动力学体系二维数据的秩分析及其应用

详细论证了动力学体系中存在的多种共线性情况,以及在此情况下二维数据阵的秩与独立反应数及组分数的关系.分析了通过增秩这一方式来判断体系组分数的条件.讨论了反应间存在物质交换对数据阵秩的影响.建立起一套通过秩分析判断未知动力学体系中存在的反应组分数、独立反应数以及可能反应机理的方法.将秩分析技术应用到聚苯胺与质子酸反应,初步分析了该体系存在的多种吸光性结构及结构变化.确定了[H＋]=0.01～0.1 mol•L－1范围内,聚苯胺与质子酸反应存在一个三结构两步互变过程.     

Determination of rank by median absolute deviation (DRMAD): a simple method for determining the number of principal factors responsible for a data matrix

Median absolute deviation (MAD) is a well‐established statistical method for determining outliers. This simple statistic can be used to determine the number of principal factors responsible for a data matrix by direct application to the residual standard deviation (RSD) obtained from principal component analysis (PCA). Unlike many other popular methods the proposed method, called determination of rank by MAD (DRMAD), does not involve the use of pseudo degrees of freedom, pseudo F‐tests, extensive calibration tables, time‐consuming iterations, nor empirical procedures. The method does not require strict adherence to normal distributions of experimental uncertainties. The computations are direct, simple to use and extremely fast, ideally suitable for online data processing. The results obtained using various sets of chemical data previously reported in the chemical literature agree with the early work. Limitations of the method, determined from model data, are discussed. An algorithm, written in MATLAB format, is presented in the Appendix. Copyright © 2008 John Wiley & Sons, Ltd.     

Rank annihilation factor analysis for spectrophotometric study of complex formation equilibria

The use rank annihilation factor analysis (RAFA) for spectrophotometric studies of complex formation equilibria are proposed. One-step complex formation and two successive and mononuclear complex formation systems studied successfully by proposed methods. When the complex stability constant acts as an optimizing object, and simply combined with the pure spectrum of ligand, the rank of original data matrix can be reduced by one by annihilating the information of the ligand from the original data matrix. The residual standard deviation (R.S.D.) of the residual matrix after bilinearization of the background matrix is regarded as the evaluation function. The performance of the method has been evaluated by using synthetic data. For two-step successive complex formation systems, the effects of noise level and equilibrium constants K₁ and K₂ on output of algorithm are investigated. The applicability of method for resolving the two-step successive complex formation systems with full spectral overlapping of two complex species also is shown. Spectrophotometric studies of murexide-calcium, dithiazone-nickel and methyl thymol blue (MTB)-copper are used as experimental model systems with different complexation stoichiometries and spectral overlapping of involved components.     

Rank annihilation factor analysis for multicomponent kinetic‐spectrophotometric determination using difference spectra

In this work rank annihilation factor analysis (RAFA) is used to analyze difference spectra of kinetic‐spectrophotometric data. Annihilation of the contribution of one chemical component from the original data matrix is a general method in RAFA. However, sometimes RAFA is not suitable for studying rank deficient data such as kinetic‐spectrophotometric measurements. On the other hand, in order to apply RAFA for the determination of an analyte in an unknown sample, a standard two‐way matrix of the analyte with rank one should generally be available. This is not usually attainable for kinetic‐spectrophotometric monitoring of complexation reactions. Processes monitored by difference spectroscopy always have the spectrum of the initial stage subtracted from each spectrum in the data matrix. In this work we show that, for kinetic‐spectrophotometric data of complexation reactions, the spectrum of ligand (reactant) itself can be used as initial spectrum for subtraction. The obtained difference matrix of sample and that of analyte of interest will be full‐rank and rank 1, respectively. Therefore the system can be analyzed by RAFA. The proposed method was investigated with simulated data at the first stage. The method was then applied in the analysis of experimental kinetic‐spectrophotometric data of a complexation reactions of Co(II) and Ni(II) with chromogenic reagent 1‐(2‐pyridylazo) 2‐naphthol in order to do multi‐component determination of these ions in various real samples. Copyright © 2009 John Wiley & Sons, Ltd.     

Quantitative estimates of precision for molecular isotopic measurements.

At least three methods of calculating the random errors or variance of molecular isotopic data are presently in use. The major components of variance are differentiated and quantified here into least three to four individual components. The measurement of error of the analyte relative to a working (whether an internal or an external) standard is quantified via the statistical pooled estimate of error. A statistical method for calculating the total variance associated with the difference of two individual isotopic compositions from two isotope laboratories is given, including the variances of the laboratory (secondary) and working standards, as well as those of the analytes. An abbreviated method for estimation of of error typical for chromatographic/isotope mass spectrometric methods is also presented.     

