C 1 Quintic Splines on Type-4 Tetrahedral Partitions

Starting with a partition of a rectangular box into subboxes, it is shown how to construct a natural tetrahedral (type-4) partition and associated trivariate C ¹ quintic polynomial spline spaces with a variety of useful properties, including stable local bases and full approximation power. It is also shown how the spaces can be used to solve certain Hermite and Lagrange interpolation problems.     

Mild template synthesis of a copper(II)-containing macrocyclic compound with 4,4,6-trimethyl-2,3,7,8-tetraazanonen-6-dithiohydrazide-1,9 in a gelatin-immobilized matrix

The complexing processes in the triple copper(II)–thiocarbohydrazide–propanone system taking place in a copper(II) hexacyanoferrate(II) gelatin-immobilized matrix in contact with aqueous-alkaline solutions (pH12), containing thiocarbohydrazide and propanone, have been studied. Template synthesis leading to a macrocyclic coordination compound with the tetradentate N,N,S,S-donor ligand, (4,4,6-trimethyl-2,3,7,8-tetraazanonen-6-dithiohydrazide-1,9), occurs under these specific conditions when thiocarbohydrazide and propanone are the ligand synthons.     

Efficient synthesis of enynecarbamates and their ring-closing metathesis/[4 + 2] Diels-Alder cycloaddition: synthesis of hexahydroisoquinolines

Enynes 5a-g were prepared in moderate to good yields from 1-(triphenylphosphoranylideneaminoalkyl)benzotriazoles. Ring-closing metathesis of 5a-f afforded functionalized dienes 6a-f, respectively, which were used in a Diels-Alder cycloaddition reaction in the synthesis of the corresponding hexahydroisoquinoline derivatives 7a-f.     

The fixed point property in ordered sets of width two

We consider the fixed point property (FPP) in an ordered set of width two (every antichain contains at most two elements). The necessary condition of the FPP and a number of equivalent conditions to the FPP in such sets is established. The product theorem is proved, as well.     

Template synthesis in the nickel(II)–thiocarbohydrazide–propanone triple system

The complexing process proceeding in the Ni^II–thiocarbohydrazide (H₂N–H–NC(=S)–NH–NH₂)–propanone triple system in EtOH solution and nickel(II)hexacyanoferrate(II) gelatin-immobilized matrix has been studied. It has been found that in the first case, template synthesis leading, as a minimum, to formation of three coordination compounds of Ni^II with (N,N,S,S)-donor tetradentate ligands having NiL¹, NiL² and NiL³compositions where L¹ is 4,6,6-trimethyl-2,3,7,8-tetraazanonen-3-di(thiohydrazide)-1,9, L² is 4,6,6,12-tetrametyl-1,9-dithio-2,3,7,8,10,11-hexaazatridekadien-3,11-hydrazide-1 and L³ is 2,8,10,10,16-pentamethyl-5,13-dithio-3,4,6,7,11,12,14,15-octaazaheptadekatrien-2,7,15 is observed, whereas in the gelatin-immobilized matrix, a complexing process in the system considered does not occur.     

Four modes competition and chaos in a shell

Steady-state chaotic vibrations of a shallow shell as a system with a nonsymmetrical restoring force and one equilibrium state are considered. Mode interaction and its effect on a chaotic behavior of the shell is studied. The terms "natural" and "imposed" chaos are introduced for the response of resonant and nonresonant modes. It is shown that such a qualitative difference is important for better understanding of chaos in systems with distributed parameters, and may be very useful for numerical investigations. Some qualitative comparisons with previous papers on chaos in distributed mechanical systems are also made. (c) 1994 American Institute of Physics.     

Resonance assignments and secondary structure analysis of E. coli thioredoxin by magic angle spinning solid-state NMR spectroscopy

De novo site-specific 13C and 15N backbone and sidechain resonance assignments are presented for uniformly enriched E. coli thioredoxin, established using two-dimensional homo- and heteronuclear solid-state magic angle spinning NMR correlation spectroscopy. Backbone dihedral angles and secondary structure were derived from the statistical analysis of the secondary chemical shifts, and are in good agreement with solution values for the intact full-length thioredoxin, with the exception of a small number of residues located at the termini of the individual secondary structure elements. A large number of cross-peaks observed in the DARR spectra with long mixing times correspond to the pairs of carbon atoms separated by 4-6 angstroms, suggesting that DARR could be efficiently employed for observation of medium- and long-range correlations. The 108 amino acid residue E. coli thioredoxin is the largest uniformly enriched protein assigned to this degree of completeness by solid-state NMR spectroscopy to date. It is anticipated that with a combination of two-dimensional correlation experiments and high magnetic fields, resonance assignments and secondary structure can be generally derived for other noncrystalline proteins.     

