Ring-closing metathesis of olefinic peptides: design, synthesis, and structural characterization of macrocyclic helical peptides

Heptapeptides containing residues with terminal olefin-derivatized side chains (3 and 4) have been treated with ruthenium alkylidene 1 and undergone facile ring-closing olefin metathesis (RCM) to give 21- and 23-membered macrocyclic peptides (5 and 6). The primary structures of peptides 3 and 4 were based upon a previously studied heptapeptide (2), which was shown to adopt a predominantly 3(10)-helical conformation in CDCl(3) solution and an alpha-helical conformation in the solid state. Circular dichroism, IR, and solution-phase (1)H NMR studies strongly suggested that acyclic precursors 3 and 4 and the fully saturated macrocyclic products 7 and 8 also adopted helical conformations in apolar organic solvents. Single-crystal X-ray diffraction of cyclic peptide 8 showed it to exist as a right-handed 3(10)-helix up to the fifth residue. Solution-phase NMR structures of both acyclic peptide 4 and cyclic peptide 8 in CD(2)Cl(2) indicated that the acyclic diene assumes a loosely 3(10)-helical conformation, which is considerably rigidified upon macrocyclization. The relative ease of introducing carbon-carbon bonds into peptide secondary structures by RCM and the predicted metabolic stability of these bonds renders olefin metathesis an exceptional methodology for the synthesis of rigidified peptide architectures.     

Fusion around the barrier for 7Li+12C

Fusion cross-sections for the ⁷Li + ¹²C reaction have been measured at energies above the Coulomb barrier by the direct detection of evaporation residues. The heavy evaporation residues with energies below 3 MeV could not be separated out from the α-particles in the spectrum and hence their contribution was estimated using statistical model calculations. The present work indicates that suppression of fusion cross-sections due to the breakup of ⁷Li may not be significant for ⁷Li + ¹²C reaction at energies around the barrier.     

On the Motion of a Dynamic System with Minimal Dissipation

The motion of a holonomic scleronomic non-conservative mechanicalsystem with minimal dissipation is considered. As applicationsof the theory several problems are studied in detail.     

Eigenanalysis of some preconditioned Helmholtz problems

Summary. In this work we calculate the eigenvalues obtained by preconditioning the discrete Helmholtz operator with Sommerfeld-like boundary conditions on a rectilinear domain, by a related operator with boundary conditions that permit the use of fast solvers. The main innovation is that the eigenvalues for two and three-dimensional domains can be calculated exactly by solving a set of one-dimensional eigenvalue problems. This permits analysis of quite large problems. For grids fine enough to resolve the solution for a given wave number, preconditioning using Neumann boundary conditions yields eigenvalues that are uniformly bounded, located in the first quadrant, and outside the unit circle. In contrast, Dirichlet boundary conditions yield eigenvalues that approach zero as the product of wave number with the mesh size is decreased. These eigenvalue properties yield the first insight into the behavior of iterative methods such as GMRES applied to these preconditioned problems. Received March 24, 1998 / Revised version received September 28, 1998     

Adaptive use of iterative methods in predictor–corrector interior point methods for linear programming

In this work we devise efficient algorithms for finding the search directions for interior point methods applied to linear programming problems. There are two innovations. The first is the use of updating of preconditioners computed for previous barrier parameters. The second is an adaptive automated procedure for determining whether to use a direct or iterative solver, whether to reinitialize or update the preconditioner, and how many updates to apply. These decisions are based on predictions of the cost of using the different solvers to determine the next search direction, given costs in determining earlier directions. We summarize earlier results using a modified version of the OB1-R code of Lustig, Marsten, and Shanno, and we present results from a predictor–corrector code PCx modified to use adaptive iteration. If a direct method is appropriate for the problem, then our procedure chooses it, but when an iterative procedure is helpful, substantial gains in efficiency can be obtained.