Steric hindrance in the synthesis and properties of the dimer of 1-(2,4,6-Tri-tert-butylphenyl)phosphole 1-oxide

Steric hindrance was observed during the oxidation of 2,4,6-tri-tert-butylphenylphosphole to the P oxide and in the dimerization of this latter species to the corresponding phosphanorbornene derivative. Single-crystal X-ray analysis of the dimer revealed considerable steric crowding around the P atoms. Deoxygenation of the dimer of the phosphole oxide by Cl₃SiH–C₆H₅N could only be accomplished under forcing conditions at 110°C. © 1997 John Wiley & Sons, Inc. Heteroatom Chem 8 : 527–531, 1997     

Homology and abelian lattice gauge theories

A simple Abelian model with both Higgs and gauge field degrees of freedom is investigated on a simplicial lattice of arbitrary dimension. We use group character expansion for both fields to get a diagrammatic expansion of the partition function. The diagrams consist of gauge group representation valued 1- and 2-chains. The diagrams are proved to satisfy the constraint that the boundary of the 2-chain representing the gauge field is equal to the 1-chain representing the Higgs field. Otherwise they identically vanish. Simple consequences of this are current conservation and the vanishing of non-null-homologous Wilson loops. Finally we use this picture for giving a lowest order estimate for the critical length of a string. This is the length at which the flux-tube string connecting two opposite charges is likely to break into two pieces due to pair creation.     

Covering of graphs by complete bipartite subgraphs; Complexity of 0–1 matrices

We prove that the edge set of an arbitrary simple graphG onn vertices can be covered by at mostn−[log₂ n]+1 complete bipartite subgraphs ofG. If the weight of a subgraph is the number of its vertices, then there always exists a cover with total weightc(n ²/logn) and this bound is sharp apart from a constant factor. Our result answers a problem of T. G. Tarján. Dedicated to Paul Erdős on his seventieth birthday     

On color critical graphs

It is shown that the minimal number of edges which have to be omitted from a (k + 1)-critical graph on n vertices in order to make it bipartite is at least ^k₂ for n large enough. This bound is best possible. Various related questions are considered.     

On inequalities for products of power sums

In the present note we investigate several inequalities concerning the product of power sums . The only restriction which is used is ₁ + ... + _k = 0. The conditions obtained are necessary and sufficient everywhere.     

Maximum bipartite subgraphs of Kneser graphs

We investigate the maximum number of edges in a bipartite subgraph of the Kneser graphK(n, r). The exact solution is given for eitherr arbitrary andn (4.3 + o(1))r, orr = 2 andn arbitrary. The problem is in connection with the study of the bipartite subgraph polytope of a graph.Research supported in part by the AKA Research Fund of the Hungarian Academy of Sciences     

Association of Cytochrome P450 Enzymes is a Determining Factor in their Catalytic Activity

Previously, our laboratory demonstrated that one cytochrome P450 isoenzyme can influence the catalytic properties of another P450 isoenzyme when combined in a reconstituted system. Moreover, our data and that of other investigators indicate that P450 interaction is required for catalytic activity even when one isoenzyme is present. The goal of the current study was to examine the possible mechanism of these interactions in more detail. Analyzing recently published X-ray data of microsomal P450 enzymes and protein docking studies, four types of dimer formations of P450 enzymes were examined in more detail. In case of two dimer types, the aggregating partner was shown to contribute to NADPH cytochrome P450 reductase (CPR) binding-a flavoprotein whose interaction with P450 is required for expressing P450 functional activity of the neighboring P450 moiety. Thus, it was shown that dimerization of P450 enzymes might result in an altered affinity towards the CPR. Two dimer types were shown to exist only in the presence of a substrate, while the other two types exist also without a substrate present. The molecular basis was established for the fact that the presence of a substrate and other P450 enzymes simultaneously determine the catalytic activity. Furthermore, a kinetic model was improved describing the catalytic activity of P450 enzymes as a function of CPR concentration based on equilibrium between different supramolecular organizations of P450 enzymes. This model was successfully applied in order to explain our experimental data and that of other investigators.Eszter Hazai and Zsolt Bikádi contributed equally to this workDavid Kupfer-Deceased