A new method for the authentication of plant samples by analyzing fingerprint chromatograms

Chemical analysis by high-performance liquid chromatography or capillary electrophoresis of plant pulverized samples, juices or extracts is an excellent method for the authentication of medicinal plant species and their products, particularly when morphological authentication is not possible. In the conventional procedure, chromatograms are integrated and the heights or areas of several peaks are used in a supervised pattern recognition method to confirm the authenticity of the product. We propose a new section approach in analysing chromatograms, where chromatograms are split into sections, which are described by four variables (number of peaks in the section, average retention time of peaks in the section, total area of peaks in the section and average area of peaks in the section), and these variables are then used in statistical analysis. The method is especially useful when the peaks on the chromatogram are not well separated and it is not easy to link individual peaks on one chromatogram with corresponding peaks on other chromatograms. In comparison with the standard procedure, our approach in analyzing chromatographic data of willow-herb (Epilobium and Chamaenerion spp.) extracts was more objective, gave better results and was also easier to perform.     

Interactive feature finding in liquid chromatography mass spectrometry data

We propose a method for finding features in liquid chromatography mass spectrometry data that is based on the isotopic pattern of peaks. Our interactive approach to feature finding is carried out across many samples simultaneously and aligns features concurrently. Our scale-independent approach prioritises potential features and is easily adaptable to look for features of a particular mass and charge, paired features in isotopically labeled samples, or differentially expressed features. We demonstrate this by identifying features from normal human adult plasma. We highlight properties of plasma data that illustrate the need to visually check the quality of features found prior to further statistical analysis.     

Stochastic processes defining sensitivity and variability of internally calibrated quantitative NASBA-based viral load assays

For quantitative assessment of virus particles in patient plasma samples various assays are commercially available. Typical performance characteristics for such assays are sensitivity, precision and the range of linearity. In order to assess these properties it is common practice to divide the range of inputs into subranges in order to apply different statistical models to evaluate these properties separately. We developed a general statistical model for internally calibrated amplification based viral load assays that combines these statistical properties in one powerful analysis. Based on the model an unambiguous definition of the lower limit of the linear range can be given. The proposed method of analysis was illustrated by a successful application to data generated by the NucliSens EasyQ HIV-1 assay.     

An empirical approach to the statistical analysis of mutagenesis data from the Salmonella test

A number of recent papers have suggested basing the statistical analysis of Salmonella (Ames) mutagenicity test results on a mathematical model of the complete dose-response curve. For most mutagens at low doses the curve increases linearly; then, as the dose increases, the curve may flatten and finally turn downwards due primarily to effects of toxicity. The exact mechanism underlying this shape is, however, not well understood and is likely to vary for different chemicals. A different approach is to assume that the initial part of the curve is linear and to base the statistical analysis solely on this region, reasoning that it contains most of the interpretable information about the mutagenesis dose response. In this paper a formal method of deciding which points are on the initial linear part of the curve is described, and a statistical method is proposed for analyzing these points. Computer simulations are used to examine the properties of the procedure and comparisons are made with a previously proposed mathematical model of the whole curve. It is concluded that the method suggested here provides a very satisfactory, robust method for the standard analysis of Salmonella data.     

Analysis of time-resolved fluorescence anisotropy decays.

We discuss the analysis of time-correlated single photon counting measurements of fluorescence anisotropy. Particular attention was paid to the statistical properties of the data. The methods used previously to analyze these experiments were examined and a new method was proposed in which parallel- and perpendicular-polarized fluorescence curves were fit simultaneously. The new method takes full advantage of the statistical properties of the measured curves; and, in some cases, it is shown to be more sensitive than other methods to systematic errors present in the data. Examples were presented using experimental and simulated data. The influence of fitting range on extracted parameters and statistical criteria for evaluating the quality of fits are also discussed.     

Superstatistics analysis of the ion current distribution function: Met3PbCl influence study

A novel analysis of ion current time series is proposed. It is shown that higher (second, third and fourth) statistical moments of the ion current probability distribution function (PDF) can yield new information about ion channel properties. The method is illustrated on a two-state model where the PDF of the compound states are given by normal distributions. The proposed method was applied to the analysis of the SV cation channels of vacuolar membrane of Beta vulgaris and the influence of trimethyllead chloride (Met₃PbCl) on the ion current probability distribution. Ion currents were measured by patch-clamp technique. It was shown that Met₃PbCl influences the variance of the open-state ion current but does not alter the PDF of the closed-state ion current. Incorporation of higher statistical moments into the standard investigation of ion channel properties is proposed.     