Study of gas-liquid partitioning of alkane solutes in several organic solvents by using principal component analysis and linear solvation energy relationships

Principal component analysis (PCA) was used to extract the number of factors which can describe the 737 gas-liquid partition coefficients of five linear, four branched, and two cyclic alkanes in 67 common solvents. Based on the reconstruction of partition coefficient data matrix, we concluded that the experimental dataset could readily be reduced to two relevant factors. Using only these two factors, there were no errors larger than 3%, 7 cases had errors larger than 2%, and in 34 cases, errors were between 1 and 2%. n-Hexane and ethylcyclohexane were chosen as the test factors, and all other partition coefficients were expressed in terms of these two test factors. Prediction of the logarithmic partition coefficient of these alkanes in seven chemically different solvents, which were originally excluded from the data matrix, was excellent: the root mean square error was 0.064, only in 11 cases the errors were larger than 1%, and only 3 had errors larger than 4%.Linear solvation energy relationships (LSERs) using both theoretical and empirical solvent parameters were used to explain the molecular interactions responsible for partition. Several combinations of parameters were tried but the standard deviations were not less than 0.31. This could be attributed to the model itself, imprecisions in the data matrix or in some of the LSER parameters. Solvent cohesive parameters and surface tension in combination with polarity-polarizability or dispersion parameters perform the best.Finally, the two principal component factors were rotated onto the most relevant physicochemical parameters that control the gas-liquid partitioning phenomena.     

A novel strategy for solving matrix effect in three-way data using parallel profiles with linear dependencies

This work presents a novel strategy for solving matrix effects using the second-order advantage and a new method called PARAllel profiles with LINear Dependencies (PARALIND). PARALIND is a generalization of parallel factor analysis (PARAFAC) and was developed to extend its use to problems with linearly dependent factors where normal PARAFAC analysis will fail to provide meaningful results. Such linearly dependent factors occur in standard addition with second-order data such as fluorescence excitation emission matrices (EEM). By successive standard addition of an analyte, the concentrations of the remaining components (interferences) remain constant and introduce linear dependency between interference concentrations in the samples. This theoretically leads to rank deficiency in the score matrix holding the relative concentrations when using PARAFAC for modeling. In practice, PARAFAC models of such data will mostly provide solutions where the score matrix is not rank deficient but a function of the noise in the data. This problem is shown to be solved by using PARALIND. In order to evaluate the applicability of the method a simulated as well as an experimental data set is tested. The results from experimental data relate to the direct determination of salicylic acid (SA), the main product of aspirin degradation, in undiluted human plasma by spectrofluorimetry.     

A software for the estimation of binding parameters of biochemical equilibria based on statistical probability model

An algorithm is proposed for the estimation of binding parameters for the interaction of biologically important macromolecules with smaller ones from electrometric titration data. The mathematical model is based on the representation of equilibria in terms of probability concepts of statistical molecular thermodynamics. The refinement of equilibrium concentrations of the components and estimation of binding parameters (log site constant and cooperativity factor) is performed using singular value decomposition, a chemometric technique which overcomes the general obstacles due to near singularity. The present software is validated with a number of biochemical systems of varying number of sites and cooperativity factors. The effect of random errors of realistic magnitude in experimental data is studied using the simulated primary data for some typical systems. The safe area within which approximate binding parameters ensure convergence has been reported for the non-self starting optimization algorithms.     

阻尼最小二乘－分光光度法用于多组分分析

基于阻尼最小二乘法原理改进ＣＰＡ法。在确定Ｐ系数矩阵时引入阻尼因子从而降低其病态程度即对偶然实验误差的敏感程度。此法用于多组分分析，如测定复合维生素Ｂ结果良好。     

Application of cause-and-effect diagrams to the interpretation of UV-Vis spectroscopic data

The application of cause-and-effect diagrams to the evaluation of thermodynamic data from UV-Vis absorption spectroscopic analysis is demonstrated. The contributions of measurement uncertainty identified from a cause-and-effect diagram are implemented into a Monte Carlo procedure based on the threshold bootstrap computer-assisted target factor analysis (TB CAT). This algorithm aims at an improvement of data comparability and accounts for non-normality, spectral, residual and parameter correlation as well as random noise in target factor analysis. The ISO Type-B measurement uncertainties are included into the process by normally distributed random numbers with specified mean values and dispersions. The TB CAT procedure is illustrated by a flow diagram and a case study of Nd(III) complexation by picolinic acid N-oxide (pic NO) in aqueous solution. Using 12 experimental spectra as input data, the single component spectra and the formation constant 1g betaML of the Nd(pic NO)2+ species are obtained together with the respective probability density distributions. The role of the cause-and-effects approach on the further development of chemical thermodynamics is discussed.     

