Nodal Surface Approximations to the Zero Equipotential Surfaces for Cubic Lattices

Models of electrostatic surfaces in atomic crystals rely on equations involving the Jacobi theta functions. Numerical integration of these is prohibitively time consuming, making it difficult to examine the properties of the fields which give rise to the surfaces. We give simple expressions for the key electrostatic surfaces using Fourier expansions in basis sets of nodal surfaces. Any surface may be computed in seconds in a form ammenable to further analysis. The distribution of the mean and Gaussian curvatures over each surface has been visualised by assigning colours so that the range from minimum to maximum value spans blue to red. We similarly explore the mean and Gaussian scalar fields over a range of triply periodic surfaces of the same morphology.     

The impact of surface area,volume, curvature,and Lennard–Jones potential to solvation modeling

This article explores the impact of surface area, volume, curvature, and Lennard–Jones (LJ) potential on solvation free energy predictions. Rigidity surfaces are utilized to generate robust analytical expressions for maximum, minimum, mean, and Gaussian curvatures of solvent–solute interfaces, and define a generalized Poisson–Boltzmann (GPB) equation with a smooth dielectric profile. Extensive correlation analysis is performed to examine the linear dependence of surface area, surface enclosed volume, maximum curvature, minimum curvature, mean curvature, and Gaussian curvature for solvation modeling. It is found that surface area and surfaces enclosed volumes are highly correlated to each other's, and poorly correlated to various curvatures for six test sets of molecules. Different curvatures are weakly correlated to each other for six test sets of molecules, but are strongly correlated to each other within each test set of molecules. Based on correlation analysis, we construct twenty six nontrivial nonpolar solvation models. Our numerical results reveal that the LJ potential plays a vital role in nonpolar solvation modeling, especially for molecules involving strong van der Waals interactions. It is found that curvatures are at least as important as surface area or surface enclosed volume in nonpolar solvation modeling. In conjugation with the GPB model, various curvature‐based nonpolar solvation models are shown to offer some of the best solvation free energy predictions for a wide range of test sets. For example, root mean square errors from a model constituting surface area, volume, mean curvature, and LJ potential are less than 0.42 kcal/mol for all test sets. © 2016 Wiley Periodicals, Inc.     

Molecular dynamics simulations of oligonucleotides in solution: Visualisation of intrinsic curvature

Summary We have undertaken molecular dynamics simulations on the d(CGCAAAAAAGCG)d(CGCTTTTTTGCG) dodecamer in solution. In this study, we focus on aspects of conformation and dynamics, including the possibility of cross-strand hydrogen bonds. We compare our results with those from crystallography as well as infrared, Raman and NMR spectroscopy and cyclization kinetics. Our method of analysis allows us to visualise the curvature of the helix as a function of time during the simulation. We find that the major distortions of the helix axis path occur at the junctions between the (essentially straight) A-tract and the CG-and GC-tracts, although at one junction this is due to hyperflexibility (i.e., regions of high flexibility with no preferred direction of curvature), while at the other junction a static curvature is found (i.e., a preferred, sustained direction of curvature).     

Curvature-regulated transmembrane anion transport by a trifluoromethylated bisbenzimidazole

In this paper,we demonstrate that modification of anion-transport active 1,3-bis(benzimidazol-2-yl)benzene with strongly electron-withdrawing trifluoromethyl and nitro groups leads to a dramatic increase in the anionophoric activity,and the activity may be greatly regulated by the curvatures of the liposomes used.     

Examining the Effects of Netropsin on the Curvature of DNA A-Tracts Using Electrophoresis

A-tracts are sequences of repeated adenine bases that, under the proper conditions, are capable of mediating DNA curvature. A-tracts occur naturally in the regulatory regions of many organisms, yet their biological functions are not fully understood. Orienting multiple A-tracts together constructively or destructively in a phase has the potential to create different shapes in the DNA helix axis. One means of detecting these molecular shape differences is from altered DNA mobilities measured using electrophoresis. The small molecule netropsin binds the minor groove of DNA, particularly at AT-rich sequences including A-tracts. Here, we systematically test the hypothesis that netropsin binding eliminates the curvature of A-tracts by measuring the electrophoretic mobilities of seven 98-base pair DNA samples containing different numbers and arrangements of centrally located A-tracts under varying conditions with netropsin. We find that netropsin binding eliminates the mobility difference between the DNA fragments with different A-tract arrangements in a concentration-dependent manner. This work provides evidence for the straightening of A-tracts upon netropsin binding and illustrates an artificial approach to re-sculpt DNA shape.     

