Pair-preferences: a Quantitative Measure of Regularities in Protein Sequences

Abstract

We present here the results obtained by applying several different methods to quantitatively measure regularities in protein sequences based on pair-preferences. We have studied the distribution of amino acid residues, singly as well as in pairs in a large data base and have attempted this task. We confirmed the existence of well-defined pair-preferences in proteins which were shown to be remarkably absent in simulated random sequences of similar amino acid distribution. The analysis of the sequences from the SWISS-PROT data base using simple statistical tests, Fourier analysis, fractal analysis and statistical thermodynamical tests were used to derive parameters to define a natural sequence. As a consequence of the existence of pair-preferences, parameters like fractal dimension (D), spectral exponent (β), scaling parameter (H) and entropy (statistical) were found to be characteristic for natural sequences. For a reference state we chose a randomised state devoid of any pair-preference. The pair-preferences qualified well to be used as quantitative measures of regularities in protein sequences.     

Statistical Comparison of Band Spectral Powers: An Aid in Stochastical Analysis of Brain Electrical Activity. Part 2: Construction of Confidence Intervals of Spectral Band Power and their Application in EEG-Analysis

Based on the result that the distribution of estimated spectral power in broad frequency bands can be approximated by x²-distribution the accuracy of the approximation was tested by different models of stochastical processes. Two significance tests for comparison of spectral band powers on the basis of this approximation and the estimation of confidence intervals were developed and tested by application on EEG data. By means of these test statistics, a new basis for statistical comparison between EEG maps of groups as well as between maps of groups and single maps can be suggested.     

Spectral analysis of distributions: finding periodic components in eukaryotic enzyme length data

We introduce the spectral analysis of distributions (SAD), a method for detecting and evaluating possible periodicity in experimental data distributions (histograms) of arbitrary shape. SAD determines whether a given empirical distribution contains a periodic component. We also propose a system of probabilistic mixture distributions to model a histogram consisting of a smooth background together with peaks at periodic intervals, with each peak corresponding to a fixed number of subunits added together. This mixture distribution model allows us to estimate the parameters of the data and to test the statistical significance of the estimated peaks. The analysis is applied to the length distribution of eukaryotic enzymes.     

Spectral vs. compartmental averaging of VA/Q distributions: confidence limits

We have investigated the method of statistical averaging as a nonparametric approach to obtain a representative ventilation-perfusion (VA/Q) distribution that exemplifies the family of compatible solutions for multiple inert gas elimination data. The variability of the compatible solutions was examined by determining the standard deviation of the statistical average. For six inert gases, it can be predicted that a distribution with up to seven contiguous nonzero VA/Q compartments can be uniquely recovered, whereas the compatible family becomes more diverse, the broader the distribution. For a given compatible family consisting of multimodal distributions with various phase relationships, the average distribution was found to display an uncharacteristically unimodal shape as a result of modal smoothing. To avoid this possible artifact, an alternative approach was adopted in which statistical averaging was performed in the frequency domain. For both deterministic and empirical data, the energy spectra of all feasible VA/Q distributions displayed a well-defined low-frequency band that was invariant within the compatible family and with a bandwidth that approximated the predicted sampling cutoff frequency. The nonuniqueness of the result was ascribable to a variable high-frequency band that was due to an aliasing effect. For a wide range of clinical data, the representative distributions resulting from compartmental and spectral averaging were indistinguishable from each other and had little variability both in the VA/Q and frequency domains. For these cases, therefore, the resolving power of the recovery algorithm was not critical. Finally, an efficient method of finding the average distribution was proposed.     

Influence of homologous disaccharides on the hydrogen-bond network of water: complementary Raman scattering experiments and molecular dynamics simulations

A comparative investigation of trehalose, sucrose, and maltose in water solution has been performed using Raman scattering experiments and Molecular Dynamics simulations. From the analysis of the O-H stretching region in the [2500,4000] cm(-1) Raman spectral range, which includes for the first time the contribution of 'free' water, and the statistical distribution of water HB probabilities from MD simulations, this study confirms the privileged interaction of trehalose with water above a peculiar threshold weight concentration of about 30%. The role of the hydration number of sugars--found higher for trehalose--on the destructuring effect of the water hydrogen bond network is also addressed. The analysis of the water O-H-O bending spectral range [1500,1800] cm(-1) reveals a change of the homogeneity of water molecules influenced by sugars, but the three investigated sugars are found to behave similarly.     

