Using the local elevation method to construct optimized umbrella sampling potentials: Calculation of the relative free energies and interconversion barriers of glucopyranose ring conformers in water

A method is proposed to combine the local elevation (LE) conformational searching and the umbrella sampling (US) conformational sampling approaches into a single local elevation umbrella sampling (LEUS) scheme for (explicit‐solvent) molecular dynamics (MD) simulations. In this approach, an initial (relatively short) LE build‐up (searching) phase is used to construct an optimized biasing potential within a subspace of conformationally relevant degrees of freedom, that is then used in a (comparatively longer) US sampling phase. This scheme dramatically enhances (in comparison with plain MD) the sampling power of MD simulations, taking advantage of the fact that the preoptimized biasing potential represents a reasonable approximation to the negative of the free energy surface in the considered conformational subspace. The method is applied to the calculation of the relative free energies of β‐D ‐glucopyranose ring conformers in water (within the GROMOS 45A4 force field). Different schemes to assign sampled conformational regions to distinct states are also compared. This approach, which bears some analogies with adaptive umbrella sampling and metadynamics (but within a very distinct implementation), is shown to be: (i) efficient (nearly all the computational effort is invested in the actual sampling phase rather than in searching and equilibration); (ii) robust (the method is only weakly sensitive to the details of the build‐up protocol, even for relatively short build‐up times); (iii) versatile (a LEUS biasing potential database could easily be preoptimized for small molecules and assembled on a fragment basis for larger ones). © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Extracting the underlying effective free energy landscape from single-molecule time series--local equilibrium states and their network

We present a new self-consistent procedure to construct a multidimensional effective free energy landscape from a scalar single molecule time series, when single molecules experience the landscape within a given timescale of "observation." The theory is based on a framework we recently developed to extract a set of local equilibrium states (LESs) and their network from a scalar time series, such as distance between dye molecules tagged in a biomolecule. We scrutinize the appropriateness of the assumptions of local equilibration and local detailed balance among LESs at the single molecule level within the given timescale, rather than postulating them a priori. The self-consistent procedure in this article incorporates the effect of local correlation of the system dynamics inside potential basins, and the effect of finiteness of the sampled data points in assigning the boundary between different LESs. We propose a new simple scheme to assign the dimensionality of the energy landscape from a single molecule time series. We also address the question of what the molecules actually "feel" from the underlying landscape at the single molecule level.     

Search strategies in structural bioinformatics

Optimisation problems pervade structural bioinformatics. In this review, we describe recent work addressing a selection of bioinformatics challenges. We begin with a discussion of research into protein structure comparison, and highlight the utility of Kolmogorov complexity as a measure of structural similarity. We then turn to research into de novo protein structure prediction, in which structures are generated from first principles. In this endeavour, there is a compromise between the detail of the model and the extent to which the conformational space of the protein can be sampled. We discuss some developments in this area, including off-lattice structure prediction using the great deluge algorithm. One strategy to reduce the size of the search space is to restrict the protein chain to sites on a regular lattice. In this context, we highlight the use of memetic algorithms, which combine genetic algorithms with local optimisation, to the study of simple protein models on the two-dimensional square lattice and the face-centred cubic lattice.     

Calculation of free energy through successive umbrella sampling

We consider an implementation of umbrella sampling in which the pertinent range of states is subdivided into small windows that are sampled consecutively and linked together. This allows us to simulate without a weight function or to extrapolate the results to the neighboring window in order to estimate a weight function. Additionally, we present a detailed error analysis in which we demonstrate that the error in umbrella sampling is controlled and, in the absence of sampling difficulties, independent of the window sizes. In this case, the efficiency of our implementation is comparable to a multicanonical simulation with a very good weight function, which in our scheme does not need to be known ahead of time. The analysis also allows us to detect sampling difficulties such as correlations between adjacent windows and provides a test of equilibration. We exemplify the scheme by simulating the liquid-vapor coexistence in a Lennard-Jones system.     

The atom assignment problem in automated de novo drug design. 2. A method for molecular graph and fragment perception

Summary If atom assignment onto 3D molecular graphs is to be optimized, an efficient scheme for placement must be developed. The strategy adopted in this paper is to analyze the molecular graphs in terms of cyclical and non-cyclical nodes; the latter are further divided into terminal and non-terminal nodes. Molecular fragments, from a fragments database, are described in a similar way. A canonical numbering scheme for the fragments and the local subgraph of the molecular graph enables fragments to be placed efficiently onto the molecular graph. Further optimization is achieved by placing similar fragments into bins using a hashing scheme based on the canonical numbering. The graph perception algorithm is illustrated in detail.     

