Time series analysis of ion dynamics in glassy ionic conductors obtained by a molecular dynamics simulation

We present several characteristics of ionic motion in glassy ionic conductors brought out by time series analysis of molecular dynamics (MD) simulation data. Time series analysis of data obtained by MD simulation can provide crucial information to describe, understand and predict the dynamics in many systems. The data have been treated by the singular spectrum analysis (SSA), which is a method to extract information from noisy short time series and thus provide insight into the unknown or partially unknown dynamics of the underlying system that generated the time series. Phase-space plot reconstructed using the principal components of SSA exhibited complex but clear structures, suggesting the deterministic nature of the dynamics.     

General framework for studying the dynamics of folded and nonfolded proteins by NMR relaxation spectroscopy and MD simulation

A general framework is presented for the interpretation of NMR relaxation data of proteins. The method, termed isotropic reorientational eigenmode dynamics (iRED), relies on a principal component analysis of the isotropically averaged covariance matrix of the lattice functions of the spin interactions responsible for spin relaxation. The covariance matrix, which is evaluated using a molecular dynamics (MD) simulation, is diagonalized yielding reorientational eigenmodes and amplitudes that reveal detailed information about correlated protein dynamics. The eigenvalue distribution allows one to quantitatively assess whether overall and internal motions are statistically separable. To each eigenmode belongs a correlation time that can be adjusted to optimally reproduce experimental relaxation parameters. A key feature of the method is that it does not require separability of overall tumbling and internal motions, which makes it applicable to a wide range of systems, such as folded, partially folded, and unfolded biomolecular systems and other macromolecules in solution. The approach was applied to NMR relaxation data of ubiquitin collected at multiple magnetic fields in the native form and in the partially folded A-state using MD trajectories with lengths of 6 and 70 ns. The relaxation data of native ubiquitin are well reproduced after adjustment of the correlation times of the 10 largest eigenmodes. For this state, a high degree of separability between internal and overall motions is present as is reflected in large amplitude and collectivity gaps between internal and overall reorientational modes. In contrast, no such separability exists for the A-state. Residual overall tumbling motion involving the N-terminal beta-sheet and the central helix is observed for two of the largest modes only. By adjusting the correlation times of the 10 largest modes, a high degree of consistency between the experimental relaxation data and the iRED model is reached for this highly flexible biomolecule.     

Application of time series analysis on molecular dynamics simulations of proteins: a study of different conformational spaces by principal component analysis

Time series analysis is applied on the collective coordinates obtained from principal component analysis of independent molecular dynamics simulations of alpha-amylase inhibitor tendamistat and immunity protein of colicin E7 based on the Calpha coordinates history. Even though the principal component directions obtained for each run are considerably different, the dynamics information obtained from these runs are surprisingly similar in terms of time series models and parameters. There are two main differences in the dynamics of the two proteins: the higher density of low frequencies and the larger step sizes for the interminima motions of colicin E7 than those of alpha-amylase inhibitor, which may be attributed to the higher number of residues of colicin E7 and/or the structural differences of the two proteins. The cumulative density function of the low frequencies in each run conforms to the expectations from the normal mode analysis. When different runs of alpha-amylase inhibitor are projected on the same set of eigenvectors, it is found that principal components obtained from a certain conformational region of a protein has a moderate explanation power in other conformational regions and the local minima are similar to a certain extent, while the height of the energy barriers in between the minima significantly change. As a final remark, time series analysis tools are further exploited in this study with the motive of explaining the equilibrium fluctuations of proteins.     

