Structure and dynamics of the homologous series of alanine peptides: a joint molecular dynamics/NMR study

The phi,psi backbone angle distribution of small homopolymeric model peptides is investigated by a joint molecular dynamics (MD) simulation and heteronuclear NMR study. Combining the accuracy of the measured scalar coupling constants and the atomistic detail of the all-atom MD simulations with explicit solvent, the thermal populations of the peptide conformational states are determined with an uncertainty of <5 %. Trialanine samples mainly ( approximately 90%) a poly-l-proline II helix-like structure, some ( approximately 10%) beta extended structure, but no alphaR helical conformations. No significant change in the distribution of conformers is observed with increasing chain length (Ala(3) to Ala(7)). Trivaline samples all three major conformations significantly. Triglycine samples the four corner regions of the Ramachandran space and exists in a slow conformational equilibrium between the cis and trans conformation of peptide bonds. The backbone angle distribution was also studied for the segment Ala3 surrounded by either three or eight amino acids on both N- and C-termini from a sequence derived from the protein hen egg white lysozyme. While the conformational distribution of the central three alanine residues in the 9mer is similar to that for the small peptides Ala(3)-Ala(7), major differences are found for the 19mer, which significantly (30-40%) samples alphaR helical stuctures.     

A study of the copolymerization of hydroxyethyl methacrylate and tetrahydrofurfuryl methacrylate

The free radical copolymerizations of hydroxyethyl methacrylate and tetrahydrofurfuryl methacrylate have been investigated at 50°C. The compositions of polymers prepared at low conversions have been determined using ¹³C-NMR, and the glass transition temperatures determined by DSC. The copolymerizations were found to be best described by a terminal model with reactivity ratios of r_H = 1.79 and r_T = 0.76. The triad fraction sequence distributions have been calculated based on the terminal model and the calculated reactivity ratios. The glass transitions have been fitted to the Gordon–Taylor equation. The best value of the Gordon–Taylor constant was found to be k_H = 1.42 ± 0.2, indicating nonideal mixing of the two monomer components in the copolymers. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 3730–3737, 1999     

Rayleigh waves in an isotropic elastic half-space coated by a thin isotropic elastic layer with smooth contact

In the present paper, we are interested in the propagation of Rayleigh waves in an isotropic elastic half-space coated with a thin isotropic elastic layer. The contact between the layer and the half space is assumed to be smooth. The main purpose of the paper is to establish an approximate secular equation of the wave. By using the effective boundary condition method, an approximate, yet highly accurate secular equation of fourth-order in terms of the dimensionless thickness of the layer is derived. From the secular equation obtained, an approximate formula of third-order for the velocity of Rayleigh waves is established. The approximate secular equation and the formula for the velocity obtained in this paper are potentially useful in many practical applications.     

Functional tolerance in an isoreticular series of highly porous metal-organic frameworks

A series of highly porous University of Michigan Crystalline Material (UMCM-1) type Zn-based metal-organic frameworks (MOFs) were synthesized from mono- and bi-functionalized benzenedicarboxylate (BDC) ligands. In total, 16 new functionalized UMCM-1 derivatives were obtained by a combination of pre- and postsynthetic functionalization. Through postsynthetic modification (PSM), amino-halo bifunctional MOFs were converted into amide-halo materials via solid-state acylation reactions. A series of bifunctional MOFs containing Cl, Br, and I groups revealed that PSM conversion is not affected by the size of the halide, only by the steric bulk of the reagent used in these solid-state organic transformations.     

Functional group effects on metal-organic framework topology

Functionalization of the ligand 1,3,5-tris(4-carboxyphenyl)benzene (H(3)BTB) has been realized with methoxy (H(3)BTB-[OMe](3)) and hydroxy (H(3)BTB-[OH](3)) groups. Combining H(3)BTB-[OMe](3) and Zn(ii) results in the formation of the first isostructural, functionalized analogue of MOF-177 (MOF-177-OMe), while the combination of H(3)BTB-[OH](3) and Zn(ii) generates a rare, interpenetrated pcu-e framework.     

Photoelectron spectroscopy and theoretical studies of UF5(-) and UF6(-)

The UF(5)(-) and UF(6)(-) anions are produced using electrospray ionization and investigated by photoelectron spectroscopy and relativistic quantum chemistry. An extensive vibrational progression is observed in the spectra of UF(5)(-), indicating significant geometry changes between the anion and neutral ground state. Franck-Condon factor simulations of the observed vibrational progression yield an adiabatic electron detachment energy of 3.82 ± 0.05 eV for UF(5)(-). Relativistic quantum calculations using density functional and ab initio theories are performed on UF(5)(-) and UF(6)(-) and their neutrals. The ground states of UF(5)(-) and UF(5) are found to have C(4v) symmetry, but with a large U-F bond length change. The ground state of UF(5)(-) is a triplet state ((3)B(2)) with the two 5f electrons occupying a 5f(z3)-based 8a(1) highest occupied molecular orbital (HOMO) and the 5f(xyz)-based 2b(2) HOMO-1 orbital. The detachment cross section from the 5f(xyz) orbital is observed to be extremely small and the detachment transition from the 2b(2) orbital is more than ten times weaker than that from the 8a(1) orbital at the photon energies available. The UF(6)(-) anion is found to be octahedral, similar to neutral UF(6) with the extra electron occupying the 5f(xyz)-based a(2u) orbital. Surprisingly, no photoelectron spectrum could be observed for UF(6)(-) due to the extremely low detachment cross section from the 5f(xyz)-based HOMO of UF(6)(-).     

Finite-sum smooth optimization with SARAH

Computational Optimization and Applications - We introduce NC-SARAH for non-convex optimization as a practical modified version of the original SARAH algorithm that was developed for convex...     

On the degree and separability of nonconvexity and applications to optimization problems

We study qualitative indications for d.c. representations of closed sets in and functions on Hilbert spaces. The first indication is an index of nonconvexity which can be regarded as a measure for the degree of nonconvexity. We show that a closed set is weakly closed if this indication is finite. Using this result we can prove the solvability of nonconvex minimization problems. By duality a minimization problem on a feasible set in which this indication is low, can be reduced to a quasi-concave minimization over a convex set in a low-dimensional space. The second indication is the separability which can be incorporated in solving dual problems. Both the index of nonconvexity and the separability can be characteristics to “good” d.c. representations. For practical computation we present a notion of clouds which enables us to obtain a good d.c. representation for a class of nonconvex sets. Using a generalized Caratheodory’s theorem we present various applications of clouds.