Remarks on a posteriori error estimation for finite element solutions

We utilize the classical hypercircle method and the lowest-order Raviart–Thomas H(div)$H(\mathrm{div})$ element to obtain a posteriori error estimates of the _P1$P_1$ finite element solutions for 2D Poisson's equation. A few other estimation methods are also discussed for comparison. We give some theoretical and numerical results to see the effectiveness of the methods.     

Selective ion binding by protein probed with the statistical mechanical integral equation theory

Selective ion binding by human lysozyme and its mutants is probed with the three-dimensional interaction site model theory which is the statistical mechanical integral equation theory. Preliminary and partial results of the study have been already published (Yoshida, N. et al. J. Am. Chem. Soc. 2006, 128, 12042-12043). The calculation was carried out for aqueous solutions of three different electrolytes, CaCl2, NaCl, and KCl, and for four different mutants of the human lysozyme: wild type, Q86D, A92D, and Q86D/A92D, which have been studied experimentally. The discussion of this article focuses on the cleft that consists of amino acid residues from Q86 to A92. For the wild type of protein in the aqueous solutions of all the electrolytes studied, there are no distributions observed for the ions inside the cleft. The Q86D mutant shows essentially the same behavior with that of the wild type. The A92D mutant shows strong binding ability to Na+ in the recognition site, which is in accord with the experimental results. There are two isomers of the Q86D/A92D mutant, e.g., apo-Q86D/A92D and holo-Q86D/A92D. Although both isomers exhibit the binding ability to the Na+ and Ca2+ ions, the holo isomer shows much greater affinity compared with the apo isomer. Regarding the selective ion binding of the holo-Q86D/A92D mutant, it shows greater affinity to Ca2+ than to Na+, which is also consistent with the experimental observation.     

Donor-acceptor distance-dependence of photoinduced electron-transfer rate in flavoproteins

Ultrafast fluorescence quenching of flavin in flavodoxin from Megasphaera elsdenii was investigated by means of a fluorescence up-conversion method. Fluorescence lifetimes of flavodoxin from M. elsdenii were estimated to be tau(1) approximately 165 fs (0.97%) and tau(2) approximately 10 ps (0.03%). Correlation of photoinduced electron-transfer rates (k(ET)) with averaged distances (D(av)) between isoalloxazine and nearby tryptophan or tyrosine was examined and obtained an empirical equation of ln k(ET) vs D(av) by means of a nonlinear least-squares method using reported data together with flavodoxin from M. elsdenii. The values of D(av) were calculated from X-ray structures of the flavoproteins. The ln k(ET) was approximately linear at D(av) shorter than 7 A. The model free empirical equation was expressed as ln k(ET) = 29.7 + (-0.327 D(av) + 2.84 x 10(-5))/(0.698 - D(av)(2)). We also analyzed the observed values of ln k(ET) with Marcus theory, but could not obtain reasonable results. Our analysis suggests that the average distance, rather than the shortest (edge to edge) distance or interplanar angles between the aromatics rings, is the key factor in the process of the photoinduced electron transfer in these flavoproteins.     

Wave optical analysis of integral method for three-dimensional images

We analyze by wave optics an integral method that produces three-dimensional (3D) images. The point light source is given at the pickup stage, and the light wave passing through each elemental lens is obtained at the display stage. The amplitude distributions of the waves from each elemental image are the same around a specific point where a 3D image is formed. Since the light waves approaching the image plane from different elemental lenses are incoherent, the synthesized value is the sum of the squared amplitudes of the waves. Therefore the modulation transfer function of this integral method is given by that of a single elemental lens.     

Drastic high magnetic field effect on suppression of Escherichia coli death

When Escherichia coli B was aerobically grown in a medium containing one-fourth the concentration of the LB medium supplemented with glutamic acid at 43 degrees C under an inhomogeneous 5.2-6.1 T magnetic field, the number of cells in the stationary phase under the high magnetic field was 100,000 times higher than that under a geomagnetic field. The finding that the amount of sigma S factor encoded by the rpoS gene under the high magnetic field was larger than that under the control geomagnetic field indicated that the activity of the rpoS gene was affected by the high magnetic field.     

