New splittings of operations of Poisson algebras and transposed Poisson algebras and related algebraic structures

There are two kinds of splittings of operations, namely, the classical splitting which is interpreted operadically as taking successors and another splitting which we call the second splitting giving the anti-structures of the successors' algebras. The algebraic structures corresponding to them respectively are characterized in terms of representations. Due to the appearance of the two bilinear operations in Poisson algebras and transposed Poisson algebras, we commence to study new splittings of operations in the ``mixed" sense that the commutative associative products and Lie brackets are splitted in different manners respectively, that is, they are splitted interlacedly in three manners: the classical splitting, the second splitting and the un-splitting. Accordingly the corresponding algebraic structures are given. More explicitly, there are 8 algebraic structures interpreted in terms of representations of Poisson algebras illustrating the mixed splittings of operations of Poisson algebras respectively, including the known pre-Poisson algebras. For illustrating the mixed splittings of operations of transposed Poisson algebras, there are 8 algebraic structures interpreted in terms of representations of transposed Poisson algebras on the spaces themselves and another 8 algebraic structures interpreted in terms of representations of transposed Poisson algebras on the dual spaces. Moreover, such a phenomenon exhibits an obvious difference between Poisson algebras and transposed Poisson algebras.Comment: 39 pages. arXiv admin note: text overlap with arXiv:2309.1617

A bialgebra theory for transposed Poisson algebras via anti-pre-Lie bialgebras and anti-pre-Lie-Poisson bialgebras

The approach for Poisson bialgebras characterized by Manin triples with respect to the invariant bilinear forms on both the commutative associative algebras and the Lie algebras is not available for giving a bialgebra theory for transposed Poisson algebras. Alternatively, we consider Manin triples with respect to the commutative 2-cocycles on the Lie algebras instead. Explicitly, we first introduce the notion of anti-pre-Lie bialgebras as the equivalent structure of Manin triples of Lie algebras with respect to the commutative 2-cocycles. Then we introduce the notion of anti-pre-Lie Poisson bialgebras, characterized by Manin triples of transposed Poisson algebras with respect to the bilinear forms which are invariant on the commutative associative algebras and commutative 2-cocycles on the Lie algebras, giving a bialgebra theory for transposed Poisson algebras. Finally the coboundary cases and the related structures such as analogues of the classical Yang-Baxter equation and $\mathcal O$-operators are studied.Comment: 34 page

Anti-dendriform algebras, new splitting of operations and Novikov type algebras

We introduce the notion of anti-dendriform algebras as a new approach of splitting the associativity. They are characterized as the algebras with two operations whose sum is associative and the negative left and right multiplication operators compose the bimodules of the sum associative algebras, justifying the notion due to the comparison with the corresponding characterization of dendriform algebras. The notions of anti-$\mathcal O$-operators and anti-Rota-Baxter operators on associative algebras are introduced to interpret anti-dendriform algebras. In particular, there are compatible anti-dendriform algebra structures on associative algebras with nondegenerate commutative Connes cocycles. There is an important observation that there are correspondences between certain subclasses of dendriform and anti-dendriform algebras in terms of $q$-algebras. As a direct consequence, we give the notion of Novikov-type dendriform algebras as an analogue of Novikov algebras for dendriform algebras, whose relationship with Novikov algebras is consistent with the one between dendriform and pre-Lie algebras. Finally we extend to provide a general framework of introducing the notions of analogues of anti-dendriform algebras, which interprets a new splitting of operations.Comment: 25 page

Biomechanical analysis of bridge combined fixation system as a novel treatment for the fixation of type A3 distal femoral fractures