Improved model-based, platform-independent feature extraction for mass spectrometry

MOTIVATION: Mass spectrometry (MS) is increasingly being used for biomedical research. The typical analysis of MS data consists of several steps. Feature extraction is a crucial step since subsequent analyses are performed only on the detected features. Current methodologies applied to low-resolution MS, in which features are peaks or wavelet functions, are parameter-sensitive and inaccurate in the sense that peaks and wavelet functions do not directly correspond to the underlying molecules under observation. In high-resolution MS, the model-based approach is more appealing as it can provide a better representation of the MS signals by incorporating information about peak shapes and isotopic distributions. Current model-based techniques are computationally expensive; various algorithms have been proposed to improve the computational efficiency of this paradigm. However, these methods cannot deal well with overlapping features, especially when they are merged to create one broad peak. In addition, no method has been proven to perform well across different MS platforms. RESULTS: We suggest a new model-based approach to feature extraction in which spectra are decomposed into a mixture of distributions derived from peptide models. By incorporating kernel-based smoothing and perceptual similarity for matching distributions, our statistical framework improves existing methodologies in terms of computational efficiency and the accuracy of the results. Our model is parameterized by physical properties and is therefore applicable to different MS instruments and settings. We validate our approach on simulated data, and show that the performance is higher than commonly used tools on real high- and low-resolution MS, and MS/MS data sets.     

A general Bayesian method for an automated signal class recognition in 2D NMR spectra combined with a multivariate discriminant analysis

Summary A generally applicable method for the automated classification of 2D NMR peaks has been developed, based on a Bayesian approach coupled to a multivariate linear discriminant analysis of the data. The method can separate true NMR signals from noise signals, solvent stripes and artefact signals. The analysis relies on the assumption that the different signal classes have different distributions of specific properties such as line shapes, line widths and intensities. As to be expected, the correlation network of the distributions of the selected properties affects the choice of the discriminant function and the final selection of signal properties. The classification rule for the signal classes was deduced from Bayes's theorem. The method was successfully tested on a NOESY spectrum of HPr protein from Staphylococcus aureus. The calculated probabilities for the different signal class memberships are realistic and reliable, with a high efficiency of discrimination between peaks that are true NOE signals and those that are not.     

Peak quantification in surface-enhanced laser desorption/ionization by using mixture models

Surface-enhanced laser desorption/ionization (SELDI) time of flight (TOF) is a mass spectrometry technology for measuring the composition of a sampled protein mixture. A mass spectrum contains peaks corresponding to proteins in the sample. The peak areas are proportional to the measured concentrations of the corresponding proteins. Quantifying peak areas is difficult for existing methods because peak shapes are not constant across a spectrum and because peaks often overlap. We present a new method for quantifying peak areas. Our method decomposes a spectrum into peaks and a baseline using so-called statistical finite mixture models. We illustrate our method in detail on 8 samples from culture media of adipose tissue and globally on 64 samples from serum to compare our method to the standard Ciphergen method. Both methods give similar estimates for singleton peaks, but not for overlapping peaks. The Ciphergen method overestimates the heights of such peaks while our method still gives appropriate estimates. Peak quantification is an important step in pre-processing SELDI-TOF data and improvements therein will pay off in the later biomarker discovery phase.     

