Exact Integral Formulas for False Discovery Rate and the Variance of False Discovery Proportion.

Multiple hypothesis testing is an integral component of data analysis for large-scale technologies such as proteomics, transcriptomics, or metabolomics, for which the false discovery rate (FDR) and positive FDR (pFDR) have been accepted as error estimation and control measures. The pFDR is the expectation of false discovery proportion (FDP), which refers to the ratio of the number of null hypotheses to that of all rejected hypotheses. In practice, the expectation of ratio is approximated by the ratio of expectation; however, the conditions for transforming the former into the latter have not been investigated. This work derives exact integral expressions for the expectation (pFDR) and variance of FDP. The widely used approximation (ratio of expectations) is shown to be a particular case (in the limit of a large sample size) of the integral formula for pFDR. A recurrence formula is provided to compute the pFDR for a predefined number of null hypotheses. The variance of FDP was approximated for a practical application in peptide identification using forward and reversed protein sequences. The simulations demonstrate that the integral expression exhibits better accuracy than the approximate formula in the case of a small number of hypotheses. For large sample sizes, the pFDRs obtained by the integral expression and approximation do not differ substantially. Applications to proteomics data sets are included.

Flexible Quality Control for Protein Turnover Rates Using d2ome.

Bioinformatics tools are used to estimate in vivo protein turnover rates from the LC-MS data of heavy water labeled samples in high throughput. The quantification includes peak detection and integration in the LC-MS domain of complex input data of the mammalian proteome, which requires the integration of results from different experiments. The existing software tools for the estimation of turnover rate use predefined, built-in, stringent filtering criteria to select well-fitted peptides and determine turnover rates for proteins. The flexible control of filtering and quality measures will help to reduce the effects of fluctuations and interferences to the signals from target peptides while retaining an adequate number of peptides. This work describes an approach for flexible error control and filtering measures implemented in the computational tool d2ome for automating protein turnover rates. The error control measures (based on spectral properties and signal features) reduced the standard deviation and tightened the confidence intervals of the estimated turnover rates.

A large-scale LC-MS dataset of murine liver proteome from time course of heavy water metabolic labeling.

Metabolic stable isotope labeling with heavy water followed by liquid chromatography coupled with mass spectrometry (LC-MS) is a powerful tool for in vivo protein turnover studies. Several algorithms and tools have been developed to determine the turnover rates of peptides and proteins from time-course stable isotope labeling experiments. The availability of benchmark mass spectrometry data is crucial to compare and validate the effectiveness of newly developed techniques and algorithms. In this work, we report a heavy water-labeled LC-MS dataset from the murine liver for protein turnover rate analysis. The dataset contains eighteen mass spectral data with their corresponding database search results from nine different labeling durations and quantification outputs from d2ome+ software. The dataset also contains eight mass spectral data from two-dimensional fractionation experiments on unlabeled samples.

Quantifying label enrichment from two mass isotopomers increases proteome coverage for in vivo protein turnover using heavy water metabolic labeling.

Heavy water metabolic labeling followed by liquid chromatography coupled with mass spectrometry is a powerful high throughput technique for measuring the turnover rates of individual proteins in vivo. The turnover rate is obtained from the exponential decay modeling of the depletion of the monoisotopic relative isotope abundance. We provide theoretical formulas for the time course dynamics of six mass isotopomers and use the formulas to introduce a method that utilizes partial isotope profiles, only two mass isotopomers, to compute protein turnover rate. The use of partial isotope profiles alleviates the interferences from co-eluting contaminants in complex proteome mixtures and improves the accuracy of the estimation of label enrichment. In five different datasets, the technique consistently doubles the number of peptides with high goodness-of-fit characteristics of the turnover rate model. We also introduce a software tool, d2ome+, which automates the protein turnover estimation from partial isotope profiles.

Retention Time Alignment for Protein Turnover Studies Using Heavy Water Metabolic Labeling.

Retention time (RT) alignment has been important for robust protein identification and quantification in proteomics. In data-dependent acquisition mode, whereby the precursor ions are semistochastically chosen for fragmentation in MS/MS, the alignment is used in an approach termed matched between runs (MBR). MBR transfers peptides, which were fragmented and identified in one experiment, to a replicate experiment where they were not identified. Before the MBR transfer, the RTs of experiments are aligned to reduce the chance of erroneous transfers. Despite its widespread use in other areas of quantitative proteomics, RT alignment has not been applied in data analyses for protein turnover using an atom-based stable isotope-labeling agent such as metabolic labeling with deuterium oxide, D2O. Deuterium incorporation changes isotope profiles of intact peptides in full scans and their fragment ions in tandem mass spectra. It reduces the peptide identification rates in current database search engines. Therefore, the MBR becomes more important. Here, we report on an approach to incorporate RT alignment with peptide quantification in studies of proteome turnover using heavy water metabolic labeling and LC-MS. The RT alignment uses correlation-optimized time warping. The alignment, followed by the MBR, improves labeling time point coverage, especially for long labeling durations.

