A proof of some conjectures of Mao on partition rank inequalities

Based on work of Atkin and Swinnerton-Dyer on partition rank difference functions, and more recent work of Lovejoy and Osburn, Mao has proved several inequalities between partition ranks modulo 10, and additional results modulo 6 and 10 for the \(M_2\) rank of partitions without repeated odd parts. Mao conjectured some additional inequalities. We prove some of Mao’s rank inequality conjectures for both the rank and the \(M_2\) rank modulo 10 using elementary methods.     

Ab initio computational study of 1-methyl-4-silatranone and attempts at its conventional synthesis

1-Methyl-4-silatranone could exhibit the structural aspects of a typical silatrane including a short N–Si bond distance reflecting a dative bond. But given the significant amide resonance in a [3.3.3] bridgehead bicyclic lactam, the lone pair could be shared with the carbonyl group leading to a very long N–Si bond, essentially a “non-silatrane.” Ab initio calculations (MP2/6-311 + G*) predict that ground state conformations of this molecule are best regarded as lactams rather than silatranes, the most stable having a calculated N–Si bond length of 2.902 Å and an N–CO bond length of 1.387 Å. The calculated transition state for inversion of the amide ring retains very little amide resonance (N–CO, 1.440 Å). Some of this loss is compensated through tightening of the N–Si bond (2.422 Å), leading to a net energy of activation of ca 8 kcal/mol. Attempts to synthesize 1-methyl-4-silatranone using conventional pathways successful for 1-methylsilatrane [condensations employing N,N-bis(2-hydroxyethyl)glycolamide in place of tris(2-hydroxyethyl)amine] were unsuccessful. This is due to the net loss in resonance energy of the amide reactant relative to that in the [3.3.3] system, the essential absence of the N–Si dative bond, and the rigidity introduced by the planar amide linkage in the starting material. A more likely pathway to successful synthesis should be formation of the amide linkage in the final step.     

Nonblinking plasmonic quantum dot assemblies for multiplex biological detection

Nonblinking nanosystems are prepared by layer-by-layer polyelectrolyte deposition, which precisely controls the stoichiometry and the distance between quantum dots (QDs) and gold nanoparticles (GNPs). Conjugation of biorecognition molecules to these nanobarcodes enables cell targeting and entry with prolonged retention and minimal toxicity.     

Evaluation of diverse α/β-backbone patterns for functional α-helix mimicry: analogues of the Bim BH3 domain

Peptidic oligomers that contain both α- and β-amino acid residues, in regular patterns throughout the backbone, are emerging as structural mimics of α-helix-forming conventional peptides (composed exclusively of α-amino acid residues). Here we describe a comprehensive evaluation of diverse α/β-peptide homologues of the Bim BH3 domain in terms of their ability to bind to the BH3-recognition sites on two partner proteins, Bcl-x(L) and Mcl-1. These proteins are members of the anti-apoptotic Bcl-2 family, and both bind tightly to the Bim BH3 domain itself. All α/β-peptide homologues retain the side-chain sequence of the Bim BH3 domain, but each homologue contains periodic α-residue → β(3)-residue substitutions. Previous work has shown that the ααβαααβ pattern, which aligns the β(3)-residues in a 'stripe' along one side of the helix, can support functional α-helix mimicry, and the results reported here strengthen this conclusion. The present study provides the first evaluation of functional mimicry by ααβ and αααβ patterns, which cause the β(3)-residues to spiral around the helix periphery. We find that the αααβ pattern can support effective mimicry of the Bim BH3 domain, as manifested by the crystal structure of an α/β-peptide bound to Bcl-x(L), affinity for a variety of Bcl-2 family proteins, and induction of apoptotic signaling in mouse embryonic fibroblast extracts. The best αααβ homologue shows substantial protection from proteolytic degradation relative to the Bim BH3 α-peptide.     

Extending foldamer design beyond α-helix mimicry: α/β-peptide inhibitors of vascular endothelial growth factor signaling

Diverse strategies have been explored to mimic the surface displayed by an α-helical segment of a protein, with the goal of creating inhibitors of helix-mediated protein-protein interactions. Many recognition surfaces on proteins, however, are topologically more complex and less regular than a single α-helix. We describe efforts to develop peptidic foldamers that bind to the irregular receptor-recognition surface of vascular endothelial growth factor (VEGF). Our approach begins with a 19-residue α-peptide previously reported by Fairbrother et al. (Biochemistry 1998, 37, 17754) to bind to this surface on VEGF. Systematic evaluation of α→β replacements throughout this 19-mer sequence enabled us to identify homologues that contain up to ~30% β residues, retain significant affinity for VEGF, and display substantial resistance to proteolysis. These α/β-peptides can block VEGF-stimulated proliferation of human umbilical vein endothelial cells.     

Probing the non-pairwise interactions between CO molecules moving on a Cu(111) surface

The coverage dependent dynamics of CO on a Cu(111) surface are studied on an atomic scale using helium spin-echo spectroscopy. CO molecules occupy top sites preferentially, but also visit intermediate bridge sites in their motion along the reaction coordinate. We observe an increase in hopping rate as the CO coverage grows; however, the motion remains uncorrelated up to at least 0.10 monolayers (ML). From the temperature dependence of the diffusion rate, we find an effective barrier of 98 ± 5 meV for diffusion. Thermal motion is modelled with Langevin molecular dynamics, using a potential energy surface having adsorption sites at top and bridge positions and the experimental data are well represented by an adiabatic barrier for hopping of 123 meV. The sites are not degenerate and the rate changes observed with coverage are modelled successfully by changing the shape of the adiabatic potential energy surface in the region of the transition state without modifying the energy barrier. The results demonstrate that sufficient detail exists in the experimental data to provide information on the principal adsorption sites as well as the energy landscape in the region of the transition state.     

Oxygen adsorption on the kinked Pt(321) surface

Oxygen adsorption and desorption were characterized on the kinked Pt(321) surface using high resolution electron energy loss spectroscopy and thermal desorption spectroscopy. Molecular oxygen adsorbs mainly as a peroxo-like species at 100K with a heat of desorption of about 22 k^J/mol. Some of the molecular oxygen also adsorbs dissociatively at 100K. Atomic oxygen is adsorbed in three states. One state is due to adsorption on the terraces and another state is due to adsorption along the rough step sites. The heat of desorption of both of these states approximately equal and decreases from 290 k^J/mol to 195kJ/mol with increasing coverage. Atomic oxygen is also observed to adsorb in another state which is interpreted as adsorption at an on-top site.