Metabolic adaptations to complex perturbations, like the response to pharmacological treatments in multifactorial diseases such as cancer, can be described through measurements of part of the fluxes and concentrations at the systemic level and individual transporter and enzyme activities at the molecular level. In the framework of Metabolic Control Analysis (MCA), ensembles of linear constraints can be built integrating these measurements at both systemic and molecular levels, which are expressed as relative differences or changes produced in the metabolic adaptation. Here, combining MCA with Linear Programming, an efficient computational strategy is developed to infer additional non-measured changes at the molecular level that are required to satisfy these constraints. An application of this strategy is illustrated by using a set of fluxes, concentrations, and differentially expressed genes that characterize the response to cyclin-dependent kinases 4 and 6 inhibition in colon cancer cells. Decreases and increases in transporter and enzyme individual activities required to reprogram the measured changes in fluxes and concentrations are compared with down-regulated and up-regulated metabolic genes to unveil those that are key molecular drivers of the metabolic response.

MOTIVATION: Developing a robust and performant data analysis workflow that integrates all necessary components whilst still being able to scale over multiple compute nodes is a challenging task. We introduce a generic method based on the microservice architecture, where software tools are encapsulated as Docker containers that can be connected into scientific workflows and executed using the Kubernetes container orchestrator. RESULTS: We developed a Virtual Research Environment (VRE) which facilitates rapid integration of new tools and developing scalable and interoperable workflows for performing metabolomics data analysis. The environment can be launched on-demand on cloud resources and desktop computers. IT-expertise requirements on the user side are kept to a minimum, and workflows can be re-used effortlessly by any novice user. We validate our method in the field of metabolomics on two mass spectrometry, one nuclear magnetic resonance spectroscopy and one fluxomics study. We showed that the method scales dynamically with increasing availability of computational resources. We demonstrated that the method facilitates interoperability using integration of the major software suites resulting in a turn-key workflow encompassing all steps for mass-spectrometry-based metabolomics including preprocessing, statistics and identification. Microservices is a generic methodology that can serve any scientific discipline and opens up for new types of large-scale integrative science. AVAILABILITY AND IMPLEMENTATION: The PhenoMeNal consortium maintains a web portal (https://portal.phenomenal-h2020.eu) providing a GUI for launching the Virtual Research Environment. The GitHub repository https://github.com/phnmnl/ hosts the source code of all projects. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Deciphering the mechanisms of regulation of metabolic networks subjected to perturbations, including disease states and drug-induced stress, relies on tracing metabolic fluxes. One of the most informative data to predict metabolic fluxes are 13C based metabolomics, which provide information about how carbons are redistributed along central carbon metabolism. Such data can be integrated using 13C Metabolic Flux Analysis (13C MFA) to provide quantitative metabolic maps of flux distributions. However, 13C MFA might be unable to reduce the solution space towards a unique solution either in large metabolic networks or when small sets of measurements are integrated. Here we present parsimonious 13C MFA (p13CMFA), an approach that runs a secondary optimization in the 13C MFA solution space to identify the solution that minimizes the total reaction flux. Furthermore, flux minimization can be weighted by gene expression measurements allowing seamless integration of gene expression data with 13C data. As proof of concept, we demonstrate how p13CMFA can be used to estimate intracellular flux distributions from 13C measurements and transcriptomics data. We have implemented p13CMFA in Iso2Flux, our in-house developed isotopic steady-state 13C MFA software. The source code is freely available on GitHub (https://github.com/cfoguet/iso2flux/releases/tag/0.7.2).

Epithelial-mesenchymal-transition promotes intra-tumoral heterogeneity, by enhancing tumor cell invasiveness and promoting drug resistance. We integrated transcriptomic data for two clonal subpopulations from a prostate cancer cell line (PC-3) into a genome-scale metabolic network model to explore their metabolic differences and potential vulnerabilities. In this dual cell model, PC-3/S cells express Epithelial-mesenchymal-transition markers and display high invasiveness and low metastatic potential, while PC-3/M cells present the opposite phenotype and higher proliferative rate. Model-driven analysis and experimental validations unveiled a marked metabolic reprogramming in long-chain fatty acids metabolism. While PC-3/M cells showed an enhanced entry of long-chain fatty acids into the mitochondria, PC-3/S cells used long-chain fatty acids as precursors of eicosanoid metabolism. We suggest that this metabolic reprogramming endows PC-3/M cells with augmented energy metabolism for fast proliferation and PC-3/S cells with increased eicosanoid production impacting angiogenesis, cell adhesion and invasion. PC-3/S metabolism also promotes the accumulation of docosahexaenoic acid, a long-chain fatty acid with antiproliferative effects. The potential therapeutic significance of our model was supported by a differential sensitivity of PC-3/M cells to etomoxir, an inhibitor of long-chain fatty acid transport to the mitochondria.

