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.     

Iterative algorithm of discrete Fourier transform for processing randomly sampled NMR data sets

Spectra obtained by application of multidimensional Fourier Transformation (MFT) to sparsely sampled nD NMR signals are usually corrupted due to missing data. In the present paper this phenomenon is investigated on simulations and experiments. An effective iterative algorithm for artifact suppression for sparse on-grid NMR data sets is discussed in detail. It includes automated peak recognition based on statistical methods. The results enable one to study NMR spectra of high dynamic range of peak intensities preserving benefits of random sampling, namely the superior resolution in indirectly measured dimensions. Experimental examples include 3D ¹⁵N- and ¹³C-edited NOESY-HSQC spectra of human ubiquitin.     

Towards automatic metabolomic profiling of high-resolution one-dimensional proton NMR spectra

Nuclear magnetic resonance (NMR) and Mass Spectroscopy (MS) are the two most common spectroscopic analytical techniques employed in metabolomics. The large spectral datasets generated by NMR and MS are often analyzed using data reduction techniques like Principal Component Analysis (PCA). Although rapid, these methods are susceptible to solvent and matrix effects, high rates of false positives, lack of reproducibility and limited data transferability from one platform to the next. Given these limitations, a growing trend in both NMR and MS-based metabolomics is towards targeted profiling or "quantitative" metabolomics, wherein compounds are identified and quantified via spectral fitting prior to any statistical analysis.?Despite the obvious advantages of this method, targeted profiling is hindered by the time required to perform manual or computer-assisted spectral fitting. In an effort to increase data analysis throughput for NMR-based metabolomics, we have developed an automatic method for identifying and quantifying metabolites in one-dimensional (1D) proton NMR spectra. This new algorithm is capable of using carefully constructed reference spectra and optimizing thousands of variables to reconstruct experimental NMR spectra of biofluids using rules and concepts derived from physical chemistry and NMR theory. The automated profiling program has been tested against spectra of synthetic mixtures as well as biological spectra of urine, serum and cerebral spinal fluid (CSF). Our results indicate that the algorithm can correctly identify compounds with high fidelity in each biofluid sample (except for urine). Furthermore, the metabolite concentrations exhibit a very high correlation with both simulated and manually-detected values.     

Multifractal Analysis for Nutritional Assessment

The concept of multifractality is currently used to describe self-similar and complex scaling properties observed in numerous biological signals. Fractals are geometric objects or dynamic variations which exhibit some degree of similarity (irregularity) to the original object in a wide range of scales. This approach determines irregularity of biologic signal as an indicator of adaptability, the capability to respond to unpredictable stress, and health. In the present work, we propose the application of multifractal analysis of wavelet-transformed proton nuclear magnetic resonance (¹H NMR) spectra of plasma to determine nutritional insufficiency. For validation of this method on ¹H NMR signal of human plasma, standard deviation from classical statistical approach and Hurst exponent (H), left slope and partition function from multifractal analysis were extracted from ¹H NMR spectra to test whether multifractal indices could discriminate healthy subjects from unhealthy, intensive care unit patients. After validation, the multifractal approach was applied to spectra of plasma from a modified crossover study of sulfur amino acid insufficiency and tested for associations with blood lipids. The results showed that standard deviation and H, but not left slope, were significantly different for sulfur amino acid sufficiency and insufficiency. Quadratic discriminant analysis of H, left slope and the partition function showed 78% overall classification accuracy according to sulfur amino acid status. Triglycerides and apolipoprotein C3 were significantly correlated with a multifractal model containing H, left slope, and standard deviation, and cholesterol and high-sensitivity C-reactive protein were significantly correlated to H. In conclusion, multifractal analysis of ¹H NMR spectra provides a new approach to characterize nutritional status.     

Solid-state NMR analysis of a peptide (Gly-Pro-Gly-Gly-Ala)6-Gly derived from a flagelliform silk sequence of Nephila clavipes

Solid-state NMR is especially useful when the structures of peptides and proteins should be analyzed by taking into account the structural distribution, that is, the distribution of the torsion angle of the individual residue. In this study, two-dimensional spin-diffusion solid-state NMR spectra of 13C-double-labeled model peptides (GPGGA)6G of flagelliform silk were observed for studying the local structure in the solid state. The spin-diffusion NMR spectra calculated by assuming the torsion angles of the beta-spiral structure exclusively could not reproduce the observed spectra. In contrast, the spectra calculated by taking into account the statistical distribution of the torsion angles of the individual central residues in the sequences Ala-Gly-Pro, Gly-Pro-Gly, Pro-Gly-Gly, Gly-Gly-Ala, and Gly-Ala-Gly from PDB data could reproduce the observed spectra well. This indicates that the statistical distribution of the torsion angles should be considered for the structural model of (GPGGA)6G similar to the case of the model peptide of elastin.     

