Biometric variability of goat populations revealed by means of principal component analysis

The aim was to analyze variation in 12 Brazilian and Moroccan goat populations, and, through principal component analysis (PCA), check the importance of body measures and their indices as a means of distinguishing among individuals and populations. The biometric measurements were wither height (WH), brisket height (BH) and ear length (EL). Thorax depth (WH-BH) and the three indices, TD/WH, EL/TD and EL/WH, were also calculated. Of the seven components extracted, the first three principal components were sufficient to explain 99.5% of the total variance of the data. Graphical dispersion by genetic groups revealed that European dairy breeds clustered together. The Moroccan breeds were separated into two groups, one comprising the Drâa and the other the Zagora and Rhâali breeds. Whereas, on the one side, the Anglo-Nubian and undefined breeds were the closest to one another the goats of the Azul were observed to have the highest variation of all the breeds. The Anglo-Nubian and Boer breeds were similar to each other. The Nambi-type goats remained distinct from all the other populations. In general, the use of graphical representation of PCA values allowed to distinguish genetic groups.     

Major structural determinants of transmembrane proteins identified by principal component analysis

We identify amino acid characteristics important in determining the secondary structures of transmembrane proteins, and compare them with characteristics important for cytoplasmic proteins. Using information derived from multiple sequence alignments, we perform a principal component analysis (PCA) to identify the directions in the 20-dimensional amino acid frequency space that comprise the most variance within each protein secondary structure. These vectors represent the important position-specific properties of the amino acids for coils, turns, beta sheets, and alpha helices. As expected, the most important axis for most of the datasets was hydrophobicity. Additional axes, distinct from hydrophobicity, are surprising, especially in the case of transmembrane alpha helices, where the effects of aromaticity and beta-branching are the next two most significant characteristics. The axis representing beta-branching also has equal importance in cytoplasmic and transmembrane helices, a finding that contrasts with some experimental results in membrane-like environments. In a further analysis, we examine trends for some of the PCA axes over averaged transmembrane alpha helices, and find interesting results for aromaticity.     

Relationships between induction of anesthesia and mitotic spindle disturbances studied by means of principal component analysis

A dataset comprising the activity of 30 compounds in 4 biological tests--anesthesia of tadpoles, anesthesia of frog heart, abnormal growth and spindle disturbances in Allium root tips--was re-evaluated by means of principal component analysis. A two-component model is required to explain the variation in biological activity of the compounds. It is found that abnormal growth is different from the other biological responses. When this test is excluded, as much as 90% of the variation is explained by a one-component model, the determining factor most probably being the lipophilic character of the compounds. Mammalian mitotic cells respond in a similar way to mitotic cells of Allium root tips. It is suggested that possible regularities in the dose-response relationships for anesthesia, teratogenic effects and generation of abnormal chromosome numbers require further exploration.     

LeuT conformational sampling utilizing accelerated molecular dynamics and principal component analysis

Monoamine transporters (MATs) function by coupling ion gradients to the transport of dopamine, norepinephrine, or serotonin. Despite their importance in regulating neurotransmission, the exact conformational mechanism by which MATs function remains elusive. To this end, we have performed seven 250 ns accelerated molecular dynamics simulations of the leucine transporter, a model for neurotransmitter MATs. By varying the presence of binding-pocket leucine substrate and sodium ions, we have sampled plausible conformational states representative of the substrate transport cycle. The resulting trajectories were analyzed using principal component analysis of transmembrane helices 1b and 6a. This analysis revealed seven unique structures: two of the obtained conformations are similar to the currently published crystallographic structures, one conformation is similar to a proposed open inward structure, and four conformations represent novel structures of potential importance to the transport cycle. Further analysis reveals that the presence of binding-pocket sodium ions is necessary to stabilize the locked-occluded and open-inward conformations.     

