Rapid parallel synthesis of dipeptide diphenyl phosphonate esters as inhibitors of dipeptidyl peptidases

In this paper, we present a parallel synthesis of several series of dipeptide diphenyl phosphonates that are known to be irreversible inhibitors of serine proteases. Polymer-assisted solution-phase synthesis (PASP) is used for the rapid and clean coupling between various alpha-aminoalkyl diphenyl phosphonate ester building blocks and commercially available or easily accessible amino acids. These compounds were used for the rapid profiling of dipeptidyl peptidase II (DPP II) and the closely related dipeptidyl peptidase IV (DPP IV). A highly selective DPP II inhibitor was identified, N-cyclopentylglycyl-NHCH(C(6)H(5))PO(OPh)(2) (9.35), that will be useful to discriminate between DPP II and DPP IV in biological systems in order to further elucidate the biological function of DPP II.     

On the length of longest chordless cycles

Upper bounds for the length of a longest (circuit) cycle without chords in a (directed) graph are given in terms of the rank of the adjacency matrix and in terms of its eigenvalues.Received: October 2003, Revised: January 2005, AMS classification: 05C     

Quantum theory as the most robust description of reproducible experiments

It is shown that the basic equations of quantum theory can be obtained from a straightforward application of logical inference to experiments for which there is uncertainty about individual events and for which the frequencies of the observed events are robust with respect to small changes in the conditions under which the experiments are carried out.