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We introduce the notion of an (α, β, γ) triple system, which generalizes the familiar generalized Jordan triple system related to a construction of simple Lie algebras. We then discuss its realization by considering some bilinear algebras and vice versa. Next, as a new concept, we study triality relations (a triality group and a triality derivation) associated with these triple systems; the relations are a generalization of the automorphisms and derivations of the triple systems. Also, we provide examples of several involutive triple systems with a tripotent element.

Ellis-van Creveld (EvC) syndrome is an autosomal-recessive skeletal dysplasia, characterized by short stature and postaxial polydactyly. A series of dental abnormalities, including hypomorphic enamel formation, has been reported in patients with EvC. Despite previous studies that attempted to uncover the mechanism leading to abnormal tooth development, little is known regarding how hypomorphic enamel is formed in patients with EvC. In the current study, using Evc2/ Limbin mutant mice we recently generated, we analyzed enamel formation in the mouse incisor. Consistent with symptoms in human patients, we observed that Evc2 mutant mice had smaller incisors with enamel hypoplasia. Histologic observations coupled with ameloblast marker analyses suggested that Evc2 mutant preameloblasts were capable of differentiating to secretory ameloblasts; this process, however, was apparently delayed, due to delayed odontoblast differentiation, mediated by a limited number of dental mesenchymal stem cells in Evc2 mutant mice. This concept was further supported by the observation that dental mesenchymal-specific deletion of Evc2 phenocopied the tooth abnormalities in Evc2 mutants. Overall, our findings suggest that mutations in Evc2 affect dental mesenchymal stem cell homeostasis, which further leads to hypomorphic enamel formation. [ABSTRACT FROM AUTHOR]

Atmospheric oxygenation and evolution of aerobic life on our earth are a result of water oxidation by oxygenic photosynthesis in photosystem II (PSII) of plants, algae and cyanobacteria. The water oxidation in the oxygen-evolving complex (OEC) in PSII is expected to proceed through five oxidation states, known as the Si(i= 0, 1, 2, 3 and 4) states in the Kok cycle, with the S1being the most stable state in the dark. The OEC in PSII involves the active catalytic site made of four Mn ions and one Ca ion, namely the CaMn4O5cluster. Past decades, molecular structures of the CaMn4O5cluster in OEC in PSII have been investigated by the extended X-ray absorption fine structure (EXAFS). The magneto-structural correlations were extensively investigated by electron paramagnetic resonance (EPR) spectroscopy. Recently, Kamiya and Shen groups made great breakthrough for determination of the S1structure of OEC of PSII by the X-ray diffraction (XRD) and X-ray free-electron laser (XFEL) experiments, providing structural foundations that are crucial for theoretical investigations of the CaMn4O5cluster. Large-scale quantum mechanics/molecular mechanics calculations starting from the XRD structures elucidated geometrical, electronic and spin structures of the CaMn4O5cluster, indicating an important role of the Jahn–Teller (JT) effect of Mn(III) ions. This paper presents theoretical formulas for estimation of the JT deformations of the CaMn4O5cluster in OEC of PSII. Scope and applicability of the formulas are examined in relation to several different structures of the CaMn4O5cluster proposed by XRD, XFEL, EXAFS and other experiments. Implications of the computational results are discussed for further refinements of geometrical parameters of the CaMn4O5cluster. [ABSTRACT FROM PUBLISHER]

Wnt proteins and beta-catenin signaling regulate major processes during embryonic development, and we hypothesized that they regulate cranial base synchondrosis development and growth. To address this issue, we analyzed cartilage-specific beta-catenin-deficient mice. Mutant synchondroses lacked typical growth plate zones, and endochondral ossification was delayed. In reciprocal transgenic experiments, cartilage overexpression of a constitutive active Lef1, a transcriptional mediator of Wnt/beta-catenin signaling, caused precocious chondrocyte hypertrophy and intermingling of immature and mature chondrocytes. The developmental changes seen in beta-catenin-deficient synchondroses were accompanied by marked reductions in Ihh and PTHrP as well as sFRP-1, an endogenous Wnt signaling antagonist and a potential Ihh signaling target. Thus, Wnt/beta-catenin signaling is essential for cranial base development and synchondrosis growth plate function. This pathway promotes chondrocyte maturation and ossification events, and may exert this important role by dampening the effects of Ihh-PTHrP together with sFRP-1. [ABSTRACT FROM AUTHOR]