Harmonicity and anharmonicity in protein dynamics: A normal mode analysis and principal component analysis

A comparison of a normal mode analysis and principal component analysis of a 200-ps molecular dynamics trajectory of bovine pancreatic trypsin inhibitor in vacuum has been made in order to further elucidate the harmonic and anharmonic aspects in the dynamics of proteins. An anharmonicity factor is defined which measures the degree of anharmonicity in the modes, be they principal modes or normal modes, and it is shown that the principal mode system naturally divides into anharmonic modes with peak frequencies below 80 cm^?1, and harmonic modes with frequencies above this value. In general the larger the mean-square fluctuation of a principal mode, the greater the degree of anharmonicity in its motion. The anharmonic modes represent only 12% of the total number of variables, but account for 98% of the total mean-square fluctuation. The transitional nature of the anharmonic motion is demonstrated. The results strongly suggest that in a large subspace, the free energy surface, as probed by the simulation, is approximated by a multi-dimensional parabola which is just a resealed version of the parabola corresponding to the harmonic approximation to the conformational energy surface at a single minimum. After 200 ps, the resealing factor, termed the “normal mode resealing factor,” has apparently converged to a value whereby the mean-square fluctuation within the subspace is about twice that predicted by the normal mode analysis. © 1995 Wiley-Liss, Inc.     

Stochastic convex sparse principal component analysis

Principal component analysis (PCA) is a dimensionality reduction and data analysis tool commonly used in many areas. The main idea of PCA is to represent high-dimensional data with a few representative components that capture most of the variance present in the data. However, there is an obvious disadvantage of traditional PCA when it is applied to analyze data where interpretability is important. In applications, where the features have some physical meanings, we lose the ability to interpret the principal components extracted by conventional PCA because each principal component is a linear combination of all the original features. For this reason, sparse PCA has been proposed to improve the interpretability of traditional PCA by introducing sparsity to the loading vectors of principal components. The sparse PCA can be formulated as an ? ₁ regularized optimization problem, which can be solved by proximal gradient methods. However, these methods do not scale well because computation of the exact gradient is generally required at each iteration. Stochastic gradient framework addresses this challenge by computing an expected gradient at each iteration. Nevertheless, stochastic approaches typically have low convergence rates due to the high variance. In this paper, we propose a convex sparse principal component analysis (Cvx-SPCA), which leverages a proximal variance reduced stochastic scheme to achieve a geometric convergence rate. We further show that the convergence analysis can be significantly simplified by using a weak condition which allows a broader class of objectives to be applied. The efficiency and effectiveness of the proposed method are demonstrated on a large-scale electronic medical record cohort.     

Normalization of single-channel DNA array data by principal component analysis

MOTIVATION: Detailed comparison and analysis of the output of DNA gene expression arrays from multiple samples require global normalization of the measured individual gene intensities from the different hybridizations. This is needed for accounting for variations in array preparation and sample hybridization conditions. RESULTS: Here, we present a simple, robust and accurate procedure for the global normalization of datasets generated with single-channel DNA arrays based on principal component analysis. The procedure makes minimal assumptions about the data and performs well in cases where other standard procedures produced biased estimates. It is also insensitive to data transformation, filtering (thresholding) and pre-screening.     

Study of xylem pressure potential daily dynamics by means of autocorrelation analysis

The xylem pressure potential (Ψ_xylem) of the leaves ofQuercus cerris, Acer campestre andCarpinus betulus was measured under anticyclonic weather types. The autocorrelation analysis revealed the daily course of the Ψ_xylem values approaching the stationary random process. A close statistical relation was found between the results obtained in three successive measurements of the Ψ_xylem (interval 2 h). A close statistical relation also between the value of the base potential (Ψ_b) measured at dawn and the actual values of the Ψ_xylem allowed the prediction of the Ψ_xylem values on the base of the known Ψ_b-values by means of a simple linear regression model.     

