Monte Carlo algorithm for least dependent non-negative mixture decomposition

We propose a simulated annealing algorithm (stochastic non-negative independent component analysis, SNICA) for blind decomposition of linear mixtures of non-negative sources with non-negative coefficients. The demixing is based on a Metropolis-type Monte Carlo search for least dependent components, with the mutual information between recovered components as a cost function and their non-negativity as a hard constraint. Elementary moves are shears in two-dimensional subspaces and rotations in three-dimensional subspaces. The algorithm is geared at decomposing signals whose probability densities peak at zero, the case typical in analytical spectroscopy and multivariate curve resolution. The decomposition performance on large samples of synthetic mixtures and experimental data is much better than that of traditional blind source separation methods based on principal component analysis (MILCA, FastICA, RADICAL) and chemometrics techniques (SIMPLISMA, ALS, BTEM).     

Molecular factor analysis applied to collections of NMR spectra

It is often useful to identify and quantify mixture components by analyzing collections of NMR spectra. Such collections arise in metabonomics and many other applications. Many mixtures studied by NMR can contain hundreds of compounds, and it is challenging to analyze the resulting complex spectra. We have approached the problem of separating signals from different molecules in complex mixtures by using self-modeling curve resolution as implemented by the alternating least-squares algorithm. Alternating least squares uses nonnegativity criteria to generate spectra and concentrations from a collection of mixture spectra. Compared to previous applications of alternating least squares, NMR spectra of complex mixtures possess unique features, such as large numbers of components and sample-to-sample variability in peak positions. To deal with these features, we developed a set of data preprocessing methods, and we made modifications to the alternating least-squares algorithm. We use the term "molecular factor analysis" to refer to the preprocessing and modified alternating least-squares methods. Molecular factor analysis was tested using an artificial data set and spectra from a metabonomics study. The results show that the tools can extract valuable information on sample composition from sets of NMR spectra.     

Deconvolution of chemical mixtures with high complexity by NMR consensus trace clustering

Identification and quantification of analytes in complex solution-state mixtures are critical procedures in many areas of chemistry, biology, and molecular medicine. Nuclear magnetic resonance (NMR) is a unique tool for this purpose providing a wealth of atomic-detail information without requiring extensive fractionation of the samples. We present three new multidimensional-NMR based approaches that are geared toward the analysis of mixtures with high complexity at natural (13)C abundance, including approaches that are encountered in metabolomics. Common to all three approaches is the concept of the extraction of one-dimensional (1D) consensus spectral traces or 2D consensus planes followed by clustering, which significantly improves the capability to identify mixture components that are affected by strong spectral overlap. The methods are demonstrated for covariance (1)H-(1)H TOCSY and (13)C-(1)H HSQC-TOCSY spectra and triple-rank correlation spectra constructed from pairs of (13)C-(1)H HSQC and (13)C-(1)H HSQC-TOCSY spectra. All methods are first demonstrated for an eight-compound metabolite model mixture before being applied to an extract from E. coli cell lysate.     

Resolution of multicomponent fluorescence emission using frequency-dependent phase angle and modulation spectra

We describe a new fluorescence method that allows the resolution of both the decay times and emission spectra of mixtures of fluorophores. This method is completely general and does not require any assumptions or knowledge of the decay times or emission spectra of the individual fluorophores. We use the phase angle spectra and modulation spectra of the mixture, measured over a range of suitable light modulation frequencies and emission wavelengths. These data are analyzed by nonlinear least-squares analysis to recover the emission spectra and the associated decay times. The principle of the method and the nature of the data are illustrated by using two-component mixtures with increasing spectral overlap. We then demonstrate the recovery of minor components, of structure emission spectra, and of a three-component mixture with completed overlapping emission spectra. And finally, we describe the resolution of a two-component mixture with decay times of 0.8 and 1.4 ns using modulation frequencies up to 774 MHz.     