Basic aspects of photon transport through matter with respect to track structure formation

After a short summary of the most important physical aspects of photon interaction with matter and of the main elements of photon transport simulation, some basic features of photon tracks in liquid water are discussed. These include the statistical distribution of the number of photon interactions caused during the complete photon slow-down, the corresponding mean value, the distance distribution of photon interactions, and the spectral distribution of secondary electrons or, which is the same, the spectral distribution of the start energy of secondary electron tracks. The latter distribution can easily be interpreted in terms of the track entity concept of Mozumder and Magee, which, therefore, proves to be the most natural concept of track structure analysis in the case of photon irradiation. Received: 20 September 1998 / Accepted in revised form: 30 April 1999     

Refining similarity scoring to enable decoy‐free validation in spectral library searching

Spectral library searching is a maturing approach for peptide identification from MS/MS, offering an alternative to traditional sequence database searching. Spectral library searching relies on direct spectrum‐to‐spectrum matching between the query data and the spectral library, which affords better discrimination of true and false matches, leading to improved sensitivity. However, due to the inherent diversity of the peak location and intensity profiles of real spectra, the resulting similarity score distributions often take on unpredictable shapes. This makes it difficult to model the scores of the false matches accurately, necessitating the use of decoy searching to sample the score distribution of the false matches. Here, we refined the similarity scoring in spectral library searching to enable the validation of spectral search results without the use of decoys. We rank‐transformed the peak intensities to standardize all spectra, making it possible to fit a parametric distribution to the scores of the nontop‐scoring spectral matches. The statistical significance of the top‐scoring match can then be estimated in a rigorous manner according to Extreme Value Theory. The overall result is a more robust and interpretable measure of the quality of the spectral match, which can be obtained without decoys. We tested this refined similarity scoring function on real datasets and demonstrated its effectiveness. This approach reduces search time, increases sensitivity, and extends spectral library searching to situations where decoy spectra cannot be readily generated, such as in searching unidentified and nonpeptide spectral libraries.     

g-Strain, ENDOR, and structure of active centers of two-iron ferredoxins

Collaborative chemical and spectroscopic work from several laboratories resulted in a qualitative structure for the active center in the two-iron ferredoxins, with each iron being in a distorted tetrahedron of sulfur atoms (two acid-labile sulfurs bridging the two iron atoms and the other two from cysteine sulfurs). Subsequent X-ray data from other laboratories confirmed this structure. Detailed EPR spectral syntheses showed that there is a distribution of structures in any given protein (even in a single crystal) resulting in a distribution of the principal values of the g tensor, which may be described by a statistical distribution of still another tensor whose principal axes are, in general, not coincident with the principal-axis frame of the g tensor.     

CoGA: An R Package to Identify Differentially Co-Expressed Gene Sets by Analyzing the Graph Spectra

Gene set analysis aims to identify predefined sets of functionally related genes that are differentially expressed between two conditions. Although gene set analysis has been very successful, by incorporating biological knowledge about the gene sets and enhancing statistical power over gene-by-gene analyses, it does not take into account the correlation (association) structure among the genes. In this work, we present CoGA (Co-expression Graph Analyzer), an R package for the identification of groups of differentially associated genes between two phenotypes. The analysis is based on concepts of Information Theory applied to the spectral distributions of the gene co-expression graphs, such as the spectral entropy to measure the randomness of a graph structure and the Jensen-Shannon divergence to discriminate classes of graphs. The package also includes common measures to compare gene co-expression networks in terms of their structural properties, such as centrality, degree distribution, shortest path length, and clustering coefficient. Besides the structural analyses, CoGA also includes graphical interfaces for visual inspection of the networks, ranking of genes according to their “importance” in the network, and the standard differential expression analysis. We show by both simulation experiments and analyses of real data that the statistical tests performed by CoGA indeed control the rate of false positives and is able to identify differentially co-expressed genes that other methods failed.     

