Limit theorem of the max-plus walk (Mathematical structures of integrable systems, its deepening and expansion)

Mathematical structures of integrable systems, its deepening and expansion. September 9-11, 2019. edited by Takao Suzuki. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.The max-plus algebra is a semiring on Rmax = R⋁{-∞} with addition ⊕ and multiplication ⊗ defined by ⊕ = max and ⊗ = +, respectively. It is known that eigenvalues of max-plus matrices are equivalent to the maximal average weight of the corresponding directed graph. In [9], authors introduced the max-plus walk which is a walk model on one dimensional lattice on Z over max-plus algebra, and discussed its properties such as the conserved quantities and the steady state. In this paper, we will discuss the limit measure of the max-plus walk

NaPi-IIc induces vacuole formation in OK cells

NaPi-IIc/SLC34A3 is a sodium-dependent inorganic phosphate (Pi) transporter in the renal proximal tubules and its mutations cause hereditary hypophosphatemic rickets with hypercalciuria (HHRH). In the present study, we created a specific antibody for opossum SLC34A3, NaPi-IIc (oNaPi-IIc), and analyzed its localization and regulation in opossum kidney cells (a tissue culture model of proximal tubular cells). Immunoreactive oNaPi-IIc protein levels increased during the proliferative phase and decreased during differentiation. Moreover, stimulating cell growth upregulated oNaPi-IIc protein levels, whereas suppressing cell proliferation downregulated oNaPi-IIc protein levels. Immunocytochemistry revealed that endogenous and exogenous oNaPi-IIc proteins localized at the protrusion of the plasma membrane, which is a phosphatidylinositol 4,5-bisphosphate (PIP2) rich-membrane, and at the intracellular vacuolar membrane. Exogenous NaPi-IIc also induced cellular vacuoles and localized in the plasma membrane. The ability to form vacuoles is specific to electroneutral NaPi-IIc, and not electrogenic NaPi-IIa or NaPi-IIb. In addition, mutations of NaPi-IIc (S138F and R468W) in HHRH did not cause cellular PIP2-rich vacuoles. In conclusion, our data anticipate that NaPi-IIc may regulate PIP2 production at the plasma membrane and cellular vesicle formation

Astrocytic dysfunction induced by ABCA1 deficiency causes optic neuropathy

Astrocyte abnormalities have received great attention for their association with various diseases in the brain but not so much in the eye. Recent independent genome-wide association studies of glaucoma, optic neuropathy characterized by retinal ganglion cell (RGC) degeneration, and vision loss found that single-nucleotide polymorphisms near the ABCA1 locus were common risk factors. Here, we show that Abca1 loss in retinal astrocytes causes glaucoma-like optic neuropathy in aged mice. ABCA1 was highly expressed in retinal astrocytes in mice. Thus, we generated macroglia-specific Abca1-deficient mice (Glia-KO) and found that aged Glia-KO mice had RGC degeneration and ocular dysfunction without affected intraocular pressure, a conventional risk factor for glaucoma. Single-cell RNA sequencing revealed that Abca1 deficiency in aged Glia-KO mice caused astrocyte-triggered inflammation and increased the susceptibility of certain RGC clusters to excitotoxicity. Together, astrocytes play a pivotal role in eye diseases, and loss of ABCA1 in astrocytes causes glaucoma-like neuropathy

Identification and functional analysis of a splice variant of mouse sodium-dependent phosphate transporter Npt2c