Improved modelling of the loading spectra using a mixture model approach

In order to perform a fatigue-life analysis of structures the parameters of the structure loading spectra must be assessed. If the load time series are counted using a two-parametric rainflow counting method, the structure loading spectrum provides a probability for the occurrence of a load-cycle with certain amplitude and mean values. It is beneficial for the prediction of the fatigue life to describe the loading spectrum by a continuous function. We have previously discovered that mixtures of Gaussian probability density functions can be used to model the loading spectra. The main problems of this approach that have not been satisfactorily resolved before are related to the estimation of the number of components in the applied mixture models, and to the modelling of the load-cycle distributions with relatively fat tails. In this article, we describe a method for estimating the parameters of mixture models, which allows automatic determination of the number of components in a mixture model. The presented method is applied for modelling simulated and measured loading spectra using mixtures of the multivariate Gaussian or t probability density functions. In the article we also show that the mixture of t probability density functions sometimes better describes the loading spectra than the mixture of Gaussian probability density functions.     

A model for random sampling and estimation of relative protein abundance in shotgun proteomics

Proteomic analysis of complex protein mixtures using proteolytic digestion and liquid chromatography in combination with tandem mass spectrometry is a standard approach in biological studies. Data-dependent acquisition is used to automatically acquire tandem mass spectra of peptides eluting into the mass spectrometer. In more complicated mixtures, for example, whole cell lysates, data-dependent acquisition incompletely samples among the peptide ions present rather than acquiring tandem mass spectra for all ions available. We analyzed the sampling process and developed a statistical model to accurately predict the level of sampling expected for mixtures of a specific complexity. The model also predicts how many analyses are required for saturated sampling of a complex protein mixture. For a yeast-soluble cell lysate 10 analyses are required to reach a 95% saturation level on protein identifications based on our model. The statistical model also suggests a relationship between the level of sampling observed for a protein and the relative abundance of the protein in the mixture. We demonstrate a linear dynamic range over 2 orders of magnitude by using the number of spectra (spectral sampling) acquired for each protein.     

Study of complexation in methanol/water mixtures by infrared and Raman spectroscopy and multivariate curve resolution-alternating least-squares analysis

The structure of the mobile phase in liquid chromatography plays an important role in the determination of retention behavior on reversed-phase stationary materials. One of the most commonly employed mobile phases is a mixture of methanol and water. In this work, infrared and Raman spectroscopic methods were used to investigate the structure of species formed in methanol/water mixtures. Chemometric methods using multivariate curve resolution by alternating least-squares analysis were used to resolve the overlapped spectra and to determine concentration profiles as a function of composition. The results showed that the structure of these mixtures could be described by a mixture model consisting of four species, namely, methanol, water, and two complexes, methanol/water (1:1) and methanol/water (1:4). The spectral frequencies and concentration profiles found from the Raman and infrared measurements were consistent with one another and with theoretical calculations.     

Qualitative and semiquantitative analysis of composite mixtures of antibodies by native mass spectrometry

Native mass spectrometry was evaluated for the qualitative and semiquantitative analysis of composite mixtures of antibodies representing biopharmaceutical products coexpressed from single cells. We show that by using automated peak fitting of the ion signals in the native mass spectra, we can quantify the relative abundance of each of the antibodies present in mixtures, with an average accuracy of 3%, comparable to a cation exchange chromatography based approach performed in parallel. Moreover, using native mass spectrometry we were able to identify, separate, and quantify 9 antibodies present in a complex mixture of 10 antibodies, whereas this complexity could not be unraveled by cation exchange chromatography. Native mass spectrometry presents a valuable alternative to existing analytical methods for qualitative and semiquantitative profiling of biopharmaceutical products. It provides both the identity of each species in a mixture by mass determination and the relative abundance through comparison of relative ion signal intensities. Native mass spectrometry is a particularly effective tool for characterization of heterogeneous biopharmaceutical products such as bispecific antibodies and antibody mixtures.     

Indirect spectral hard modeling for the analysis of reactive and interacting mixtures

We present an indirect hard modeling (IHM) approach for the quantitative analysis of reactive multicomponent mixtures with intermolecular interaction. It can be used when it is not possible to obtain calibration data in the composition region of interest. The goal of this work, specifically, is to analyze reactive systems, although the validation of the method is done with nonreactive systems. Compared to conventional hard modeling, the new approach reduces the manual work required for modeling and renders unnecessary the assignment of bands in mixture spectra to individual components. It is based on parametric models of the pure component spectra that are made just flexible enough to fit the spectra of the unknown mixtures, and it only requires small calibration data sets that may lie in different regions of the composition space. The application to infrared (IR) and Raman spectra of multicomponent systems is discussed.     