Carbon-13 NMR studies of chloroplast membranes: carbon-13 enrichment without 13C-13C couplings

A novel approach to carbon-13 (13C) enrichment of chloroplast membranes (and plant materials in general) is presented for 13C-nuclear magnetic resonance (13C-NMR) studies. The method minimizes the occurrence of spectral complications arising from 13C-13C couplings resulting from a statistical distribution of 13C within the molecule with low probability of encountering two 13C atoms adjacent to each other. This is achieved by growing the plants in light surrounded by an atmosphere containing 1/3rd 12CO2 and 2/3rd 13CO2, liberated by weak acid-treatment of a mixture of corresponding barium carbonate salts.     

Abacus: a computational tool for extracting and pre-processing spectral count data for label-free quantitative proteomic analysis

We describe Abacus, a computational tool for extracting spectral counts from MS/MS data sets. The program aggregates data from multiple experiments, adjusts spectral counts to accurately account for peptides shared across multiple proteins, and performs common normalization steps. It can also output the spectral count data at the gene level, thus simplifying the integration and comparison between gene and protein expression data. Abacus is compatible with the widely used Trans-Proteomic Pipeline suite of tools and comes with a graphical user interface making it easy to interact with the program. The main aim of Abacus is to streamline the analysis of spectral count data by providing an automated, easy to use solution for extracting this information from proteomic data sets for subsequent, more sophisticated statistical analysis.     

Spectral mapping tools from the earth sciences applied to spectral microscopy data.

BACKGROUND: Spectral imaging, originating from the field of earth remote sensing, is a powerful tool that is being increasingly used in a wide variety of applications for material identification. Several workers have used techniques like linear spectral unmixing (LSU) to discriminate materials in images derived from spectral microscopy. However, many spectral analysis algorithms rely on assumptions that are often violated in microscopy applications. This study explores algorithms originally developed as improvements on early earth imaging techniques that can be easily translated for use with spectral microscopy. METHODS: To best demonstrate the application of earth remote sensing spectral analysis tools to spectral microscopy data, earth imaging software was used to analyze data acquired with a Leica confocal microscope with mechanical spectral scanning. For this study, spectral training signatures (often referred to as endmembers) were selected with the ENVI (ITT Visual Information Solutions, Boulder, CO) "spectral hourglass" processing flow, a series of tools that use the spectrally over-determined nature of hyperspectral data to find the most spectrally pure (or spectrally unique) pixels within the data set. This set of endmember signatures was then used in the full range of mapping algorithms available in ENVI to determine locations, and in some cases subpixel abundances of endmembers. RESULTS: Mapping and abundance images showed a broad agreement between the spectral analysis algorithms, supported through visual assessment of output classification images and through statistical analysis of the distribution of pixels within each endmember class. CONCLUSIONS: The powerful spectral analysis algorithms available in COTS software, the result of decades of research in earth imaging, are easily translated to new sources of spectral data. Although the scale between earth imagery and spectral microscopy is radically different, the problem is the same: mapping material locations and abundances based on unique spectral signatures.     

Spectral kinetics ratiometry: a simple approach for real-time monitoring of fluorophore distributions in living cells.

BACKGROUND: Spectral Imaging Microscopy is gaining attention in biological research. Most of the commercial systems in vogue employ linear spectral un-mixing algorithms and/or spectral profile matching algorithms to extract the component spectral information from the measured specimen spectra. The need to accurately deconvolve multiple spectra with minimal cross-contamination is always accompanied by an increase in system complexity and cost. METHODS: We describe here a variant of the spectral waveform cross-correlation analysis (SWCCA) method where the master reference spectral library is constructed by composite spectra with varying ratios of component spectra, unlike the conventional spectral library where pure spectra form the components. We demonstrate that this spectral kinetics ratiometric approach gives realistic estimates of fluorophore distribution in living cells with a better spectral correlation as compared with pure component spectral libraries. RESULTS: Biological applications demonstrated in this article include acceptor photobleaching FRET, caspase activity during cell death and mitochondrial membrane polarization kinetics during substrate metabolism. CONCLUSIONS: Beyond the representative applications presented in this article, we think the proposed approach can be valuable in dynamic studies of a variety of other cellular processes such as pH oscillations, photobleaching and quenching kinetics. Besides giving better spectral correlation and real-time monitoring of biophysical processes in living cells, this method can serve as an economical solution for high-throughput spectral classification requirements.     

