Some problems in metric fixed point theory

Three papers, published coincidentally and independently by Felix Browder, Dietrich G?hde, and W. A. Kirk in 1965, triggered a branch of mathematical research now called metric fixed point theory. This is a survey of some of the highlights of that theory, with a special emphasis on some of the problems that remain open. Dedicated to Felix Browder on the occasion of his 80th birthday     

Photophysics of diplatinum polyynediyl oligomers: chain length dependence of the triplet state in sp carbon chains

The series of polyynes with the structure trans, trans-[Ar-Pt(P 2)-(C[triple bond]C) n -Pt(P 2)-Ar], where P = tri( p-tolyl)phosphine, Ar = p-tolyl, and n = 3, 4, 5, 6 (6, 8, 10, 12 sp carbon atoms), has been subjected to a comprehensive photophysical investigation. At low temperature ( T < 140 K) in a 2-methyltetrahydrofuran (MTHF) glass, the complexes exhibit moderately efficient phosphorescence appearing as a series of narrow (fwhm < 200 cm (-1)) vibronic bands separated by ca. 2100 cm (-1). The emission is assigned to a (3)pi,pi* triplet state that is concentrated on the sp carbon chain, and the vibronic progression arises from coupling of the excitation to the -C[triple bond]C- stretch. The 0-0 energy of the phosphorescence decreases with increasing sp carbon chain length, spanning a range of over 6000 cm (-1) across the series. Transient absorption spectroscopy carried out at ambient temperature confirms that the (3)pi,pi* triplet is produced efficiently, and it displays a strongly allowed triplet-triplet absorption. In the MTHF solvent glass ( T < 140 K), the emission lifetimes increase with emission energy. Analysis of the triplet nonradiative decay rates reveals a quantitative energy gap law correlation. The nonradiative decay rates can be calculated by using parameters recovered from a single-mode Franck-Condon fit of the emission spectra.     

Donor-acceptor biradicals as ground state analogues of photoinduced charge separated states

A Valence Bond Configuration Interaction (VBCI) model is used to relate the intraligand magnetic exchange interaction (J) to the electronic coupling matrix element (HAB) in Tp(Cum,MeZn)(SQNN), a compound that possesses a Donor-Acceptor (D-A) SemiQuinone-NitronylNitroxide (SQNN) biradical ligand. Within this framework, an SQ --> NN charge transfer state mixes with the ground state and stabilizes the spin triplet (S = 1). This charge-transfer transition is observed spectroscopically and probed using resonance Raman spectroscopy. In addition, the temperature-dependent electronic absorption spectrum of the Ni(II) complex, Tp(Cum,MeNi)(SQNN), has been studied. Exchange coupling between the S = 1 Ni(II) ion and S = 1 SQNN provides a mechanism for observing the formally spin-forbidden, ligand-based 3GC --> 1CTC transition. This provides a means of determining U, the mean GC --> CTC energy, and a one-center exchange integral, K(0). The experimental determination of J, U, and K(0) permits facile calculation of HAB, and we show that this methodology can be extended to determine the electronic coupling matrix element in related SQ-Bridge-NN molecules. As magnetic susceptibility measurements are easily acquired in the solid state, H(AB) may be effectively determined for single molecules in a known geometry, provided a crystal structure exists for the biradical complex. Thus, SQ-Bridge-NN molecules possess considerable potential for probing both geometric and electronic structure contributions to the magnitude of the electronic coupling matrix element associated with a given bridge fragment.     