Statistical correlation and projection methods for improved information recovery from diffusion-edited NMR spectra of biological samples

Although NMR spectroscopic techniques coupled with multivariate statistics can yield much useful information for classifying biological samples based on metabolic profiles, biomarker identification remains a time-consuming and complex procedure involving separation methods, two-dimensional NMR, and other spectroscopic tools. We present a new approach to aid complex biomixture analysis that combines diffusion ordered (DO) NMR spectroscopy with statistical total correlation spectroscopy (STOCSY) and demonstrate its application in the characterization of urinary biomarkers and enhanced information recovery from plasma NMR spectra. This method relies on calculation and display of the covariance of signal intensities from the various nuclei on the same molecule across a series of spectra collected under different pulsed field gradient conditions that differentially attenuate the signal intensities according to translational molecular diffusion rates. We term this statistical diffusion-ordered spectroscopy (S-DOSY). We also have developed a new visualization tool in which the apparent diffusion coefficients from DO spectra are projected onto a 1D NMR spectrum (diffusion-ordered projection spectroscopy, DOPY). Both methods either alone or in combination have the potential for general applications to any complex mixture analysis where the sample contains compounds with a range of diffusion coefficients.     

Targeted profiling: quantitative analysis of 1H NMR metabolomics data

Extracting meaningful information from complex spectroscopic data of metabolite mixtures is an area of active research in the emerging field of "metabolomics", which combines metabolism, spectroscopy, and multivariate statistical analysis (pattern recognition) methods. Chemometric analysis and comparison of 1H NMR1 spectra is commonly hampered by intersample peak position and line width variation due to matrix effects (pH, ionic strength, etc.). Here a novel method for mixture analysis is presented, defined as "targeted profiling". Individual NMR resonances of interest are mathematically modeled from pure compound spectra. This database is then interrogated to identify and quantify metabolites in complex spectra of mixtures, such as biofluids. The technique is validated against a traditional "spectral binning" analysis on the basis of sensitivity to water suppression (presaturation, NOESY-presaturation, WET, and CPMG), relaxation effects, and NMR spectral acquisition times (3, 4, 5, and 6 s/scan) using PCA pattern recognition analysis. In addition, a quantitative validation is performed against various metabolites at physiological concentrations (9 microM-8 mM). "Targeted profiling" is highly stable in PCA-based pattern recognition, insensitive to water suppression, relaxation times (within the ranges examined), and scaling factors; hence, direct comparison of data acquired under varying conditions is made possible. In particular, analysis of metabolites at low concentration and overlapping regions are well suited to this analysis. We discuss how targeted profiling can be applied for mixture analysis and examine the effect of various acquisition parameters on the accuracy of quantification.     

Sign constraints improve the detection of differences between complex spectral data sets: LC-IR as an example

Spectroscopy is a fast and rich analytical tool. On many occasions, spectra are acquired of two or more sets of samples that differ only slightly. These data sets then need to be compared and analyzed, but sometimes it is difficult to find the differences. We present a simple and effective method that detects and extracts new spectral features in a spectrum coming from one set with respect to spectra of another set on the basis of the fact that these new spectral features are essentially positive quantities. The proposed procedure (i) characterizes the spectra of the reference set by a component model and (ii) uses asymmetric least squares (ASLS) to find differences with respect to this component model. It should be stressed that the method only focuses on new features and does not trace relative changes of spectral features that occur in both sets of spectra. A comparison is made with the conventional ordinary least squares (OLS) approach. Both methods (OLS and ASLS) are illustrated with simulations and are tested for size-exclusion chromatography with infrared detection (SEC-IR) of mixtures of polymer standards. Both methods are able to provide information about new spectral features. It is shown that the ASLS-based procedure yields the best recovery of new features in the simulations and in the SEC-IR experiments. Band positions and band shapes of new spectral features are better retrieved with the ASLS than with the OLS method, even those which could hardly be detected visually. Depending on the spectroscopic technique used, the ASLS-based method facilitates identification of the new chemical compounds.     