Local and nonlocal contributions to molecular first-order hyperpolarizability: a Hirshfeld partitioning analysis

Based on first-principles calculations, a decomposition scheme is proposed to investigate the molecular site-specific first-order hyperpolarizability (β) responses by means of Hirshfeld population analysis and finite field method. For a molecule, its β is decomposed into local and nonlocal contributions of individual atoms or groups. The former describes the response within the atomic sphere, while the latter describes the contributions from interatomic charge transfer. This scheme is then applied to six prototypical donor-acceptor (D-A) or D-π-A molecules for which the local and nonlocal hyperpolarizabilities are evaluated based on their MP2 density. Both the local and nonlocal parts exhibit site-specific characteristics, but vary differently with molecular structures. The local part depends mainly on the atomic attributes such as electronegativity and charge state, as well as its location in the molecule, while the nonlocal part relates to the ability and distance of charge delocalization within the molecule, increasing rapidly with molecular size. The proposed decomposition scheme provides a way to distinguish atomic or group contributions to molecular hyperpolarizabilities, which is useful in the molecular design for organic nonlinear optical materials.     

线性反馈抑制螺旋波

A class of excitable media described by the Fitzhugh-Nagumo equation is investigated. Based on the stable and self adaptive theory, the error between the systems grid variables and the standard sampling of the periodical signal or constant signal was feed back into the system both globally and locally. When the controller was then shut off, automatically, the whole system became homogeneous. Additionally, the scheme was tested under noisy conditions. The numerical simulations results demonstrate its effectiveness. The system reached a homogeneous state and a spiral wave was converted into a target wave, resulting in a wonderful pattern emerging using a different controller. The scheme proved robust in resisting the effects of noise.     

Measurement of gas diffusion coefficient in liquid-saturated porous media using magnetic resonance imaging

In this study, the dual-chamber pressure decay method and magnetic resonance imaging (MRI) were used to dynamically visualize the gas diffusion process in liquid-saturated porous media, and the relationship of concentration-distance for gas diffusing into liquid-saturated porous media at different times were obtained by MR images quantitative analysis. A non-iterative finite volume method was successfully applied to calculate the local gas diffusion coefficient in liquid-saturated porous media. The results agreed very well with the conventional pressure decay method, thus it demonstrates that the method was feasible of determining the local diffusion coefficient of gas in liquid-saturated porous media at different times during diffusion process.     

Hydrogen Peroxide Formation in Boiling Water Plasma of Electrolyte-Cathode Discharge

A mechanism is proposed for the formation of hydrogen peroxide in an electrolyte-cathode atmospheric-pressure direct-current discharge. A local increase in the temperature of water in the area of liquid contact with the gas discharge causes its boiling, and strong electric fields due to unevenness of the turbulent surface appear on the splashes. As a result, a local breakdown of the hemispherical region of boiling water beneath the electrolyte-cathode spot is possible. The kinetic scheme of the reactions for water vapor plasma has been considered, and hydrogen peroxide concentrations have been calculated, the calculation results being in satisfactory agreement with experimental data.     

A hybrid approach combining energy density analysis with the interaction energy decomposition method

We propose a new analysis technique for characterizing molecular interactions that combines an energy decomposition scheme, such as the Kitaura-Morokuma decomposition method, with energy density analysis, which partitions the total energy of the system into atomic contributions. The combined scheme, termed Interaction-EDA, enables us to estimate the local contribution of interaction energy components, such as electrostatic, exchange, polarization, and charge transfer. The evaluation of the local interaction energy is rather important in large systems. For a numerical assessment, the Interaction-EDA method is applied to the process of CO adsorption on Si(100) - (2 x 1) surface.     

森林泥炭的热解特性及热解动力学

泥炭阴燃是森林地下火的主要燃烧形式之一, 研究泥炭的热解规律对认识其阴燃机理及地下火蔓延机理有重要意义. 本文使用荧光光谱分析技术测定了我国东北林区一种典型泥炭样品的主要元素组成, 并使用热重-差热分析(TG-DTA)技术研究了泥炭样品在惰性气氛中的热解规律. 实验结果表明, 泥炭样品主要由45种元素构成. 从常温到1073 K高温的升温过程中, 泥炭样品的质量损失过程可以分为三个阶段, 依次为水分损失阶段、有机质热解阶段和矿物质分解阶段. 对于泥炭阴燃密切相关的有机质热解阶段, 结合热分析动力学理论和优化计算方法, 建立了描述泥炭有机质热解动力学规律的三组分叠加反应模型.     