BackgroundTo compare the biomechanical parameters of AO/OTA type A3 distal femoral fractures fixed bilaterally with a bridge combined fixation system (BCFS) and lateral locking compression plate + locking reconstruction plate (LCP + LRP).MethodsTwelve A3 distal femoral fracture models with medial cortical defects of the distal femur were created using synthetic femoral Sawbones. BCFS and LCP + LRP were used for bilateral fixation, with six in each group. Axial compression and torsion tests were performed on the two groups of fracture models to determine their stiffness during axial compression and the Torsional stiffness during torsion tests. Axial compression failure tests were performed to collect the vertical loads of the ultimate failure tests.ResultsIn the test conducted on the fixed type A3 distal femoral fracture models, the axial stiffness in the BCFS group (group A) (1,072.61 ± 113.5 N/mm) was not significantly different from that in the LCP + LRP group (group B) (1,184.13 ± 110.24 N/mm) (t = 1.726, P = 0.115), the Torsional stiffness in group A (3.73 ± 0.12 N.m/deg) was higher than that in group B (3.37 ± 0.04 N.m/deg) (t = 6.825, P < 0.001),and the ultimate failure test of type A3 fracture model showed that the vertical load to destroy group A fixation (5,290.45 ± 109.63 N) was higher than that for group B (3,978.43 ± 17.1 N) (t = 23.28, P < 0.05). Notably, intertrochanteric fractures occurred in groups A and B.ConclusionsIn the fixation of type A3 distal femoral fractures, the anti-axial compression of the BCFS group was similar to that of the LCP + LRP group, but the anti-torsion was better

Involvement of Ca2+ Activated Cl- Channel Ano6 in Platelet Activation and Apoptosis

Background/Aims: The ubiquitously expressed Ca2+ Activated Cl- Channel Ano6 participates in the stimulation of cell membrane scrambling. Defective Ano6 underlies the Scott syndrome, an inherited bleeding disorder with impaired scrambling of plasma membrane phospholipids. At least in theory, the bleeding disorder of Scott syndrome may result from impaired platelet function. Activators of platelets include thrombin and collagen related peptide (CRP), which trigger increase of cytosolic Ca2+-activity ([Ca2+]i), production of reactive oxygen species (ROS), degranulation, integrin activation, as well as cell shrinkage and phospholipid scrambling of the cell membrane. The present study thus explored whether Ano6 modifies activation-induced alterations of cytosolic Ca2+-activity ([Ca2+]i), degranulation (P-selectin exposure), integrin activation, phosphatidylserine exposure on the platelet surface and platelet volume. Methods: Platelets from mice lacking Ano6 (ano6-/-) were compared to platelets from corresponding wild-type mice (ano6+/+). [Ca2+]i was estimated from Fluo-3 fluorescence, ROS from DCFDA fluorescence, degranulation from P-selectin abundance, integrin activation from αIIbβ3-integrin abundance, phosphatidylserine abundance from annexin-V-binding, and cell volume from forward scatter. Results: Platelet number in blood was slightly higher in ano6-/- mice than in ano6+/+ mice. Without activation [Ca2+]i and volume were similar in ano6-/- and ano6+/+ platelets as well as ROS abundance, P-selectin abundance, αIIbβ3 integrin activation, and phosphatidylserine exposure were negligible in both genotypes. Thrombin (0.01 U/ml) and CRP (2 or 5 µg/ml) increased [Ca2+]i, ROS abundance, platelet degranulation, αIIbβ3 integrin activation, and triggered annexin-V-binding as well as cell shrinkage, all effects less pronounced in ano6-/- than in ano6+/+ platelets. Conclusions: Genetic knockout of Ano6 blunts thrombin- and CRP-induced activation and apoptosis of blood platelets

Blunted apoptosis of erythrocytes in mice deficient in the heterotrimeric G-protein subunit Gαi2

Putative functions of the heterotrimeric G-protein subunit Gαi2-dependent signaling include ion channel regulation, cell differentiation, proliferation and apoptosis. Erythrocytes may, similar to apoptosis of nucleated cells, undergo eryptosis, characterized by cell shrinkage and cell membrane scrambling with phosphatidylserine (PS) exposure. Eryptosis may be triggered by increased cytosolic Ca2+ activity and ceramide. In the present study, we show that Gαi2 is expressed in both murine and human erythrocytes and further examined the survival of erythrocytes drawn from Gαi2-deficient mice (Gαi2−/−) and corresponding wild-type mice (Gαi2+/+). Our data show that plasma erythropoietin levels, erythrocyte maturation markers, erythrocyte counts, hematocrit and hemoglobin concentration were similar in Gαi2−/− and Gαi2+/+ mice but the mean corpuscular volume was significantly larger in Gαi2−/− mice. Spontaneous PS exposure of circulating Gαi2−/− erythrocytes was significantly lower than that of circulating Gαi2+/+ erythrocytes. PS exposure was significantly lower in Gαi2−/− than in Gαi2+/+ erythrocytes following ex vivo exposure to hyperosmotic shock, bacterial sphingomyelinase or C6 ceramide. Erythrocyte Gαi2 deficiency further attenuated hyperosmotic shock-induced increase of cytosolic Ca2+ activity and cell shrinkage. Moreover, Gαi2−/− erythrocytes were more resistant to osmosensitive hemolysis as compared to Gαi2+/+ erythrocytes. In conclusion, Gαi2 deficiency in erythrocytes confers partial protection against suicidal cell death