Assignments of carbon NMR resonances for microcrystalline ubiquitin

Solid-state NMR 2D spectroscopy was used to correlate carbon backbone and side-chain chemical shifts for uniformly (13)C,(15)N-enriched microcrystalline ubiquitin. High applied field strengths, 800 MHz for protons, moderate proton decoupling fields, 80-100 kHz, and high magic angle sample spinning frequencies, 20 kHz, were used to narrow the most of the carbon line widths to 0.5-0.8 ppm. Homonuclear magnetization transfer was effected by matching the proton RF field to the spinning frequency, the so-called dipolar-assisted rotational resonance (DARR) (Takegoshi, K.; Nakamura, S.; Terao, T. Chem. Phys. Lett. 2001, 344, 631-637), and a mixing time of 20 ms was used to maximize the intensity of one-bond transfers between carbon atoms. This polarization transfer sequence resulted in roughly 14% transfer efficiencies for directly bonded carbon pairs and 4% transfer efficiencies for carbons separated by a third carbon. With this simple procedure, the majority of the one-bond correlations was observed with moderate transfer efficiencies, and many two-bond correlations were also observed with weaker intensities. Spin systems could be identified for more than half of the amino acid side chains, and site-specific assignments were readily possible via comparison with 400 MHz (15)N-(13)C-(13)C correlation spectroscopy (described separately).     

Comparative study of photodynamic properties of 13,15-N-cycloimide derivatives of chlorin p6

Comparative study of 13,15-[N-(2-hydroxyethyl)]cycloimide chlorin p6 (2), 13,15-(N-acetoxy)cycloimide chlorin p6 (3), 13,15-(N-hydroxy)cycloimide chlorin p6 methyl ester (4) and 13,15-(N-methoxy)cycloimide chlorin p6 methyl ester (5) together with the previously investigated 13,15-[N-(3-hydroxypropyl)]cycloimide chlorin p6 (1) was performed. The dependence of the key photodynamic properties of 1-5 on the introduced substituents was analyzed. The photoinduced cell-killing activity of 4 is 100- and 280-fold higher than that of chlorin p6 and Photogem, respectively, as estimated on A549 human lung adenocarcinoma cells. The activity is reduced eight times in the order 4 > 5 > 1 > 2 > 3. The intracellular accumulation of 1-5 occurs in cytoplasm in a monomeric form bound to the lipids of cellular membranes. This form of 1, 2, 3, 4 and 5 is characterized by the high quantum yield of singlet oxygen generation, which depends on the introduced substituents, 0.66, 0.59, 0.35, 0.51 and 0.73, respectively. The photostability is two-fold less for 1 and four-fold less for 2, 3 and 5 than for 4. The rates of cellular uptake and efflux of 1-5 vary widely, thus providing the way to optimize the pharmacological properties of the photosensitizer (PS) using the respective substituents. Modifying the substituents, 1-5 were targeted to different cellular organelles. The enhanced accumulation in the Golgi apparatus and mitochondria complemented with diffuse staining of intracellular membranous structures is a property of 1-4. Compound 5 accumulates selectively in the lipid droplets and stains weakly perinuclear structures. Temperature-sensitive mechanisms of transport are responsible for the 1-4 uptake. Diffusion can play a role in the internalization of 5 but not of 1-4. Endocytosis via caveolae, clathrin-dependent and adenosine triphosphate-dependent pathways are not noticeably involved in the 1-5 internalization. Independently from their intracellular localization 1, 4 and 5 are highly efficient near-IR PS, which induce predominantly an apoptotic type of cell death under conditions providing ca 50% level of phototoxicity and necrosis at the 100% level of phototoxicity.