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This paper develops L p - L q decay estimates of the gradient of the Stokes semigroup (T (t)) t ≥ 0 generated by the negative of the Stokes operator in exterior Lipschitz domains Ω ⊂ R n , n ≥ 3. More precisely, the L p - L q estimates of ∇ T (t) with optimal rates are proved if p and q satisfy | 1 / p − 1 / 2 | < 1 / (2 n) + ε , | 1 / q − 1 / 2 | < 1 / (2 n) + ε , and p ≤ q ≤ n with some ε > 0 , which should be useful for the study of stability of the several physically relevant flows. As an application, we obtain the existence theorem of global-in-time strong solutions to the three-dimensional Navier–Stokes equations in the critical space L ∞ (0 , ∞ ; L σ 3 (Ω)) provided that the initial velocity is small in the L 3 -norm. [ABSTRACT FROM AUTHOR]

We show that the Stokes operator defined on L σ p (Ω) for an exterior Lipschitz domain Ω ⊂ R n (n ≥ 3) admits maximal regularity provided that p satisfies | 1 / p − 1 / 2 | < 1 / (2 n) + ε for some ε > 0. In particular, we prove that the negative of the Stokes operator generates a bounded analytic semigroup on L σ p (Ω) for such p. In addition, L p - L q -mapping properties of the Stokes semigroup and its gradient with optimal decay estimates are obtained. This enables us to prove the existence of mild solutions to the Navier–Stokes equations in the critical space L ∞ (0 , T ; L σ 3 (Ω)) (locally in time and globally in time for small initial data). [ABSTRACT FROM AUTHOR]

In this study, we show that any finitely generated gyrovector subspace in the Möbius gyrovector space coincides with the intersection of the vector subspace generated by the same generators and the Möbius ball. As an application, we present a notion of orthogonal gyrodecomposition and clarify the relationship with the orthogonal decomposition. [ABSTRACT FROM AUTHOR]

To investigate how the conformational flexibility of subtilisin affects its ability to discriminate between enantiomeric amino acid and ester substrates for the subtilisin-catalyzed reaction in an organic solvent, the flexibility around the active site and the surface of subtilisin was estimated from the mobility of a spin label bound to subtilisin by ESR spectroscopy. Many studies on enzyme flexibility focus on the active site. Both the surface and active site flexibility play an important role in the enantioselectivity enhancement of the enzyme-catalyzed reaction. It was found, however, that the different behavior observed for the enantioselectivity between the amino acid and ester substrates could be correlated with the flexibility around the surface rather than the flexibility at the active site of subtilisin. In other words, for the ester substrates, the greater flexibility around the surface of subtilisin induced by a conformational change resulting from the presence of an additive such as DMSO is essential for the enantioselectivity enhancement. This model is also supported by the Michaelis–Menten kinetic parameters for each enantiomeric substrate. Our findings provide insight into the enantioselectivity enhancement for the resolution of enantiomers for enzyme-catalyzed reactions in organic solvents. [Copyright &y& Elsevier]

NK1 is a splice variant of the polypeptide growth factor HGF/SF that consists of the N terminal (N) and first kringle (K) domains and retains receptor binding and signalling. While NK1 behaves as a monomer in solution, two independent crystallographic structures have previously shown an identical, tightly packed dimer. Here we report a novel orthorhombic crystal form of NK1 at 2.5 A˚ resolution in which four NK1 protomers are packed in two distinct dimers in the asymmetric unit. Although the basic architecture of the new NK1 dimers is similar to the two described earlier, the new crystal form demonstrates extensive hinge movement between the N and K domain that leads to re-orientation of the receptor-binding sites. The hinge bending is evidence of the paucity of strong interactions between domains within the protomer, in contrast to the extensive interactions between protomers in the dimer. These observations are consistent with domain swapping in the dimer, such that the interdomain interactions of the monomer are replaced by equivalent interprotomer interactions in the dimer and offer a route for protein engineering of NK1 variants which may act as receptor antagonists. [Copyright &y& Elsevier]

[Display omitted] • We discovered a ricefish species from a river in central Sulawesi. • This river shares estuarine waters with another river where its sister species occurs. • These two species are genetically isolated despite freshwater drainage connectivity. • Coalescent-based demographic inference demonstrated that they are of lake-origin. • They are probably relic species left in these rivers due to lost dispersal ability. Sulawesi is a biodiversity hotspot for ricefishes (Adrianichthyidae), with many species endemic to the central part of this island in single ancient lakes or lake systems. Frequent vicariance by lake fragmentation since the Pliocene may be largely responsible for diversification in this family. In this study, we demonstrate that not only lacustrine species but also riverine species in this area are also deeply divergent even within a single river system. A mitochondrial phylogeny revealed that a ricefish population newly discovered from Cerekang River is sister to Oryzias dopingdopingensis Mandagi, Mokodongan, Tanaka, & Yamahira, another riverine species endemic to Doping-doping River. However, the Cerekang Oryzias was genetically isolated from O. dopingdopingensis , despite that Cerekang River and Doping-doping River share a connection across estuarine waters. This separation was supported by phylogenomic trees and population genetic structure analyses based on genome-wide single nucleotide polymorphisms. Coalescent-based demographic inference demonstrated that the ancestral population of these two riverine ricefishes had experienced a substantial population decrease and subsequently diverged into two sub-populations. Because the Cerekang Oryzias was also morphologically distinguished from O. dopingdopingensis , we described it as a new species, O. landangiensis. We infer that O. landangiensis and O. dopingdopingensis are of lake-origin and are relic species which were left in these rivers after the lake disappeared, and that they have lost their dispersal ability when inhabiting the ancient lake. The lost dispersal ability possibly contributed to the formation of the biodiversity hotspot for this fish group on this island. [ABSTRACT FROM AUTHOR]