Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution

Collocation type methods are studied for the numerical solutionof the weakly singular Volterra integral equation of the secondkind: where the solution (t) is assumedto have the form f(t) = x(t)+r^?(t), x and being sufficientlysmooth. The solution is approximated near zero by a linear combinationof powers of t?, and away from zero by the usual polynomialrepresentation. Convergence is proved and many numerical experimentsare carried out with examples from the literature. A comparisonis made with a method of Brunner & Norsett (1981), originallydeveloped for (1) with a smooth solution. Special attentionis paid to the numerical approximation of the so-called momentintegrals which emerge in the collocation scheme.     

Insight into G-DNA structural polymorphism and folding from sequence and loop connectivity through free energy analysis

The lengths of G-tracts and their connecting loop sequences determine G-quadruplex folding and stability. Complete understanding of the sequence-structure relationships remains elusive. Here, single-loop G-quadruplexes were investigated using explicit solvent molecular dynamics (MD) simulations to characterize the effect of loop length, loop sequence, and G-tract length on the folding topologies and stability of G-quadruplexes. Eight loop types, including different variants of lateral, diagonal, and propeller loops, and six different loop sequences [d0 (i.e., no intervening residues in the loop), dT, dT(2), dT(3), dTTA, and dT(4)] were considered through MD simulation and free energy analysis. In most cases the free energetic estimates agree well with the experimental observations. The work also provides new insight into G-quadruplex folding and stability. This includes reporting the observed instability of the left propeller loop, which extends the rules for G-quadruplex folding. We also suggest a plausible explanation why human telomere sequences predominantly form hybrid-I and hybrid-II type structures in K(+) solution. Overall, our calculation results indicate that short loops generally are less stable than longer loops, and we hypothesize that the extreme stability of sequences with very short loops could possibly derive from the formation of parallel multimers. The results suggest that free energy differences, estimated from MD and free energy analysis with current force fields and simulation protocols, are able to complement experiment and to help dissect and explain loop sequence, loop length, and G-tract length and orientation influences on G-quadruplex structure.     

The quotient field as a torsion-free covering module

R will denote a commutative integral domain with quotient fieldQ. A torsion-free cover of a moduleM is a torsion-free moduleF and anR-epimorphism σ:F→M such that given any torsion-free moduleG and λ∈Hom _R (G, M) there exists μ∈Hom _R (G,F) such that σμ=λ. It is known that ifM is a maximal ideal ofR, R→R/M is a torsion-free cover if and only ifR is a maximal valuation ring. LetE denote the injective hull ofR/M thenR→R/M extends to a homomorphismQ→E. We give necessary and sufficient conditions forQ→E to be a torsion-free cover.     

无机酸洗脱对胜利褐煤微晶结构及其自燃倾向性的影响

利用XRD、Raman、XPS和FT-IR表征技术,研究无机酸洗脱(HCl、H2SO4、HCl-HF)处理的胜利褐煤微晶结构的变化,采用自行设计的表面吸附仪-GC联用装置,对样品进行不同温度的低温脉冲氧化实验,考察了煤样在不同温度下氧吸附量的变化规律,通过低温脉冲氧吸附规律与TG/DTG和固定床燃烧实验关联,考察了煤样的自燃倾向。结果表明,无机酸洗脱对矿物质的脱除使得煤结构的有序度增加,石墨化程度提高,无机酸洗脱煤样与原煤相比吸氧量明显下降。随着吸附温度的升高,各煤样吸氧量明显增加,且随着脱除矿物质程度的增加,吸氧量呈减小的趋势,导致自燃倾向降低。     

An accurate and simple quantum model for liquid water

The path-integral molecular dynamics and centroid molecular dynamics methods have been applied to investigate the behavior of liquid water at ambient conditions starting from a recently developed simple point charge/flexible (SPC/Fw) model. Several quantum structural, thermodynamic, and dynamical properties have been computed and compared to the corresponding classical values, as well as to the available experimental data. The path-integral molecular dynamics simulations show that the inclusion of quantum effects results in a less structured liquid with a reduced amount of hydrogen bonding in comparison to its classical analog. The nuclear quantization also leads to a smaller dielectric constant and a larger diffusion coefficient relative to the corresponding classical values. Collective and single molecule time correlation functions show a faster decay than their classical counterparts. Good agreement with the experimental measurements in the low-frequency region is obtained for the quantum infrared spectrum, which also shows a higher intensity and a redshift relative to its classical analog. A modification of the original parametrization of the SPC/Fw model is suggested and tested in order to construct an accurate quantum model, called q-SPC/Fw, for liquid water. The quantum results for several thermodynamic and dynamical properties computed with the new model are shown to be in a significantly better agreement with the experimental data. Finally, a force-matching approach was applied to the q-SPC/Fw model to derive an effective quantum force field for liquid water in which the effects due to the nuclear quantization are explicitly distinguished from those due to the underlying molecular interactions. Thermodynamic and dynamical properties computed using standard classical simulations with this effective quantum potential are found in excellent agreement with those obtained from significantly more computationally demanding full centroid molecular dynamics simulations. The present results suggest that the inclusion of nuclear quantum effects into an empirical model for water enhances the ability of such model to faithfully represent experimental data, presumably through an increased ability of the model itself to capture realistic physical effects.     

Quantum mechanically derived AMBER-compatible heme parameters for various states of the cytochrome P450 catalytic cycle

Molecular mechanics (MM) methods are computationally affordable tools for screening chemical libraries of novel compounds for sites of P450 metabolism. One challenge for MM methods has been the absence of a consistent and transferable set of parameters for the heme within the P450 active site. Experimental data indicate that mammalian P450 enzymes vary greatly in the size, architecture, and plasticity of their active sites. Thus, obtaining X-ray-based geometries for the development of accurate MM parameters for the major classes of hepatic P450 remains a daunting task. Our previous work with preliminary gas-phase quantum mechanics (QM)-derived atomic partial charges greatly improved the accuracy of docking studies of raloxifene to CYP3A4. We have therefore developed and tested a consistent set of transferable MM parameters based on gas-phase QM calculations of two model systems of the heme-a truncated (T-HM) and a full (F-HM) for four states of the P450 catalytic cycle. Our results indicate that the use of the atomic partial charges from the F-HM further improves the accuracy of docked predictions for raloxifene to CYP3A4. Different patterns for substrate docking are also observed depending on the choice of heme model and state. Newly parameterized heme models are tested in implicit and explicitly solvated MD simulations in the absence and presence of enzyme structures, for CYP3A4, and appear to be stable on the nanosecond simulation timescale. The new force field for the various heme states may aid the community for simulations of P450 enzymes and other heme-containing enzymes.     

Assignment of oxime and hydrazone configuration using 1H‐15N and 13C‐15N coupling measurements at natural abundance

Measurement of ¹H‐¹⁵N and ¹³C‐¹⁵N coupling constants at natural abundance is demonstrated to be a reliable and generic method to determine the configuration of oximes, hydrazines, and related systems. Data on ¹H‐¹⁵N and ¹³C‐¹⁵N coupling constants on a variety of systems obtained at natural abundance confirm the geometric dependence of the measured ¹H‐¹⁵N and ¹³C‐¹⁵N coupling constants. In addition, we summarize a simple “decision‐tree” for determining configuration based on practical considerations of sample quantity, solubility, and complexity. Copyright © 2016 John Wiley & Sons, Ltd.