Software Tool for Visualization and Validation of Protein Turnover Rates Using Heavy Water Metabolic Labeling and LC-MS.

Metabolic stable isotope labeling followed by liquid chromatography coupled with mass spectrometry (LC-MS) is a powerful tool for in vivo protein turnover studies of individual proteins on a large scale and with high throughput. Turnover rates of thousands of proteins from dozens of time course experiments are determined by data processing tools, which are essential components of the workflows for automated extraction of turnover rates. The development of sophisticated algorithms for estimating protein turnover has been emphasized. However, the visualization and annotation of the time series data are no less important. The visualization tools help to validate the quality of the model fits, their goodness-of-fit characteristics, mass spectral features of peptides, and consistency of peptide identifications, among others. Here, we describe a graphical user interface (GUI) to visualize the results from the protein turnover analysis tool, d2ome, which determines protein turnover rates from metabolic D2O labeling followed by LC-MS. We emphasize the specific features of the time series data and their visualization in the GUI. The time series data visualized by the GUI can be saved in JPEG format for storage and further dissemination.

Protein turnover models for LC-MS data of heavy water metabolic labeling.

Protein turnover is vital for cellular functioning and is often associated with the pathophysiology of a variety of diseases. Metabolic labeling with heavy water followed by liquid chromatography coupled to mass spectrometry is a powerful tool to study in vivo protein turnover in high throughput and large scale. Heavy water is a cost-effective and easy to use labeling agent. It labels all nonessential amino acids. Due to its toxicity in high concentrations (20% or higher), small enrichments (8% or smaller) of heavy water are used with most organisms. The low concentration results in incomplete labeling of peptides/proteins. Therefore, the data processing is more challenging and requires accurate quantification of labeled and unlabeled forms of a peptide from overlapping mass isotopomer distributions. The work describes the bioinformatics aspects of the analysis of heavy water labeled mass spectral data, available software tools and current challenges and opportunities.

Using Heavy Mass Isotopomers for Protein Turnover in Heavy Water Metabolic Labeling.

Metabolic labeling followed by LC-MS-based proteomics is a powerful tool to study proteome dynamics in high-throughput experiments both in vivo and in vitro. High mass resolution and accuracy allow differentiation in isotope profiles and the quantification of partially labeled peptide species. Metabolic labeling duration introduces a time domain in which the gradual incorporation of labeled isotopes is recorded. Different stable isotopes are used for labeling. Labeling with heavy water has advantages because it is cost-effective and easy to use. The protein degradation rate constant has been modeled using exponential decay models for the relative abundances of mass isotopomers. The recently developed closed-form equations were applied to study the analytic behavior of the heavy mass isotopomers in the time domain of metabolic labeling. The predictions from the closed-form equations are compared with the practices that have been used to extract degradation rate constants from the time-course profiles of heavy mass isotopomers. It is shown that all mass isotopomers, except for the monoisotope, require data transformations to obtain the exponential depletion, which serves as a basis for the rate constant model. Heavy mass isotopomers may be preferable choices for modeling high-mass peptides or peptides with a high number of labeling sites. The results are also applicable to stable isotope labeling with other atom-based labeling agents.

A novel estimator of the interaction matrix in Graphical Gaussian Model of omics data using the entropy of non-equilibrium systems.

MOTIVATION: Inferring the direct relationships between biomolecules from omics datasets is essential for the understanding of biological and disease mechanisms. Gaussian Graphical Model (GGM) provides a fairly simple and accurate representation of these interactions. However, estimation of the associated interaction matrix using data is challenging due to a high number of measured molecules and a low number of samples. RESULTS: In this article, we use the thermodynamic entropy of the non-equilibrium system of molecules and the data-driven constraints among their expressions to derive an analytic formula for the interaction matrix of Gaussian models. Through a data simulation, we show that our method returns an improved estimation of the interaction matrix. Also, using the developed method, we estimate the interaction matrix associated with plasma proteome and construct the corresponding GGM and show that known NAFLD-related proteins like ADIPOQ, APOC, APOE, DPP4, CAT, GC, HP, CETP, SERPINA1, COLA1, PIGR, IGHD, SAA1 and FCGBP are among the top 15% most interacting proteins of the dataset. AVAILABILITY AND IMPLEMENTATION: The supplementary materials can be found in the following URL: http://dynamic-proteome.utmb.edu/PrecisionMatrixEstimater/PrecisionMatrixEstimater.aspx. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Partial Isotope Profiles Are Sufficient for Protein Turnover Analysis Using Closed-Form Equations of Mass Isotopomer Dynamics.

