Numerical methods for solving the eigenvalue problem for a positive branch confocal unstable resonator

The resonator problem for a positive branch confocal unstable resonator reduces to a Fredholm homogeneous integral equation of the second kind, whose numerical solution here is based on a sequence of algebraic eigenvalue problems. We compare two algorithms for the solution of an optical resonator problem. These are obtained by (i) successive degenerate kernel approximation by Taylor polynomials of the Fredholm kernel and (ii) Nyström’s method with Simpson’s rule as the subordinate numerical integration method. The numerical results arising from these routines compare well with other published results, and have the added advantage of simplicity and easy adaptability to other resonator problems.     

Effects on peptide binding affinity for TNFα by PEGylation and conjugation to hyaluronic acid

Conjugation of cytokine-neutralizing monoclonal antibodies (mAb) to hyaluronic acid (HA) having M_w of 1.6 MDa was previously shown to be an effective strategy for localized delivery to sites of inflammation. Despite the disparity in size of the mAb and HA, the mAb–HA conjugate was found bind tumor necrosis factor-α (TNFα) as strongly as the non-conjugated antibody, suggesting conjugation to this charged polysaccharide can provide an alternative to poly(ethylene glycol) (PEG) conjugation, which has been shown to reduce binding interactions for many proteins. To explore conjugation chemistries more systematically, we report a study on a model peptide inhibitor of tumor necrosis factor-α to investigate the effects of site-specific conjugation to HA and PEG. We compared the binding affinities of a variety of WP9QY peptide–polymer conjugates for TNFα in order to examine the effects of PEG molecular weight as well as the effects of PEG versus functionalized hyaluronic acid (HA) conjugation. The results indicate that the binding affinity of the PEG conjugates decreases in comparing PEG with mass 2 k, 10 k, and 30 k, which was attributed to PEG shrouding of the peptide, while conjugation to a 66 kDa HA chain preserved peptide binding affinity. We attribute this difference to the increased solubility of HA compared to PEG, potentially due to the carboxylic acid functional groups. In addition, the results demonstrate that conjugation to HA via a short PEG linker significantly enhances the association rate k_on, which may reflect an increased peptide accessibility. By balancing both the advantages associated with the PEG conjugates and with the HA conjugates, the HA–PEG2k–WP9QY conjugate was able to improve the binding affinity of the peptide for TNFα by a factor of two. Optimization of polymer chemistry could be used to improve delivery of protein therapeutics for localized and systemic administration.     

Cryogenic OrbiSIMS Localizes Semi‐Volatile Molecules in Biological Tissues

OrbiSIMS is a recently developed instrument for label‐free imaging of chemicals with micron spatial resolution and high mass resolution. We report a cryogenic workflow for OrbiSIMS (Cryo‐OrbiSIMS) that improves chemical detection of lipids and other biomolecules in tissues. Cryo‐OrbiSIMS boosts ionization yield and decreases ion‐beam induced fragmentation, greatly improving the detection of biomolecules such as triacylglycerides. It also increases chemical coverage to include molecules with intermediate or high vapor pressures, such as free fatty acids and semi‐volatile organic compounds (SVOCs). We find that Cryo‐OrbiSIMS reveals the hitherto unknown localization patterns of SVOCs with high spatial and chemical resolution in diverse plant, animal, and human tissues. We also show that Cryo‐OrbiSIMS can be combined with genetic analysis to identify enzymes regulating SVOC metabolism. Cryo‐OrbiSIMS is applicable to high resolution imaging of a wide variety of non‐volatile and semi‐volatile molecules across many areas of biomedicine.     

Quantum: Einstein,Bohr and the Great Debate About the Nature of Reality,by Manjit Kumar

The history of absolute measurements of gravity is mentioned and the reasons for making absolute measurements are indicated. The principles and main advantages and difficulties of the main method—reversible pendulum, free fall, symmetrical free motion—are discussed and examples of each method are described. Problems of comparison of different determinations and of estimating systematic errors are considered.     

Synthesis and biological properties of 3-methyl-10-propargyl-5,8-dideazafolic acid

The synthesis of N³-methyl-10-propargyl-5,8-dideazafolic acid ( 1b ) is described. Ring closure of methyl-5-methylanthranilate with chloroformamidine hydrochloride gave a high yield of pure 2-amino-4-hydroxy-6-methylquinazoline treatment of which with iodomethane/sodium hydroxide provided the corresponding 3-methylquinazoline (6) which was converted to its 2-pivaloylamino derivative. This synthetic approach, next involving functionalisation of the 6-methyl group, was not further pursued because of difficulty encountered in removing the pivaloyl group. Methyl 5-methylanthranilate was treated with p-toluenesulfonyl chloride and the product then N-methylated. The tosyl group was cleaved with hydrogen bromide/phenol and the resulting methylamine ring-closed with chloroformamidine hydrochloride to provide 2-amino-1,4-dihydro-1,6-dimethyl-4-oxoquinazoline ( 11 ). The 2-pivaloylamino derivative of 11 was prone to hydrolytic deamination when attempts were made to remove the pivaloyl group and further elaboration of this heterocycle, with the intention of obtaining N¹-methyl-10-propargyl-5,8-dideazafolic acid was, too, not attempted. Di-t-butyl N-(4-propargylamino)benzoyl)-L-glutamate was therefore prepared and coupled with 2-amino-6-bromomethyl-4-hydroxyquinazoline hydrobromide. The resulting antifolate diester was N-monomethylated. Removal of the t-butyl groups with trifluoracetic acid afforded the target compound 1b and its structure was proved by degradation to the quinazoline 6 . Its IC₅₀ for L1210 thymidylate synthase (TS) was 26 μM; the control value for 10-propargyl-5,8-dideazafolic acid ( 1a ) was 0.02 μM. Thus the substitution of the lactam hydrogen in 1a by a methyl group reduced the TS inhibition by 1300-fold. Compound 1b was poorly cytotoxic to L1210 cells in culture (ID₅₀ > 100 μM). An unperturbed lactam group in this class of antifolate is important for binding to TS.     

Cationic polymerization of α-methylstyrene from polydienes. I. Synthesis and characterization of poly(butadiene-g-α-methylstyrene) copolymers

The preparation of poly(butadiene-g-α-methylstyrene) copolymers was investigated with three different alkylaluminum coinitiators. The alkylaluminum compounds in conjunction with polybutadiene which contained a low concentration of labile chlorine atoms initiated the polymerization of α-methylstyrene to produce graft copolymers. Trimethylaluminum gave higher grafting efficiencies than diethylaluminum chloride at comparable monomer conversions. Triethylaluminum produced only very low monomer conversions (<5%), even at long reaction times, and for this reason was not studied extensively. The number of grafts per polybutadiene backbone was determined for a number of copolymers and found to increase slightly as the allylic chlorine concentration in the polybutadiene backbone was increased. In all cases, however, only a low percentage of the available labile chlorine sites along the polybutadiene backbone resulted in grafted α-methylstyrene side chains. The addition of small quantities of water to the polymerization solvent greatly enhanced the grafting rate and ultimate monomer conversion during the synthesis of these poly(butadiene-g-α-methylstyrene) copolymers. The mechanistic role of water during these grafting reactions is unknown at the present time.