2D NMR metabonomic analysis: a novel method for automated peak alignment

MOTIVATION: Comparative metabolic profiling by nuclear magnetic resonance (NMR) is showing increasing promise for identifying inter-individual differences to drug response. Two dimensional (2D) (1)H (13)C NMR can reduce spectral overlap, a common problem of 1D (1)H NMR. However, the peak alignment tools for 1D NMR spectra are not well suited for 2D NMR. An automated and statistically robust method for aligning 2D NMR peaks is required to enable comparative metabonomic analysis using 2D NMR. RESULTS: A novel statistical method was developed to align NMR peaks that represent the same chemical groups across multiple 2D NMR spectra. The degree of local pattern match among peaks in different spectra is assessed using a similarity measure, and a heuristic algorithm maximizes the similarity measure for peaks across the whole spectrum. This peak alignment method was used to align peaks in 2D NMR spectra of endogenous metabolites in liver extracts obtained from four inbred mouse strains in the study of acetaminophen-induced liver toxicity. This automated alignment method was validated by manual examination of the top 50 peaks as ranked by signal intensity. Manual inspection of 1872 peaks in 39 different spectra demonstrated that the automated algorithm correctly aligned 1810 (96.7%) peaks. AVAILABILITY: Algorithm is available upon request.     

The use of the Mexican Hat and the Morlet wavelets for detection of ecological patterns

In this paper, we compare the relationship between scale and period in ecological pattern analysis and wavelet analysis. We also adapt a commonly used wavelet, the Morlet, to ecological pattern analysis. Using Monte Carlo assessments, we apply methods of statistical significance test to wavelet analysis for pattern analysis. In order to understand the inherent strength and weakness of the Morlet and the Mexican Hat wavelets, we also investigate and compare the properties of two frequently used wavelets by testing with field data and four artificial transects of different typical patterns which is often encountered in ecological research. It is shown that the Mexican Hat provides better detection and localization of patch and gap events over the Morlet, whereas the Morlet offers improved detection and localization of scale over the Mexican Hat. There is always a trade-off between the detection and localization of scale versus patch and gap events. Therefore, the best composite analysis is the combination of their advantages. The properties of wavelet in dealing with ecological data may be affected by characteristics intrinsic to wavelet itself. The peaks of different scales in isograms of wavelet power spectrum from the Mexican Hat may overlap with each other. Alternatively, these peaks of different scales in isograms of wavelet power spectrum may combine with each other unless the size of the analyzed scales is significantly different. These overlapping or combining lead to combining of peaks for different scales, or the masking of trough between peaks of different scales in the scalogram. Ecologists should combine all the information in scalogram and isograms of wavelet coefficient and wavelet power spectrum from different wavelets, which can provide us a broader view and precise pattern information.     

Detection and separation of heterogeneity in molecular complexes by statistical analysis of their two-dimensional projections

Progress in molecular structure determination by cryo electron microscopy and single particle analysis has led to improvements in the resolution achievable. However, in many cases the limiting factor is structural heterogeneity of the sample. To address this problem, we have developed a method based on statistical analysis of the two-dimensional images to detect and sort localised structural variations caused, for example, by variable occupancy of a ligand. Images are sorted by two consecutive stages of multivariate statistical analysis (MSA) to dissect out the two main sources of variation, namely out of plane orientation and local structural changes. Heterogeneity caused by local changes is detected by MSA that reveals significant peaks in the higher order eigenimages. The eigenimages revealing local peaks are used for automated classification. Evaluation of differences between classes allows discrimination of molecular images with and without ligand. This method is very rapid, independent of any initial three-dimensional model, and can detect even minor subpopulations in an image ensemble. A strategy for using this technique was developed on model data sets. Here, we demonstrate the successful application of this method to both model and real EM data on chaperonin-substrate and ribosome-ligand complexes.     

Combined experimental and statistical strategy for mass spectrometry based serum protein profiling for diagnosis of breast cancer: a case-control study

Serum protein profiling by mass spectrometry is a promising method for early detection of cancer. We have implemented a combined strategy based on matrix-assisted laser desorption ionization mass spectrometry (MALDI MS) and statistical data analysis for serum protein profiling and applied it in a well-described breast cancer case-control study. A rigorous sample collection protocol ensured high quality specimen and reduced bias from preanalytical factors. Preoperative serum samples obtained from 48 breast cancer patients and 28 controls were used to generate MALDI MS protein profiles. A total of nine mass spectrometric protein profiles were obtained for each serum sample. A total of 533 common peaks were defined and represented a 'reference protein profile'. Among these 533 common peaks, we identified 72 peaks exhibiting statistically significant intensity differences ( p < 0.01) between cases and controls. A diagnostic rule based on these 72 mass values was constructed and exhibited a cross-validated sensitivity and specificity of approximately 85% for the detection of breast cancer. With this method, it was possible to distinguish early stage cancers from controls without major loss of sensitivity and specificity. We conclude that optimized serum sample handling and mass spectrometry data acquisition strategies in combination with statistical analysis provide a viable platform for serum protein profiling in cancer diagnosis.     

