Principal components of functional connectivity: A new approach to study dynamic brain connectivity during rest.

Functional connectivity (FC) as measured by correlation between fMRI BOLD time courses of distinct brain regions has revealed meaningful organization of spontaneous fluctuations in the resting brain. However, an increasing amount of evidence points to non-stationarity of FC; i.e., FC dynamically changes over time reflecting additional and rich information about brain organization, but representing new challenges for analysis and interpretation. Here, we propose a data-driven approach based on principal component analysis (PCA) to reveal hidden patterns of coherent FC dynamics across multiple subjects. We demonstrate the feasibility and relevance of this new approach by examining the differences in dynamic FC between 13 healthy control subjects and 15 minimally disabled relapse-remitting multiple sclerosis patients. We estimated whole-brain dynamic FC of regionally-averaged BOLD activity using sliding time windows. We then used PCA to identify FC patterns, termed "eigenconnectivities", that reflect meaningful patterns in FC fluctuations. We then assessed the contributions of these patterns to the dynamic FC at any given time point and identified a network of connections centered on the default-mode network with altered contribution in patients. Our results complement traditional stationary analyses, and reveal novel insights into brain connectivity dynamics and their modulation in a neurodegenerative disease.

Suitability of GRIND-based principal properties for the description of molecular similarity and ligand-based virtual screening

The information provided by the alignment-independent GRid Independent Descriptors (GRIND) can be condensed by the application of principal component analysis, obtaining a small number of principal properties (GRIND-PP), which is more suitable for describing molecular similarity. The objective of the present study is to optimize diverse parameters involved in the obtention of the GRIND-PP and validate their suitability for applications, requiring a biologically relevant description of the molecular similarity. With this aim, GRIND-PP computed with a collection of diverse settings were used to carry out ligand-based virtual screening (LBVS) on standard conditions. The quality of the results obtained was remarkable and comparable with other LBVS methods, and their detailed statistical analysis allowed to identify the method settings more determinant for the quality of the results and their optimum. Remarkably, some of these optimum settings differ significantly from those used in previously published applications, revealing their unexplored potential. Their applicability in large compound database was also explored by comparing the equivalence of the results obtained using either computed or projected principal properties. In general, the results of the study confirm the suitability of the GRIND-PP for practical applications and provide useful hints about how they should be computed for obtaining optimum results.

Proteomic analysis of peach fruit mesocarp softening and chilling injury using difference gel electrophoresis (DIGE)

Background: Peach fruit undergoes a rapid softening process that involves a number of metabolic changes. Storing fruit at low temperatures has been widely used to extend its postharvest life. However, this leads to undesired changes, such as mealiness and browning, which affect the quality of the fruit. In this study, a 2-D DIGE approach was designed to screen for differentially accumulated proteins in peach fruit during normal softening as well as under conditions that led to fruit chilling injury. Results:The analysis allowed us to identify 43 spots -representing about 18% of the total number analyzed- that show statistically significant changes. Thirty-nine of the proteins could be identified by mass spectrometry. Some of the proteins that changed during postharvest had been related to peach fruit ripening and cold stress in the past. However, we identified other proteins that had not been linked to these processes. A graphical display of the relationship between the differentially accumulated proteins was obtained using pairwise average-linkage cluster analysis and principal component analysis. Proteins such as endopolygalacturonase, catalase, NADP-dependent isocitrate dehydrogenase, pectin methylesterase and dehydrins were found to be very important for distinguishing between healthy and chill injured fruit. A categorization of the differentially accumulated proteins was performed using Gene Ontology annotation. The results showed that the 'response to stress', 'cellular homeostasis', 'metabolism of carbohydrates' and 'amino acid metabolism' biological processes were affected the most during the postharvest. Conclusions: Using a comparative proteomic approach with 2-D DIGE allowed us to identify proteins that showed stage-specific changes in their accumulation pattern. Several proteins that are related to response to stress, cellular homeostasis, cellular component organization and carbohydrate metabolism were detected as being differentially accumulated. Finally, a significant proportion of the proteins identified had not been associated with softening, cold storage or chilling injury-altered fruit before; thus, comparative proteomics has proven to be a valuable tool for understanding fruit softening and postharvest.

Identification of molecular apocrine breast tumours by microarray analysis.

