Direct Participation of a Peripheral Side Chain of a Corrin Ring in Coenzyme B12 Catalysis

The crystal structures of the B₁₂‐dependent isomerases (eliminating) diol dehydratase and ethanolamine ammonia‐lyase complexed with adenosylcobalamin were solved with and without substrates. The structures revealed that the peripheral a‐acetamide side chain of the corrin ring directly interacts with the adenosyl group to maintain the group in the catalytic position, and that this side chain swings between the original and catalytic positions in a synchronized manner with the radical shuttling between the coenzyme and substrate/product. Mutations involving key residues that cooperatively participate in the positioning of the adenosyl group, directly or indirectly through the interaction with the a‐side chain, decreased the turnover rate and increased the relative rate of irreversible inactivation caused by undesirable side reactions. These findings guide the engineering of enzymes for improved catalysis and producing useful chemicals by utilizing the high reactivity of radical species.     

Comproportionation reaction and hindered rotation of coordinated pyridine rings in an acetate-bridged tetraplatinum(II) cluster with pyridine-based ligands in the cluster plane

A series of pyridine-substituted derivatives of octaacetatotetraplatinum(II), [Pt4(CH3COO)8-n(L)2n]n+ (L= 4-dimethylaminopyridine (dmap), pyridine (py), 4-cyanopyridine (cpy); n = 1-4) were prepared, and the tetra- and octasubstituted forms (n = 2 and 4) were isolated. 1HNMR spectra showed that this type of cluster undergoes a comproportionation reaction. Reactions between clusters in which n = 0 and 2, n = 0 and 4, and n = 2 and 4 afforded Pt4 clusters with n = 1, 2, and 3, respectively, as a main product in acetonitrile. The dmap-substituted clusters, trans-[Pt4(CH3COO)6(dmap)4](ClO4)2 x 3CH3NO2 (3a(ClO4)2 x 3CH3NO2) and [Pt4(CH3COO)4(dmap)8](ClO4)4 x 4 H2O (5a(ClO4)4-4H2O), have been structurally characterized. Both 3a and 5a have a square-planar cluster core comprised of four PtII ions, and all eight out-of-plane coordination sites are occupied by acetate ligands in a bridging mode. In 5a, all of the in-plane sites are occupied by dmap ligands. In 3a, four dmap ligands occupy the coordination sites at the two mutually opposite edges of the square planar cluster skeleton, giving a trans tetrasubstituted form of [Pt4(CH3COO)8-] (1). In octasubstituted 5a, adjacent dmap ligands are so closely arranged that the Pt-N distances (2.20(3), 2.30(3) A) are longer than those in tetrasubstituted 3a (2.13(1), 2.15(1) A) and related Pt4 clusters. Furthermore, rotation of the dmap ligand about the Pt-N bond in 5a was restricted, and the rate constant of the rotation was 4.5s(-1) at 20 degrees C from dynamic NMR study. Cluster [Pt4(CH3COO)5(dmap)6]3+ (4a) also exhibited similar hindered rotation with the rate constants of 2.0s(-1), 12s(-1) and approximately 10(4)s(-1) at 20 degrees C depending on the coordination sites of the dmap ligands in 4a.     

Antiandrogen. I. 2-azapregnane and 2-oxapregnane steroids.

2-Azachlormadinone acetate (5a, 17-acetoxy-6-chloro-2-azapregna-4,6-diene- 3,20-dione), 2-oxachlormadinone acetate (6, 17-acetoxy-6-chloro-2-oxapregna-4,6-diene-3,20-dione) and the derivatives were prepared as potential antiandrogenic agents. Biological evaluation showed that 5a and 6 had a potent antiandrogenic activity when tested in the castrated male rat.     

Inverse bifurcation problems for diffusive Holling–Tanner population model

We consider the equation which is called Holling–Tanner population model where is a bifurcation parameter and are unknown constants. In this paper, we determine the unknown constants from the asymptotic behavior of the bifurcation curve , where .     

A superconvergence result of the natural convection equations

This paper presents a superconvergence result of the stationary natural convection equations. The superconvergence result is obtained by applying a coarse mesh projection for finite element approximation. This projection method is actually a postprocessing procedure that constructs a new approximation based on a high order polynomial on coarse mesh, under some regularity assumption. Finally, numerical experiment is presented for testing, which confirms the theoretic analysis. Copyright © 2015 John Wiley & Sons, Ltd.     

On the pagenumber of trivalent Cayley graphs

Book embedding of graphs is one of the graph layout problem. It is useful for the multiprocessor network layout or the fault-tolerant processor arrays. We show that the trivalent Cayley graphs proposed by Vadapalli and Srimani can be embedded in five pages, and show some additional results on cube-connected cycles.     

Interior transition layers of solutions to the perturbed elliptic Sine-Gordon equation on an interval

We consider the perturbed elliptic Sine-Gordon equation on an interval-u″t+γsinu(t)=μf(u(t)),t ∈I := (-T, T),u(t) > 0,t ∈I,u(±T)=0 where λ, μ>0 are parameters andT>0 is a constant. By applying variational methods subject to the constraint depending on λ, we obtain eigenpairs (μ,u)=(μ(λ),u _λ) which solve this eigenvalue problem for a given λ>0. Then we study the asymptotic behavior ofu _λ and μ(λ) as λ→∞. Especially, we study the location of interior transition layers ofu _λ as λ→∞. This research has been supported by the Japan Society for the Promotion of Science.     

Asymptotic behavior of eigenvalues of two-parameter nonlinear Sturm-Liouville problems

The nonlinear two-parameter Sturm-Liouville problemu ^"+μg(u)=λf(u) is studied for μ, λ>0. By using Ljusternik-Schnirelman theory on the general level set developed by Zeidler, we shall show the existence of ann-th variational eigenvalue λ=λ_n(μ). Furthermore, for specialf andg, the asymptotic formula of λ₁(μ)) as μ→∞ is established.     

On a resolvent estimate of the Stokes system in a half space arising from a free boundary problem for the Navier–Stokes equations

In this paper we consider a resolvent problem of the Stokes operator with some boundary condition in the half space, which is obtained as a model problem arising in evolution free boundary problems for viscous, incompressible fluid flow. We show standard resolvent estimates in the L_q framework (1 < q < ∞), applying some kernel estimates to concrete solution formulas. The Volevich trick in [21] plays a fundamental role in estimating solutions (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)