MOTIVATION: Skeletal muscle dysfunction is a systemic effect in one-third of patients with chronic obstructive pulmonary disease (COPD), characterized by high reactive-oxygen-species (ROS) production and abnormal endurance training-induced adaptive changes. However, the role of ROS in COPD remains unclear, not least because of the lack of appropriate tools to study multifactorial diseases. RESULTS: We describe a discrete model-driven method combining mechanistic and probabilistic approaches to decipher the role of ROS on the activity state of skeletal muscle regulatory network, assessed before and after an 8-week endurance training program in COPD patients and healthy subjects. In COPD, our computational analysis indicates abnormal training-induced regulatory responses leading to defective tissue remodeling and abnormal energy metabolism. Moreover, we identified tnf, insr, inha and myc as key regulators of abnormal training-induced adaptations in COPD. The tnf-insr pair was identified as a promising target for therapeutic interventions. Our work sheds new light on skeletal muscle dysfunction in COPD, opening new avenues for cost-effective therapies. It overcomes limitations of previous computational approaches showing high potential for the study of other multi-factorial diseases such as diabetes or cancer. CONTACT: [email protected] or [email protected] information: Supplementary data are available at Bioinformatics online.

Tracing stable isotopes, such as 13C using various mass spectrometry (MS) methods provides a valuable information necessary for the study of biochemical processes in cells. However, extracting such information requires special care, such as a correction for naturally occurring isotopes, or overlapping mass spectra of various components of the cell culture medium. Developing a method for a correction of overlapping peaks is the primary objective of this study. Our computer program-MIDcor (free at https://github.com/seliv55/mid_correct) written in the R programming language, corrects the raw MS spectra both for the naturally occurring isotopes and for the overlapping of peaks corresponding to various substances. To this end, the mass spectra of unlabeled metabolites measured in two media are necessary: in a minimal medium containing only derivatized metabolites and chemicals for derivatization, and in a complete cell incubated medium. The MIDcor program calculates the difference (D) between the theoretical and experimentally measured spectra of metabolites containing only the naturally occurring isotopes. The result of comparison of D in the two media determines a way of deciphering the true spectra. (1) If D in the complete medium is greater than that in the minimal medium in at least one peak, then unchanged D is subtracted from the raw spectra of the labeled metabolite. (2) If D does not depend on the medium, then the spectrum probably overlaps with a derivatized fragment of the same metabolite, and D is modified proportionally to the metabolite labeling. The program automatically reaches a decision regarding the way of correction. For some metabolites/fragments in the case (2) D was found to decrease when the tested substance was 13C labeled, and this isotopic effect also can be corrected automatically, if the user provides a measured spectrum of the substance in which the 13C labeling is known a priori. Using the developed program improves the reliability of stable isotope tracer data analysis.

BACKGROUND: Advances in high throughput technologies and growth of biomedical knowledge have contributed to an exponential increase in associative data. These data can be represented in the form of complex networks of biological associations, which are suitable for systems analyses. However, these networks usually lack both, context specificity in time and space as well as the distinctive borders, which are usually assigned in the classical pathway view of molecular events (e.g. signal transduction). This complexity and high interconnectedness call for automated techniques that can identify smaller targeted subnetworks specific to a given research context (e.g. a disease scenario). RESULTS: Our method, named ChainRank, finds relevant subnetworks by identifying and scoring chains of interactions that link specific network components. Scores can be generated from integrating multiple general and context specific measures (e.g. experimental molecular data from expression to proteomics and metabolomics, literature evidence, network topology). The performance of the novel ChainRank method was evaluated on recreating selected signalling pathways from a human protein interaction network. Specifically, we recreated skeletal muscle specific signaling networks in healthy and chronic obstructive pulmonary disease (COPD) contexts. The analysis showed that ChainRank can identify main mediators of context specific molecular signalling. An improvement of up to factor 2.5 was shown in the precision of finding proteins of the recreated pathways compared to random simulation. CONCLUSIONS: ChainRank provides a framework, which can integrate several user-defined scores and evaluate their combined effect on ranking interaction chains linking input data sets. It can be used to contextualise networks, identify signaling and regulatory path amongst targeted genes or to analyse synthetic lethality in the context of anticancer therapy. ChainRank is implemented in R programming language and freely available at https://github.com/atenyi/ChainRank.