ESTIMATION Of PARTICLE SIZE bY DRIFTS and FTIR-PAS

ABSTRACT

Diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) and Fourier transform infrared photoacoustic spectroscopy (FTIR-PAS) were used to study particle size and distribution of sucrose powder. Partial least squares (PLS) regression was used to correlate spectral data with particle size. FTIR-PAS spectra were similar to the spectra obtained using DRIFTS when the sample is mixed with 95% potassium bromide (KBr). Both DRIFTS and FTIR-PAS methods can successfully predict the mean panicle size and concentration in binary and quaternary mixtures. R-square values for both DRIFTS and FTIR-PAS are greater than 0.9.     

Charger: combination of signal processing and statistical learning algorithms for precursor charge-state determination from electron-transfer dissociation spectra

Tandem mass spectrometry in combination with liquid chromatography has emerged as a powerful tool for characterization of complex protein mixtures in a high-throughput manner. One of the bioinformatics challenges posed by the mass spectral data analysis is the determination of precursor charge when unit mass resolution is used for detecting fragment ions. The charge-state information is used to filter database sequences before they are correlated to experimental data. In the absence of the accurate charge state, several charge states are assumed. This dramatically increases database search times. To address this problem, we have developed an approach for charge-state determination of peptides from their tandem mass spectra obtained in fragmentations via electron-transfer dissociation (ETD) reactions. Protein analysis by ETD is thought to enhance the range of amino acid sequences that can be analyzed by mass spectrometry-based proteomics. One example is the improved capability to characterize phosphorylated peptides. Our approach to charge-state determination uses a combination of signal processing and statistical machine learning. The signal processing employs correlation and convolution analyses to determine precursor masses and charge states of peptides. We discuss applicability of these methods to spectra of different charge states. We note that in our applications correlation analysis outperforms the convolution in determining peptide charge states. The correlation analysis is best suited for spectra with prevalence of complementary ions. It is highly specific but is dependent on quality of spectra. The linear discriminant analysis (LDA) approach uses a number of other spectral features to predict charge states. We train LDA classifier on a set of manually curated spectral data from a mixture of proteins of known identity. There are over 5000 spectra in the training set. A number of features, pertinent to spectra of peptides obtained via ETD reactions, have been used in the training. The loading coefficients of LDA indicate the relative importance of different features for charge-state determination. We have applied our model to a test data set generated from a mixture of 49 proteins. We search the spectra with and without use of the charge-state determination. The charge-state determination helps to significantly save the database search times. We discuss the cost associated with the possible misclassification of charge states.     

Determination of enantiomeric excess using the ultraviolet-circular dichroism and the high-performance liquid chromatography-circular dichroism methods

Two useful numerical methods using ultraviolet (UV) and circular dichroism (CD) spectroscopies are proposed to determine enantiomeric excess (e.e). An algorithm is also proposed to generate self-consistent pure R and S enantiomer reference spectra. After all pure reference spectra are generated, a simulated annealing algorithm is applied to minimize the mismatch between the experimental spectra and the spectra after a least-squares fit. Optimal factors for R and S enantiomers are then used to determine e.e. The ultraviolet-circular dichroism (UV-CD) method uses the combined UV and CD spectra in a composite form, while the high-performance liquid chromatography (HPLC)-CD method only employs the CD spectra with the total concentrations of R plus S enantiomers provided by HPLC using a non-chiral stationary phase. Both methods were successfully tested on mixtures with known composition and then applied to real experimental data (unknown compositions). Compared with the UV-CD method, the results show that excellent results are more readily obtained using the HPLC-CD method. With the systems studied, the latter usually provided outstanding estimations of e.e with low error percentages.     

ESTIMATION Of PARTICLE SIZE bY DRIFTS and FTIR-PAS

Diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) and Fourier transform infrared photoacoustic spectroscopy (FTIR-PAS) were used to study particle size and distribution of sucrose powder. Partial least squares (PLS) regression was used to correlate spectral data with particle size. FTIR-PAS spectra were similar to the spectra obtained using DRIFTS when the sample is mixed with 95% potassium bromide (KBr). Both DRIFTS and FTIR-PAS methods can successfully predict the mean panicle size and concentration in binary and quaternary mixtures. R-square values for both DRIFTS and FTIR-PAS are greater than 0.9.     