Metabolic labeling with atom-based heavy isotopes, followed by liquid chromatography coupled with mass spectrometry (LC-MS), has been a powerful technique for studies of proteome and metabolome. In proteomics, the protein turnover of thousands of proteins can be estimated from the gradual incorporation of 2H or 15N in the diet. Software tools have been developed to automate the estimation of protein turnover. Traditionally, the turnover has been estimated using the time course of the depletion of the normalized abundance of monoisotopes. While the bioinformatic aspects of peak detection and integration, time course modeling, and uncertainty estimation have progressed, mass isotopomer dynamics during label incorporation has only been modeled from approximate approaches or numerical simulations. We derive closed-form equations that describe the dynamics of mass isotopomers during metabolic labeling with an atom-based stable isotope. The derived equations create an alternative method for estimating label incorporation. They also provide opportunities for estimation of precursor-product relationships in species or systems where they are unknown. The equations are useful in bioinformatic tools for analyzing mass spectral data from metabolic labeling.

High-Resolution Mass Spectrometry for In Vivo Proteome Dynamics using Heavy Water Metabolic Labeling.

Cellular proteins are continuously degraded and synthesized. The turnover of proteins is essential to many cellular functions. Combined with metabolic labeling using stable isotopes, LC-MS estimates proteome dynamics in high-throughput and on a large scale. Modern mass spectrometers allow a range of instrumental settings to optimize experimental output for specific research goals. One such setting which affects the results for dynamic proteome studies is the mass resolution. The resolution is vital for distinguishing target species from co-eluting contaminants with close mass-to-charge ratios. However, for estimations of proteome dynamics from metabolic labeling with stable isotopes, the spectral accuracy is highly important. Studies examining the effects of increased mass resolutions (in modern mass spectrometers) on the proteome turnover output and accuracy have been lacking. Here, we use a publicly available heavy water labeling and mass spectral data sets of murine serum proteome (acquired on Orbitrap Fusion and Agilent 6530 QToF) to analyze the effect of mass resolution of the Orbitrap mass analyzer on the proteome dynamics estimation. Increased mass resolution affected the spectral accuracy and the number acquired tandem mass spectra.

Timepoint Selection Strategy for In Vivo Proteome Dynamics from Heavy Water Metabolic Labeling and LC-MS.

Protein homeostasis, proteostasis, is essential for healthy cell functioning and is dysregulated in many diseases. Metabolic labeling with heavy water followed by liquid chromatography coupled online to mass spectrometry (LC-MS) is a powerful high-throughput technique to study proteome dynamics in vivo. Longer labeling duration and dense timepoint sampling (TPS) of tissues provide accurate proteome dynamics estimations. However, the experiments are expensive, and they require animal housing and care, as well as labeling with stable isotopes. Often, the animals are sacrificed at selected timepoints to collect tissues. Therefore, it is necessary to optimize TPS for a given number of sampling points and labeling duration and target a specific tissue of study. Currently, such techniques are missing in proteomics. Here, we report on a formula-based stochastic simulation strategy for TPS for in vivo studies with heavy water metabolic labeling and LC-MS. We model the rate constant (lognormal), measurement error (Laplace), peptide length (gamma), relative abundance of the monoisotopic peak (beta regression), and the number of exchangeable hydrogens (gamma regression). The parameters of the distributions are determined using the corresponding empirical probability density functions from a large-scale dataset of murine heart proteome. The models are used in the simulations of the rate constant to minimize the root-mean-square error (rmse). The rmse for different TPSs shows structured patterns. They are analyzed to elucidate common features in the patterns.

Calculation of the Protein Turnover Rate Using the Number of Incorporated 2H Atoms and Proteomics Analysis of a Single Labeled Sample.

