<Emphasis Type="Bold">NP</Emphasis> -Hardness of Largest Contained and Smallest Containing Simplices for <Emphasis Type="Italic">V</Emphasis>- and <Emphasis Type="Italic">H</Emphasis>-Polytopes

   Abstract. The problem of finding a d -simplex of maximum volume in an arbitrary d -dimensional V -polytope, for arbitrary d , was shown by Gritzmann et al. [GKL] in 1995 to be NP-hard. They conjectured that the corresponding problem for H -polytopes is also NP-hard. This paper presents a unified way of proving the NP-hardness of both these problems. The approach also yields NP-hardness proofs for the problems of finding d -simplices of minimum volume containing d -dimensional V - or H -polytopes. The polytopes that play the key role in the hardness proofs are truncations of simplices. A construction is presented which associates a truncated simplex to a given directed graph, and the hardness results follow from the hardness of detecting whether a directed graph has a partition into directed triangles.     

Site-Specific <Emphasis Type="Italic">N</Emphasis>-Glycosylation of Recombinant Pentameric and Hexameric Human IgM

Glycosylation is known to play an important role in IgG antibody structure and function. Polymeric IgM, the largest known antibody in humans, displays five potential N-glycosylation sites on each heavy chain monomer. IgM can exist as a pentamer with a connecting singly N-glycosylated J-chain (with a total of 51 glycosylation sites) or as a hexamer (60 glycosylation sites). In this study, the N-glycosylation of recombinant pentameric and hexameric IgM produced by the same human cell type and culture conditions was site-specifically profiled by RP-LC-CID/ETD-MS/MS using HILIC-enriched tryptic and GluC glycopeptides. The occupancy of all putative N-glycosylation sites on the pentameric and hexameric IgM were able to be determined. Distinct glycosylation differences were observed between each of the five N-linked sites on the IgM heavy chains. While Asn171, Asn332, and Asn395 all had predominantly complex type glycans, differences in glycan branching and sialylation were observed between the sites. Asn563, a high mannose-rich glycosylation site that locates in the center of the IgM polymer, was only approximately 60% occupied in both the pentameric and hexameric IgM forms, with a difference in relative abundance of the glycan structures between the pentamer and hexamer. This study highlights the information obtained by characterization of the site-heterogeneity of a highly glycosylated protein of high molecular mass with quaternary structure, revealing differences that would not be seen by global glycan or deglycosylated peptide profiling.

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Quaternary suppression via difference spectroscopy for 13C CP/MAR of organic solids: Application to a phenylazonaphthol

A pulse sequence for obtaining solid-state NMR spectra of proton-bearing ¹³C nuclei only, based on a difference method, is proposed. As an example, spectra of the dyestuff CI Pigment Red 57:1 [monohydrated calcium salt of 1-(2-sulpho-4-methylphenylazo)-2-hydroxnaphthyalene 3-carboxylic acid] are illustrated. The difference method reveals a peak which is otherwise severely overlapped by others. Its presence is confirmed by higher field spectra. The results show that the dyestuff is present as the keto-hydrazo tautomer.     

THE EFFECT OF CROSS-LINKING ON PHOTOCYCLING ACTIVITY OF BACTERIORHODOPSIN

Abstract— Purple membrane preparations from Halobacterium halobium were chemically modified with imidoesters. Dimethyl adipimidate (8.3 Å chain length) amidinates about five of the six free lysine residues whereas dimethyl suberimidate (11.3 Å) under the same conditions reacts with only 2–3 residues. Gel electrophoresis showed that the shorter chain length imidoesters were less effective than dimethyl suberimidate in oligomer formation. However, dimethyl adipimidate resulted in a more marked inhibition of the photoreaction activity. Monofunctional imidates, methyl acetimidate and methyl butyrimi-date, at comparable degrees of amidination, did not appreciably affect activity indicating that the presence of bulky groups on the exposed lysine residues does not cause the effects observed. Hence, the introduction of molecular mobility constraints by intramolecular cross-linking slows photocycling, and, therefore, inhibits proton pumping activity of bacteriorhodopsin. This indicates that conforma-tional changes of the protein moiety of bacteriorhodopsin occur during photocycling activity.     