Determination of barrier heights and prefactors from protein folding rate data

We determine both barrier heights and prefactors for protein folding by applying constraints determined from experimental rate measurements to a Kramers theory for folding rate. The theoretical values are required to match the experimental values at two conditions of temperature and denaturant that induce the same stability. Several expressions for the prefactor in the Kramers rate equation are examined: a random energy approximation, a correlated energy approximation, and an approximation using a single Arrhenius activation energy. Barriers and prefactors are generally found to be large as a result of implementing this recipe, i.e., the folding landscape is cooperative and smooth. Interestingly, a prefactor with a single Arrhenius activation energy admits no formal solution.     

Rapid identification of Candida species by using nuclear magnetic resonance spectroscopy and a statistical classification strategy

Nuclear magnetic resonance (NMR) spectra were acquired from suspensions of clinically important yeast species of the genus Candida to characterize the relationship between metabolite profiles and species identification. Major metabolites were identified by using two-dimensional correlation NMR spectroscopy. One-dimensional proton NMR spectra were analyzed by using a staged statistical classification strategy. Analysis of NMR spectra from 442 isolates of Candida albicans, C. glabrata, C. krusei, C. parapsilosis, and C. tropicalis resulted in rapid, accurate identification when compared with conventional and DNA-based identification. Spectral regions used for the classification of the five yeast species revealed species-specific differences in relative amounts of lipids, trehalose, polyols, and other metabolites. Isolates of C. parapsilosis and C. glabrata with unusual PCR fingerprinting patterns also generated atypical NMR spectra, suggesting the possibility of intraspecies discontinuity. We conclude that NMR spectroscopy combined with a statistical classification strategy is a rapid, nondestructive, and potentially valuable method for identification and chemotaxonomic characterization that may be broadly applicable to fungi and other microorganisms.     

On a mathematical procedure for detecting significant parameters in the classification of a statistical ensemble of phenomena and its applications

Summary The paper is concerned with a procedure for detecting the uncorrelated linear combinations of a given set of random variables. The linear transformation which is used is related to the eigenvectors of the covariance matrix for the original random variables. If the significant non correlated signals are in number less than the original ones (which have often a high degree of redundancy) the possibility arises for an application of this procedure to some branches of communication theory. The most important applications should be to vocoder for a further compression of information, for masking messages and also for building a machine which should be able to classify a statistical ensemble after suitable coding. The procedure has been tested by trying to extract significant parameters from a special coding of spoken Italian vowels in view of an improvement in the efficiency of speech recognition.     

Metabolic differentiation of Arabidopsis treated with methyl jasmonate using nuclear magnetic resonance spectroscopy

NMR spectroscopy combined with principal component analysis was applied to Arabidopsis thaliana treated with methyl jasmonate in order to obtain macroscopic metabolic changes caused by the treatment. As the first step several chromatographic and NMR spectroscopic techniques were utilized to identify metabolites of Arabidopsis. Sephadex LH-20 showed a high efficiency in the separation of phenolic metabolites in the plant. For identification of minor metabolites two-dimensional J-resolved NMR technique was directly applied to the plant extract and results in a number of elucidation of the metabolites of which signals overlap in ¹H NMR spectra. The chemical structure of the identified metabolites were confirmed by various two-dimensional NMR spectroscopy including correlated spectroscopy, heteronuclear single quantum coherence, and heternuclear multiple bond correlation. As next step, a statistical approach, principal component analysis based on projected J-resolved NMR spectra was performed for metabolic alteration of methyl jasmonate-treated Arabidopsis. The results show that methyl jasmonate caused an increase of flavonoids, fumaric acid, sinapoyl malate, sinigrin, tryptophan, valine, threonine, and alanine and a decrease of malic acid, feruloyl malate, glutamine, and carbohydrates after 24 h treatment.     

Synthesis and luminescence properties of pyrazolone derivatives and their terbium complexes

Seven novel pyrazolone derivatives were synthesized and characterized by ¹H NMR and ¹³C NMR spectra, mass spectra, infrared spectra and elemental analysis. Their terbium complexes were prepared and characterized by elemental analysis, EDTA titrimetric analysis, UV/vis spectra, infrared spectra and molar conductivity, as well as thermal analysis. The fluorescence properties and fluorescence quantum yields of the complexes were investigated at room temperature. The results indicated that pyrazolone derivatives had good energy‐transfer efficiency for the terbium ion. All the terbium complexes emitted green fluorescence characteristic of terbium ions, possessed strong fluorescence intensity, and showed relatively high fluorescence quantum yields. Cyclic voltammograms of the terbium complexes were studied and the highest occupied molecular orbital (HOMO) and lowest occupied molecular orbital (LUMO) energy levels of these complexes were estimated. Copyright © 2014 John Wiley & Sons, Ltd.     