The Determination of Ampicillin in Epicillin by the Curvature Inversion Method

Abstract

A method based on the curvature inversion technique has been developed for the determination of ampicillin in epicillin. The results for four epicillin samples are compared with the results obtained by thin-layer chromatography.     

Comparison between hydrogen-transfer and fluoro-transfer reactions on the microcanonical unimolecular rate constants

The microcanonical rate constants for the hydrogen-transfer process of HCCF (reaction 7) and the fluoro-transfer process of FCCF (reaction 8) are carried out with tunneling correction and curvature correction. The results show that the tunneling effects and curvature effects on the rate constant of reaction 7 is quite different from that of reaction 8. The rate constants for different rotational states are also studied for these reactions.     

Thermodynamic issues associated with combined cyclic voltammetry and wafer curvature measurements in electrolytes

A thermodynamic framework has been provided for the interpretation of combined cyclic voltammetry and surface stress measurements, the latter being obtained from wafer curvature or beam deflection measurements of a solid electrode as a function of applied potential (so-called voltstressograms). Firstly, the derivation of electrocapillarity equations for solid electrodes has been critically reviewed by starting from the Gibbs adsorption equation appropriate for solid–electrolyte interfaces. This allowed us to demonstrate the critical importance of elastic surface strain in the thermodynamic boundary conditions of the partial derivatives intervening in the interpretation of voltstressograms. From these considerations, it was shown for the first time that the electrocapillarity equations for solid electrodes are not appropriate for describing the variation of surface stress with potential obtained from wafer curvature measurements, because such measurements are intrinsically incompatible with the constant strain condition implied in the electrocapillarity equations. An alternative explanation is provided for the experimentally observed proportionality between the current density, measured in cyclic voltammograms, and the first derivative of surface stress with respect to potential, obtained from voltstressograms.     

A reasonable criterion of reactivities at the defective region of single‐walled carbon nanotubes

Defect directional curvature K_D‐def was proposed as a reasonable criterion for the reactivities and adduct structures at the defective region of single‐walled carbon nanotubes (SWCNTs). B3LYP/6‐31G* calculations for the [2 + 1] and [1 + 1] additions of a series of 11‐layer (n, n) (n = 4–8) and six‐layer (10,0) SWCNTs with Stone‐Wales defects showed that the K_D‐def or its mean K_M‐def was a good index to judge the adduct structures and the reactivities. Adducts of the [2 + 1] additions were divided into two types: one was the adduct with the C‐X‐C configuration and corresponding to the large K_D‐def and the large binding energy, and another was the adduct with the closed ?3MR structure and corresponding to the small K_D‐def and the small binding energy. It must be pointed out that, besides mainly relying on the K_D‐def, the adduct structures and the reactivities of the [2 + 1] additions had been weakly affected by topologic structures. The calculated results for the [1 + 1] additions of the 11‐layer (5,5) SWCNT with defect A revealed that the binding energies monotonously increased with the K_M‐def. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

计算富勒烯结构的新方法:曲率定理*

介绍了利用曲率定理计算富勒烯结构的方法,证明了富勒烯结构中五元环数恒为12,与传统的欧拉定理法进行了对比,凸显了曲率定理法在研究多面体结构时直观形象的特点,强调了数学方法对解决化学问题和认识化学模型的重要性。     

A Chiral Polycyclic Aromatic Hydrocarbon Monkey Saddle

A contorted polycyclic aromatic hydrocarbon (PAH) in the shape of a monkey saddle has been synthesized in three steps from a readily available truxene precursor. The monkey saddle PAH is consisting of three five‐, seven six‐, and three eight‐membered rings and has been unambiguously characterized by single‐crystal X‐ray diffraction. Owing to the three biaryl axes the monkey saddle PAH is inherently chiral. The inversion of the two enantiomeric structures into each other preferably occurs through a twisting of peripheral rings rather than by a fully planar intermediate, as has been calculated by DFT methods. Enantiomers were separated by chiral HPLC and inversion barriers determined by variable temperature circular dichroism spectroscopy, supporting the twisting mechanism.     