Extracting effective normal modes from equilibrium dynamics at finite temperature

A general method for obtaining effective normal modes of a molecular system from molecular dynamics simulations is presented. The method is based on a localization criterion for the Fourier transformed velocity time-correlation functions of the effective modes. For a given choice of the localization function used, the method becomes equivalent to the principal mode analysis (PMA) based on covariance matrix diagonalization. On the other hand, a proper choice of the localization function leads to a novel method with a strong analogy with the usual normal mode analysis of equilibrium structures, where the Hessian system at the minimum energy structure is replaced by the thermal averaged Hessian, although the Hessian itself is never actually calculated. This method does not introduce any extra numerical cost during the simulation and bears the same simplicity as PMA itself. It can thus be readily applied to ab initio molecular dynamics simulations. Three such examples are provided here. First we recover effective normal modes of an isolated formaldehyde molecule computed at 20 K in very good agreement with the results of a normal mode analysis performed at its equilibrium structure. We then illustrate the applicability of the method for liquid phase studies. The effective normal modes of a water molecule in liquid water and of a uracil molecule in aqueous solution can be extracted from ab initio molecular dynamics simulations of these two systems at 300 K.     

Reorientational eigenmode dynamics: a combined MD/NMR relaxation analysis method for flexible parts in globular proteins

An approach is presented for the interpretation of heteronuclear NMR spin relaxation data in mobile protein parts in terms of reorientational eigenmode dynamics. The method is based on the covariance matrix of the spatial functions of the nuclear spin interactions that cause relaxation expressed as spherical harmonics of rank 2. The approach was applied to characterize the dynamics of a loop region of ubiquitin. The covariance matrix was determined from a conformational ensemble generated by a 5 ns molecular dynamics simulation. It was found that the time correlation functions of the dominant eigenmodes decay in good approximation with a single correlation time. From the reorientational eigenmodes, their eigenvalues, and correlation times, NMR relaxation data were calculated in accordance with Bloch-Wangsness-Redfield relaxation theory and directly compared with experimental (15)N relaxation parameters. Using a fitting procedure, agreement between calculated and experimental data was improved significantly by adjusting eigenvalues and correlation times of the dominant modes. The presented procedure provides detailed information on correlated reorientational dynamics of flexible parts in globular proteins. The covariance matrix was linked to the covariance matrix of backbone dihedral angle fluctuations, allowing one to study the motional behavior of these degrees of freedom on nano- and subnanosecond time scales.     

A New kHz Velocity Map Ion/Electron Imaging Spectrometer for Femtosecond Time-Resolved Molecular Reaction Dynamics Studies

A new velocity map imaging spectrometer is constructed for molecular reaction dynamics studies using time-resolved photoelectron/ion spectroscopy method.By combining a kHz pulsed valve and an ICCD camera,this velocity map imaging spectrometer can be run at a repetition rate of 1 kHz,totally compatible with the fs Ti:Sapphire laser system,facilitating time-resolved studies in gas phase which are usually time-consuming.Time-resolved velocity map imaging study of NH₃ photodissociation at 200 nm was performed and the time-resolved total kinetic energy release spectrum of H+NH₂ products provides rich information about the dissociation dynamics of NH₃.These results show that this new apparatus is a powerful tool for investigating the molecular reaction dynamics using time-resolved methods.     

The automotive system — a complex coupling of matter and energy networks

Linear equations are shown with schematic diagrams which together describe the automotive dynamic model. However, the principal intent of the paper is not to study the dynamics of automotive operations. The schematic diagrams of each sub-system are presented to indicate the possible points of energy storage and dissipation and how they relate to the continuity of energy.From the sub-system diagrams it is now possible to generate energy and matter balances for the automotive system. The final energie matrix expression (eqn 49), which relates to all components of the system, is developed.     

基于地统计学与支持向量回归的QSAR建模

基于主成分分析(PCA)、地统计学(GS)和支持向量回归(SVR), 提出了一种新的定量构效关系(QSAR)个体化预测方法——Weight-PCA-GS-SVR. 其基本思路是: 先以PCA降维并消除自变量间的信息冗余, 继以SVR经非线性主成分筛选去除与因变量无关的主成分, 再以保留主成分计算样本间的加权距离, 然后以高维GS确定公用变程; 每一个待测样本都以自身为中心从训练集中找出加权距离小于公用变程的私有k个近邻, 以SVR训练建模完成个体化预测. Weight-PCA-GS-SVR从行、列两个方向对模型进行了优化, 为自变量提供了一种新的加权方法, 为解决最优k近邻选择难题提供了新的思路, 并具有SVR原来的优点. 经3个化合物活性实例数据集验证, 新方法在所有参比模型中预测精度最高, 且明显优于文献报道结果, Weight-PCA-GS-SVR在QSAR等回归预测领域有较广泛的应用前景.     