Effects of the anti-cancer drug adriamycin on the energy metabolism of rat heart as measured by in vivo 31P-NMR and implications for adriamycin-induced cardiotoxicity

In vivo 31P-NMR was used to measure the effects of the anti-tumor drug adriamycin on the energy metabolism of rat heart. The exclusive acquisition of NMR signal from cardiac muscle was assured by positioning a solenoidal radio-frequency NMR coil around the heart. Appropriate control experiments verified that 31P-NMR spectra solely originated from this organ. Acute effects occurring shortly after adriamycin administration are expressed in 31P spectra as a dose-dependent decline in the cardiac levels of phosphocreatine, after which stabilization at a new steady-state level occurs. These acute effects of a single dose are complete in 30-60 min and no significant further changes take place within 150 min after drug introduction. Longer-term effects of single high doses and of multiple lower doses were measured up to a week after the initiation of treatment. It seemed that at a total dose of 20 mg/kg, drug-induced interference with cardiac energy metabolism was more pronounced than at the same dose in the acute phase. These 31P-NMR data demonstrate that adriamycin treatment is accompanied by a decrease of the cardiac phosphocreatine/ATP ratio which might be an expression of the well-established cardiotoxicity of the drug.     

Studies of yeast phenylalanine-accepting transfer ribonucleic acid backbone structure in solution by phosphorus-31 nuclear magnetic resonance spectroscopy.

Approximately 17 diester phosphates from the backbone structure of yeast tRNAPhe give rise to phosphorus resonances, which are resolved in its 31P NMR spectrum. To localize these diester phosphates within the tRNA structure, 31P NMR spectra of several chemically or enzymatically modified yeast tRNAPhe species were recorded. To this end selective modifications were performed in the anticodon, the DHU, and the T psi C loop. Modifications, performed in different loop regions, give rise to perturbation of different characteristic 31P resonances. The 31P spectra were correlated with the corresponding 1H NMR spectra of the ring N hydrogen-bonded protons and interpreted in view of the X-ray results obtained on yeast tRNAPhe. It is concluded that the diester phosphate groups, which experience an unusual shift, can be accounted for in the X-ray structure in terms of hydrogen-bonded phosphates groups and diester phosphates with a diester geometry, deviating from the normal double-helical conformation.     

Use of multiple 13C-labeling strategies and 13C NMR to detect low levels of exogenous metabolites in the presence of large endogenous pools: measurement of glucose turnover in a human subject

A significant problem which may be encountered in 13C NMR studies of metabolism is the contribution that background levels of 13C may make to the observed spectra when low or tracer levels of the 13C label are used. We propose that the introduction of two or more labeled sites in the same tracer molecule is an effective strategy for eliminating or reducing this difficulty and demonstrate its feasibility in an isotope dilution study of glucose turnover in a human volunteer. This approach has two significant advantages over the more common use of a singly enriched labeling strategy: (i) as a consequence of the scalar coupling interactions, multiple-labeled metabolites will yield spectra distinct from those containing natural abundance 13C, and (ii) at a 99% level of enrichment for the precursor, concentration levels which are approximately 1% of the endogenous pools can be detected with approximately equal sensitivity. As a demonstration of this strategy, glucose production in a human subject was determined by continuous infusion of tracer levels of [U-13C6]glucose over a 4-h period and subsequent analysis of plasma levels of the tracer in vitro by NMR. Mass spectroscopy was used on the same samples to provide a basis for comparison of the precision and accuracy of the NMR technique. The results demonstrate the feasibility of the multiply labeled approach for detection by NMR of tracer amounts of label in the presence of a much larger endogenous pool of glucose. The NMR and mass spectrometric data gave quantitatively identical results for the glucose production rate demonstrating that equivalent data may be obtained by both methods.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

Distribution of parental genome blocks in recombinant inbred lines

We consider recombinant inbred lines obtained by crossing two given homozygous parents and then applying multiple generations of self-crossings or full-sib matings. The chromosomal content of any such line forms a mosaic of blocks, each alternatively inherited identically by descent from one of the parents. Quantifying the statistical properties of such mosaic genomes has remained an open challenge for many years. Here, we solve this problem by taking a continuous chromosome picture and assuming crossovers to be noninterfering. Using a continuous-time random walk framework and Markov chain theory, we determine the statistical properties of these identical-by-descent blocks. We find that successive block lengths are only very slightly correlated. Furthermore, the blocks on the ends of chromosomes are larger on average than the others, a feature understandable from the nonexponential distribution of block lengths.     