Previous microarray studies on breast cancer identified multiple tumour classes, of which the most prominent, named luminal and basal, differ in expression of the oestrogen receptor alpha gene (ER). We report here the identification of a group of breast tumours with increased androgen signalling and a 'molecular apocrine' gene expression profile. Tumour samples from 49 patients with large operable or locally advanced breast cancers were tested on Affymetrix U133A gene expression microarrays. Principal components analysis and hierarchical clustering split the tumours into three groups: basal, luminal and a group we call molecular apocrine. All of the molecular apocrine tumours have strong apocrine features on histological examination (P=0.0002). The molecular apocrine group is androgen receptor (AR) positive and contains all of the ER-negative tumours outside the basal group. Kolmogorov-Smirnov testing indicates that oestrogen signalling is most active in the luminal group, and androgen signalling is most active in the molecular apocrine group. ERBB2 amplification is commoner in the molecular apocrine than the other groups. Genes that best split the three groups were identified by Wilcoxon test. Correlation of the average expression profile of these genes in our data with the expression profile of individual tumours in four published breast cancer studies suggest that molecular apocrine tumours represent 8-14% of tumours in these studies. Our data show that it is possible with microarray data to divide mammary tumour cells into three groups based on steroid receptor activity: luminal (ER+ AR+), basal (ER- AR-) and molecular apocrine (ER- AR+).

Characterization of olive oil by carbon isotope analysis of individual fatty acids: Implications for authentication

The fatty acids of olive oils of distinct quality grade from the most important European Union (EU) producer countries were chemically and isotopically characterized. The analytical approach utilized combined capillary column gas chromatography-mass spectrometry (GC/MS) and the novel technique of compound-specific isotope analysis (CSIA) through gas chromatography coupled to a stable isotope ratio mass spectrometer (IRMS) via a combustion (C) interface (GC/C/IRMS). This approach provides further insights into the control of the purity and geographical origin of oils sold as cold-pressed extra virgin olive oil with certified origin appellation. The results indicate that substantial enrichment in heavy carbon isotope (C-13) of the bulk oil and of individual fatty acids are related to (1) a thermally induced degradation due to deodorization or steam washing of the olive oils and (2) the potential blend with refined olive oil or other vegetable oils. The interpretation of the data is based on principal component analysis of the fatty acids concentrations and isotopic data (delta(13)C(oil), delta(13)C(16:0), delta(13)C(18:1)) and on the delta(13)C(16:0) vs delta(13)C(18:1) covariations. The differences in the delta(13)C values of palmitic and oleic acids are discussed in terms of biosynthesis of these acids in the plant tissue and admixture of distinct oils.

The Standard Biplot

Biplots are graphical displays of data matrices based on the decomposition of a matrix as the product of two matrices. Elements of these two matrices are used as coordinates for the rows and columns of the data matrix, with an interpretation of the joint presentation that relies on the properties of the scalar product. Because the decomposition is not unique, there are several alternative ways to scale the row and column points of the biplot, which can cause confusion amongst users, especially when software packages are not united in their approach to this issue. We propose a new scaling of the solution, called the standard biplot, which applies equally well to a wide variety of analyses such as correspondence analysis, principal component analysis, log-ratio analysis and the graphical results of a discriminant analysis/MANOVA, in fact to any method based on the singular-value decomposition. The standard biplot also handles data matrices with widely different levels of inherent variance. Two concepts taken from correspondence analysis are important to this idea: the weighting of row and column points, and the contributions made by the points to the solution. In the standard biplot one set of points, usually the rows of the data matrix, optimally represent the positions of the cases or sample units, which are weighted and usually standardized in some way unless the matrix contains values that are comparable in their raw form. The other set of points, usually the columns, is represented in accordance with their contributions to the low-dimensional solution. As for any biplot, the projections of the row points onto vectors defined by the column points approximate the centred and (optionally) standardized data. The method is illustrated with several examples to demonstrate how the standard biplot copes in different situations to give a joint map which needs only one common scale on the principal axes, thus avoiding the problem of enlarging or contracting the scale of one set of points to make the biplot readable. The proposal also solves the problem in correspondence analysis of low-frequency categories that are located on the periphery of the map, giving the false impression that they are important.