One pot, two phases: iron-catalyzed cyclopropanation with in situ generated diazomethane

Tamed! The safe handling of diazomethane can be accomplished by a two-phase reaction. After being generated in aqueous media, the highly reactive species transfers to the organic phase and directly converts alkenes into cyclopropanes (see scheme). An air-stable iron(III) porphyrin complex serves as the catalyst.     

Selective removal of chlorine from chloroaromatic pollutants by electrocatalytic reduction over palladium-loaded carbon felt

This brief review outlines work on effective hydrodechlorination of environmentally persistent chlorine-containing aromatic pollutants by electrocatalytic reduction at Pd-loaded carbon felt. The selective removal of chlorine from phenoxy herbicides 2,4-D and 2,4,5-T, chlorinated biphenyls and naphthalene was readily achieved (i) at room temperature and (ii) directly in aqueous media. No highly active reducing chemicals were required for such a treatment. The use of carbon felt of high surface area as a solution-permeable cathode offered high adsorption capacity for chloroaromatics, while supported palladium provided the system with a highly reactive reducing species supposed to be a surface-bound hydride, which was generated upon electrochemical reductive decomposition of water. A facilitating effect of bulky tetraalkylammonium cations of a supporting electrolyte on substrate conversion and product recovery is considered. The reaction mechanism for selective hydrodechlorination of chloroaromatics in aqueous media and scheme for activation of Pd-loaded carbon felt by electrolytic pre-treatment are proposed and discussed.     

Robust and high‐resolution simulations of nonlinear electrokinetic processes in variable cross‐section channels

We present a model and an associated numerical scheme to simulate complex electrokinetic processes in channels with nonuniform cross‐sectional area. We develop a quasi‐1D model based on local cross‐sectional area averaging of the equations describing unsteady, multispecies, electromigration‐diffusion transport. Our approach uses techniques of lubrication theory to approximate electrokinetic flows in channels with arbitrary variations in cross‐section; and we include chemical equilibrium calculations for weak electrolytes, Taylor–Aris type dispersion due of nonuniform bulk flow, and the effects of ionic strength on species mobility and on acid–base equilibrium constants. To solve the quasi‐1D governing equations, we provide a dissipative finite volume scheme that adds numerical dissipation at selective locations to ensure both unconditional stability and high accuracy. We couple the numerical scheme with a novel adaptive grid refinement algorithm that further improves the accuracy of simulations by minimizing numerical dissipation. We benchmark our numerical scheme with existing numerical schemes by simulating nonlinear electrokinetic problems, including ITP and electromigration dispersion in CZE. Simulation results show that our approach yields fast, stable, and high‐resolution solutions using an order of magnitude less grid points compared to the existing dissipative schemes. To highlight our model's capabilities, we demonstrate simulations that predict increase in detection sensitivity of ITP in converging cross‐sectional area channels. We also show that our simulations of ITP in variable cross‐sectional area channels have very good quantitative agreement with published experimental data.     

Scheme for adding electron-nucleus cusps to Gaussian orbitals

A simple scheme is described for introducing the correct cusps at nuclei into orbitals obtained from Gaussian basis set electronic structure calculations. The scheme is tested with all-electron variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods for the Ne atom, the H2 molecule, and 55 molecules from a standard benchmark set. It greatly reduces the variance of the local energy in all cases and slightly improves the variational energy. This scheme yields a general improvement in the efficiency of all-electron VMC and DMC calculations using Gaussian basis sets.     

Analytic first and second derivatives of the energy in the fragment molecular orbital method combined with molecular mechanics

Analytic first and second derivatives of the energy are developed for the fragment molecular orbital method interfaced with molecular mechanics in the electrostatic embedding scheme at the level of Hartree-Fock and density functional theory. The importance of the orbital response terms is demonstrated. The role of electrostatic embedding upon molecular vibrations is analyzed, comparing force field and quantum mechanical treatments for an ionic liquid and a solvated protein. The method is applied for 100 protein conformations sampled in molecular dynamics (MD) to take into account the complexity of a flexible protein structure in solution, and a good agreement with experimental data is obtained: Frequencies from an experimental infrared (IR) spectrum are reproduced within 17 cm⁻¹ .     

