FRT Construction for Dynamical Yang-Baxter Maps

Notions of an (H, X)-bialgebroid and of its dynamical representation are proposed. The dynamical representations of each (H, X)-bialgebroid form a tensor category. Every dynamical Yang-Baxter map R(lambda) satisfying suitable conditions, a generalization of the set-theoretical solution to the quantum Yang-Baxter equation, gives birth to an (H, X)-bialgebroid A_R. The categories of L-operators for R(lambda) and of dynamical representations of A_R are isomorphic as tensor categories

Commutative Hopf algebras and cocommutative Hopf algebras in positive characteristic

AbstractLet A be a commutative Hopf algebra over a field k of characteristic p > 0. Let ϑ: C → B be a surjective map of commutative algebras such that xp = 0 for any x in Ker(ϑ), so that the map Fc:k1p ⊗ C → C, λ ⊗ a ↦ λpap factors through k1p ⊗ ϑ, yielding a map FCB: k1p ⊗ B → C. A map of algebras f:A → B can be lifted to an algebra map \̄tf: A → C such that f = ϑ ∘ \̄tf if and only if Ker(FA)⊂ Ker(FCB ∘ (k1p ⊗ f)). In particular, if FA is injective, any algebra map A → B can be lifted to A → C. The dual results will be given for cocommutative Hopf algebras and coalgebra maps

Transient and permanent gene transfer into the brain of the teleost fish medaka (Oryzias latipes) using human adenovirus and the Cre-loxP system

AbstractIn this study, we demonstrated that human type-5 adenovirus infected the brain of the teleost fish, medaka (Oryzias latipes), in vivo. Injection of adenoviral vector into the mesencephalic ventricle of medaka larvae induced the expression of reporter genes in some parts of the telencephalon, the periventricular area of the mesencephalon and diencephalon, and the cerebellum. Additionally, the Cre-loxP system works in medaka brains using transgenic medaka carrying a vector containing DsRed2, flanked by loxP sites under control of the β-actin promoter and downstream promoterless enhanced green fluorescent protein (EGFP). We demonstrated that the presence of green fluorescence depended on injection of adenoviral vector expressing the Cre gene and confirmed that EGFP mRNA was transcribed in the virus-injected larvae

CYK4 relaxes the bias in the off-axis motion by MKLP1 kinesin-6

Centralspindlin, a complex of the MKLP1 kinesin-6 and CYK4 GAP subunits, plays key roles in metazoan cytokinesis. CYK4-binding to the long neck region of MKLP1 restricts the configuration of the two MKLP1 motor domains in the centralspindlin. However, it is unclear how the CYK4-binding modulates the interaction of MKLP1 with a microtubule. Here, we performed three-dimensional nanometry of a microbead coated with multiple MKLP1 molecules on a freely suspended microtubule. We found that beads driven by dimeric MKLP1 exhibited persistently left-handed helical trajectories around the microtubule axis, indicating torque generation. By contrast, centralspindlin, like monomeric MKLP1, showed similarly left-handed but less persistent helical movement with occasional rightward movements. Analysis of the fluctuating helical movement indicated that the MKLP1 stochastically makes off-axis motions biased towards the protofilament on the left. CYK4-binding to the neck domains in MKLP1 enables more flexible off-axis motion of centralspindlin, which would help to avoid obstacles along crowded spindle microtubules