Molecular nanopolaritonics: cross manipulation of near-field plasmons and molecules. I. Theory and application to junction control

Near-field interactions between plasmons and molecules are treated in a simple unified approach. The density matrix of a molecule is treated with linear-response random phase approximation and the plasmons are treated classically. The equations of motion for the combined system are linear, governed by a simple Liouvillian operator for the polariton (plasmon+molecule excitation) dynamics. The dynamics can be followed in time or directly in frequency space where a trace formula for the transmission is presented. A model system is studied, metal dots in a forklike arrangement, coupled to a two level system with a large transition-dipole moment. A Fano-type resonance [Phys. Rev. 103, 1202 (1956)] develops when the molecular response is narrower than the width of the absorption spectrum for the plasmons. We show that the direction of the dipole of the molecule determines the direction the polariton chooses. Further, the precise position of the molecule has a significant effect on the transfer.     

Hierarchical structure of the energy landscape of proteins revisited by time series analysis. I. Mimicking protein dynamics in different time scales

Time series models, which are constructed from the projections of the molecular-dynamics (MD) runs on principal components (modes), are used to mimic the dynamics of two proteins: tendamistat and immunity protein of colicin E7 (ImmE7). Four independent MD runs of tendamistat and three independent runs of ImmE7 protein in vacuum are used to investigate the energy landscapes of these proteins. It is found that mean-square displacements of residues along the modes in different time scales can be mimicked by time series models, which are utilized in dividing protein dynamics into different regimes with respect to the dominating motion type. The first two regimes constitute the dominance of intraminimum motions during the first 5 ps and the random walk motion in a hierarchically higher-level energy minimum, which comprise the initial time period of the trajectories up to 20-40 ps for tendamistat and 80-120 ps for ImmE7. These are also the time ranges within which the linear nonstationary time series are completely satisfactory in explaining protein dynamics. Encountering energy barriers enclosing higher-level energy minima constrains the random walk motion of the proteins, and pseudorelaxation processes at different levels of minima are detected in tendamistat, depending on the sampling window size. Correlation (relaxation) times of 30-40 ps and 150-200 ps are detected for two energy envelopes of successive levels for tendamistat, which gives an overall idea about the hierarchical structure of the energy landscape. However, it should be stressed that correlation times of the modes are highly variable with respect to conformational subspaces and sampling window sizes, indicating the absence of an actual relaxation. The random-walk step sizes and the time length of the second regime are used to illuminate an important difference between the dynamics of the two proteins, which cannot be clarified by the investigation of relaxation times alone: ImmE7 has lower-energy barriers enclosing the higher-level energy minimum, preventing the protein to relax and letting it move in a random-walk fashion for a longer period of time.     

Principal component analysis of polarity and interaction parameters in inverse gas chromatography

Inverse gas chromatography is used in the characterization of aliphatic-aromatic and aromatic ketones, their oximes, and ketone-oxime or oxime-oxime mixtures. All these organic materials are used as liquid stationary phases in gas chromatographic columns. A series of polarity and Flory-Huggins interaction parameters are determined and used to describe the physicochemical properties of examined materials, metal extractants, and products of their degradation. Principal component analysis (PCA) is performed on a data matrix consisting of polarity and interaction parameters for ketones, their oximes, and mixtures. The calculations are carried out on the correlation matrix. It is found that seven principal components account for more than 95% of the total variance in the data, indicating that the polarity (interaction) parameters are not correlating well. Physical meanings are attributed to the principal components, the most influential ones being that the first and the second principal components account for several Flory-Huggins interaction parameters, whereas the fifth is correlated with criterion "A". The plots of component loadings show characteristic groupings of polarity indicators, whereas that of component scores show several groupings of stationary phases. Cluster analysis provides mainly the same groupings. PCA allows for the grouping of polarity and solubility parameters based on the information carried within those parameters. There is no need to use more than one parameter from each cluster. McReynolds polarity and the partial molar excess Gibbs free energy of solution per methylene group carry the same information. The groups of ketones, oximes, and their mixtures can be distinguished with the use of PCA on the basis of the measured polarity, solubility parameters, or both.     

