Peptide mimetics as enzyme inhibitors: Use of free energy perturbation calculations to evaluate isosteric replacement for amide bonds in a potent HIV protease inhibitor

Summary We present the application of free energy perturbation theory/molecular dynamics to predict the consequence of replacing each of the seven peptide bonds in the potent HIV protease inhibitor JG365: ACE (acetyl)-Ser-Leu-Asn-HEA (hydroxyethylamine analog of Phe-Pro)-Ile-Val-NME (N-methyl) by ethylene or fluoroethylene isosteres. Replacing two of these bonds may well lead to significantly tighter binding; replacing two others is predicted to significantly diminish the binding affinity. Also, for three of the peptide bonds fluoroethylene replacements could lead to increased binding of free energies of the inhibitors. Our results should be considered as predictive since there are, as yet, no experimental results on such peptide replacements as enzyme inhibitors.     

Transfer hydrogenation of phenanthrene in the presence of boron modified alumina or silica-alumina

Reactions of phenanthrene with hydrogen donors carried out in the presence of boron trifluoride etherate modified catalysts: silica, alumina or silica-alumina have been studied. Di-, tetra- and octahydrophenanthrenes as well as some bicyclic hydrocarbons were the reactions products. Their yields were strongly influenced by hydrogen donor polarity.     

Equivalent statement of the Poincaré Conjecture

We find an equivalent statement of the Poincaré Conjecture in an analytical form involving the notion of the Sobolev mappings between manifolds.This work is supported by KBN grant no. 2 1057 91 01.     

Segre classes of a vector bundle spanned by global sections

We show that the Segre polynomial determines the minimal number of sections spanning a vector bundle spanned by global sections.The author was an NSERC Postdoctoral Fellow while preparing this paper.     

Strained delocalized carbenoid ring systems — A theoretical investigation

A number of ring compounds containing a divalent carbon center (carbenes) have been studied usingab initio quantum chemical methods. The studied systems include: imidazol-2-ylidene, 4-pyranylidene, 9-xanthylidene, cyclohexa-2,5-dienylidene and 4-oxocyclohexa-2,5-dienylidene. Extended ANO type basis sets were used. Wave functions and energies were obtained with a multiconfigurational approach (CASSCF), where dynamic correlation effects are treated by using second-order perturbation theory (CASPT2).The singlet-triplet splitting has been found to depend linearly on the energy separation between the two carbene orbitals. All systems, where this splitting is larger than about 10 eV have been found to have a singlet ground state, while those with a smaller gap have a triplet ground state. A number of excited states have been characterized. Computed excitation energies are in agreement with experiment in cases where such information is available.     

One‐pot synthesis of the indole derivative 4‐chloro‐3‐sulphamoyl‐N‐(2,3‐dihydro‐2‐methyl‐1H‐indol‐1‐yl)benzamide (indapamide)

New methods for the synthesis the indole derivative, Indapamide (1), using mixed anhydrides of the general formula R1COOCOOR2 (2) or DCC (N,N'‐dicyclohexylcarbodiimide) (3), are described.     

Diporphyrinyl derivatives of 1,10-phenanthroline and 2,2′-bipyridyl

The title derivatives were synthesized containing two meso-tri-p-tolylpheneleneporphyrin units attached via amide bridges to 4, 7- and 4,4′ positions of the respective heteroaromatic spacers.     

Bezoutians, Euclidean Algorithm, and Orthogonal Polynomials

We prove a quadratic expression for the Bezoutian of two univariate polynomials in terms of the remainders for the Euclidean algorithm. In case of two polynomials of the same degree, or of consecutive degrees, this allows us to interpret their Bezoutian as the Christoffel- Darboux kernel for a finite family of orthogonal polynomials, arising from the Euclidean algorithm. We give orthogonality properties of remainders, and reproducing properties of Bezoutians. Received December 13, 2004