Model systems for flavoenzyme activity: relationships between cofactor structure, binding and redox properties

A series of flavins were synthesized bearing electron-withdrawing and -donating substituents. The electrochemical properties of these flavins in a nonpolar solvent were determined. The recognition of these flavins by a diamidopyridine (DAP) receptor and the effect this receptor has on flavin redox potential was also quantified. It was found that the DAP-flavin binding affinity and the reduction potentials (E(1/2)) for both the DAP-bound and unbound flavins correlated well with functions derived from linear free energy relationships (LFERs). These results provide insight and predictive capability for the interplay of electronics and redox state-specific interactions for both abiotic and enzymatic systems.     

Studies on the Lewis acid mediated cleavage of alpha-aminoacetals: synthesis of novel 1,2-aminoethers,and evidence for alpha-alkoxy aziridinium ion intermediates

The nucleophilic cleavage of alpha-amino acetals induced by TMSOTf can be used to prepare a wide range of substituted 1,2-aminoethers. In particular, organometallic reagents, N-heterocycles, and enamines all react efficiently to give products in good yield. In appropriate cases, good levels of stereocontrol are possible, but this is very dependent on the nature of the nucleophile and the substrate, with diethylzinc proving particularly effective across a range of substrates. The degree of stereocontrol can be used to infer the nature of the reactive intermediates involved in the reaction. With diethylzinc, it is most likely that the reaction proceeds by coordination of the nucleophile to the amino group followed by transfer of an ethyl group to an alpha-oxocarbenium ion. With non-coordinating nucleophiles, the stereochemical outcome can be rationalised in terms of addition to the possible alpha-alkoxy aziridinium ion intermediates.     

Palladium-catalyzed sequential alkylation-alkenylation reactions: new three-component coupling leading to oxacycles

A new three-component domino reaction catalyzed by palladium was devised, producing polysubstituted bicyclic molecules in good yields from readily available substrates. The reaction conditions and the scope of the process were examined, and a possible mechanism is proposed. [reaction: see text]     

Recycling solid supports – A head-to-tail linker

The concept of a `head-to-tail linker' designed to allow the regeneration and reuse of a variety of solid supports is introduced. The synthesis of this linker, its coupling to various solid supports, its application in a number of standard solid phase reactions and resin regeneration are presented.     

On the deficiency indices and self-adjointness of symmetric Hamiltonian systems

The main purpose of this paper is to investigate the formal deficiency indices of a symmetric first-order system

     

Hausdorff dimension and asymptotic cycles

We carry out a multifractal analysis for the asymptotic cycles for compact Riemann surfaces of genus . This describes the set of unit tangent vectors for which the associated orbit has a given asymptotic cycle in homology.

     

Ascending Hnn Extensions of Finitely Generated Free Groups Are Hopfian

It is shown that every ascending HNN extension of a finitelygenerated free group is Hopfian. An important ingredient inthe proof is that under certain hypotheses on the group H, ifG is an ascending HNN extension of H, then cd(G) = cd(H) + 1.     

Hilbert schemes, polygraphs and the Macdonald positivity conjecture

We study the isospectral Hilbert scheme , defined as the reduced fiber product of with the Hilbert scheme of points in the plane , over the symmetric power . By a theorem of Fogarty, is smooth. We prove that is normal, Cohen-Macaulay and Gorenstein, and hence flat over . We derive two important consequences.

(1) We prove the strong form of the conjecture of Garsia and the author, giving a representation-theoretic interpretation of the Kostka-Macdonald coefficients . This establishes the Macdonald positivity conjecture, namely that .

(2) We show that the Hilbert scheme is isomorphic to the -Hilbert scheme of Nakamura, in such a way that is identified with the universal family over . From this point of view, describes the fiber of a character sheaf at a torus-fixed point of corresponding to .

The proofs rely on a study of certain subspace arrangements , called polygraphs, whose coordinate rings carry geometric information about . The key result is that is a free module over the polynomial ring in one set of coordinates on . This is proven by an intricate inductive argument based on elementary commutative algebra.

     

Derived Lengths of Solvable Groups Having Five Irreducible Character Degrees I

Let G be a solvable group with five character degrees. We show that the derived length of G is at most 5. This verifies that the Taketa inequality, dl(G)|cd(G)|, is valid for solvable groups with at most five character degrees.