A Symmetric Generalization of Linear B\"acklund Transformation associated with the Hirota Bilinear Difference Equation

The Hirota bilinear difference equation is generalized to discrete space of arbitrary dimension. Solutions to the nonlinear difference equations can be obtained via B\"acklund transformation of the corresponding linear problems.Comment: Latex, 12 pages, 1 figur

From nothing to something: discrete integrable systems

Chinese ancient sage Laozi said that everything comes from `nothing'. Einstein believes the principle of nature is simple. Quantum physics proves that the world is discrete. And computer science takes continuous systems as discrete ones. This report is devoted to deriving a number of discrete models, including well-known integrable systems such as the KdV, KP, Toda, BKP, CKP, and special Viallet equations, from `nothing' via simple principles. It is conjectured that the discrete models generated from nothing may be integrable because they are identities of simple algebra, model-independent nonlinear superpositions of a trivial integrable system (Riccati equation), index homogeneous decompositions of the simplest geometric theorem (the angle bisector theorem), as well as the M\"obious transformation invariants.Comment: 11 pages, side 10 repor

T-systems and Y-systems in integrable systems

The T and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer matrices in solvable lattice models, q-characters of Kirillov-Reshetikhin modules of quantum affine algebras, cluster algebras with coefficients, periodicity conjectures of Zamolodchikov and others, dilogarithm identities in conformal field theory, difference analogue of L-operators in KP hierarchy, Stokes phenomena in 1d Schr\"odinger problem, AdS/CFT correspondence, Toda field equations on discrete space-time, Laplace sequence in discrete geometry, Fermionic character formulas and combinatorial completeness of Bethe ansatz, Q-system and ideal gas with exclusion statistics, analytic and thermodynamic Bethe ans\"atze, quantum transfer matrix method and so forth. This review article is a collection of short reviews on these topics which can be read more or less independently.Comment: 156 pages. Minor corrections including the last paragraph of sec.3.5, eqs.(4.1), (5.28), (9.37) and (13.54). The published version (JPA topical review) also needs these correction

Catalytic Function of PLA2G6 Is Impaired by Mutations Associated with Infantile Neuroaxonal Dystrophy but Not Dystonia-Parkinsonism

Mutations in the PLA2G6 gene have been identified in autosomal recessive neurodegenerative diseases classified as infantile neuroaxonal dystrophy (INAD), neurodegeneration with brain iron accumulation (NBIA), and dystonia-parkinsonism. These clinical syndromes display two significantly different disease phenotypes. NBIA and INAD are very similar, involving widespread neurodegeneration that begins within the first 1-2 years of life. In contrast, patients with dystonia-parkinsonism present with a parkinsonian movement disorder beginning at 15 to 30 years of age. The PLA2G6 gene encodes the PLA2G6 enzyme, also known as group VIA calcium-independent phospholipase A(2), which has previously been shown to hydrolyze the sn-2 acyl chain of phospholipids, generating free fatty acids and lysophospholipids.We produced purified recombinant wildtype (WT) and mutant human PLA2G6 proteins and examined their catalytic function using in vitro assays with radiolabeled lipid substrates. We find that human PLA2G6 enzyme hydrolyzes both phospholipids and lysophospholipids, releasing free fatty acids. Mutations associated with different disease phenotypes have different effects on catalytic activity. Mutations associated with INAD/NBIA cause loss of enzyme activity, with mutant proteins exhibiting less than 20% of the specific activity of WT protein in both lysophospholipase and phospholipase assays. In contrast, mutations associated with dystonia-parkinsonism do not impair catalytic activity, and two mutations produce a significant increase in specific activity for phospholipid but not lysophospholipid substrates.These results indicate that different alterations in PLA2G6 function produce the different disease phenotypes of NBIA/INAD and dystonia-parkinsonism. INAD/NBIA is caused by loss of the ability of PLA2G6 to catalyze fatty acid release from phospholipids, which predicts accumulation of PLA2G6 phospholipid substrates and provides a mechanistic explanation for the accumulation of membranes in neuroaxonal spheroids previously observed in histopathological studies of INAD/NBIA. In contrast, dystonia-parkinsonism mutations do not appear to directly impair catalytic function, but may modify substrate preferences or regulatory mechanisms for PLA2G6

