Bradley Worley

Multivariate Analysis in Metabolomics

Metabolomics aims to provide a global snapshot of all small-molecule metabolites in cells and biological fluids, free of observational biases inherent to more focused studies of metabolism. However, the staggeringly high information content of such global analyses introduces a challenge of its own; efficiently forming biologically relevant conclusions from any given metabolomics dataset indeed requires specialized forms of data analysis. One approach to finding meaning in metabolomics datasets involves multivariate analysis (MVA) methods such as principal component analysis (PCA) and partial least squares projection to latent structures (PLS), where spectral features contributing most to variation or separation are identified for further analysis. However, as with any mathematical treatment, these methods are not a panacea; this review discusses the use of multivariate analysis for metabolomics, as well as common pitfalls and misconceptions.

Utilities for Quantifying Separation in PCA/PLS-DA Scores Plots

Metabolic fingerprinting studies rely on interpretations drawn from low-dimensional representations of spectral data generated by methods of multivariate analysis such as principal components analysis and projection to latent structures discriminant analysis. The growth of metabolic fingerprinting and chemometric analyses involving these low-dimensional scores plots necessitates the use of quantitative statistical measures to describe significant differences between experimental groups. Our updated version of the PCAtoTree software provides methods to reliably visualize and quantify separations in scores plots through dendrograms employing both nonparametric and parametric hypothesis testing to assess node significance, as well as scores plots identifying 95% confidence ellipsoids for all experimental groups.

MVAPACK: A Complete Data Handling Package for NMR Metabolomics

Data handling in the field of NMR metabolomics has historically been reliant on either in-house mathematical routines or long chains of expensive commercial software. Thus, while the relatively simple biochemical protocols of metabolomics maintain a low barrier to entry, new practitioners of metabolomics experiments are forced to either purchase expensive software packages or craft their own data handling solutions from scratch. This inevitably complicates the standardization and communication of data handling protocols in the field. We report a newly developed open-source platform for complete NMR metabolomics data handling, MVAPACK, and describe its application on an example metabolic fingerprinting data set.

Combining DI-ESI–MS and NMR datasets for metabolic profiling

Metabolomics datasets are commonly acquired by either mass spectrometry (MS) or nuclear magnetic resonance spectroscopy (NMR), despite their fundamental complementarity. In fact, combining MS and NMR datasets greatly improves the coverage of the metabolome and enhances the accuracy of metabolite identification, providing a detailed and high-throughput analysis of metabolic changes due to disease, drug treatment, or a variety of other environmental stimuli. Ideally, a single metabolomics sample would be simultaneously used for both MS and NMR analyses, minimizing the potential for variability between the two datasets. This necessitates the optimization of sample preparation, data collection and data handling protocols to effectively integrate direct-infusion MS data with one-dimensional (1D) 1H NMR spectra. To achieve this goal, we report for the first time the optimization of (i) metabolomics sample preparation for dual analysis by NMR and MS, (ii) high throughput, positive-ion direct infusion electrospray ionization mass spectrometry (DI-ESI–MS) for the analysis of complex metabolite mixtures, and (iii) data handling protocols to simultaneously analyze DI-ESI–MS and 1D 1H NMR spectral data using multiblock bilinear factorizations, namely multiblock principal component analysis (MB-PCA) and multiblock partial least squares (MB-PLS). Finally, we demonstrate the combined use of backscaled loadings, accurate mass measurements and tandem MS experiments to identify metabolites significantly contributing to class separation in MB-PLS-DA scores. We show that integration of NMR and DI-ESI–MS datasets yields a substantial improvement in the analysis of metabolome alterations induced by neurotoxin treatment.Graphical abstract

PCA as a practical indicator of OPLS-DA model reliability

BACKGROUND Principal Component Analysis (PCA) and Orthogonal Projections to Latent Structures Discriminant Analysis (OPLS-DA) are powerful statistical modeling tools that provide insights into separations between experimental groups based on high-dimensional spectral measurements from NMR, MS or other analytical instrumentation. However, when used without validation, these tools may lead investigators to statistically unreliable conclusions. This danger is especially real for Partial Least Squares (PLS) and OPLS, which aggressively force separations between experimental groups. As a result, OPLS-DA is often used as an alternative method when PCA fails to expose group separation, but this practice is highly dangerous. Without rigorous validation, OPLS-DA can easily yield statistically unreliable group separation. METHODS A Monte Carlo analysis of PCA group separations and OPLS-DA cross-validation metrics was performed on NMR datasets with statistically significant separations in scores-space. A linearly increasing amount of Gaussian noise was added to each data matrix followed by the construction and validation of PCA and OPLS-DA models. RESULTS With increasing added noise, the PCA scores-space distance between groups rapidly decreased and the OPLS-DA cross-validation statistics simultaneously deteriorated. A decrease in correlation between the estimated loadings (added noise) and the true (original) loadings was also observed. While the validity of the OPLS-DA model diminished with increasing added noise, the group separation in scores-space remained basically unaffected. CONCLUSION Supported by the results of Monte Carlo analyses of PCA group separations and OPLS-DA cross-validation metrics, we provide practical guidelines and cross-validatory recommendations for reliable inference from PCA and OPLS-DA models.

