmetric dimers. Furthermore, nonlinear gain/loss terms enable the existence of both symmetric and asymmetric solution profiles (and of bifurcations between them), while only symmetric solutions are present in the linear PT-symmetric dimers and trimers. The linear stability analysis around the obtained solutions is discussed and their dynamical evolution is explored by means of direct numerical simulations. Finally, a brief discussion is also given of recent progress in the context of PT-symmetric quadrimers.

Lysosomal acid lipase-deficient mice: depletion of white and brown fat, severe hepatosplenomegaly, and shortened life span

Lysosomal acid lipase (LAL) is essential for the hydrolysis of triglycerides (TG) and cholesteryl esters (CE) in lysosomes. A mouse model created by gene targeting produces no LAL mRNA, protein, or enzyme activity. The lal-/- mice appear normal at birth, survive into adulthood, and are fertile. Massive storage of TG and CE is observed in adult liver, adrenal glands, and small intestine. The age-dependent tissue and gross progression in this mouse model are detailed here. Although lal-/- mice can be bred to give homozygous litters, they die at ages of 7 to 8 months. The lal-/- mice develop enlargement of a single mesenteric lymph node that is full of stored lipids. At 6;-8 months of age, the lal-/- mice have completely absent inguinal, interscapular, and retroperitoneal white adipose tissue. In addition, brown adipose tissue is progressively lost. The plasma free fatty acid levels are significantly higher in lal-/- mice than age-matched lal+/+ mice, and plasma insulin levels were more elevated upon glucose challenge. Energy intake was also higher in lal-/- male mice, although age-matched body weights were not significantly altered from age-matched lal+/+ mice. Early in the disease course, hepatocytes are the main storage cell in the liver; by 3;-8 months, the lipid-stored Kupffer cells progressively fill the liver. The involvement of macrophages throughout the body of lal-/- mice provide evidence for a critical nonappreciated role of LAL in cellular cholesterol and fatty acid metabolism, adipocyte differentiation, and fat mobilization.

Targeted disruption of the mouse lysosomal acid lipase gene: long-term survival with massive cholesteryl ester and triglyceride storage

Lysosomal acid lipase (LAL) is essential for the hydrolysis of the triglycerides and cholesteryl esters in lysosomes. Its deficiency produces two phenotypes, a severe infantile-onset variant, Wolman disease (WD), and a later onset variant, cholesteryl ester storage disease (CESD). A mouse model with a LAL null mutation was produced by targeting disruption of the mouse gene. Homozygote knockout mice (lal -/lal-) produce no LAL mRNA, protein or enzyme activity. The lal-/lal- mice are born in Mendelian ratios, are normal appearing at birth, and follow normal development into adulthood. However, massive accumulation of triglycerides and cholesteryl esters occurs in several organs. By 21 days, the liver develops a yellow-orange color and is approximately 1.5-2.0x larger than normal. The accumulated cholesteryl esters and triglycerides are approximately 30-fold greater than normal. The lal+/lal- mice have approximately 50% of normal LAL activity and do not show lipid accumulation. Male and female lal-/lal- mice are fertile and can be bred to produce progeny. This mouse model is a phenotypic model of human CESD, and a biochemical and histopathologic mimic of human WD. The lal-/lal- mice provide a model to determine the role of LAL in lipid metabolism and the pathogenesis of its deficiency states.

Mouse lysosomal acid lipase: characterization of the gene and analysis of promoter activity

Lysosomal acid lipase (LAL) is required for the hydrolysis of intracellular cholesteryl esters and triglycerides that are delivered to lysosomes by low density lipoprotein (LDL) receptor-mediated endocytosis. To understand that the expression of LAL mRNA and protein is tissue and cell specifically regulated in mice, genomic clones for the mouse lysosomal acid lipase (mLAL) gene were isolated and characterized. The 6.8 kb of the mLAL gene 5'-flanking region was sequenced. Comparisons of mouse and human LAL genes organization revealed identical intron/exon boundaries, except for intron 1 of the mouse gene, and identical exonic length of exons 3-9. The transcription start sites and exon 1 of mLAL were characterized by 5'-RACE-PCR and S1 nuclease mapping. Transfection of 5' flanking deletions of mLAL luciferase reporter gene construct identified positive and negative regulatory elements that varied with cell type. Transfection of three progressively smaller pieces of intron 1 inserted into an SV40 promoter and luciferase reporter gene revealed an enhancer-like activity in intron 1 that is also cell type specific. These studies provide insight into the basis for regulation of this critical enzyme in lipid metabolism.