Selective removal of chlorine from chloroaromatic pollutants by electrocatalytic reduction over palladium-loaded carbon felt

This brief review outlines work on effective hydrodechlorination of environmentally persistent chlorine-containing aromatic pollutants by electrocatalytic reduction at Pd-loaded carbon felt. The selective removal of chlorine from phenoxy herbicides 2,4-D and 2,4,5-T, chlorinated biphenyls and naphthalene was readily achieved (i) at room temperature and (ii) directly in aqueous media. No highly active reducing chemicals were required for such a treatment. The use of carbon felt of high surface area as a solution-permeable cathode offered high adsorption capacity for chloroaromatics, while supported palladium provided the system with a highly reactive reducing species supposed to be a surface-bound hydride, which was generated upon electrochemical reductive decomposition of water. A facilitating effect of bulky tetraalky lammonium cations of a supporting electrolyte on substrate conversion and product recovery is considered. The reaction mechanism for selective hydrodechlorination of chloroaromatics in aqueous media and scheme for activation of Pd-loaded carbon felt by electrolytic pre-treatment are proposed and discussed.     

Relating normal vibrational modes to local vibrational modes with the help of an adiabatic connection scheme

Information on the electronic structure of a molecule and its chemical bonds is encoded in the molecular normal vibrational modes. However, normal vibrational modes result from a coupling of local vibrational modes, which means that only the latter can provide detailed insight into bonding and other structural features. In this work, it is proven that the adiabatic internal coordinate vibrational modes of Konkoli and Cremer [Int. J. Quantum Chem. 67, 29 (1998)] represent a unique set of local modes that is directly related to the normal vibrational modes. The missing link between these two sets of modes are the compliance constants of Decius, which turn out to be the reciprocals of the local mode force constants of Konkoli and Cremer. Using the compliance constants matrix, the local mode frequencies of any molecule can be converted into its normal mode frequencies with the help of an adiabatic connection scheme that defines the coupling of the local modes in terms of coupling frequencies and reveals how avoided crossings between the local modes lead to changes in the character of the normal modes.     

Proton evolved local field solid-state nuclear magnetic resonance using Hadamard encoding: theory and application to membrane proteins

NMR anisotropic parameters such as dipolar couplings and chemical shifts are central to structure and orientation determination of aligned membrane proteins and liquid crystals. Among the separated local field experiments, the proton evolved local field (PELF) scheme is particularly suitable to measure dynamically averaged dipolar couplings and give information on local molecular motions. However, the PELF experiment requires the acquisition of several 2D datasets at different mixing times to optimize the sensitivity for the complete range of dipolar couplings of the resonances in the spectrum. Here, we propose a new PELF experiment that takes the advantage of the Hadamard encoding (HE) to obtain higher sensitivity for a broad range of dipolar couplings using a single 2D experiment. The HE scheme is obtained by selecting the spin operators with phase switching of hard pulses. This approach enables one to detect four spin operators, simultaneously, which can be processed into two 2D spectra covering a broader range of dipolar couplings. The advantages of the new approach are illustrated for a U-(15)N NAL single crystal and the U-(15)N labeled single-pass membrane protein sarcolipin reconstituted in oriented lipid bicelles. The HE-PELF scheme can be implemented in other multidimensional experiments to speed up the characterization of the structure and dynamics of oriented membrane proteins and liquid crystalline samples.     

Numerical approximation of AR‐XPS spectra for rough surfaces considering the effect of electron shadowing

A computational scheme is presented that takes into account the topography, i.e. the shadowing and hence the local emission angle of the electrons when evaluating AR‐XPS data of macroscopic rough surfaces. The topography of the sample surface is supposed to be recorded by atomic force microscopy and/or optical microscopy. The emitted photoelectrons are simulated based on an extension of the Beer–Lambert law that includes the shadowing, the current local emission angle, and the geometrical instrument setup. The obtained angle‐resolved XPS spectra are optimized in accordance with experimental ones via a self‐consistent minimization algorithm that also allows one to determine the layer thicknesses of the corrugated sample. In order to validate the proposed numerical scheme, the simulation program simulation of electron spectra for surface analysis is used. An additional analysis is then performed considering only experimental data. The numerical scheme gives good agreement in simulation–simulation as well as simulation–experiment comparisons and permits a comprehensible interpretation of the measured data. Copyright © 2014 John Wiley & Sons, Ltd.