Deterministic multidimensional nonuniform gap sampling.

Born from empirical observations in nonuniformly sampled multidimensional NMR data relating to gaps between sampled points, the Poisson-gap sampling method has enjoyed widespread use in biomolecular NMR. While the majority of nonuniform sampling schemes are fully randomly drawn from probability densities that vary over a Nyquist grid, the Poisson-gap scheme employs constrained random deviates to minimize the gaps between sampled grid points. We describe a deterministic gap sampling method, based on the average behavior of Poisson-gap sampling, which performs comparably to its random counterpart with the additional benefit of completely deterministic behavior. We also introduce a general algorithm for multidimensional nonuniform sampling based on a gap equation, and apply it to yield a deterministic sampling scheme that combines burst-mode sampling features with those of Poisson-gap schemes. Finally, we derive a relationship between stochastic gap equations and the expectation value of their sampling probability densities.

13C NMR Reveals No Evidence of n−π* Interactions in Proteins

An interaction between neighboring carbonyl groups has been postulated to stabilize protein structures. Such an interaction would affect the C chemical shielding of the carbonyl groups, whose paramagnetic component is dominated by and excitations. Model compound calculations indicate that both the interaction energetics and the chemical shielding of the carbonyl group are instead dominated by a classical dipole-dipole interaction. A set of high-resolution protein structures with associated carbonyl C chemical shift assignments verifies this correlation and provides no evidence for an inter-carbonyl interaction.

Convex accelerated maximum entropy reconstruction.

Maximum entropy (MaxEnt) spectral reconstruction methods provide a powerful framework for spectral estimation of nonuniformly sampled datasets. Many methods exist within this framework, usually defined based on the magnitude of a Lagrange multiplier in the MaxEnt objective function. An algorithm is presented here that utilizes accelerated first-order convex optimization techniques to rapidly and reliably reconstruct nonuniformly sampled NMR datasets using the principle of maximum entropy. This algorithm - called CAMERA for Convex Accelerated Maximum Entropy Reconstruction Algorithm - is a new approach to spectral reconstruction that exhibits fast, tunable convergence in both constant-aim and constant-lambda modes. A high-performance, open source NMR data processing tool is described that implements CAMERA, and brief comparisons to existing reconstruction methods are made on several example spectra.

Subrandom methods for multidimensional nonuniform sampling

Methods of nonuniform sampling that utilize pseudorandom number sequences to select points from a weighted Nyquist grid are commonplace in biomolecular NMR studies, due to the beneficial incoherence introduced by pseudorandom sampling. However, these methods require the specification of a non-arbitrary seed number in order to initialize a pseudorandom number generator. Because the performance of pseudorandom sampling schedules can substantially vary based on seed number, this can complicate the task of routine data collection. Approaches such as jittered sampling and stochastic gap sampling are effective at reducing random seed dependence of nonuniform sampling schedules, but still require the specification of a seed number. This work formalizes the use of subrandom number sequences in nonuniform sampling as a means of seed-independent sampling, and compares the performance of three subrandom methods to their pseudorandom counterparts using commonly applied schedule performance metrics. Reconstruction results using experimental datasets are also provided to validate claims made using these performance metrics.

Metabolic Investigations of the Molecular Mechanisms Associated with Parkinson’s Disease

Parkinson’s disease (PD) is a neurodegenerative disorder characterized by fibrillar cytoplasmic aggregates of α-synuclein (i.e., Lewy bodies) and the associated loss of dopaminergic cells in the substantia nigra. Mutations in genes such as α-synuclein (SNCA) account for only 10% of PD occurrences. Exposure to environmental toxicants including pesticides and metals (e.g., paraquat (PQ) and manganese (Mn)) is also recognized as an important PD risk factor. Thus, aging, genetic alterations, and environmental factors all contribute to the etiology of PD. In fact, both genetic and environmental factors are thought to interact in the promotion of idiopathic PD, but the mechanisms involved are still unclear. In this study, we summarize our findings to date regarding the toxic synergistic effect between α-synuclein and paraquat treatment. We identified an essential role for central carbon (glucose) metabolism in dopaminergic cell death induced by paraquat treatment that is enhanced by the overexpression of α-synuclein. PQ “hijacks” the pentose phosphate pathway (PPP) to increase NADPH reducing equivalents and stimulate paraquat redox cycling, oxidative stress, and cell death. PQ also stimulated an increase in glucose uptake, the translocation of glucose transporters to the plasma membrane, and AMP-activated protein kinase (AMPK) activation. The overexpression of α-synuclein further stimulated an increase in glucose uptake and AMPK activity, but impaired glucose metabolism, likely directing additional carbon to the PPP to supply paraquat redox cycling.