Dynamics of peptides with fixed geometry: Kinetic energy terms and potential energy derivatives as functions of dihedral angles

Expressions are derived for computing the kinetic energy of a peptide with fixed geometry, in terms of dihedral angles as generalized coordinates; other expressions required for the solution of Lagrange's equations are also presented. The peptide is regarded as held stationary at one end. We also outline the computations that are needed in calculating the components of the third derivative of a potential energy function that consists of a sum of pairwise interatomic interactions.     

Letter to the Editor: Stockwell and Wavelet Transforms

Recent applied literature introduces the Stockwell transform (S-transform) as a new approach to time-frequency analysis. It is the purpose of this letter to encourage the interaction between the wavelet and the Stockwell communities by demonstrating that—up to minor modifications—the S-transform is a special case of the well-known continuous wavelet transform via a Morlet-type mother wavelet, with the features of a linear frequency scale, and an amplitude and modulation adjustment in phase space. The extensive research and applications obtained for the continuous wavelet transform can therefore be directly applied to the Stockwell domain.     

The First Turbulence and First Fossil Turbulence

A model is proposed connecting turbulence, fossil turbulence and the big-bang origin of the universe. While details are incomplete, the model is consistent with our knowledge of these processes and is supported by observations. Turbulence arises in a hot big-bang quantum gravitational dynamics scenario at Planck scales. Chaotic, eddy-like motions produce an exothermic Planck particle cascade from 10^?35 m at 10³² K to 10⁸ larger, 10⁴ cooler, quark-gluon scales. A Planck-Kerr instability gives high Reynolds number (Re ～ 10⁶) turbulent combustion, space-time-energy-entropy and turbulent mixing. Batchelor-Obukhov-Corrsin turbulent-temperature fluctuations are preserved as the first fossil turbulence by inflation stretching the patterns beyond the horizon ct of causal connection faster than light speed c in time t～ 10^?33 sec. Fossil big-bang temperature turbulence reenters the horizon and imprints nucleosynthesis of H-He densities that seed fragmentation by gravity at 10¹² s in the low Reynolds number plasma before its transition to gas at t～ 10¹³ s and T～ 3000 K. Multiscaling coefficients of the cosmic microwave background (CMB) temperature anisotropies closely match those for high Reynolds number turbulence, Bershadskii, A. and Sreenivasan, K.R., Phys. Lett. A 299 (2002) 149-152; Bershadskii, A. and Sreenivasan, K.R., Phys. Lett. A 319 (2003) 21-23. CMB spectra support the interpretation that big-bang turbulence fossils triggered fragmentation of the viscous plasma at supercluster to galaxy mass scales from 10⁴⁶ to 10⁴² kg, Gibson, C.H., Appl. Mech. Rev. 49 (5) (1996) 299-315; Gibson, C.H., J. Fluids Eng. 122 (2000) 830-835; Gibson, C.H., Combust. Sci. Technol. (2004, to be published).     

Turbulent boundary layer on a mildly curved convex surface

Mean flow and turbulence measurements have been made in a boundary layer which grows first on a flat' wall and then on a convex wall of radius of curvature approximately 100 times the boundary layer thickness. The turbulence data include profiles of the four non-zero components of the Reynolds stress tensor and three triple velocity products obtained at five stream-wise positions. A number of measurements were also made for comparison in the boundary layer on a flat wall under the same conditions. The effects of convex curvature are to reduce turbulent intensities, shear stress and wall friction by approximately 10% of their plane flow values; the triple velocity products are halved in the curved layer. The measurements supplement the small quantity of previously published data available for testing mathematical models of turbulence. The results show the same general trends that have been observed in earlier investigations but there are significant differences in detail, notably in respect of levels of the normal stresses.     