Ansig for Windows: An interactive computer program for semiautomatic assignment of protein NMR spectra

Assignment of NMR spectra is a prerequisite for structure determination of proteins using NMR. The time spent on the assignment is comparatively long compared to that spent on other parts in the protein structure determination process, but it can be shortened by using either interactive or fully automated computer programs. To benefit from the advantages of both types of program we have developed a version of the interactive assignment program ANSIG to include automatized, yet user-supervised, routines. The new program includes tools for (i) semiautomatic sequential assignment, (ii) plotting of distances from PDB structure files directly in NMR spectra and (iii) statistical analysis of distance restraint violations with the possibility to directly zoom to violated NOEs in NOESY spectra.     

Bayesian signal extraction from noisy FT NMR spectra

Summary The statistical interpretation of the histogram representation of NMR spectra is described, leading to an estimation of the probability density function of the noise. The white-noise and Gaussian hypotheses are discussed, and a new estimator of the noise standard deviation is derived from the histogram strategy. The Bayesian approach to NMR signal detection is presented. This approach homogeneously combines prior knowledge, obtained from the histogram strategy, together with the posterior information resulting from the test of presence of a set of reference shapes in the neighbourhood of each data point. This scheme leads to a new strategy in the local detection of NMR signals in 2D and 3D spectra, which is illustrated by a complete peak-picking algorithm.     

ASICS: an automatic method for identification and quantification of metabolites in complex 1D <Superscript>1</Superscript>H NMR spectra

Introduction

Experiments in metabolomics rely on the identification and quantification of metabolites in complex biological mixtures. This remains one of the major challenges in NMR/mass spectrometry analysis of metabolic profiles. These features are mandatory to make metabolomics asserting a general approach to test a priori formulated hypotheses on the basis of exhaustive metabolome characterization rather than an exploratory tool dealing with unknown metabolic features.

Objectives

In this article we propose a method, named ASICS, based on a strong statistical theory that handles automatically the metabolites identification and quantification in proton NMR spectra.

Methods

A statistical linear model is built to explain a complex spectrum using a library containing pure metabolite spectra. This model can handle local or global chemical shift variations due to experimental conditions using a warping function. A statistical lasso-type estimator identifies and quantifies the metabolites in the complex spectrum. This estimator shows good statistical properties and handles peak overlapping issues.

Results

The performances of the method were investigated on known mixtures (such as synthetic urine) and on plasma datasets from duck and human. Results show noteworthy performances, outperforming current existing methods.

Conclusion

ASICS is a completely automated procedure to identify and quantify metabolites in ¹H NMR spectra of biological mixtures. It will enable empowering NMR-based metabolomics by quickly and accurately helping experts to obtain metabolic profiles.

     

Comparison of 1D and 2D NMR spectroscopy for metabolic profiling

High-resolution, liquid state nuclear magnetic resonance (NMR) spectroscopy is a popular platform for metabolic profiling because the technique is nondestructive, quantitative, reproducible, and the spectra contain a wealth of biochemical information. Because of the large dynamic range of metabolite concentrations in biofluids, statistical analyses of one-dimensional (1D) proton NMR data tend to be biased toward selecting changes in more abundant metabolites. Although two-dimensional (2D) proton-proton experiments can alleviate spectral crowding, they have been mainly used for structural determination. In this study, 2D total correlation spectroscopy NMR was used to compare the global metabolic profiles of urine obtained from wild-type and Abcc6-knockout mice. The 2D data were compared to an improved 1D experiment in which signal contributions from macromolecules and the urea peak have been spectroscopically removed for more accurate quantitation of low-abundance metabolites. Although statistical models from both 1D and 2D data could differentiate samples acquired from the two groups of mice, only the 2D spectra allowed the characterization of statistically relevant changes in the low-abundance metabolites. While acquisition of the 2D data require more time, the data obtained resulted in a more meaningful and comprehensive metabolic profile, aided in metabolite identifications, and minimized ambiguities in peak assignments.     

A docking analysis of the statistical physics of protein-protein recognition

We describe protein-protein recognition within the frame of the random energy model of statistical physics. We simulate, by docking the component proteins, the process of association of two proteins that form a complex. We obtain the energy spectrum of a set of protein-protein complexes of known three-dimensional structure by performing docking in random orientations and scoring the models thus generated. We use a coarse protein representation where each amino acid residue is replaced by its Vorono? cell, and derive a scoring function by applying the evolutionary learning program ROGER to a set of parameters measured on that representation. Taking the scores of the docking models to be interaction energies, we obtain energy spectra for the complexes and fit them to a Gaussian distribution, from which we derive physical parameters such as a glass transition temperature and a specificity transition temperature.