New insights into the meaning and usefulness of principal component analysis of concatenated trajectories

A comparison between different conformations of a given protein, relating both structure and dynamics, can be performed in terms of combined principal component analysis (combined‐PCA). To that end, a trajectory is obtained by concatenating molecular dynamics trajectories of the individual conformations under comparison. Then, the principal components are calculated by diagonalizing the correlation matrix of the concatenated trajectory. Since the introduction of this approach in 1995 it has had a large number of applications. However, the interpretation of the eigenvectors and eigenvalues so obtained is based on intuitive foundations, because analytical expressions relating the concatenated correlation matrix with those of the individual trajectories under consideration have not been provided yet. In this article, we present such expressions for the cases of two, three, and an arbitrary number of concatenated trajectories. The formulas are simple and show what is to be expected and what is not to be expected from a combined‐PCA. Their correctness and usefulness is demonstrated by discussing some representative examples. The results can be summarized in a simple sentence: the correlation matrix of a concatenated trajectory is given by the average of the individual correlation matrices plus the correlation matrix of the individual averages. From this it follows that the combined‐PCA of trajectories belonging to different free energy basins provides information that could also be obtained by alternative and more straightforward means. © 2014 Wiley Periodicals, Inc.     

Analysis of complex oscillatory dynamics of a pH oscillator

Reaction systems that display pronounced periodic and aperiodic variations in the pH value of the reaction medium are known as pH oscillators. A member of this family of reactions studied here, the Cu(II)-catalyzed oxidation of thiosulfate by hydrogen peroxide in acidic solution, is known to display a rich variety of oscillatory dynamics. We focus on experimental time series showing complex aperiodic dynamics that simultaneously possesses the characteristics of period-doubled large-amplitude oscillations and irregular small-amplitude oscillations reminiscent of mixed-mode dynamics. An analysis based on the reconstruction of the attractor from the measured time series by two different methods and subsequent calculation of the maximal Lyapunov exponent reveals that this interesting dynamical regime is a manifestation of deterministic chaos. The text was submitted by the authors in English.     

Use of Chemometrics: Principal Component Analysis (PCA) and Principal Component Regression (PCR) for the Authentication of Orange Juice

ABSTRACT

Principal Component Analysis (PCA) was applied to a set of physico-chemical variables obtained from 41 samples of summer orange juice, in order to reduce the number of variables. Working with the covariance matrix, three components (which explained 98.27% of the variance) were taken. With the correlation matrix, four components which explained: 85.65% of the variance were taken. With the scores corresponding to both matrixes a principal component regression (PCR) was carried out against the dependent variable of Brix grades, so as to obtain two statistical models that would allow the detection of adulterations in pure orange juice, based on dilution and later masking by the addition of sugar. The models were tested with simulated dilutions of 41 samples of juice, to assess the effectiveness of each for the detection of adulterations. Both models turned out to be equally effective, detecting adulterations starting from about 15 % of dilution.     

A Synergistic Approach towards Optimization of Coupled Cluster Amplitudes by Exploiting Dynamical Hierarchy

The coupled cluster iteration scheme for determining the cluster amplitudes involves a set of nonlinearly coupled difference equations. In the space spanned by the amplitudes, the set of equations are analyzed as a multivariate time-discrete map where the concept of time appears in an implicit manner. With the observation that the cluster amplitudes have difference in their relaxation timescales with respect to the distributions of their magnitudes, the coupled cluster iteration dynamics are considered as a synergistic motion of coexisting slow and fast relaxing modes, manifesting a dynamical hierarchical structure. With the identification of the highly damped auxiliary amplitudes, their time variation can be neglected compared to the principal amplitudes which take much longer time to reach the fixed points. We analytically establish the adiabatic approximation where each of these auxiliary amplitudes are expressed as unique parametric functions of the collective principal amplitudes, allowing us to study the optimization with the latter taken as the independent degrees of freedom. Such decoupling of the amplitudes significantly reduces the computational scaling without sacrificing the accuracy in the ground state energy as demonstrated by a number of challenging molecular applications. A road-map to treat higher order post-adiabatic effects is also discussed.     

