The Geometry of the Newton Method on Non-Compact Lie Groups

An important class of optimization problems involve minimizing a cost function on a Lie group. In the case where the Lie group is non-compact there is no natural choice of a Riemannian metric and it is not possible to apply recent results on the optimization of functions on Riemannian manifolds. In this paper the invariant structure of a Lie group is exploited to provide a strong interpretation of a Newton iteration on a general Lie group. The paper unifies several previous algorithms proposed in the literature in a single theoretical framework. Local asymptotic quadratic convergence is proved for the algorithms considered.     

Definitive identification of cysteine and glutathione complexes of bismuth by mass spectrometry: assessing the biochemical fate of bismuth pharmaceutical agents

Solutions containing BiCl3, bismuth subsalicylate or Bi(NO3)3 with L-cysteine, DL-homocysteine, D-methionine or glutathione have been examined by electrospray mass spectrometry. Prominent peaks are assigned to bismuth complexes of these biomolecules and provide insight towards understanding the bioactivity of bismuth compounds.     

Rheological and Solubility Properties of Soy Protein Isolate

Soy protein isolate (SPI) powders often have poor water solubility, particularly at pH values close to neutral, which is an attribute that is an issue for its incorporation into complex nutritional systems. Therefore, the objective of this study was to improve SPI solubility while maintaining low viscosity. Thus, the intention was to examine the solubility and rheological properties of a commercial SPI powder at pH values of 2.0, 6.9, and 9.0, and determine if heat treatment at acidic or alkaline conditions might positively influence protein solubility, once re-adjusted back to pH 6.9. Adjusting the pH of SPI dispersions from pH 6.9 to 2.0 or 9.0 led to an increase in protein solubility with a concomitant increase in viscosity at 20 °C. Meanwhile, heat treatment at 90 °C significantly improved the solubility at all pH values and resulted in a decrease in viscosity in samples heated at pH 9.0. All SPI dispersions measured under low-amplitude rheological conditions showed elastic-like behaviour (i.e., G′ > G″), indicating a weak “gel-like” structure at frequencies less than 10 Hz. In summary, the physical properties of SPI can be manipulated through heat treatment under acidic or alkaline conditions when the protein subunits are dissociated, before re-adjusting to pH 6.9.     

Silica–gelatin hybrids for tissue regeneration: inter-relationships between the process variables

Owing to their diverse range of highly tailorable material properties, inorganic/organic hybrids have the potential to meet the needs of biodegradable porous scaffolds across a range of tissue engineering applications. One such hybrid platform, the silica–gelatin sol–gel system, was examined and developed in this study. These hybrid scaffolds exhibit covalently linked interpenetrating networks of organic and inorganic components, which allows for independent control over their mechanical and degradation properties. A combination of the sol–gel foaming process and freeze drying was used to create an interconnected pore network. The synthesis and processing of the scaffolds has many variables that affect their structure and properties. The focus of this study was to develop a matrix tool that shows the inter-relationship between process variables by correlating the key hybrid material properties with the synthesis parameters that govern them. This was achieved by investigating the effect of the organic (gelatin) molecular weight and collating previously reported data. Control of molecular weight of the polymer is as an avenue that allows the modification of hybrid material properties without changing the surface chemistry of the material, which is a factor that governs the cell and tissue interaction with the scaffold. This presents a significant step forward in understanding the complete potential of the silica–gelatin hybrid system as a medical device.     

A shortest path-based approach to the multileaf collimator sequencing problem

The multileaf collimator sequencing problem is an important component in effective cancer treatment delivery. The problem can be formulated as finding a decomposition of an integer matrix into a weighted sequence of binary matrices whose rows satisfy a consecutive ones property. Minimising the cardinality of the decomposition is an important objective and has been shown to be strongly NP-hard, even for a matrix restricted to a single column or row. We show that in this latter case it can be solved efficiently as a shortest path problem, giving a simple proof that the one-row problem is fixed-parameter tractable in the maximum intensity. We develop new linear and constraint programming models exploiting this result. Our approaches significantly improve the best known for the problem, bringing real-world sized problem instances within reach of exact algorithms.     

Discovering New Classes of <Emphasis Type="Italic">Brugia malayi</Emphasis> Asparaginyl-tRNA Synthetase Inhibitors and Relating Specificity to Conformational Change

SLIDE software, which models the flexibility of protein and ligand side chains while docking, was used to screen several large databases to identify inhibitors of Brugia malayi asparaginyl-tRNA synthetase (AsnRS), a target for anti-parasitic drug design. Seven classes of compounds identified by SLIDE were confirmed as micromolar inhibitors of the enzyme. Analogs of one of these classes of inhibitors, the long side-chain variolins, cannot bind to the adenosyl pocket of the closed conformation of AsnRS due to steric clashes, though the short side-chain variolins identified by SLIDE␣apparently bind isosterically with adenosine. We hypothesized that an open conformation of the motif 2 loop also permits the long side-chain variolins to bind in the adenosine pocket and that their selectivity for Brugia relative to human AsnRS can be explained by differences in the sequence and conformation of this loop. Loop flexibility sampling using Rigidity Optimized Conformational Kinetics (ROCK) confirms this possibility, while scoring of the relative affinities of the different ligands by SLIDE correlates well with the compounds’ ranks in inhibition assays. Combining ROCK and SLIDE provides a promising approach for exploiting conformational flexibility in structure-based screening and design of species selective inhibitors.