Hg+Br-->HgBr recombination and collision-induced dissociation dynamics

A global potential energy surface has been constructed for the system HgBr+Ar-->Hg+Br+Ar to determine temperature dependent rate constants for the collision-induced dissociation (CID) and recombination of Hg and Br atoms. The surface was decomposed using a many-body expansion. Accurate two-body potentials for HgBr, HgAr, and ArBr were calculated using coupled cluster theory with single and double excitations and a perturbative treatment of triple excitations [CCSD(T)], as well as the multireference averaged coupled pair functional method. Correlation consistent basis sets were used to extrapolate to the complete basis set limit and corrections were included to account for scalar and spin-orbit relativistic effects, core-valence correlation, and the Lamb shift. The three-body potential was computed with the CCSD(T) method and triple-zeta quality basis sets. Quasiclassical trajectories using the final analytical potential surface were directly carried out on the CID of HgBr by Ar for a large sampling of initial rotational, vibrational, and collision energies. The recombination rate of Hg and Br atoms is a likely first step in mercury depletion events that have been observed in the Arctic troposphere during polar sunrise. The effective second order rate constant for this process was determined in this work from the calculated CID rate as a function of temperature using the principle of detailed balance, which resulted in k(T) = 1.2 x 10(-12) cm(3) molecule(-1) s(-1) at 260 K and 1 bar pressure.     

Membrane Cholesterol and the Formation of Cholesterol Domains in the Pathogenesis of Cardiovascular Disease

At least three types of cholesterol-rich membrane domains have been described in biological membranes including cholesterol rafts, membrane caveolae and crystalline cholesterol domains,. While clear biological functions have been ascribed to both rafts and caveolae, little attention has been directed to the biological consequences of cholesterol enrichment of cell membranes and the formation of cholesterol domains. Elevated blood cholesterol levels have been shown to result in the enrichment of the cell plasma membrane with cholesterol in arterial smooth muscle cells (SMC), endothelial cells (EC) and cardiac myocytes. In the early period of cholesterol feeding (within days), the cell membrane enriches with cholesterol and membrane viscosity and membrane bilayer width increase. This latter effect severely alters membrane protein function, and recent data indicates that this induces the modulation of vascular cells (SMC and EC) to the atherosclerotic phenotype. In cardiac myocytes these membrane modifications appear to induce alterations in gene expression patterns that lead to the development of a heart failure phenotype. In addition, as the cholesterol content increases, phase separation of cholesterol occurs resulting in the formation of immiscible cholesterol domains within the membrane. These domains likely initiate nucleation of cholesterol crystals which would explain the origin of “cholesterol clefts” in atherosclerotic lesions. Taken together, these membrane alterations secondary to cholesterol enrichment constitute a “membrane lesion” which contribute to the very early pathogenic events underlying major human diseases including coronary artery disease, stroke and heart failure.     

The Implications of (2S,4S)‐Hydroxyproline 4‐O‐Glycosylation for Prolyl Amide Isomerization

The conformations of peptides and proteins are often influenced by glycans O‐linked to serine (Ser) or threonine (Thr). (2S,4R)‐4‐Hydroxyproline (Hyp), together with L ‐proline (Pro), are interesting targets for O‐glycosylation because they have a unique influence on peptide and protein conformation. In previous work we found that glycosylation of Hyp does not affect the N‐terminal amide trans/cis ratios (K_trans/cis) or the rates of amide isomerization in model amides. The stereoisomer of Hyp—(2S,4S)‐4‐hydroxyproline (hyp)—is rarely found in nature, and has a different influence both on the conformation of the pyrrolidine ring and on K_trans/cis. Glycans attached to hyp would be expected to be projected from the opposite face of the prolyl side chain relative to Hyp; the impact this would have on K_trans/cis was unknown. Measurements of ³J coupling constants indicate that the glycan has little impact on the C^γ‐endo conformation produced by hyp. As a result, it was found that the D ‐galactose residue extending from a C^γ‐endo pucker affects both K_trans/cis and the rate of isomerization, which is not found to occur when it is projected from a C^γ‐exo pucker; this reflects the different environments delineated by the proline side chain. The enthalpic contributions to the stabilization of the trans amide isomer may be due to disruption of intramolecular interactions present in hyp; the change in enthalpy is balanced by a decrease in entropy incurred upon glycosylation. Because the different stereoisomers—Hyp and hyp—project the O‐linked carbohydrates in opposite spatial orientations, these glycosylated amino acids may be useful for understanding of how the projection of a glycan from the peptide or protein backbone exerts its influence.