Ferromagnetic Intermolecular Interaction of N-Protonated Pyridylphenylcarbene

Abstract

The HCl and DCl salts of pheny1-4-pyridyldiazomethane were prepared and irradiated at 6 K to generate the carbenes. Their ESR spectra indicated presence of plural triplet carbenes with slightly-different zero-field splitting constants. Besides the triplet species, we found a quintet species whose signal intensity decreases with increasing temperature. The quintet spin state was concluded to be a ground state which was produced by an intermolecular ferromagnetic interaction of the triplet carbenes. The ferromagnetic interaction would be explained by the McConnell mechanism, judging from the crystal structure of the HCl salt of phenyl-4-pyridylketone.     

Titanium(IV) chloride-mediated ring cleavage and Michael addition of 3,3-dialkylcyclobutanones and 3-[(trimethylsilyl)methyl]-cyclobutanones

β'-Chloro and β',γ'-unsaturated trichlorotitanium enolates, which were formed in situ by titanium(IV) chloride-mediated ring cleavage of 3,3-dialkylcyclobutanones and 3-[(trimethylsilyl)methyl]cyclobutanones, reacted with enones to give Michael adducts with keeping a labile β'-chloro or β',γ'-unsaturated group.     

Single-step fabrication of patterned gold film array by an engineered multi-functional peptide

This study constitutes a demonstration of the biological route to controlled nano-fabrication via modular multi-functional inorganic-binding peptides. Specifically, we use gold- and silica-binding peptide sequences, fused into a single molecule via a structural peptide spacer, to assemble pre-synthesized gold nanoparticles on silica surface, as well as to synthesize nanometallic particles in situ on the peptide-patterned regions. The resulting film-like gold nanoparticle arrays with controlled spatial organization are characterized by various microscopy and spectroscopy techniques. The described bio-enabled, single-step synthetic process offers many advantages over conventional approaches for surface modifications, self-assembly and device fabrication due to the peptides' modularity, inherent biocompatibility, material specificity and catalytic activity in aqueous environments. Our results showcase the potential of artificially-derived peptides to play a key role in simplifying the assembly and synthesis of multi-material nano-systems in environmentally benign processes.     

Indium(III) triflate-catalyzed reaction of 2-carbomethoxycyclobutanone with nitrones

2-Carbomethoxycyclobutanone reacted with N-phenyl-C-arylnitrones to afford methyl 5-oxo-2-[aryl(phenylamino)methyl]tetrahydrofuran-2-carboxylates by the catalysis of indium(III) triflate in the presence of magnesium sulfate.     

Placevent: An algorithm for prediction of explicit solvent atom distribution—Application to HIV‐1 protease and F‐ATP synthase

We have created a simple algorithm for automatically predicting the explicit solvent atom distribution of biomolecules. The explicit distribution is coerced from the three‐dimensional (3D) continuous distribution resulting from a 3D reference interaction site model (3D‐RISM) calculation. This procedure predicts optimal location of solvent molecules and ions given a rigid biomolecular structure and the solvent composition. We show examples of predicting water molecules near the KNI‐272 bound form of HIV‐1 protease and predicting both sodium ions and water molecules near the rotor ring of F‐adenosine triphosphate (ATP) synthase. Our results give excellent agreement with experimental structure with an average prediction error of 0.39–0.65 Å. Further, unlike experimental methods, this method does not suffer from the partial occupancy limit. Our method can be performed directly on 3D‐RISM output within minutes. It is extremely useful for examining multiple specific solvent–solute interactions, as a convenient method for generating initial solvent structures for molecular dynamics calculations, and may assist in refinement of experimental structures. © 2012 Wiley Periodicals, Inc.