Modelling plant species distribution in alpine grasslands using airborne imaging spectroscopy

Remote sensing using airborne imaging spectroscopy (AIS) is known to retrieve fundamental optical properties of ecosystems. However, the value of these properties for predicting plant species distribution remains unclear. Here, we assess whether such data can add value to topographic variables for predicting plant distributions in French and Swiss alpine grasslands. We fitted statistical models with high spectral and spatial resolution reflectance data and tested four optical indices sensitive to leaf chlorophyll content, leaf water content and leaf area index. We found moderate added-value of AIS data for predicting alpine plant species distribution. Contrary to expectations, differences between species distribution models (SDMs) were not linked to their local abundance or phylogenetic/functional similarity. Moreover, spectral signatures of species were found to be partly site-specific. We discuss current limits of AIS-based SDMs, highlighting issues of scale and informational content of AIS data.     

Less label, more free: approaches in label-free quantitative mass spectrometry

In this review we examine techniques, software, and statistical analyses used in label-free quantitative proteomics studies for area under the curve and spectral counting approaches. Recent advances in the field are discussed in an order that reflects a logical workflow design. Examples of studies that follow this design are presented to highlight the requirement for statistical assessment and further experiments to validate results from label-free quantitation. Limitations of label-free approaches are considered, label-free approaches are compared with labelling techniques, and forward-looking applications for label-free quantitative data are presented. We conclude that label-free quantitative proteomics is a reliable, versatile, and cost-effective alternative to labelled quantitation.     

Ciclograma: a tool for detection of rhythmicities in sleep/wake cycles

The Fourier spectral analysis of binary time series (or rectangular signals) causes methodological problems, due to the fact that it is based on sinusoidal functions. We propose a new tool for the detection of periodicities in binary time series, focusing on sleep/wake cycles. This methodology is based on a weighted histogram of cycle durations. In this paper, we compare our methodology with the Fourier spectral analysis on the basis of simulated and real binary data sets of various lengths. We also provide an approach to statistical validation of the periodicities determined with our methodology. Furthermore, we analyze the discriminating power of both methods in terms of standard deviation. Our results indicate that the Ciclograma is much more powerful than Fourier analysis when applied on this type of time series.     

谱分析在DNA序列分析中的应用

目的：谱分析是信号处理的常用方法,其中的统计相关分析、傅里叶变换、小波变换和数字滤波等手段已逐渐应用到DNA序列的分析中,这些应用包括DNA序列的周期性分析、基因识别和同源性分析等方面。本文对谱分析方法在DNA序列分析中的应用情况进行简单的综述。     

Scaling in biological nuclear magnetic resonance spectral distributions

A statistical analysis of the distribution of the eigenvalues of the chemical shift interaction as detected by nuclear magnetic resonance (NMR) spectroscopy in large biological systems is presented in the light of random matrix theory. A power law dependence is experimentally observed for the distribution of the number of eigenvalues, N, of the shielding hamiltonian with epsilon i less than or equal to E as a function of the energy E. From this cumulative distribution of energy levels, N(E), we also obtain a density of states rho(E). The exponent of the energy variation of N(E) and rho(E) are correlated with the dimensionality of the molecular system. A crossover in the values of the exponents is found in passing from low to higher energy in the spectra. Our method classifies and reduces the chemical shift data base of proteins and also demonstrates a degree of regularity in seemingly irregular spectral patterns.     

生物组织拉曼光谱数据的统计分析

拉曼光谱技术在生命科学领域已取得较为广泛的研究与应用,如何从低信噪比、质量差的拉曼光谱信号提取并充分利用谱图中所含信息,对光谱后续分析、样品的归类等至关重要.本文首先明确了生物组织拉曼光谱统计分析中几个重要的概念,进而对拉曼光谱数据的预处理,光谱分析研究中较为常用的几种多元统计方法进行了归纳、对比与分析.     

Informational and statistical measures of the self-organization of the heart regulation systems in the analysis of heart rate variability

The results of orthostatic tests measuring heart rate variability (HRV) in athletes are outlined here, using the Dirichlet distribution and the properties of information entropy. It has been shown that informational and statistical measures used for the analysis of HRV reflect the state of homeostasis regulating the cardiac activity and its dynamics with a higher degree of accuracy than the conventional indicators of variation statistics and spectral analysis.