Blunted apoptosis of erythrocytes in mice deficient in the heterotrimeric G-protein subunit Gαi2

Putative functions of the heterotrimeric G-protein subunit Gαi2-dependent signaling include ion channel regulation, cell differentiation, proliferation and apoptosis. Erythrocytes may, similar to apoptosis of nucleated cells, undergo eryptosis, characterized by cell shrinkage and cell membrane scrambling with phosphatidylserine (PS) exposure. Eryptosis may be triggered by increased cytosolic Ca2+ activity and ceramide. In the present study, we show that Gαi2 is expressed in both murine and human erythrocytes and further examined the survival of erythrocytes drawn from Gαi2-deficient mice (Gαi2−/−) and corresponding wild-type mice (Gαi2+/+). Our data show that plasma erythropoietin levels, erythrocyte maturation markers, erythrocyte counts, hematocrit and hemoglobin concentration were similar in Gαi2−/− and Gαi2+/+ mice but the mean corpuscular volume was significantly larger in Gαi2−/− mice. Spontaneous PS exposure of circulating Gαi2−/− erythrocytes was significantly lower than that of circulating Gαi2+/+ erythrocytes. PS exposure was significantly lower in Gαi2−/− than in Gαi2+/+ erythrocytes following ex vivo exposure to hyperosmotic shock, bacterial sphingomyelinase or C6 ceramide. Erythrocyte Gαi2 deficiency further attenuated hyperosmotic shock-induced increase of cytosolic Ca2+ activity and cell shrinkage. Moreover, Gαi2−/− erythrocytes were more resistant to osmosensitive hemolysis as compared to Gαi2+/+ erythrocytes. In conclusion, Gαi2 deficiency in erythrocytes confers partial protection against suicidal cell death.Fil: Bissinger, Rosi. Eberhard Karls Universität Tübingen; AlemaniaFil: Lang, Elisabeth. Universitat Dusseldorf; AlemaniaFil: Ghashghaeinia, Mehrdad. Eberhard Karls Universität Tübingen; AlemaniaFil: Singh, Yogesh. Eberhard Karls Universität Tübingen; AlemaniaFil: Zelenak, Christine. Charité Medical University; AlemaniaFil: Fehrenbacher, Birgit. Eberhard Karls Universität Tübingen; AlemaniaFil: Honisch, Sabina. Eberhard Karls Universität Tübingen; AlemaniaFil: Chen, Hong. Eberhard Karls Universität Tübingen; AlemaniaFil: Fakhri, Hajar. Eberhard Karls Universität Tübingen; AlemaniaFil: Umbach, Anja T.. Eberhard Karls Universität Tübingen; AlemaniaFil: Liu, Guilai. Eberhard Karls Universität Tübingen; AlemaniaFil: Rexhepaj, Rexhep. Universitat Bonn; AlemaniaFil: Liu, Guoxing. Eberhard Karls Universität Tübingen; AlemaniaFil: Schaller, Martin. Eberhard Karls Universität Tübingen; AlemaniaFil: Mack, Andreas F.. Eberhard Karls Universität Tübingen; AlemaniaFil: Lupescu, Adrian. Eberhard Karls Universität Tübingen; AlemaniaFil: Birnbaumer, Lutz. National Institutes of Health; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay; ArgentinaFil: Lang, Florian. Eberhard Karls Universität Tübingen; AlemaniaFil: Qadri, Syed M.. Eberhard Karls Universität Tübingen; Alemania. Pontificia Universidad Católica Argentina "Santa María de los Buenos Aires". Facultad de Ciencias Médicas. Instituto de Investigaciones Biomédicas; Argentin