The liver performs many essential metabolic functions, which can be studied using computational models of hepatocytes. Here we present HepatoDyn, a highly detailed dynamic model of hepatocyte metabolism. HepatoDyn includes a large metabolic network, highly detailed kinetic laws, and is capable of dynamically simulating the redox and energy metabolism of hepatocytes. Furthermore, the model was coupled to the module for isotopic label propagation of the software package IsoDyn, allowing HepatoDyn to integrate data derived from 13C based experiments. As an example of dynamical simulations applied to hepatocytes, we studied the effects of high fructose concentrations on hepatocyte metabolism by integrating data from experiments in which rat hepatocytes were incubated with 20 mM glucose supplemented with either 3 mM or 20 mM fructose. These experiments showed that glycogen accumulation was significantly lower in hepatocytes incubated with medium supplemented with 20 mM fructose than in hepatocytes incubated with medium supplemented with 3 mM fructose. Through the integration of extracellular fluxes and 13C enrichment measurements, HepatoDyn predicted that this phenomenon can be attributed to a depletion of cytosolic ATP and phosphate induced by high fructose concentrations in the medium.

BACKGROUND: Flux balance analysis is traditionally implemented to identify the maximum theoretical flux for some specified reaction and a single distribution of flux values for all the reactions present which achieve this maximum value. However it is well known that the uncertainty in reaction networks due to branches, cycles and experimental errors results in a large number of combinations of internal reaction fluxes which can achieve the same optimal flux value. RESULTS: In this work, we have modified the applied linear objective of flux balance analysis to include a poling penalty function, which pushes each new set of reaction fluxes away from previous solutions generated. Repeated poling-based flux balance analysis generates a sample of different solutions (a characteristic set), which represents all the possible functionality of the reaction network. Compared to existing sampling methods, for the purpose of generating a relatively "small" characteristic set, our new method is shown to obtain a higher coverage than competing methods under most conditions. The influence of the linear objective function on the sampling (the linear bias) constrains optimisation results to a subspace of optimal solutions all producing the same maximal fluxes. Visualisation of reaction fluxes plotted against each other in 2 dimensions with and without the linear bias indicates the existence of correlations between fluxes. This method of sampling is applied to the organism Actinobacillus succinogenes for the production of succinic acid from glycerol. CONCLUSIONS: A new method of sampling for the generation of different flux distributions (sets of individual fluxes satisfying constraints on the steady-state mass balances of intermediates) has been developed using a relatively simple modification of flux balance analysis to include a poling penalty function inside the resulting optimisation objective function. This new methodology can achieve a high coverage of the possible flux space and can be used with and without linear bias to show optimal versus sub-optimal solution spaces. Basic analysis of the Actinobacillus succinogenes system using sampling shows that in order to achieve the maximal succinic acid production CO₂ must be taken into the system. Solutions involving release of CO₂ all give sub-optimal succinic acid production.

The mitochondrial electron transport chain transforms energy satisfying cellular demand and generates reactive oxygen species (ROS) that act as metabolic signals or destructive factors. Therefore, knowledge of the possible modes and bifurcations of electron transport that affect ROS signaling provides insight into the interrelationship of mitochondrial respiration with cellular metabolism. Here, a bifurcation analysis of a sequence of the electron transport chain models of increasing complexity was used to analyze the contribution of individual components to the modes of respiratory chain behavior. Our algorithm constructed models as large systems of ordinary differential equations describing the time evolution of the distribution of redox states of the respiratory complexes. The most complete model of the respiratory chain and linked metabolic reactions predicted that condensed mitochondria produce more ROS at low succinate concentration and less ROS at high succinate levels than swelled mitochondria. This prediction was validated by measuring ROS production under various swelling conditions. A numerical bifurcation analysis revealed qualitatively different types of multistationary behavior and sustained oscillations in the parameter space near a region that was previously found to describe the behavior of isolated mitochondria. The oscillations in transmembrane potential and ROS generation, observed in living cells were reproduced in the model that includes interaction of respiratory complexes with the reactions of TCA cycle. Whereas multistationarity is an internal characteristic of the respiratory chain, the functional link of respiration with central metabolism creates oscillations, which can be understood as a means of auto-regulation of cell metabolism.

Reactive oxygen species (ROS) produced in the mitochondrial respiratory chain (RC) are primary signals that modulate cellular adaptation to environment, and are also destructive factors that damage cells under the conditions of hypoxia/reoxygenation relevant for various systemic diseases or transplantation. The important role of ROS in cell survival requires detailed investigation of mechanism and determinants of ROS production. To perform such an investigation we extended our rule-based model of complex III in order to account for electron transport in the whole RC coupled to proton translocation, transmembrane electrochemical potential generation, TCA cycle reactions, and substrate transport to mitochondria. It fits respiratory electron fluxes measured in rat brain mitochondria fueled by succinate or pyruvate and malate, and the dynamics of NAD(+) reduction by reverse electron transport from succinate through complex I. The fitting of measured characteristics gave an insight into the mechanism of underlying processes governing the formation of free radicals that can transfer an unpaired electron to oxygen-producing superoxide and thus can initiate the generation of ROS. Our analysis revealed an association of ROS production with levels of specific radicals of individual electron transporters and their combinations in species of complexes I and III. It was found that the phenomenon of bistability, revealed previously as a property of complex III, remains valid for the whole RC. The conditions for switching to a state with a high content of free radicals in complex III were predicted based on theoretical analysis and were confirmed experimentally. These findings provide a new insight into the mechanisms of ROS production in RC.

