Conjugacy invariant pseudo-norms,representability and RNA secondary structures

To a reasonable approximation, a secondary structures of RNA is determined by Watson-Crick pairing without pseudo-knots in such a way as to minimise the number of unpaired bases. We show that this minimal number is determined by the maximal conjugacy-invariant pseudo-norm on the free group on two generators subject to bounds on the generators. This allows us to construct lower bounds on the minimal number of unpaired bases by constructing conjugacy invariant pseudo-norms.     

Development of a turbulent near-wall temperature model and its application to channel flow

A numerical study of fluid flow and heat transfer in a two-dimensional channel under fully developed turbulent conditions is reported. A computer program which is capable of treating both forced and natural convection problems under turbulent conditions has been developed. The code uses the high-Reynolds-number form of the two equation turbulent model(k-?) in which a turbulent kinetic energy near-wall model is incorporated in order to accurately represent the behavior of the flow near the wall, particularly in the viscous sublayer where the turbulent Reynolds number is small. A near-wall temperature model has been developed and incorporated into the energy equation to allow accurate prediction of the temperature distribution near the wall and, therefore, accurate calculation of heat transfer coefficients. The sensitivity of the prediction of flow and heat transfer to variations in the coefficients used in the turbulence model is investigated. The predictions of the model are compared to available experimental and theoretical results; good agreement is obtained. The inclusion of the near-wall temperature model has further improved the predictions of the temperature profile and heat transfer coefficient. The results indicate that the turbulent kinetic energy Prandtl number should be a function of Reynolds number.     

Comparison of LC and LC/MS methods for quantifying <Emphasis Type="Italic">N</Emphasis>-glycosylation in recombinant IgGs

High-performance liquid chromatography (LC) and liquid chromatography/electrospray ionization time-of-flight mass spectrometry (LC/ESI-MS) methods with various sample preparation schemes were compared for their ability to identify and quantify glycoforms in two different production lots of a recombinant monoclonal IgG1 antibody. IgG1s contain a conserved N-glycosylation site in the fragment crystallizable (Fc) subunit. Six methods were compared: (1) LC/ESI-MS analysis of intact IgG, (2) LC/ESI-MS analysis of the Fc fragment produced by limited proteolysis with Lys-C, (3) LC/ESI-MS analysis of the IgG heavy chain produced by reduction, (4) LC/ESI-MS analysis of Fc/2 fragment produced by limited proteolysis and reduction, (5) LC/MS analysis of the glycosylated tryptic fragment (293EEQYNSTYR301) using extracted ion chromatograms, and (6) normal phase HPLC analysis of N-glycans cleaved from the IgG using PNGase F. The results suggest that MS quantitation based on the analysis of Fc/2 (4) is accurate and gives results that are comparable to normal phase HPLC analysis of N-glycans (6).     

Gas‐Phase Electron‐Diffraction Investigation and Quantum‐Chemical Calculations of the Structure of 1,5‐Dimethylsemibullvalene‐2,4,6,8‐tetracarboxylic Dianhydride

The bridged homotropilidines have been of interest for decades because their molecules offer the potential for homoaromaticity. Although many of these have been shown not to be homoaromatic, the energy differences of the delocalized (homoaromatic) forms and the localized (nonhomoaromatic) ones, and the barriers to the interconversion of the localized forms via a Cope rearrangement, have been found to vary greatly. The title compound is a strong candidate for homoaromaticity, and, since the structures of the possible localized and delocalized forms could differ significantly, we have carried out an electron‐diffraction investigation of it augmented by quantum‐mechanical calculations with different basis sets at several levels of theory. Three models were explored: one representing a localized form of C_s symmetry, one a delocalized form of C_2v symmetry, and one a 2 : 1 mixture of the localized/delocalized forms. Although none of the models could be ruled out, the experimental evidence slightly favors the C_s form. These results are consistent with those from the DFT B3PW91 calculations with basis sets ranging from 6‐31G(d) to cc‐pVTZ, which, surprisingly, predict essentially equal thermally corrected free energies for each. The results are discussed.     

Crystal structure of a bulky cyclic sulfite

The structure of the cyclic sulfite derived from the reaction of thionyl chloride withendo-8-hydroxy-exo-8-(endo-8-hydroxypentacyclo[5.4.0.0.^2,6.0^3,10.0^5,9]undec-exo-8-yl)pentacyclo-[5.4.0.0.^2,6.0^3,10.0^5,9]undecane is reported. All bond lengths and angles are consistent with the strained cage geometry. A static disorder of the terminal oxygen was found to be present.     

Homeomorphisms and the homology of non-orientable surfaces

We show that, for a closed non-orientable surfaceF, an automorphism ofH ₁(F, ℤ) is induced by a homeomorphism ofF if and only if it preserves the (mod 2) intersection pairing. We shall also prove the corresponding result for punctured surfaces.