Simultaneous and exact interval estimates for the contrast of two groups based on an extremely high dimensional variable: application to mass spec data

MOTIVATION: Analysis of high-throughput proteomic/genomic data, in particular, surface-enhanced laser desorption/ionization time-of-flight mass spectrometry (SELDI-TOF MS) data and microarray data, has led to a multitude of techniques aimed at identifying potential biomarkers. Most of the statistical techniques for comparing two groups are based on qualitative measures such as P-value. A quantitative way such as interval estimation for the contrasts of two groups is more appealing. RESULTS: We have devised a simultaneous confidence bands method capable of detecting potential biomarkers, while controlling for overall confidence coverage level, in high-dimensional datasets that discriminate two treatment groups using a permutation scheme. For example, for the SELDI-TOF MS data, we deal with the entire spectrum simultaneously and construct (1 - alpha) confidence bands for the mean differences between groups. Furthermore, peaks were identified based on the maximal differences between the groups as determined by the confidence bands. The analysis method herein described gives both qualitative (P-value) and quantitative data (magnitude of difference). The Clinical Proteomics Programs Databank's ovarian cancer dataset and data from in-house samples containing known spiked-in proteins were analyzed. We were able to identify potential biomarkers similar to those described in previous analysis of the ovarian cancer data, however, while these markers are highly significant between cancer and normal groups, our analysis indicated the absolute difference between the two groups was minimal. In addition, we found additional markers than those previously described with greater differences in average intensities. The proposed confidence bands method successfully detected the spiked-in peaks, as well as, secondary peaks generated by adducts and double-charged species. We also illustrate our method utilizing paired gene expression data from a prostate cancer microarray experiment by constructing confidence bands for the fold changes between cancer and normal samples. AVAILABILITY: R-package, 'seie.zip' (license: GNU GPL), is publiclly available at http://research2.dfci.harvard.edu/dfci/MS_spike-in_data/     

Analysis of comparative data using generalized estimating equations

It is widely acknowledged that the analysis of comparative data from related species should be performed taking into account their phylogenetic relationships. We introduce a new method, based on the use of generalized estimating equations (GEE), for the analysis of comparative data. The principle is to incorporate, in the modelling process, a correlation matrix that specifies the dependence among observations. This matrix is obtained from the phylogenetic tree of the studied species. Using this approach, a variety of distributions (discrete or continuous) can be analysed using a generalized linear modelling framework, phylogenies with multichotomies can be analysed, and there is no need to estimate ancestral character state. A simulation study showed that the proposed approach has good statistical properties with a type-I error rate close to the nominal 5%, and statistical power to detect correlated evolution between two characters which increases with the strength of the correlation. The proposed approach performs well for the analysis of discrete characters. We illustrate our approach with some data on macro-ecological correlates in birds. Some extensions of the use of GEE are discussed.     

Multivariate Dimensionality Reduction Approaches to Identify Gene-Gene and Gene-Environment Interactions Underlying Multiple Complex Traits

The elusive but ubiquitous multifactor interactions represent a stumbling block that urgently needs to be removed in searching for determinants involved in human complex diseases. The dimensionality reduction approaches are a promising tool for this task. Many complex diseases exhibit composite syndromes required to be measured in a cluster of clinical traits with varying correlations and/or are inherently longitudinal in nature (changing over time and measured dynamically at multiple time points). A multivariate approach for detecting interactions is thus greatly needed on the purposes of handling a multifaceted phenotype and longitudinal data, as well as improving statistical power for multiple significance testing via a two-stage testing procedure that involves a multivariate analysis for grouped phenotypes followed by univariate analysis for the phenotypes in the significant group(s). In this article, we propose a multivariate extension of generalized multifactor dimensionality reduction (GMDR) based on multivariate generalized linear, multivariate quasi-likelihood and generalized estimating equations models. Simulations and real data analysis for the cohort from the Study of Addiction: Genetics and Environment are performed to investigate the properties and performance of the proposed method, as compared with the univariate method. The results suggest that the proposed multivariate GMDR substantially boosts statistical power.     