Sequence-dependent correction of random coil NMR chemical shifts.

Random coil chemical shifts are commonly used to detect secondary structure elements in proteins in chemical shift index calculations. While this technique is very reliable for folded proteins, application to unfolded proteins reveals significant deviations from measured random coil shifts for certain nuclei. While some of these deviations can be ascribed to residual structure in the unfolded protein, others are clearly caused by local sequence effects. In particular, the amide nitrogen, amide proton, and carbonyl carbon chemical shifts are highly sensitive to the local amino acid sequence. We present a detailed, quantitative analysis of the effect of the 20 naturally occurring amino acids on the random coil shifts of (15)N(H), (1)H(N), and (13)CO resonances of neighboring residues, utilizing complete resonance assignments for a set of five-residue peptides Ac-G-G-X-G-G-NH(2). The work includes a validation of the concepts used to derive sequence-dependent correction factors for random coil chemical shifts, and a comprehensive tabulation of sequence-dependent correction factors that can be applied for amino acids up to two residues from a given position. This new set of correction factors will have important applications to folded proteins as well as to short, unstructured peptides and unfolded proteins.     

Estimating the chemical rank of three-way data arrays by a simple linear transform incorporating Monte Carlo simulation

Estimating an appropriate chemical rank of a three-way data array is very important to second-order calibration. In this paper, a simple linear transform incorporating Monte Carlo simulation approach (LTMC) to estimate the chemical rank of a three-way data array was suggested. The new method determines the chemical rank through performing a simple linear transform procedure on the original cube matrix to produce two subspaces by singular value decomposition. One of two subspaces is derived from the original three-way data array itself and the other is derived from a new three-way data array produced by the linear transformation of the original one. Projection technique incorporating the Monte Carlo approach acts as distinguishing criterion to choose the appropriate component number of the system. Simulated three-way trilinear data arrays with different noise types (homoscedastic and heteroscedastic), various noise level as well as high collinearity are used to illustrate the feasibility of the new method. The results have shown that the new method could yield accurate results with different conditions appended. The feasibility of the new method is also confirmed by two real arrays, HPLC-DAD data and excitation-emission fluorescent data. All the results are compared with the other three factor-determining methods: factor indicator function (IND), core consistency diagnostic (CORCONDIA) and two-mode subspace comparison (TMSC) approach. It shows that the newly proposed algorithm can objectively and quickly determine the chemical rank to fit the trilinear model.     

Multivariate standard addition method solved by net analyte signal calculation and rank annihilation factor analysis

This article describes the use of the net analyte signal (NAS) concept and rank annihilation factor analysis (RAFA) for building two different multivariate standard addition models called “SANAS” and “SARAF.” In the former, by the definition of a new subspace, the NAS vector of the analyte of interest in an unknown sample as well as the NAS vectors of samples spiked with various amounts of the standard solutions are calculated and then their Euclidean norms are plotted against the concentration of added standard. In this way, a simple linear standard addition graph similar to that in univariate calibration is obtained, from which the concentration of the analyte in the unknown sample and the analytical figures of merit are readily calculated. In the SARAF method, the concentration of the analyte in the unknown sample is varied iteratively until the contribution of the analyte in the response data matrix is completely annihilated. The proposed methods were evaluated by analyzing simulated absorbance data as well as by the analysis of two indicators in synthetic matrices as experimental data. The resultant predicted concentrations of unknown samples showed that the SANAS and SARAF methods both produced accurate results with relative errors of prediction lower than 5% in most cases.     

A new approach to the prediction of RP-HPLC retention times in gradient elution from isocratic data

Summary A general chromatographic model has been set up starting from a set of equations based on the concept of the velocity of a solute along the column. The composition of the mobile phase is taken into account solely as a numerical factor entering into suitable equations and totally independent of the chemical-properties of the constituents. A few isocratic experimental runs are necessary as input data, and subsequently a small amount of computational effort is sufficient to make predictions of retention times under gradient elution conditions for solutes of whatever chemical structure. The prediction errors are dependent on the steepness of the linear gradient chosen but are, in any case, acceptably low.     