Formation of dissipative structures upon homogenous oxidation of biosubstrata: Evaluation of dynamic characteristics and parameterization of time series

The possibility of formation of dissipative structures in the system consisting of biosubstrate and oxygenated iron (II) complexes is shown by the example of liquid-phase oxidation of cysteine. The results of evaluation of dynamic characteristics of the investigated processes (type of dynamics, dimensions of phase space and attractor, Lyapunov indicators, and the Kolmogorov-Sinai entropy) are given. Parameterization of the resulting time series was carried out using the approaches of flicker-noise spectroscopy.     

Effect of ligand binding on the intraminimum dynamics of proteins

Effects of ligand binding on protein dynamics are studied via molecular dynamics (MD) simulations on two different enzymes, dihydrofolate reductase (DHFR) and triosephosphate isomerase (TIM), in their unliganded (free) and liganded states. Domain motions in MD trajectories are analyzed by collectivities and rotation angles along the principal components (PCs). DHFR in the free state has well‐defined domain rotations, whereas rotations are slightly damped in the binary complex with nicotinamide adenine dinucleotide phosphate (NADPH), and remarkably distorted in the presence of NADP⁺, showing that NADP⁺ is solely responsible for the loss of correlation of the domains in DHFR. Although mean square fluctuations of MD simulations in the same PC subspaces are similar for different ligation states, linear stochastic time series models show that backbone flexibility along the first five PCs is decreased upon NADPH and NADP⁺ binding in subpicosecond scale. This shows that mobility of the protein along the PCs is closely related with intraminimum dynamics, and alterations in ligation states may change the intraminimum dynamics significantly. Low vibrational frequencies of the alpha‐carbon atoms of DHFR are determined from the time series models of a larger number of low indexed PCs, and it is found that number of modes in the lowest frequencies is reduced upon ligand binding. A similar result is obtained for TIM in the unliganded and dihydroxyacetone phosphate bound states. We suggest that stochastic time series modeling is a promising method to be used in determining subtle perturbations in protein dynamics. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Covariance nuclear magnetic resonance spectroscopy

Covariance nuclear magnetic resonance (NMR) spectroscopy is introduced, which is a new scheme for establishing nuclear spin correlations from NMR experiments. In this method correlated spin dynamics is directly displayed in terms of a covariance matrix of a series of one-dimensional (1D) spectra. In contrast to two-dimensional (2D) Fourier transform NMR, in a covariance spectrum the spectral resolution along the indirect dimension is determined by the favorable spectral resolution obtainable along the detection dimension, thereby reducing the time-consuming sampling requirement along the indirect dimension. The covariance method neither involves a second Fourier transformation nor does it require separate phase correction or apodization along the indirect dimension. The new scheme is demonstrated for cross-relaxation (NOESY) and J-coupling based magnetization transfer (TOCSY) experiments.     

Imaging fingerprinting of excitation emission matrices

The spectral fingerprinting of the excitation emission matrix (EEM) of fluorescent substances is demonstrated using polychromatic light sources and tri-chromatic image detectors. A model of the measured fingerprints explaining their features and classification performance, based on the polychromatic excitation of the indicators is proposed.Substantial amount of spectral information is retained in the fingerprints as corroborated by multivariate analysis and experimental conditions that favor such situation are identified.In average, for five different substances, the model shows a fitting goodness measured by the Pearson's r coefficient and the root mean square deviation of 0.8541 and 0.0247 respectively, while principal component classification patterns satisfactorily compare with the EEM spectroscopy classification and respectively explain 96% and 93% of the information in the fist two principal components.The measurements can be performed using regular computer screens as illumination and web cameras as detectors, which constitute ubiquitous and affordable platforms compatible with distributed evaluations, in contrast to regular instrumentation for EEM measurements.