An iterative Lavrentiev regularization method

This paper presents an iterative method for the computation of approximate solutions of large linear discrete ill-posed problems by Lavrentiev regularization. The method exploits the connection between Lanczos tridiagonalization and Gauss quadrature to determine inexpensively computable lower and upper bounds for certain functionals. This approach to bound functionals was first described in a paper by Dahlquist, Eisenstat, and Golub. A suitable value of the regularization parameter is determined by a modification of the discrepancy principle. In memory of Germund Dahlquist (1925–2005).AMS subject classification (2000) 65R30, 65R32, 65F10     

Orthogonal projection regularization operators

Tikhonov regularization often is applied with a finite difference regularization operator that approximates a low-order derivative. This paper proposes the use of orthogonal projections as regularization operators, e.g., with the same null space as commonly used finite difference operators. Applications to iterative and SVD-based methods for Tikhonov regularization are described. Truncated iterative and SVD methods are also considered. Research of L. Reichel was supported in part by an OBR Research Challenge Grant. Research of F. Sgallari was supported in part by PRIN 2004 grant 2004014411-005.     

A truncated projected SVD method for linear discrete ill-posed problems

Truncated singular value decomposition is a popular solution method for linear discrete ill-posed problems. However, since the singular value decomposition of the matrix is independent of the right-hand side, there are linear discrete ill-posed problems for which this method fails to yield an accurate approximate solution. This paper describes a new approach to incorporating knowledge about properties of the desired solution into the solution process through an initial projection of the linear discrete ill-posed problem. The projected problem is solved by truncated singular value decomposition. Computed examples illustrate that suitably chosen projections can enhance the accuracy of the computed solution.     

Enantioseparation of 2-aryloxypropionic acids on chiral porous monolithic columns by capillary electrochromatography. Evaluation of column performance and enantioselectivity

The enantioseparation of 2-aryloxypropionic acids by capillary electrochromatography was tested on columns with a monolithic stationary phase prepared from silanized fused-silica capillaries (100 microm I.D.) by in situ copolymerization of glycidyl methacrylate, ethylene glycol dimethacrylate and methyl methacrylate in the presence of formamide and 1-propanol as the porogen solvents. The porous chiral monolithic stationary phases were prepared by reaction of the epoxy-groups at the surface of the monolith with (+)-1-(4-aminobutyl)-(5R,8S,10R)-terguride. To attain the minimum HETP values for the enantiodiscrimination of 2-phenoxypropionic acid, the influence of the composition of polymerization solution on column total porosity and efficiency was investigated. Optimum mobile phase conditions were found for all analytes tested using acetonitrile-methanol mixtures containing triethylamine and acetic acid as the buffer components. Furthermore, the chemical and mechanical stabilities of the columns were satisfactory, allowing hundreds of analyses.     

An Outline of the Latest Crystallographic Studies on Inhibitor-Enzyme Complexes for the Design and Development of New Therapeutics against Tuberculosis

The elucidation of the structure of enzymes and their complexes with ligands continues to provide invaluable insights for the development of drugs against many diseases, including bacterial infections. After nearly three decades since the World Health Organization’s (WHO) declaration of tuberculosis (TB) as a global health emergency, Mycobacterium tuberculosis (Mtb) continues to claim millions of lives, remaining among the leading causes of death worldwide. In the last years, several efforts have been devoted to shortening and improving treatment outcomes, and to overcoming the increasing resistance phenomenon. The structural elucidation of enzyme-ligand complexes is fundamental to identify hot-spots, define possible interaction sites, and elaborate strategies to develop optimized molecules with high affinity. This review offers a critical and comprehensive overview of the most recent structural information on traditional and emerging mycobacterial enzymatic targets. A selection of more than twenty enzymes is here discussed, with a special emphasis on the analysis of their binding sites, the definition of the structure–activity relationships (SARs) of their inhibitors, and the study of their main intermolecular interactions. This work corroborates the potential of structural studies, substantiating their relevance in future anti-mycobacterial drug discovery and development efforts.     

Identification and refinement of a peptide affinity ligand with unique specificity for a monoclonal anti-tenascin-C antibody by screening of a phage display library

Using phage display technology, a 22-mer peptide was selected as a ligand with unique specificity for the murine monoclonal ST2146 antibody that recognizes the EGF repeats region of the human tumor-associated antigen tenascin-C. This peptide, synthesized in an 8-branched form to enhance its binding properties, is useful in replacing the native antigen in the affinity and immunoreactivity characterization of the ST2146 antibody and its biotinylated derivatives. Affinity resins, prepared by immobilizing the mimotope or its shorter 10-mer binding unit on a chromatographic support, were able to capture ST2146 directly from the hybridoma supernatant, with antibody recovery and host cell protein (HCP) reduction similar to or better than protein A sorbent, a purity degree exceeding 95%, and full recovery of antibody activity. The affinity constants of both peptides, as determined by frontal analysis of broad-zone elution affinity chromatography and BiaCore measurements, were very similar and included in a range suitable for affinity ligands. Column capacity, determined by applying a large excess of purified ST2146 to 1 mL of column bed volume, was close to 50 mg/mL for both resins. These matrices retain their ST2146 binding properties after various treatments, including sanitization, thus indicating very high stability in terms of ligand leakage and degradation. Moreover, the short form shows higher enzymatic stability, thus proving more suitable as ligand for ST2146 affinity purification.     

Transition-Metal Complexes with Bidentate Ligands Spanning trans-Positions. Part XVII. Some platinum(II) complexes with anionic ligands such as methoxide,formate, carboxylate,hydride, and borohydride,and the X-ray crystal structure of [PtHCl( )] (PP = 2,11-bis(diphenylphosphinomethyl)benzo[c]phenanthrene)

The complexes trans-[PtXY( 2 ] (X = H or Me; Y = OMe, OCHO, CO₂H, and BH₄; 2 = 2,11-bis{bis[3-(trifluoromethyl)phenyl]phosphinomethyl}benzo[c]phenanthrene) were prepared, and their decompositions to trans[PtHX( 2 )] were studied. Some binuclear hydrido-bridged complexes, e.g.[( 2 )HPt(μ-H)PtH( 2 )]⁺, were also obtained. The preparation of complexes trans-[PtHX( 28 )₂] (X = H or Me, 28 = bis[3-(trifluoromethyl)phenyl]benzylphosphine) is also reported. The X-ray crystal structure of trans-[PtHCl 1 )] ( 1 = 2,11-bis(diphenylphosphinomethyl)benzo[c]phenanthrene) was carried out.     

Molecular Complexes for the Study of Enantiodiscriminative Processes

The structure of the molecular complex between the chiral selector (+)1-(3-allylpropyl)-(5R,8S,10R)-N,N-diethyl-N-[6-methylergolin-8-yl]urea, C₂₃H₃₃N₄O, (allyl-terguride) and the more retained (S) isomer of dansyl-serine, C₁₅H₁₉N₂O₅S, has been determined. It is part of a study on the chiral recognition mechanism of ergot alkaloids, when used in chiral stationary phases for the separation of racemic mixture of organic acids by liquid chromatographic methods. At the pH of the crystallization conditions, which mimick those corresponding to the best enantiodiscriminative activity, each molecule of (S)-dansyl-serine is locked by hydrogen bonds between two translation related molecules of allyl-terguride forming a infinite chains in a 1:1 molecular ratio.