Using Self-referencing Interlaced Submatrices to Determine the Number of Chemical Species in a Mixture

Determining the number of chemical species is the first step in analyses of a chemical or biological system. A novel method is proposed to address this issue by taking advantage of frequency differences between chemical information and noise. Two interlaced submatrices were obtained by downsampling an original data spectra matrix in an interlacing manner. The two interlaced submatrices contained similar chemical information but different noise levels. The number of relevant chemical species was determined through pairwise comparisons of principal components obtained by principal component analysis of the two interlaced submatrices. The proposed method, referred to as SRISM, uses two self-referencing interlaced submatrices to make the determination. SRISM was able to selectively distinguish relevant chemical species from various types of interference factors such as signal overlapping, minor components and noise in simulated datasets. Its performance was further validated using experimental datasets that contained high-levels of instrument aberrations, signal overlapping and collinearity. SRISM was also applied to infrared spectral data obtained from atmospheric monitoring. It has great potential for overcoming various types of interference factor. This method is mathematically rigorous, computationally efficient, and readily automated.     

基于化学子空间对线性变换稳定的秩估计方法

提出了一个新的化学计量学方法,即线性变换下稳定的化学子空间法,用于二维数据的化学秩估计.该方法的基本思想是具有化学意义的子空间对在一个方向上的二维数据的线性变换是最稳定的.据此,两个新的定量指标投影残差法和子空间夹角法被提出用于衡量两个子空间之间的差异性.对两个近红外数据的分析结果表明,这一方法为二维数据的化学秩估计提供了一个很有价值的工具.     

Use of factor analysis and liquid chromatography to determine the number of species in reactions of potassium ions with selected polyethers

Abstract factor analysis is used to determine the number of species in chemical systems from data obtained by high-performance liquid chromatography. Retention data for the systems involving the reaction between potassium ions and three polyethers, benzo-5-crown-5, dibenzo-18-crown-6, and dibenzo-24-crown-8, were obtained in methanol at room temperature. The experimental data were factor-analyzed in order to yield the number of species in the reacting system. In addition to the usual criteria, it is proposed that tree-dimensional graphs of calculated data be compared to three-dimensional graphs of raw data in order to evaluate the factor space. It is also suggested that the three-dimensional graphs showing the residual error matrix be examined as a tool in the evaluation of the factor space. Two species were found from the reaction between benzo-15-crown-5 and potassium, one from dibenzo-18-crown-6-, and there from dibenzo-24-crown-8 in methanol.     

Multiple alignment tensors from a denatured protein

The structural content of the denatured state has yet to be fully characterized. In recent years, large residual dipolar couplings (RDCs) from denatured proteins have been observed under alignment conditions produced by bicelles and strained polyacrylamide gels. In this report, we describe efforts to extend our picture of the residual structure in denatured nuclease by measuring RDCs with multiple alignment tensors. Backbone amide 15N-1H RDCs were collected from 4 M urea for a total of eight RDC data sets. The RDCs were analyzed by singular value decomposition (SVD) to determine the number of independent alignment tensors present in the data. On the basis of the resultant singular values and propagated error estimates, it is clear that there are at least three independent alignment tensors. These three independent RDC datasets can be reconstituted as orthogonal linear combinations, (OLC)-RDC datasets, of the eight actually recorded. The first, second, and third OLC-RDC datasets are highly robust to the removal of any single experimental RDC dataset, establishing the presence of three independent alignment tensors, sampled well above the level of experimental uncertainty. The observation that the RDC data span three or more dimensions of the five-dimensional parameter space demonstrates that the ensemble average structure of denatured nuclease must be asymmetric with respect to these three orthogonal principal axes, which is not inconsistent with earlier work demonstrating that it has a nativelike topology.     

Multi-wavelength spectrophotometric determination of the protolytic constants of tetracycline hydrochloride in some nonaqueous-water mixed solvents: a solvatochromism study

Annihilation of the contribution of one chemical component from the original data matrix is a general method in rank annihilation factor analysis (RAFA). However, RAFA is not applicable for studying the protonation equilibria of multiprotic acids but in this study two-rank annihilation factor analysis (TRAFA) was used as an efficient chemometrics algorithm for determination of the protolytic constants (pKa) of tetracycline hydrochloride (TCHC) in some nonaqueous-water mixed solvents such as acetonitrile (AN)-water and methanol (MeOH)-water from the spectral pH-absorbance data. The spectral data was obtained from spectrophotometric acid-base titrations of different solutions of TCHC at (25.0±0.10)°C and an ionic strength of 0.10 M. In TRAFA algorithm the pKa values were obtained with relationship between residual standard deviation (R.S.D.) and hypothetical pKa values. In the case of TCHC, the spectra were divided in two consecutive subdivisions according to their pH range having two pKa and TRAFA was run twice. The validity of the obtained pKa values was checked with well-known chemometrics algorithms such as DATAN, EQUSPEC, SPECFIT/32 and SQUAD. The effects of changing solvent composition on the protolytic constants were explained by linear solvation energy relationships (LSER) utilizing solvatochromic parameters.