Comparison between principal component analysis and independent component analysis in electroencephalograms modelling

Principal Component Analysis (PCA) is a classical technique in statistical data analysis, feature extraction and data reduction, aiming at explaining observed signals as a linear combination of orthogonal principal components. Independent Component Analysis (ICA) is a technique of array processing and data analysis, aiming at recovering unobserved signals or 'sources' from observed mixtures, exploiting only the assumption of mutual independence between the signals. The separation of the sources by ICA has great potential in applications such as the separation of sound signals (like voices mixed in simultaneous multiple records, for example), in telecommunication or in the treatment of medical signals. However, ICA is not yet often used by statisticians. In this paper, we shall present ICA in a statistical framework and compare this method with PCA for electroencephalograms (EEG) analysis.We shall see that ICA provides a more useful data representation than PCA, for instance, for the representation of a particular characteristic of the EEG named event-related potential (ERP).     

Classification of chili powders by thin-layer chromatography and principal component analysis

Silica gel, aluminium oxide, diatomaceous earth, polyamide, cyano, diol and amino plates have been tested for their capacity to separate the color pigments of six chili powders of different origin by both adsorption and reversed-phase thin-layer chromatography. The plates were evaluated at 340 and 440 nm wavelengths. Best separation of color pigments was obtained on impregnated diatomaceous earth layer using acetone-water 17:3 v/v eluent. It was found that the pigment composition of chili powders showed marked differences. Principal component analysis employed for the classification of the chili powders according to their pigment composition indicated that these differences can be used for the determination of the similarity or dissimilarity of the chili powders.     

Probabilistic principal component analysis for metabolomic data

Background  

Data from metabolomic studies are typically complex and high-dimensional. Principal component analysis (PCA) is currently the most widely used statistical technique for analyzing metabolomic data. However, PCA is limited by the fact that it is not based on a statistical model.     

Functional roles of magnesium binding to extracellular signal-regulated kinase 2 explored by molecular dynamics simulations and principal component analysis

Molecular dynamics (MD) simulations coupled with principal component (PC) analysis were carried out to study functional roles of Mg²⁺ binding to extracellular signal-regulated kinase 2 (ERK2). The results suggest that Mg²⁺ binding heavily decreases eigenvalue of the first principal component and totally inhibits motion strength of ERK2, which favors stabilization of ERK2 structure. Binding free energy predictions indicate that Mg²⁺ binding produces an important effect on binding ability of adenosine triphosphate (ATP) to ERK2 and strengthens the ATP binding. The calculations of residue-based free energy decomposition show that lack of Mg²⁺ weakens interactions between the hydrophobic rings of ATP and five residues I29, V37, A50, L105, and L154. Hydrogen bond analyses also prove that Mg²⁺ binding increases occupancies of hydrogen bonds formed between ATP and residues K52, Q103, D104, and M106. We expect that this study can provide a significant theoretical hint for designs of anticancer drugs targeting ERK2.     

A principal component analysis of the dynamics of subdomains and binding sites in human serum albumin

The conformational dynamics of human serum albumin (HSA) was investigated by principal component analysis (PCA) applied to three molecular dynamics trajectories of 200 ns each. The overlap of the essential subspaces spanned by the first 10 principal components (PC) of different trajectories was about 0.3 showing that the PCA based on a trajectory length of 200 ns is not completely convergent for this protein. The contributions of the relative motion of subdomains and of the subdomains (internal) distortion to the first 10 PCs were found to be comparable. Based on the distribution of the first 3 PC, 10 protein conformers are identified showing relative root mean square deviations (RMSD) between 2.3 and 4.6 Å. The main PCs are found to be delocalized over the whole protein structure indicating that the motions of different protein subdomains are coupled. This coupling is considered as being related to the allosteric effects observed upon ligand binding to HSA. On the other hand, the first PC of one of the three trajectories describes a conformational transition of the protein domain I that is close to that experimentally observed upon myristate binding. This is a theoretical support for the older hypothesis stating that changes of the protein onformation favorable to binding can precede the ligand complexation. A detailed all atoms PCA performed on the primary Sites 1 and 2 confirms the multiconformational character of the HSA binding sites as well as the significant coupling of their motions. © 2013 Wiley Periodicals, Inc. Biopolymers 101: 561–572, 2014.     