Distributional equivalence and subcompositional coherence in the analysis of contingency tables, ratio-scale measurements and compositional data

We consider two fundamental properties in the analysis of two-way tables of positive data: the principle of distributional equivalence, one of the cornerstones of correspondence analysis of contingency tables, and the principle of subcompositional coherence, which forms the basis of compositional data analysis. For an analysis to be subcompositionally coherent, it suffices to analyse the ratios of the data values. The usual approach to dimension reduction in compositional data analysis is to perform principal component analysis on the logarithms of ratios, but this method does not obey the principle of distributional equivalence. We show that by introducing weights for the rows and columns, the method achieves this desirable property. This weighted log-ratio analysis is theoretically equivalent to spectral mapping , a multivariate method developed almost 30 years ago for displaying ratio-scale data from biological activity spectra. The close relationship between spectral mapping and correspondence analysis is also explained, as well as their connection with association modelling. The weighted log-ratio methodology is applied here to frequency data in linguistics and to chemical compositional data in archaeology.

Analysis of matched matrices

We consider the joint visualization of two matrices which have common rowsand columns, for example multivariate data observed at two time pointsor split accord-ing to a dichotomous variable. Methods of interest includeprincipal components analysis for interval-scaled data, or correspondenceanalysis for frequency data or ratio-scaled variables on commensuratescales. A simple result in matrix algebra shows that by setting up thematrices in a particular block format, matrix sum and difference componentscan be visualized. The case when we have more than two matrices is alsodiscussed and the methodology is applied to data from the InternationalSocial Survey Program.

A note on the dual scaling of dominance data and its relationship to correspondence analysis

Dual scaling of a subjects-by-objects table of dominance data (preferences,paired comparisons and successive categories data) has been contrasted with correspondence analysis, as if the two techniques were somehow different. In this note we show that dual scaling of dominance data is equivalent to the correspondence analysis of a table which is doubled with respect to subjects. We also show that the results of both methods can be recovered from a principal components analysis of the undoubled dominance table which is centred with respect to subject means.

Multivariate analysis and geostatistics of the fertility of a humic rhodic hapludox under coffee cultivation

The spatial variability of soil and plant properties exerts great influence on the yeld of agricultural crops. This study analyzed the spatial variability of the fertility of a Humic Rhodic Hapludox with Arabic coffee, using principal component analysis, cluster analysis and geostatistics in combination. The experiment was carried out in an area under Coffea arabica L., variety Catucai 20/15 - 479. The soil was sampled at a depth 0.20 m, at 50 points of a sampling grid. The following chemical properties were determined: P, K+, Ca2+, Mg2+, Na+, S, Al3+, pH, H + Al, SB, t, T, V, m, OM, Na saturation index (SSI), remaining phosphorus (P-rem), and micronutrients (Zn, Fe, Mn, Cu and B). The data were analyzed with descriptive statistics, followed by principal component and cluster analyses. Geostatistics were used to check and quantify the degree of spatial dependence of properties, represented by principal components. The principal component analysis allowed a dimensional reduction of the problem, providing interpretable components, with little information loss. Despite the characteristic information loss of principal component analysis, the combination of this technique with geostatistical analysis was efficient for the quantification and determination of the structure of spatial dependence of soil fertility. In general, the availability of soil mineral nutrients was low and the levels of acidity and exchangeable Al were high.

Development of a two-step screening ESI-TOF-MS method for rapid determination of significant stress-induced metabolome modifications in plant leaf extracts: the wound response in Arabidopsis thaliana as a case study.

To study the stress-induced effects caused by wounding under a new perspective, a metabolomic strategy based on HPLC-MS has been devised for the model plant Arabidopsis thaliana. To detect induced metabolites and precisely localise these compounds among the numerous constitutive metabolites, HPLC-MS analyses were performed in a two-step strategy. In a first step, rapid direct TOF-MS measurements of the crude leaf extract were performed with a ballistic gradient on a short LC-column. The HPLC-MS data were investigated by multivariate analysis as total mass spectra (TMS). Principal components analysis (PCA) and hierarchical cluster analysis (HCA) on principal coordinates were combined for data treatment. PCA and HCA demonstrated a clear clustering of plant specimens selecting the highest discriminating ions given by the complete data analysis, leading to the specific detection of discrete-induced ions (m/z values). Furthermore, pool constitution with plants of homogeneous behaviour was achieved for confirmatory analysis. In this second step, long high-resolution LC profilings on an UPLC-TOF-MS system were used on pooled samples. This allowed to precisely localise the putative biological marker induced by wounding and by specific extraction of accurate m/z values detected in the screening procedure with the TMS spectra.