Rate constant estimation with heavy water requires a long-term experiment with data collection at multiple time points (3-4 weeks for mitochondrial proteome dynamics in mice and much longer in other species). When tissue proteins are analyzed, this approach requires euthanizing animals at each time point or multiple tissue biopsies in humans. Although short-term protocols are available, they require knowledge of the maximum number of isotope labels (N) and accurate quantification of observed 2H-enrichment in the peptide. The high-resolution accurate mass spectrometers used for proteome dynamics studies are characterized by a systematic spectral error that compromises these measurements. To circumvent these issues, we developed a simple algorithm for the rate constant calculation based on a single labeled sample and comparable unlabeled (time 0) sample. The algorithm determines N for all proteogenic amino acids from a long-term experiment to calculate the predicted plateau 2H-labeling of peptides for a short-term protocol and estimates the rate constant based on the measured baseline and the predicted plateau 2H-labeling of peptides. The method was validated based on the rate constant estimation in a long-term experiment in mice and dogs. The improved 2 time-point method enables the rate constant calculation with less than 10% relative error compared to the bench-marked multi-point method in mice and dogs and allows us to detect diet-induced subtle changes in ApoAI turnover in mice. In conclusion, we have developed and validated a new algorithm for protein rate constant calculation based on 2-time point measurements that could also be applied to other biomolecules.

Another look at matrix correlations.

MOTIVATION: High throughput technologies are widely employed in modern biomedical research. They yield measurements of a large number of biomolecules in a single experiment. The number of experiments usually is much smaller than the number of measurements in each experiment. The simultaneous measurements of biomolecules provide a basis for a comprehensive, systems view for describing relevant biological processes. Often it is necessary to determine correlations between the data matrices under different conditions or pathways. However, the techniques for analyzing the data with a low number of samples for possible correlations within or between conditions are still in development. Earlier developed correlative measures, such as the RV coefficient, use the trace of the product of data matrices as the most relevant characteristic. However, a recent study has shown that the RV coefficient consistently overestimates the correlations in the case of low sample numbers. To correct for this bias, it was suggested to discard the diagonal elements of the outer products of each data matrix. In this work, a principled approach based on the matrix decomposition generates three trace-independent parts for every matrix. These components are unique, and they are used to determine different aspects of correlations between the original datasets. RESULTS: Simulations show that the decomposition results in the removal of high correlation bias and the dependence on the sample number intrinsic to the RV coefficient. We then use the correlations to analyze a real proteomics dataset. AVAILABILITY AND IMPLEMENTATION: The python code can be downloaded from http://dynamic-proteome.utmb.edu/MatrixCorrelations.aspx. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Proteome Dynamics from Heavy Water Metabolic Labeling and Peptide Tandem Mass Spectrometry.

Protein homeostasis (proteostasis) is a result of a dynamic equilibrium between protein synthesis and degradation. It is important for healthy cell/organ functioning and is often associated with diseases such as neurodegenerative diseases and non-Alcoholic Fatty Liver disease. Heavy water metabolic labeling, combined with liquid-chromatography and mass spectrometry (LC-MS), is a powerful approach to study proteostasis in vivo in high throughput. Traditionally, intact peptide signals are used to estimate stable isotope incorporation in time-course experiments. The time-course of label incorporation is used to extract protein decay rate constant (DRC). Intact peptide signals, computed from integration in chromatographic time and mass-to-charge ratio (m/z) domains, usually, provide an accurate estimate of label incorporation. However, sample complexity (co-elution), limited dynamic range, and low signal-to-noise ratio (S/N) may adversely interfere with the peptide signals. These artifacts complicate the DRC estimations by distorting peak shape in chromatographic time and m/z domains. Fragment ions, on the other hand, are less prone to these artifacts and are potentially well suited in aiding DRC estimations. Here, we show that the label incorporation encoded into the isotope distributions of fragment ions reflect the isotope enrichment during the metabolic labeling with heavy water. We explore the label incorporation statistics for devising practical approaches for DRC estimations.

d2ome, Software for in Vivo Protein Turnover Analysis Using Heavy Water Labeling and LC-MS, Reveals Alterations of Hepatic Proteome Dynamics in a Mouse Model of NAFLD.

Metabolic labeling with heavy water followed by LC-MS is a high throughput approach to study proteostasis in vivo. Advances in mass spectrometry and sample processing have allowed consistent detection of thousands of proteins at multiple time points. However, freely available automated bioinformatics tools to analyze and extract protein decay rate constants are lacking. Here, we describe d2ome-a robust, automated software solution for in vivo protein turnover analysis. d2ome is highly scalable, uses innovative approaches to nonlinear fitting, implements Grubbs' outlier detection and removal, uses weighted-averaging of replicates, applies a data dependent elution time windowing, and uses mass accuracy in peak detection. Here, we discuss the application of d2ome in a comparative study of protein turnover in the livers of normal vs Western diet-fed LDLR-/- mice (mouse model of nonalcoholic fatty liver disease), which contained 256 LC-MS experiments. The study revealed reduced stability of 40S ribosomal protein subunits in the Western diet-fed mice.