Mutations in the SLC34A3 gene, a sodium-dependent inorganic phosphate (Pi) cotransporter, also referred to as NaPi IIc, causes hereditary hypophosphatemic rickets with hypercalciuria (HHRH), an autosomal recessive disorder. In human and rodent, NaPi IIc is mainly localized in the apical membrane of renal proximal tubular cells. In this study, we identified mouse NaPi IIc variant (Npt2c-v1) that lacks the part of the exon 3 sequence that includes the assumed translation initiation site of Npt2c. Microinjection of mouse Npt2c-v1 cRNA into Xenopus oocytes demonstrated that Npt2c-v1 showed sodium-dependent Pi cotransport activity. The characterization of pH dependency showed activation at extracellular alkaline-pH. Furthermore, Npt2c-v1 mediated Pi transport activity was significantly higher at any pH value than those of Npt2c. In an in vitro study, the localization of the Npt2c-v1 protein was detected in the apical membrane in opossum kidney cells. The expression of Npt2c-v1 mRNA was detected in the heart, spleen, testis, uterus, placenta, femur, cerebellum, hippocampus, diencephalon and brain stem of mouse. Using mouse bone primary cultured cells, we showed the expression of Npt2c-v1 mRNA. In addition, the Npt2c protein was detected in the spermatozoa head. Thus, Npt2c-v1 was expressed in extra-renal tissues such as epididymal spermatozoa and may function as a sodium-dependent phosphate transporter

Characterization of a Conformation-Restricted Amyloid β Peptide and Immunoreactivity of Its Antibody in Human AD brain.

Characterization of amyloid β (Aβ) oligomers, the transition species present prior to the formation of Aβ fibrils and that have cytotoxicity, has become one of the major topics in the investigations of Alzheimer\u27s disease (AD) pathogenesis. However, studying pathophysiological properties of Aβ oligomers is challenging due to the instability of these protein complexes in vitro. Here, we report that conformation-restricted Aβ42 with an intramolecular disulfide bond at positions 17 and 28 (SS-Aβ42) formed stable Aβ oligomers in vitro. Thioflavin T binding assays, nondenaturing gel electrophoresis, and morphological analyses revealed that SS-Aβ42 maintained oligomeric structure, whereas wild-type Aβ42 and the highly aggregative Aβ42 mutant with E22P substitution (E22P-Aβ42) formed Aβ fibrils. In agreement with these observations, SS-Aβ42 was more cytotoxic compared to the wild-type and E22P-Aβ42 in cell cultures. Furthermore, we developed a monoclonal antibody, designated TxCo-1, using the toxic conformation of SS-Aβ42 as immunogen. X-ray crystallography of the TxCo-1/SS-Aβ42 complex, enzyme immunoassay, and immunohistochemical studies confirmed the recognition site and specificity of TxCo-1 to SS-Aβ42. Immunohistochemistry with TxCo-1 antibody identified structures resembling senile plaques and vascular Aβ in brain samples of AD subjects. However, TxCo-1 immunoreactivity did not colocalize extensively with Aβ plaques identified with conventional Aβ antibodies. Together, these findings indicate that Aβ with a turn at positions 22 and 23, which is prone to form Aβ oligomers, could show strong cytotoxicity and accumulated in brains of AD subjects. The SS-Aβ42 and TxCo-1 antibody should facilitate understanding of the pathological role of Aβ with toxic conformation in AD

A Non-alternant Aromatic Belt: Methylene-bridged [6]Cycloparaphenylene Synthesized from Pillar[6]arene

The synthesis, structure, and properties of methylene-bridged [6]cycloparaphenylene ([6]CPP), a non-alternant aromatic belt, are described. This belt-shaped methylene-bridged [6]CPP, in which each phenylene unit is tethered to its neighbors by methylene bridges, was constructed through six-fold intramolecular nickel-mediated aryl-aryl coupling of triflate-functionalized pillar[6]arene in 15% isolated yield. Compared with the analogous [6]CPP, the methylene bridges co-planarize neighboring paraphenylene units and enhance the degree of p-conjugation, resulting in a significant decrease in energy gap. Moreover, the incorporation of small molecules in the defined pocket of methylene-bridged [6]CPP makes it an attractive supramolecular architecture. Methylene-bridged [6]CPP is characterized by high internal strain energy reaching 110.2 kcal·mol–1, attributed to its restricted structure. This work not only exhibits an efficient strategy to construct a new family of aromatic belt, but also showcases their properties, which combine the merits of CPPs and pillararenes

スペイン語の非人称性の表現について ―SE構文と3PL構文―

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