Genetic Ablation of PLA2G6 in Mice Leads to Cerebellar Atrophy Characterized by Purkinje Cell Loss and Glial Cell Activation

Infantile neuroaxonal dystrophy (INAD) is a progressive, autosomal recessive neurodegenerative disease characterized by axonal dystrophy, abnormal iron deposition and cerebellar atrophy. This disease was recently mapped to PLA2G6, which encodes group VI Ca2+-independent phospholipase A2 (iPLA2 or iPLA2β). Here we show that genetic ablation of PLA2G6 in mice (iPLA2β-/-) leads to the development of cerebellar atrophy by the age of 13 months. Atrophied cerebella exhibited significant loss of Purkinje cells, as well as reactive astrogliosis, the activation of microglial cells, and the pronounced up-regulation of the pro-inflammatory cytokines tumor necrosis factor-α (TNF-α) and interleukin-1β (IL-1β). Moreover, glial cell activation and the elevation in TNF-α and IL-1β expression occurred before apparent cerebellar atrophy. Our findings indicate that the absence of PLA2G6 causes neuroinflammation and Purkinje cell loss and ultimately leads to cerebellar atrophy. Our study suggests that iPLA2β-/- mice are a valuable model for cerebellar atrophy in INAD and that early anti-inflammatory therapy may help slow the progression of cerebellar atrophy in this deadly neurodegenerative disease

Protein Crosslinking by Transglutaminase Controls Cuticle Morphogenesis in Drosophila

Transglutaminase (TG) plays important and diverse roles in mammals, such as blood coagulation and formation of the skin barrier, by catalyzing protein crosslinking. In invertebrates, TG is known to be involved in immobilization of invading pathogens at sites of injury. Here we demonstrate that Drosophila TG is an important enzyme for cuticle morphogenesis. Although TG activity was undetectable before the second instar larval stage, it dramatically increased in the third instar larval stage. RNA interference (RNAi) of the TG gene caused a pupal semi-lethal phenotype and abnormal morphology. Furthermore, TG-RNAi flies showed a significantly shorter life span than their counterparts, and approximately 90% of flies died within 30 days after eclosion. Stage-specific TG-RNAi before the third instar larval stage resulted in cuticle abnormality, but the TG-RNAi after the late pupal stage did not, indicating that TG plays a key role at or before the early pupal stage. Immediately following eclosion, acid-extractable protein from wild-type wings was nearly all converted to non-extractable protein due to wing maturation, whereas several proteins remained acid-extractable in the mature wings of TG-RNAi flies. We identified four proteins—two cuticular chitin-binding proteins, larval serum protein 2, and a putative C-type lectin—as TG substrates. RNAi of their corresponding genes caused a lethal phenotype or cuticle abnormality. Our results indicate that TG-dependent protein crosslinking in Drosophila plays a key role in cuticle morphogenesis and sclerotization

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

The Drosophila melanogaster host model

The deleterious and sometimes fatal outcomes of bacterial infectious diseases are the net result of the interactions between the pathogen and the host, and the genetically tractable fruit fly, Drosophila melanogaster, has emerged as a valuable tool for modeling the pathogen–host interactions of a wide variety of bacteria. These studies have revealed that there is a remarkable conservation of bacterial pathogenesis and host defence mechanisms between higher host organisms and Drosophila. This review presents an in-depth discussion of the Drosophila immune response, the Drosophila killing model, and the use of the model to examine bacterial–host interactions. The recent introduction of the Drosophila model into the oral microbiology field is discussed, specifically the use of the model to examine Porphyromonas gingivalis–host interactions, and finally the potential uses of this powerful model system to further elucidate oral bacterial-host interactions are addressed