Multiple-breed genomic evaluation by principal component analysis in small size populations

In this study, the effects of breed composition and predictor dimensionality on the accuracy of direct genomic values (DGV) in a multiple breed (MB) cattle population were investigated. A total of 3559 bulls of three breeds were genotyped at 54 001 single nucleotide polymorphisms: 2093 Holstein (H), 749 Brown Swiss (B) and 717 Simmental (S). DGV were calculated using a principal component (PC) approach for either single (SB) or MB scenarios. Moreover, DGV were computed using all SNP genotypes simultaneously with SNPBLUP model as comparison. A total of seven data sets were used: three with a SB each, three with different pairs of breeds (HB, HS and BS), and one with all the three breeds together (HBS), respectively. Editing was performed separately for each scenario. Reference populations differed in breed composition, whereas the validation bulls were the same for all scenarios. The number of SNPs retained after data editing ranged from 36 521 to 41 360. PCs were extracted from actual genotypes. The total number of retained PCs ranged from 4029 to 7284 in Brown Swiss and HBS respectively, reducing the number of predictors by about 85% (from 82% to 89%). In all, three traits were considered: milk, fat and protein yield. Correlations between deregressed proofs and DGV were used to assess prediction accuracy in validation animals. In the SB scenarios, average DGV accuracy did not substantially change when either SNPBLUP or PC were used. Improvement of DGV accuracy were observed for some traits in Brown Swiss, only when MB reference populations and PC approach were used instead of SB-SNPBLUP (+10% HBS, +16%HB for milk yield and +3% HBS and +7% HB for protein yield, respectively). With the exclusion of the abovementioned cases, similar accuracies were observed using MB reference population, under the PC or SNPBLUP models. Random variation owing to sampling effect or size and composition of the reference population may explain the difficulty in finding a defined pattern in the results.     

Neuronal assembly detection and cell membership specification by principal component analysis

In 1949, Donald Hebb postulated that assemblies of synchronously activated neurons are the elementary units of information processing in the brain. Despite being one of the most influential theories in neuroscience, Hebb's cell assembly hypothesis only started to become testable in the past two decades due to technological advances. However, while the technology for the simultaneous recording of large neuronal populations undergoes fast development, there is still a paucity of analytical methods that can properly detect and track the activity of cell assemblies. Here we describe a principal component-based method that is able to (1) identify all cell assemblies present in the neuronal population investigated, (2) determine the number of neurons involved in ensemble activity, (3) specify the precise identity of the neurons pertaining to each cell assembly, and (4) unravel the time course of the individual activity of multiple assemblies. Application of the method to multielectrode recordings of awake and behaving rats revealed that assemblies detected in the cerebral cortex and hippocampus typically contain overlapping neurons. The results indicate that the PCA method presented here is able to properly detect, track and specify neuronal assemblies, irrespective of overlapping membership.     

Pre-processing of chromatographic data for principal component analysis

This paper examines the selection of the appropriate representation of chromatogram data prior to using principal component analysis (PCA), a multivariate statistical technique, for the diagnosis of chromatogram data sets. The effects of four process variables were investigated; flow rate, temperature, loading concentration and loading volume, for a size exclusion chromatography system used to separate three components (monomer, dimer, trimer). The study showed that major positional shifts in the elution peaks that result when running the separation at different flow rates caused the effects of other variables to be masked if the PCA is performed using elapsed time as the comparative basis. Two alternative methods of representing the data in chromatograms are proposed. In the first data were converted to a volumetric basis prior to performing the PCA, while in the second, having made this transformation the data were adjusted to account for the total material loaded during each separation. Two datasets were analysed to demonstrate the approaches. The results show that by appropriate selection of the basis prior to the analysis, significantly greater process insight can be gained from the PCA and demonstrates the importance of pre-processing prior to such analysis.