Iterating the number of intersection points of the diagonals of irregular convex polygons, or C(n,4) the hard way !

Counting the number of internal intersection points made bythe diagonals of irregular convex polygons where no three diagonalsare concurrent is an interesting problem in discrete mathematics.This paper uses an iterative approach to develop a summationrelation which tallies the total number of intersections, andshows that this total can be expressed as a simple sum of products.This iterative approach also motivates solutions for the numberof internal regions and number of line segments produced bythe diagonals     

Qualitative characterization of biomolecular zinc complexes by collisionally induced dissociation

Nanospray and collisionally induced dissociation (CID) on a quadrupole/time-of-flight mass spectrometer were used to examine the complexes formed between the zinc ion binding protein metallothionein and a series of peptides related to glutathione. The objective of the study was to determine if CID could be used to distinguish complexes that are stabilized by co-chelation of a zinc ion from non-covalent complexes that were formed in some other way. Differences in the collision energy required for dissociation and, more importantly, differences in the distribution of zinc ions between the pairs of dissociation products suggest that mass spectrometry can provide qualitative information about the bimolecular chelation of metal ions. The potential application to zinc chelates is particularly important, since biological chelates do not provide signals directly detectable by NMR, M?ssbauer or other spectroscopies. The observations reported here also allowed a molecular mechanism to be proposed to explain the differences observed by others in the physiological interactions of reduced and oxidized glutathione with metallothionein.