RESUMO
An outline is given of how to split the n-dimensional space of torsion angles occurring in flexible (bio-)polymers (like alkanes, nucleic acids, or proteins, for instance) into n one-dimensional potential curves. Forthcoming applications will focus on the "protein folding problem," beginning with polyglycine. CONTEXT: In accordance with Euler's topology rules, molecules are considered to be composed of "vertices" (atoms, ligands, bonding sites, functional groups, and bigger fragments). Following Hückel, each vertex is represented by only one basis function. Starting from the "monofocal" hydrids CH[Formula: see text], NH[Formula: see text], OH[Formula: see text], FH, and SiH[Formula: see text], PH[Formula: see text], SH[Formula: see text], ClH as anchor units, "chemionic" Hamiltonians (of individual "chemion ensembles" and proportional nuclear charges) are constructed recursively, together with an appropriate basis set for the first five (normal) alkanes and some related oligomers like primary alcohols, alkyl amines, and alkyl chlorides. METHODS: Standard methods ("Restricted Hartree-Fock RHF" and "Full Configuration Interaction FCI") are used to solve the various stationary Schrödinger equations. Two software packages are indispensable: "SMILES" for integral evaluations over Slater-type orbitals (STO), and "Numerical Recipes" for matrix diagonalizations and inversions. While managing with only two-center repulsion integrals, "implicit multi-center integrations" lead us to the non-empirical fundament of Hoffmann's "Extended-Hückel Theory."
RESUMO
The postulated transition of Bis-Maltolato-OxoVanadium(IV) (BMOV) from its inactive trans- into its cis-aquo-BMOV isomeric form in solution was simulated by means of computational molecular modeling. The rotational barrier was calculated with DFT - B3LYP under a stepwise optimization protocol with STO-3G, 3-21G, 3-21G*, and 6-31G ab initio basis sets. Our computed results are consistent with reports on the putative molecular mechanism of BMOV triggering the insulin-like cellular response (insulin mimetic) as a potent inhibitor of the protein tyrosine phosphatase-1B (PTP-1B). Initially, trans-BMOV is present in its solid dosage form but in aqueous solution, and during oral administration, it is readily converted into a mixture of "open-type" and "closed-type" complexes of cis-aquo-BMOV under equilibrium conditions. However, in the same measure as the "closed-type" complex binds to the cytosolic PTP-1B, it disappears from solution, and the equilibrium shifts towards the "closed-type" species. In full accordance, the computed binding mode of cis-BMOV is energetically favored over sterically hindered trans-BMOV. In view of our earlier report on prodrug hypothesis of vanadium organic compounds the present results suggest that cis-BMOV is the bioactive species.