Strategy for automated analysis of dynamic metabolic mixtures by NMR. Application to an insect venom

Elucidation of the composition of chemical-biological samples is a main focus of systems biology and metabolomics. Due to the inherent complexity of these mixtures, reliable, efficient, and potentially automatable methods are needed to identify the underlying metabolites and natural products. Because of its rich chemical information content, nuclear magnetic resonance (NMR) spectroscopy has a unique potential for this task. Here we present a generalization and application of a recently introduced NMR data collection, processing, and analysis strategy that circumvents the need for extensive purification and hyphenation prior to analysis. It uses covariance TOCSY NMR spectra measured on a 1-mm high-temperature cryogenic probe that are analyzed by a spectral trace clustering algorithm yielding 1D NMR spectra of the individual components for their unambiguous identification. The method is demonstrated on a metabolic model mixture and is then applied to the unpurified venom mixture of an individual walking stick insect that contains several slowly interconverting and closely related metabolites.     

Three-way analysis of fluorescence spectra of polycyclic aromatic hydrocarbons with quenching by nitromethane

The application of trilinear decomposition (TLD) to the analysis of fluorescence excitation-emission matrices of mixtures of polycyclic aromatic hydrocarbons (PAHs) is described. The variables constituting the third-order tensor are excitation wavelength, emission wavelength, and concentration of a fluorescence quencher (nitromethane). The addition of a quencher to PAH mixtures selectively reduces the fluorescence intensity of mixture components according to the Stern-Volmer equation. TLD allows the three-way matrix to be decomposed to give unique solutions for the excitation spectrum, emission spectrum, and quenching profiles for each component. The availability of spectra and calculated Stern-Volmer constants can aid in the identification of unknown components. Preprocessing of the data to correct for Rayleigh/Raman scatter and primary absorption by the quencher is necessary. Both three-component (anthracene, pyrene, 1-methylpyrene) and four-component (fluoranthene, anthracene, pyrene, 2,3-benzofluorene) synthetic mixtures are successfully resolved by TLD using quencher concentrations up to 100 mM. Results are compared using both alternating least-squares and direct trilinear decomposition algorithms. The reproducibility of extracted Stern-Volmer constants is determined from replicate experiments. To illustrate the application of TLD to a real sample, a chromatographic cut from the analysis of a light gas oil sample was used. Analysis of the TLD extracted spectra and quenching constants suggests the presence of three classes of polycyclic aromatic hydrocarbons consistent with data from a second dimension of chromatography and mass spectrometry.     

Attenuated total reflection infrared difference spectroscopy (ATR-IRDS) for quantitative reaction monitoring

Monitoring of chemical reactors is key to optimizing yield and efficiency of chemical transformation processes. Aside from tracking pressure and temperature, the measurement of the chemical composition is essential in this context. We present an infrared difference spectroscopy approach for determining the reactant (cyclooctene) and product (cyclooctane) concentrations during a catalytic hydrogenation reaction in the solvent cyclohexane, which is present in large excess. Subtracting the spectrum of the pure solvent from the reactor mixture spectra yields infrared (IR) spectra, which can ultimately be evaluated using a curve-fitting procedure based on spectral soft modeling. An important feature of our evaluation approach is that the calibration only requires recording the pure component spectra of the reactants, products, and solvent. Hence, no time-consuming preparation of mixtures for calibration is necessary. The IR concentration results are in good agreement with gas chromatography measurements.     

Vibration milling of TiB<Subscript>2</Subscript> + TiNi powder mixtures

We have studied how the duration of the vibration comilling of a 80 vol % TiB₂ + 20 vol % TiNi powder mixture influences the particle size, morphology, and fine-structure parameters of its components. At a milling time of 60 h, we obtained a mixture containing 27 vol % nanoparticles, in which the cubic TiNi phase had a crystallite size of 1.1 nm. We believe that vibration-milled TiB₂ + TiNi mixtures are potentially attractive for the fabrication of composite materials by powder metallurgy methods.