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.

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.

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.

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.

Cocaine diminishes functional network robustness and destabilizes the energy landscape of neuronal activity in the medial prefrontal cortex.

We present analysis of neuronal activity recordings from a subset of neurons in the medial prefrontal cortex of rats before and after the administration of cocaine. Using an underlying modern Hopfield model as a description for the neuronal network, combined with a machine learning approach, we compute the underlying functional connectivity of the neuronal network. We find that the functional connectivity changes after the administration of cocaine with both functional-excitatory and functional-inhibitory neurons being affected. Using conventional network analysis, we find that the diameter of the graph, or the shortest length between the two most distant nodes, increases with cocaine, suggesting that the neuronal network is less robust. We also find that the betweenness centrality scores for several of the functional-excitatory and functional-inhibitory neurons decrease significantly, while other scores remain essentially unchanged, to also suggest that the neuronal network is less robust. Finally, we study the distribution of neuronal activity and relate it to energy to find that cocaine drives the neuronal network towards destabilization in the energy landscape of neuronal activation. While this destabilization is presumably temporary given one administration of cocaine, perhaps this initial destabilization indicates a transition towards a new stable state with repeated cocaine administration. However, such analyses are useful more generally to understand how neuronal networks respond to perturbations.

The neuroanatomical organization of the hypothalamus is driven by spatial and topological efficiency.

The hypothalamus in the mammalian brain is responsible for regulating functions associated with survival and reproduction representing a complex set of highly interconnected, yet anatomically and functionally distinct, sub-regions. It remains unclear what factors drive the spatial organization of sub-regions within the hypothalamus. One potential factor may be structural connectivity of the network that promotes efficient function with well-connected sub-regions placed closer together geometrically, i.e., the strongest axonal signal transferred through the shortest geometrical distance. To empirically test for such efficiency, we use hypothalamic data derived from the Allen Mouse Brain Connectivity Atlas, which provides a structural connectivity map of mouse brain regions derived from a series of viral tracing experiments. Using both cost function minimization and comparison with a weighted, sphere-packing ensemble, we demonstrate that the sum of the distances between hypothalamic sub-regions are not close to the minimum possible distance, consistent with prior whole brain studies. However, if such distances are weighted by the inverse of the magnitude of the connectivity, their sum is among the lowest possible values. Specifically, the hypothalamus appears within the top 94th percentile of neural efficiencies of randomly packed configurations and within one standard deviation of the median efficiency when packings are optimized for maximal neural efficiency. Our results, therefore, indicate that a combination of geometrical and topological constraints help govern the structure of the hypothalamus.