Families of Line-Graphs and Their Quantization

Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L ⁿ (G). We give necessary and sufficient conditions for a line-graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions. Line-graphs may therefore serve as models to study the semiclassical limit (of large matrix size) of a quantum dynamics on graphs with fixed classical behaviour.     

The effect of ph and gas composition on the bubble fractionation of proteins

Studies were conducted to establish the effect of the variation of environmental factors on the separation occurring in protein systems, resulting from bubble fractionation in a bioreactor. The measure of separation was selected to be the separation ratio. This is defined to be the ratio of either the top or the middle position concentration in the vessel to the bottom concentration of the vessel. Invertase and α-amylase were the two “model” enzymes considered. It was observed that, under certain conditions, i.e., a combination of the nature of the sparging gas and the medium pH, varying degrees of protein separation were achieved. The pH of the system dramatically influenced the separation. It was found that the best separation occurred at a certain pH, assumed to be at or close to thepI of the protein in question. Furthermore, it was observed that systems sparged with CO₂ exhibited greater separation than systems sparged with air. In fact, in the case of invertase, almost threefold separation was observed at the top port when the solution was sparged with CO₂.     

Dehydroalanine-based inhibition of a peptide epimerase from spider venom

Ribosomally produced peptides that contain D-amino acids have been isolated from a number of vertebrate and invertebrate sources. In each case, the D-amino acids are introduced by a posttranslational modification of a parent peptide containing only amino acids of the L-configuration. The only known enzyme to catalyze such a reaction is the peptide epimerase (also known as peptide isomerase) from the venom of the funnel web spider, Agelenopsis aperta. This enzyme interconverts two 48-amino-acid-long peptide toxins that differ only by the stereochemistry at a single serine residue. In this paper we report the synthesis and testing of two pentapeptide analogues that contain modified amino acids at the site normally occupied by the substrate serine residue. When the L-chloroalanine-containing peptide 3 was incubated with the epimerase it was converted into the dehydroalanine-containing peptide 4 via an elimination of HCl. The dehydroalanine peptide 4 was independently synthesized and found to act as a potent inhibitor of the epimerase (IC50 = 0.5 microM). These results support a direct deprotonation/reprotonation mechanism in which a carbanionic intermediate is formed. The observed inhibition by 4 can be attributed to the sp(2)-hybridization of the alpha-carbon in the dehydroalanine unit that mimics the planar geometry of the anionic intermediate.