Rapid Dihydrogen Cleavage by Persistent Nitroxide Radicals under Frustrated Lewis Pair Conditions

Persistent radicals undergo hydrogen atom abstraction reactions with a great variety of substrates, but not with dihydrogen. It has now been found that the TEMPO radical splits dihydrogen under mild conditions in the presence of the strong bulky B(C₆F₅)₃ boron Lewis acid. The reaction is thought to proceed by a typical frustrated Lewis pair mechanism with the TEMPO radical acting as the active Lewis base. The reaction was analyzed by DFT, which indicates that no significant spin density on the hydrogen atoms is accumulated along the H₂ splitting reaction path.     

The geometric genus of splice-quotient singularities

We prove a formula for the geometric genus of splice-quotient singularities (in the sense of Neumann and Wahl). This formula enables us to compute the invariant from the resolution graph; in fact, it reduces the computation to that for splice-quotient singularities with smaller resolution graphs. We also discuss the dimension of the first cohomology groups of certain invertible sheaves on a resolution of a splice-quotient singularity.

     

Hochschild Homology of Singular Algebras

One of the main properties of Hochschild homology of the algebra of smooth functions on a smooth manifold is its local character. In this paper, we consider subalgebras of smooth functions which are significant for singular spaces such that simplicial complexes or cones over smooth manifolds. We compute their Hochschild homology and investigate the local character. Our computations show that, in opposition with the smooth case, the (local part of the) Hochschild homology is not always isomorphic to the corresponding de Rham complex of differential forms. The method we use is a slight modification of the localization procedure introduced in by Sullivan.     

On the kinematics of protein folding

We offer simple solutions to three kinematic problems that occur in the folding of proteins. We show how to construct suitably local elementary Monte Carlo moves, how to close a loop, and how to fold a loop without breaking the bond that closes it.     

On Existence of Solutions to Differential Equations or Inclusions Remaining in a Prescribed Closed Subset of a Finite-Dimensional Space

This paper is devoted to existence of trajectories to differential equations and inclusions remaining in a given closed (or compact) set. Topological properties of the boundary of this set enables us to conclude the existence of such trajectories in many cases.     

Common Features of the Onset of the Persistent Chaos in Nonlinear Oscillators: A Phenomenological Approach

Bifurcational precedences of generating the persistent,crossing-the-potential-barrier chaos in nonautonomous, dissipative nonlinearoscillators are examined. The comparative computational study covers thetwin-well oscillator, pendulum with parametric excitation, and pendulumdriven by external harmonic force. The study reveals common features of thesystem response properties and of the bifurcational scenarios, prior to theonset of the chaos. It is pointed out that, in the three considered systems,the chaos is preceded by the two and only two asymmetric periodicattractors, which are simultaneously annihilated via theperiod-doubling-crisis scenario. However, the generating of the chaos is notnecessarily related directly to the escape from a potential well. We alsoshow that, in all three systems, the persistent chaos can be viewed as anirregular combination of the `crossing the potential barrier' and theoscillatory component of motion.     

Periodic Cyclic Homology of Iwahori–Hecke Algebras

We determine the periodic cyclic homology of the Iwahori–Hecke algebras H _q , for q * not a proper root of unity. (In this paper, by a proper root of unity we shall mean a root of unity other than 1.) Our method is based on a general result on periodic cyclic homology, which states that a weakly spectrum preserving morphism of finite type algebras induces an isomorphism in periodic cyclic homology. The concept of a weakly spectrum preserving morphism is defined in this paper, and most of our work is devoted to understanding this class of morphisms. Results of Kazhdan and Lusztig and Lusztig show that, for the indicated values of q, there exists a weakly spectrum preserving morphism _q : H _q J, to a fixed finite type algebra J. This proves that _q induces an isomorphism in periodic cyclic homology and, in particular, that all algebras H _q have the same periodic cyclic homology, for the indicated values of q. The periodic cyclic homology groups of the algebra H ₁ can then be determined directly, using results of Karoubi and Burghelea, because it is the group algebra of an extended affine Weyl group.     

Molecular design of two sterol 14α-demethylase homology models and their interactions with the azole antifungals ketoconazole and bifonazole

Summary Sterol 14α-demethylase (CYP51) is one of the known major targets for azole antifungals. Therapeutic side effects of these antifungals are based on interactions of the azoles with the human analogue enzyme. This study describes for the first time a comparison of a human CYP51 (HU-CYP51) homology model with a homology model of the fungal CYP51 of Candida albicans (CA-CYP51). Both models are constructed by using the crystal structure of Mycobacterium tuberculosis MT-CYP51 (PDB code: 1EA1).The binding mode of the azole ketoconazole is investigated in molecular dynamics simulations with the GROMACS force field. The usage of special parameters for the iron azole complex binding is necessary to obtain the correct complex geometry in the active site of the enzyme models. Based on the dynamics simulations it is possible to explain the enantioselectivity of the human enzyme and also to predict the binding mode of the isomers of ketoconazole in the active site of the fungal model.