Retaining principal components for discrete variables

The present study discusses retention criteria for principal components analysis (PCA) applied to Likert scale items typical in psychological questionnaires. The main aim is to recommend applied researchers to restrain from relying only on the eigenvalue-than-one criterion; alternative procedures are suggested for adjusting for sampling error. An additional objective is to add evidence on the consequences of applying this rule when PCA is used with discrete variables. The experimental conditions were studied by means of Monte Carlo sampling including several sample sizes, different number of variables and answer alternatives, and four non-normal distributions. The results suggest that even when all the items and thus the underlying dimensions are independent, eigenvalues greater than one are frequent and they can explain up to 80% of the variance in data, meeting the empirical criterion. The consequences of using Kaiser"s rule are illustrated with a clinical psychology example. The size of the eigenvalues resulted to be a function of the sample size and the number of variables, which is also the case for parallel analysis as previous research shows. To enhance the application of alternative criteria, an R package was developed for deciding the number of principal components to retain by means of confidence intervals constructed about the eigenvalues corresponding to lack of relationship between discrete variables.

Genetic divergence among tomato leafminer populations based on AFLP analysis

The objective of this work was to determine the genetic differences among eight Brazilian populations of the tomato leafminer Tuta absoluta (Meyrick) (Lepidoptera: Gelechiidae), from the states of Espírito Santo (Santa Tereza), Goiás (Goianápolis), Minas Gerais (Uberlândia and Viçosa), Pernambuco (Camocim de São Félix), Rio de Janeiro (São João da Barra) and São Paulo (Paulínia and Sumaré), using the amplified fragment length polymorphism (AFLP) technique. Fifteen combinations of EcoRI and MseI primers were used to assess divergence among populations. The data were analyzed using unweighted pair-group method, based on arithmetic averages (UPGMA) bootstrap analysis and principal coordinate analysis. Using a multilocus approach, these populations were divided in two groups, based on genetic fingerprints. Populations from Goianápolis, Santa Tereza, and Viçosa formed one group. Populations from Camocim de São Félix, Paulínia, São João da Barra, Sumaré, and Uberlândia fitted in the second group. These results were congruent with differences in susceptibility of this insect to insecticides, previously identified by other authors.

UPLC-TOF-MS for plant metabolomics: a sequential approach for wound marker analysis in Arabidopsis thaliana.

The model plant Arabidopsis thaliana was studied for the search of new metabolites involved in wound signalling. Diverse LC approaches were considered in terms of efficiency and analysis time and a 7-min gradient on a UPLC-TOF-MS system with a short column was chosen for metabolite fingerprinting. This screening step was designed to allow the comparison of a high number of samples over a wide range of time points after stress induction in positive and negative ionisation modes. Thanks to data treatment, clear discrimination was obtained, providing lists of potential stress-induced ions. In a second step, the fingerprinting conditions were transferred to longer column, providing a higher peak capacity able to demonstrate the presence of isomers among the highlighted compounds.

Raman analysis of multilayer automotive paints in forensic science: measurement variability and depth profile?

The aim of this work is to study the influence of several analytical parameters on the variability of Raman spectra of paint samples. In the present study, microtome thin section and direct (no preparation) analysis are considered as sample preparation. In order to evaluate their influence on the measures, an experimental design such as 'fractional full factorial' with seven factors (including the sampling process) is applied, for a total of 32 experiments representing 160 measures. Once the influence of sample preparation highlighted, a depth profile of a paint sample is carried out by changing the focusing plane in order to measure the colored layer under a clearcoat. This is undertaken in order to avoid sample preparation such a microtome sectioning. Finally, chemometric treatments such as principal component analysis are applied to the resulting spectra. The findings of this study indicate the importance of sample preparation, or more specifically, the surface roughness, on the variability of the measurements on a same sample. Moreover, the depth profile experiment highlights the influence of the refractive index of the upper layer (clearcoat) when measuring through a transparent layer.