Trees with Equal Domination and Restrained Domination Numbers

Let G = (V,E) be a graph and let S V. The set S is a packing in G if the vertices of S are pairwise at distance at least three apart in G. The set S is a dominating set (DS) if every vertex in V − S is adjacent to a vertex in S. Further, if every vertex in V − S is also adjacent to a vertex in V − S, then S is a restrained dominating set (RDS). The domination number of G, denoted by γ(G), is the minimum cardinality of a DS of G, while the restrained domination number of G, denoted by γ_r(G), is the minimum cardinality of a RDS of G. The graph G is γ-excellent if every vertex of G belongs to some minimum DS of G. A constructive characterization of trees with equal domination and restrained domination numbers is presented. As a consequence of this characterization we show that the following statements are equivalent: (i) T is a tree with γ(T)=γ_r(T); (ii) T is a γ-excellent tree and T ≠ K₂; and (iii) T is a tree that has a unique maximum packing and this set is a dominating set of T. We show that if T is a tree of order n with ℓ leaves, then γ_r(T) ≤ (n + ℓ + 1)/2, and we characterize those trees achieving equality.     

The synthesis of new weakly coordinating diborate anions: anion stability as a function of linker structure and steric bulk

The successive addition of KCN and Ph3CCl to B(C6F4-C6F5-2)3 (PBB) affords triphenylmethyl salts of the [NC-PBB]- anion. By contrast, the analogous reaction with sodium dicyanamide followed by treatment with Ph(3)CCl leads to the zwitterionic aminoborane H2NB(C12F9)2C12F8, via nucleophilic attack on an o-F atom, together with CPh3[F-PBB]. Whereas treatment of [NC-PBB]- with either PBB or B(C6F5)3 fails to give isolable cyano-bridged diborates, the reaction of Me3SiNC-B(C6F5)3 with PBB in the presence of Ph3CCl affords [Ph3C][PBB-NC-B(C6F5)3]. Due to steric hindrance this anion is prone to borane dissociation. The longer linking group N(CN)2- gives the very voluminous anions [N[CNB(C6F5)3]2]- and [N(CN-PBB)2]-. A comparison of propylene polymerisations with rac-Me2Si(Ind)2ZrMe2 activated with the various boranes or trityl borates gives an anion-dependent activity sequence, in the order [NC-PBB]- < [MeB(C6F5)3]- < [MePBB]- approximately [PBB-NCB(C6F5)3]- approximately [N[CNB(C6F5)3]2]- < [F-PBB]-< [B(C6F5)4]- < [N(CN-PBB)2]-. The anion [N(CN-PBB)2]- gives a catalyst productivity about 2500 times higher than that of [NC-PBB]- and exceeds that of [B(C6F5)4]- based catalysts. The van der Waals volumes and surface areas of the anions have been calculated and provide a rationale for the observed reactivity trends in polymerisation reactions.     

15N CIDNP investigations of the peroxynitric acid nitration of L-tyrosine and of related compounds

Peroxynitric acid (O2NOOH) nitrates L-tyrosine and related compounds at pH 2-5. During reaction with O2(15)NOOH in the probe of a 15N NMR spectrometer, the NMR signals of the nitration products of L-tyrosine, N-acetyl-L-tyrosine, 4-fluorophenol and 4-methoxyphenylacetic acid appear in emission indicating a nitration via free radicals. Nuclear polarizations are built up in radical pairs [15NO2* , PhO*]F or [15NO2* , ArH*+]F formed by diffusive encounters of 15NO2 with phenoxyl-type radicals PhO or with aromatic radical cations ArH*+. Quantitative 15N CIDNP investigations with N-acetyl-L-tyrosine and 4-fluorophenol show that the radical-dependent nitration is the only reaction pathway. During the nitration reaction, the 15N NMR signal of 15NO3- also appears in emission. This is explained by singlet-triplet transitions in radical pairs [15NO2* , 15NO3*]S generated by electron transfer between O2(15)NOOH and H15NO2 formed as a reaction intermediate. During reaction of peroxynitric acid with ascorbic acid, 15N CIDNP is again observed in the 15N NMR signal of 15NO3- showing that ascorbic acid is oxidized by free radicals. In contrast to this, O2(15)NOOH reacts with glutathione and cysteine without the appearance of 15N CIDNP, indicating a direct oxidation without participation of free radicals.     

Multipolar interactions in the D pocket of thrombin: large differences between tricyclic imide and lactam inhibitors

Two series of tricyclic inhibitors of the serine protease thrombin, imides (+/-)-1-(+/-)-8 and lactams (+/-)-9-(+/-)-13, were analysed to evaluate contributions of orthogonal multipolar interactions with the backbone C=O moiety of Asn98 to the free enthalpy of protein-ligand complexation. The lactam derivatives are much more potent and more selective inhibitors (K(i) values between 0.065 and 0.005 microM, selectivity for thrombin over trypsin between 361- and 1609-fold) than the imide compounds (Ki values between 0.057 and 23.7 microM, selectivity for thrombin over trypsin between 3- and 67-fold). The increase in potency and selectivity is explained by the favorable occupancy of the P-pocket of thrombin by the additional isopropyl substituent in the lactam derivatives. The nature of the substituent on the benzyl ring filling the D pocket strongly influences binding potency in the imide series, with Ki values increasing in the sequence: F < OCH2O < Cl < H < OMe < OH < N(pyr)< Br. This sequence can be explained by both steric fit and the occurrence of orthogonal multipolar interactions with the backbone C[double bond, length as m-dash]O moiety of Asn98. In contrast, the substituent on the benzyl ring hardly affects the ligand potency in the lactam series. This discrepancy was clarified by the comparison of X-ray structures solved for co-crystals of thrombin with imide and lactam ligands. Whereas the benzyl substituents in the imide inhibitors are sufficiently close (< or =3.5 Angstroms) to the C=O group of Asn98 to allow for attractive orthogonal multipolar interactions, the distances in the lactam series are too large (> or =4 Angstroms) for attractive dipolar contacts to be effective.     

Differential proteome analysis of colon carcinoma cell line SW480 after reconstitution of the tumour suppressor Smad4

The tumour suppressor gene Smad4 is frequently inactivated in gastrointestinal carcinomas. Smad4 plays a pivotal role in transducing signals of the transforming growth factor-β (TGF-β) superfamily of proteins. Inactivation of Smad4 seems to occur late during tumour progression when tumours acquire invasive and metastatic properties. Identification of proteins directly or indirectly regulated by Smad4 would, therefore, ease the future design of new diagnostic and therapeutic strategies for gastrointestinal carcinoma. We have used human colon carcinoma cell line SW480 stably transfected with Smad4 as an in-vitro model system to identify Smad4-regulated proteins by applying two-dimensional gel electrophoresis (2DE) then MALDI-PMF/PFF-MS. We identified a total of 47 protein species with a Smad4-dependent expression. From the functions of the candidate proteins we obtained new insights into Smad4’s participation in processes, for example apoptosis, differentiation, and proliferation.     

Directed evolution of hybrid enzymes: Evolving enantioselectivity of an achiral Rh-complex anchored to a protein

The concept of utilizing the methods of directed evolution for tuning the enantioselectivity of synthetic achiral metal-ligand centers anchored to proteins has been implemented experimentally for the first time.