η1- and η2-coordination in phosphaalkeneplatinum(0) complexes. High resolution solid state 31P NMR spectrum of mesityl(diphenylmethylene)phosphinebis(triphenylphosphine)platinum(0)

The high resolution solid state ³¹P NMR spectrum of Pt(PPh₃)₂(P(mesityl)=CPh₂) shows the expected features for an η¹-coordinated phosphaalkene ligand and is completely different from that of the η²-complex which exists in solution.     

Interactions between Vitamin E Homologues and Ascorbate Free Radicals in Murine Skin Homogenates Irradiated with Ultraviolet Light

The mechanism of oxidation of ascorbic acid in mouse skin homogenates by UV light was investigated by measuring ascorbate free radical formation using electron spin resonance signal formation. Addition of vitamin E (α-tocopherol or α-tocotrienol) had no effect, whereas short-chain homologues (2,5,7,8-tetramethyl-6-hydroxy-chroman-2-carboxylic acid [Trolox] and 2,2,5,7,8-penta-methyl-6-hydroxychromane [PMC]) accelerated ascorbate oxidation. The similar hydrophilicity of ascorbate, Trolox and PMC increased their interaction, thus rapidly depleting ascorbate. When dihydrolipoic acid was added simultaneously with the vitamin E homologues, the accelerated ascorbate oxidation was prevented. This was due to the regeneration of ascorbate and PMC from their free radicals by a recycling mechanism between ascorbate, vitamin E homologues and dihydrolipoic acid. Potentiation of antioxidant recycling may be protective against UV irradiation-induced damage. The rate of ascorbate oxidation in the presence of vitamin E homologues was enhanced by a photosensitizer (riboflavin) but was not influenced by reactive oxygen radical quenchers, superoxide dismutase or 5,5-dimethyl-l-pyrroline-iV-ox-ide. These experimental results suggest that the UV irradiation-induced ascorbate oxidation in murine skin homogenates is caused by photoactivated reactions rather than reactive oxygen radical reactions.     

[MESITYL]BACTERIORHODOPSIN. THE PROPERTIES OF AN ANALOGUE OF THE PURPLE MEMBRANE CONTAINING [MESITYL] RETINAL AS THE CHROMOPHORE

Abstract— A new synthesis of all-trans-[mesityl]retinal, II , (all-trans-3,7-dimethyl-9-(2',4',6'-trimethylphenyl)-2,4,6,8,-nonatetraenal) and 13-cis-[mesityl]retinal, VI , (3,7-dimethyl-9-(2'4'6'-trimethylphenyl)-2Z,4E,6E,8E-nonatetraenal) is reported. Combination of all-trans-[mesityl]retinal with bacterioopsin results in the formation of a synthetic membrane (Λ_max 460) which has photocycling properties similar to the purple membrane although its cycling rate is very much slower. An M-type intermediate can be trapped at -60°C. Photoreversal of the M-intermediate to the wavelength of initial absorption is observed. Phototransformation of the initial [mesityl]bacteriorhodopsin is accompanied by conversion of the all-frans to the 13- cis -isomer.     

Correlated dipole polarizabilities and dipole moments of the halides HX and CH3X (X=F,Cl and Br)

Summary We report values of the correlated dynamic dipole polarizability for the halides HX and CH₃X (X = F, Cl and Br). The polarizabilities are calculated within the second-order polarization propagator approximation (SOPPA). The correlated results are in much better agreement with the available experimental results, compared to RPA. We also report the second-order dipole moments using both the relaxed and unrelaxed MP2 density matrices. The relaxed results are in better agreement with experiment.     

Generalized Multiresolution Analyses with Given Multiplicity Functions

Generalized multiresolution analyses are increasing sequences of subspaces of a Hilbert space ℋ that fail to be multiresolution analyses in the sense of wavelet theory because the core subspace does not have an orthonormal basis generated by a fixed scaling function. Previous authors have studied a multiplicity function m which, loosely speaking, measures the failure of the GMRA to be an MRA. When the Hilbert space ℋ is L ²(ℝ ⁿ ), the possible multiplicity functions have been characterized by Baggett and Merrill. Here we start with a function m satisfying a consistency condition, which is known to be necessary, and build a GMRA in an abstract Hilbert space with multiplicity function m.