Fabrication and activity of silicate nanoparticles and nanosilicate-entrapped enzymes using polyethyleneimine as a biomimetic polymer

In nature, some peptides induce precipitation of silicic acid into silica nanoparticles such as is found in marine algae called diatoms. However, polybasic polymers can act as peptide mimics; one such polymer, polyethyleneimine (PEI), has the advantage that it is stable at room temperature and is inexpensive, in comparison with synthetic peptides. We describe the fabrication and characterization of biosilicate nanoparticles formed by mimicking the peptides using PEI. Brownian motion nanoparticle tracking analysis and field emission gun scanning electron microscopy have been used for the first time to characterize nanoparticles made with tetramethyl orthosilicate (TMOS) and PEI to investigate the fundamental factors that affect particle properties. These factors include the effect of phosphate concentration, PEI molecular weight, TMOS concentration, and species of alkoxy-silane used. The properties of the particles are compared with other particles made with polymers that induce silication. Our results show that using PEI gives differences in particle size compared with previous work using other polymers that induce silication. The entrapment of enzymes during the silication process, rationale for using nonphosphate and phosphate buffers during enzyme entrapment, and the analysis of enzyme activity are also presented. Because enzymes can be entrapped during fabrication, it means that there are many future possibilities for the use of silicate nanoparticles containing enzymes, such as biosensors and biocatalytic reactors.     

Diversity oriented synthesis: substitution at C5 in unreactive pyrimidines by Claisen rearrangement and reactivity in nucleophilic substitution at C2 and C4 in pteridines and pyrido[2,3-d]pyrimidines

Diversity oriented synthesis of fused pyrimidines leads to scaffolds with many biological activities. In the case of the preparation of pyrido[2,3-d]pyrimidines from 2-alkylthiopyrimidines, the formation of a new carbon-carbon bond at C5 is required, a reaction, that is, very limited in scope. However Claisen type rearrangement of simple 4-allylic ethers affords C5 substituted pyrimidines readily; in cases with an ester substituent, rearrangement occurs at room temperature. Subsequent cyclisation to afford 6-methylpyrido[2,3-d]pyrimidin-7(8H)-ones was achieved in high yield. Using allylic ethers derived from 3-chloromethyl-4-arylbut-3-en-2-ones as substrates, a new titanium[IV]chloride catalysed reaction affording 6-arylmethyl-7-methylpyrido[2,3-d]pyrimidines was discovered. In contrast, 2-alkylthiopteridines are readily available. In both cases, substitution at C2 and C4 to generate diversity has been carried out and the reactivity compared; yields of substitution products were generally higher with pteridine substrates. In biological assays unexpected hits were found for activity against the Gram positive bacterium, Nocardia farcinia, and against the parasite Trypanosoma brucei brucei, illustrating the value of diversity oriented synthesis in the discovery of biologically active compounds.     

Evaluation of direct analysis in real time mass spectrometry for onsite monitoring of batch slurry reactions

Batch slurry reactions are widely used in the industrial manufacturing of chemicals, pharmaceuticals, petrochemicals and polymers. However, onsite monitoring of batch slurry reactions is still not feasible in production plants due to the challenge in analyzing heterogeneous samples without complicated sample preparation procedures. In this study, direct analysis in real time mass spectrometry (DART-MS) has been evaluated for the onsite monitoring of a model batch slurry reaction. The results suggested that automation of the sampling process of DART-MS is important to achieve quantitative results. With a sampling technique of manual sample deposition on melting point capillaries followed by automatic sample introduction across the helium beam, relative standard deviation (RSD) of the protonated molecule signals from the reaction product of the model batch slurry reaction ranged from 6 to 30%. This RSD range is improved greatly over a sampling technique of manual sample deposition followed by manual sample introduction where the RSDs are up to 110%. Furthermore, with the semi-automated sampling approach, semi-quantitative analysis of slurry samples has been achieved. Better quantification is expected with a fully automated sampling approach.     

QMS in the Third Stability Zone with a Transverse Magnetic Field Applied

We report here a study using a quadrupole mass spectrometer (QMS) in which a static magnetic field is applied transversely to the body of the mass filter operating in stability zone 3. Significant improvement in QMS performance was obtained under certain magnetic field conditions, and these have been explained in terms of our theoretical model. The theoretical approach assumed in the model is that the QMS contains hyperbolic rods as electrodes and that the magnetic field acts over the full length of the mass filter assembly. Our latest analysis also predicts for what values of operating parameters an enhancement of the quadrupole resolution is achieved when a transverse magnetic field is applied. The model predicts instrument resolution R > 5000 for Ar with a 100 mm long mass filter and R > 3500 for a HT and D₂ mixture with a 200 mm long mass filter via application of a transverse magnetic field.     

Optimally Decomposing Coverings with Translates of a Convex Polygon

We show that any k-fold covering using translates of an arbitrary convex polygon can be decomposed into Ω(k) covers. Such a decomposition can be computed using an efficient (polynomial-time) algorithm.