The Fukui matrix: a simple approach to the analysis of the Fukui function and its positive character

The Fukui matrix is introduced as the derivative of the one-electron reduced density matrix with respect to a change in the number of electrons under constant external potential. The Fukui matrix extends the Fukui function concept: the diagonal of the Fukui matrix is the Fukui function. Diagonalizing the Fukui matrix gives a set of eigenvectors, the Fukui orbitals, and accompanying eigenvalues. At the level of theory used, there is always one dominant eigenvector, with an eigenvalue equal to 1. The remaining eigenvalues are either zero or come in pairs with eigenvalues of the same magnitude but opposite sign. Analysis of the frontier molecular orbital coefficient in the eigenvector with eigenvalue 1 gives information on the quality of the frontier molecular orbital picture. The occurrence of negative Fukui functions can be easily interpreted in terms of the nodal character of the dominant eigenvector versus the characteristics of the remaining eigenvectors and eigenvalues.     

Green chemistry: solvent- and metal-free Prins cyclization. Application to sequential reactions

Prins cyclization between a homoallylic alcohol and an aldehyde, promoted by trimethylsilyl halide, afforded 4-halo-tetrahydropyrans with good to excellent yields. Thanks to the absence of the solvent and metal, the THP thus obtained have been implicated without purification in several other reactions, in a sequential way, affording in particular new indole derivatives.     

Polyvalent Transition-State Analogues of Sialyl Substrates Strongly Inhibit Bacterial Sialidases**

Bacterial sialidases (SA) are validated drug targets expressed by common human pathogens such as Streptococcus pneumoniae, Vibrio cholerae, or Clostridium perfringens. Noncovalent inhibitors of bacterial SA capable of reaching the submicromolar level are rarely reported. In this work, multi- and polyvalent compounds are developed, based on the transition-state analogue 2-deoxy-2,3-didehydro-N-acetylneuraminic (DANA). Poly-DANA inhibits the catalytic activity of SA from S. pneumoniae (NanA) and the symbiotic microorganism B. thetaiotaomicron (BtSA) at the picomolar and low nanomolar levels (expressed in moles of molecules and of DANA, respectively). Each DANA grafted to the polymer surpasses the inhibitory potential of the monovalent analogue by more than four orders of magnitude, which represents the highest multivalent effect reported so far for an enzyme inhibition. The synergistic interaction is shown to operate exclusively in the catalytic domain, and not in the flanked carbohydrate-binding module (CBM). These results offer interesting perspectives for the multivalent inhibition of other SA families lacking a CBM, such as viral, parasitic, or human SA.