Integrating overlapping structures and background information of words significantly improves biological sequence comparison

Word-based models have achieved promising results in sequence comparison. However, as the important statistical properties of words in biological sequence, how to use the overlapping structures and background information of the words to improve sequence comparison is still a problem. This paper proposed a new statistical method that integrates the overlapping structures and the background information of the words in biological sequences. To assess the effectiveness of this integration for sequence comparison, two sets of evaluation experiments were taken to test the proposed model. The first one, performed via receiver operating curve analysis, is the application of proposed method in discrimination between functionally related regulatory sequences and unrelated sequences, intron and exon. The second experiment is to evaluate the performance of the proposed method with f-measure for clustering Hepatitis E virus genotypes. It was demonstrated that the proposed method integrating the overlapping structures and the background information of words significantly improves biological sequence comparison and outperforms the existing models.     

Application of Taylor''s hypothesis to an unsteady convective field for the spectral analysis of turbulence in the aorta

Two types of unsteadiness must be considered when spectral analysis is applied to unsteady turbulence such as that found in the aorta. Firstly, the statistical properties of the turbulence itself change in time and so the definition of spectral density must be reconsidered. Secondly, the turbulent velocity fluctuations, whether they are steady or unsteady, are carried by an unsteady convective velocity which alters their properties as seen by a stationary observer.

In the present study, unsteadiness of turbulence in the latter sense is discussed by applying Taylor's hypothesis of ‘frozen turbulence’ to turbulence with an unsteady convective velocity. If both a ‘frozen’ pattern of turbulence and a constant convective velocity are assumed, measured frequency spectra can be easily transformed into wavenumber (spatial) spectra, usually as a trivial part of normalisation. In the case of unsteady turbulence, however, the convection velocity is no longer constant and the conventional method can not be used. A new method of estimating the spatial properties of unsteady turbulence is proposed in which the temporal fluctuations of the turbulent velocity are transformed into spatial fluctuations using a nonlinear transformation based upon the unsteady convective velocity. The transformed data are then Fourier analysed to yield a wavenumber spectrum directly.

The proposed method is applied to data obtained in the canine ascending aorta. Spectra calculated by the proposed method differ significantly from those obtained by the conventional method, particularly in the high wavenumber (or frequency) range. This difference is discussed as an ‘aliasing’ phenomenon that has also been known in steady turbulence.     

Determination of cross relaxation rates by 3D NOE-NOE spectroscopy

Summary A method for quantitative determination of cross-relaxation rates of macromolecules in solution is developed. The method is based on the analysis of the intensities of cross peaks in 3D NOE-NOE spectra. The linear combination of the intensities of 3D peaks (spin-diffusion peaks, back-transfer peaks) results in an expression directly proportional to the cross-relaxation rate. The proposed approach allows to determine interproton distances in macromolecules more accurately.     

Size distribution of submicron particles by dynamic light scattering measurements: analyses considering normalization errors

Errors in the experimental baseline used to normalize dynamic light scattering data can seriously affect the size distribution resulting from the data analysis. A revised method, which incorporates the characteristics of this error into the size distribution algorithm CONTIN (Ruf 1989), is tested with experimental data of high statistical accuracy obtained from a sample of phospholipid vesicles. It is shown that the various commonly used ways of accumulating and normalizing dynamic light scattering data are associated with rather different normalization errors. As a consequence a variety of solutions differing in modality, as well as in width, are obtained on carrying out data analysis in the common way. It is demonstrated that a single monomodal solution is retrieved from all these data sets when the new method is applied, which in addition provides the corresponding baseline errors quantitatively. Furthermore, stable solutions are obtainable with data of lower statistical accuracy which results from measurements of shorter duration. The use of an additional parameter in data inversion reduces the occurrence of spurious peaks. This stabilizing effect is accompanied by larger uncertainties in the width of the size distribution. It is demonstrated that these uncertainties are reduced by nearly a factor of two on using the normalization error function instead of the ‘dust term’ option for the analysis of noisy data sets.