Engineering cosmetics using the Net-Average-Curvature (NAC) model

The hydrophilic–lipophilic balance (HLB) and the packing parameter have been guiding formulators for the last 70 years. However, these indicators look at the surfactant only without considering formulation conditions such as temperature, salinity, and oil hydrophobicity. The hydrophilic–lipophilic difference (HLD) consists of two empirical correlations that consider the entire set of formulation conditions, serving as a unified theory of hydrophobicity that connects to HLB, packing parameter, and phase inversion temperature (PIT). Target HLD values for cosmetic formulations are discussed. The HLD alone, however, does not provide formulation properties such as solubilization capacity, phase diagrams, or interfacial tension. To this end, the net-average curvature (NAC) model interprets the HLD as a dimensionless interfacial curvature, using this approach to predict formulation properties and phase diagrams. The use of the HLD-NAC model in the design of a skin cleansing formula is illustrated via a predicted ‘fish’ phase diagram required to identify preferred compositions.     

Molecular‐Curvature‐Induced Spontaneous Formation of Curved and Concentric Lamellae through Nucleation

Spontaneous formation of concentric lamellae was observed in self‐assembling giant surfactants consisting of a fluorinated polyhedral oligomeric silsesquioxane (FPOSS) head and flexible polymer tail(s). Owing to the asymmetrical sizes of the head and tail blocks and the rectangular molecular interface, the giant surfactants assumed a truncated‐wedge‐like molecular shape, which induced morphological curvature during self‐assembly, thus resulting in the formation of curved and concentric lamellae. These curved/concentric lamellae were observed in FPOSS‐based giant surfactants with different architectures and compositions. The spontaneous curvature formation not only promotes our fundamental understanding of assembly principles, but also provides a promising and efficient approach to the fabrication of a wide range of high‐performance devices.     

表面活性剂体系中电荷诱导的层状相向囊泡相的转化

向一种非离子表面活性剂LA070(英文名AlcoholC12-C16Poly(1-6)Ethoxylate)复配体系LA070/C8H17OH/H2O形成的层状相中加入离子型表面活性剂使其电荷化,在电荷诱导下,双分子层的曲率发生变化,闭合形成具有黏弹性的囊泡相.离子型表面活性剂的加入量增大到一定程度时,由于反离子的屏蔽作用,囊泡结构被破坏,溶液的黏弹性消失,澄清的溶液逐渐变混浊,然后分为两相.     

Monte Carlo study of the translocation of a polymer chain through a hole

The translocation of a polymer chain through a narrow hole in a rigid obstacle has been studied by the static Monte Carlo simulations. A modified self-avoiding walk on a cubic lattice has been used to model the polymer in an athermal solution. The entropy of the chain before, in the course, and after the translocation process has been estimated by the statistical counting method. The thermodynamic generalized forces governing the translocation have been calculated. The influence of the system geometry on the entropic barrier landscape is discussed.     

Evaluation of DNA bending models in their capacity to predict electrophoretic migration anomalies of satellite DNA sequences

DNA containing a sequence that generates a local curvature exhibits a pronounced retardation in electrophoretic mobility. Various theoretical models have been proposed to explain relationship between DNA structural features and migration anomaly. Here, we studied the capacity of 15 static wedge‐bending models to predict electrophoretic behavior of 69 satellite monomers derived from four divergent families. All monomers exhibited retarded mobility in PAGE corresponding to retardation factors ranging 1.02–1.54. The curvature varied both within and across the groups and correlated with the number, position, and lengths of A‐tracts. Two dinucleotide models provided strong correlation between gel mobility and curvature prediction; two trinucleotide models were satisfactory while remaining dinucleotide models provided intermediate results with reliable prediction for subsets of sequences only. In some cases, similarly shaped molecules exhibited relatively large differences in mobility and vice versa. Generally less accurate predictions were obtained in groups containing less homogeneous sequences possessing distinct structural features. In conclusion, relatively universal theoretical models were identified suitable for the analysis of natural sequences known to harbor relatively moderate curvature. These models could be potentially applied to genome wide studies. However, in silico predictions should be viewed in context of experimental measurement of intrinsic DNA curvature.