Hepatic Mitochondrial Defects in a Nonalcoholic Fatty Liver Disease Mouse Model Are Associated with Increased Degradation of Oxidative Phosphorylation Subunits.

Nonalcoholic fatty liver disease (NAFLD) is associated with hepatic mitochondrial dysfunction characterized by reduced ATP synthesis. We applied the 2H2O-metabolic labeling approach to test the hypothesis that the reduced stability of oxidative phosphorylation proteins contributes to mitochondrial dysfunction in a diet-induced mouse model of NAFLD. A high fat diet containing cholesterol (a so-called Western diet (WD)) led to hepatic oxidative stress, steatosis, inflammation and mild fibrosis, all markers of NAFLD, in low density cholesterol (LDL) receptor deficient (LDLR-/-) mice. In addition, compared with controls (LDLR-/- mice on normal diet), livers from NAFLD mice had reduced citrate synthase activity and ATP content, suggesting mitochondrial impairment. Proteome dynamics study revealed that mitochondrial defects are associated with reduced average half-lives of mitochondrial proteins in NAFLD mice (5.41 ± 0.46 versus 5.15 ± 0.49 day, p < 0.05). In particular, the WD reduced stability of oxidative phosphorylation subunits, including cytochrome b-c1 complex subunit 1 (5.9 ± 0.1 versus 3.4 ± 0.8 day), ATP synthase subunit α (6.3 ± 0.4 versus 5.5 ± 0.4 day) and ATP synthase F(0) complex subunit B1 of complex V (8.5 ± 0.6 versus 6.5 ± 0.2 day) (p < 0.05). These changes were associated with impaired complex III and F0F1-ATP synthase activities. Markers of mitophagy were increased, but proteasomal degradation activity were reduced in NAFLD mice liver, suggesting that ATP deficiency because of reduced stability of oxidative phosphorylation complex subunits contributed to inhibition of ubiquitin-proteasome and activation of mitophagy. In conclusion, the 2H2O-metabolic labeling approach shows that increased degradation of hepatic oxidative phosphorylation subunits contributed to mitochondrial impairment in NAFLD mice.

Poisson Model To Generate Isotope Distribution for Biomolecules.

We introduce a simplified computational algorithm for computing isotope distributions (relative abundances and masses) of biomolecules. The algorithm is based on Poisson approximation to binomial and multinomial distributions. It leads to a small number of arithmetic operations to compute isotope distributions of molecules. The approach uses three embedded loops to compute the isotope distributions, as compared with the eight embedded loops in exact calculations. The speed improvement is about 3-fold compared to the fast Fourier transformation-based isotope calculations, often termed as ultrafast isotope calculation. The approach naturally incorporates the determination of the masses of each molecular isotopomer. It is applicable to high mass accuracy and resolution mass spectrometry data. The application to tryptic peptides in a UniProt protein database revealed that the mass accuracy of the computed isotopomers is better than 1 ppm. Even better mass accuracy (below 1 ppm) is achievable when the method is paired with the exact calculations, which we term a hybrid approach. The algorithms have been implemented in a freely available C/C++ code.

Increased serotransferrin and ceruloplasmin turnover in diet-controlled patients with type 2 diabetes.

Type 2 diabetes mellitus (T2DM) is associated with oxidative stress and perturbed iron metabolism. Serotransferrin (Trf) and ceruloplasmin (Cp) are two key proteins involved in iron metabolism and anti-oxidant defense. Non-enzymatic glycation and oxidative modification of plasma proteins are known to occur under hyperglycemia and oxidative stress. In this study, shotgun proteomics and 2H2O-based metabolic labeling were used to characterize post-translational modifications and assess the kinetics of Trf and Cp in T2DM patients and matched controls in vivo. Six early lysine (Amadori) and one advanced arginine glycation were detected in Trf. No glycation, but five asparagine deamidations, were found in Cp. T2DM patients had increased fractional catabolic rates of both Trf and Cp that correlated with HbA1c (p < 0.05). The glycated Trf population was subject to an even faster degradation compared to the total Trf pool, suggesting that hyperglycemia contributed to an increased Trf degradation in T2DM patients. Enhanced production of Trf and Cp kept their levels stable. The changes in Trf and Cp turnover were associated with increased systemic oxidative stress without any alteration in iron status in T2DM. These findings can help better understand the potential role of altered Trf and Cp metabolism in the pathogenesis of T2DM and other diseases.