Chronic Obstructive Pulmonary Disease (COPD) is an inflammatory process of the lung inducing persistent airflow limitation. Extensive systemic effects, such as skeletal muscle dysfunction, often characterize these patients and severely limit life expectancy. Despite considerable research efforts, the molecular basis of muscle degeneration in COPD is still a matter of intense debate. In this study, we have applied a network biology approach to model the relationship between muscle molecular and physiological response to training and systemic inflammatory mediators. Our model shows that failure to co-ordinately activate expression of several tissue remodelling and bioenergetics pathways is a specific landmark of COPD diseased muscles. Our findings also suggest that this phenomenon may be linked to an abnormal expression of a number of histone modifiers, which we discovered correlate with oxygen utilization. These observations raised the interesting possibility that cell hypoxia may be a key factor driving skeletal muscle degeneration in COPD patients.

Increased production of reactive oxygen species (ROS) in mitochondria underlies major systemic diseases, and this clinical problem stimulates a great scientific interest in the mechanism of ROS generation. However, the mechanism of hypoxia-induced change in ROS production is not fully understood. To mathematically analyze this mechanism in details, taking into consideration all the possible redox states formed in the process of electron transport, even for respiratory complex III, a system of hundreds of differential equations must be constructed. Aimed to facilitate such tasks, we developed a new methodology of modeling, which resides in the automated construction of large sets of differential equations. The detailed modeling of electron transport in mitochondria allowed for the identification of two steady state modes of operation (bistability) of respiratory complex III at the same microenvironmental conditions. Various perturbations could induce the transition of respiratory chain from one steady state to another. While normally complex III is in a low ROS producing mode, temporal anoxia could switch it to a high ROS producing state, which persists after the return to normal oxygen supply. This prediction, which we qualitatively validated experimentally, explains the mechanism of anoxia-induced cell damage. Recognition of bistability of complex III operation may enable novel therapeutic strategies for oxidative stress and our method of modeling could be widely used in systems biology studies.

MOTIVATION: A very promising approach in drug discovery involves the integration of available biomedical data through mathematical modelling and data mining. We have developed a method called optimization program for drug discovery (OPDD) that allows new enzyme targets to be identified in enzymopathies through the integration of metabolic models and biomedical data in a mathematical optimization program. The method involves four steps: (i) collection of the necessary information about the metabolic system and disease; (ii) translation of the information into mathematical terms; (iii) computation of the optimization programs prioritizing the solutions that propose the inhibition of a reduced number of enzymes and (iv) application of additional biomedical criteria to select and classify the solutions. Each solution consists of a set of predicted values for metabolites, initial substrates and enzyme activities, which describe a biologically acceptable steady state of the system that shifts the pathologic state towards a healthy state. RESULTS: The OPDD was used to detect target enzymes in an enzymopathy, the human hyperuricemia. An existing S-system model and bibliographic information about the disease were used. The method detected six single-target enzyme solutions involving dietary modification, one of them coinciding with the conventional clinical treatment using allopurinol. The OPDD detected a large number of possible solutions involving two enzyme targets. All except one contained one of the previously detected six enzyme targets. The purpose of this work was not to obtain solutions for direct clinical implementation but to illustrate how increasing levels of biomedical information can be integrated together with mathematical models in drug discovery. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Metabolic flux analysis of biochemical reaction networks using isotope tracers requires software tools that can analyze the dynamics of isotopic isomer (isotopomer) accumulation in metabolites and reveal the underlying kinetic mechanisms of metabolism regulation. Since existing tools are restricted by the isotopic steady state and remain disconnected from the underlying kinetic mechanisms, we have recently developed a novel approach for the analysis of tracer-based metabolomic data that meets these requirements. The present contribution describes the last step of this development: implementation of (i) the algorithms for the determination of the kinetic parameters and respective metabolic fluxes consistent with the experimental data and (ii) statistical analysis of both fluxes and parameters, thereby lending it a practical application. RESULTS: The C++ applications package for dynamic isotopomer distribution data analysis was supplemented by (i) five distinct methods for resolving a large system of differential equations; (ii) the 'simulated annealing' algorithm adopted to estimate the set of parameters and metabolic fluxes, which corresponds to the global minimum of the difference between the computed and measured isotopomer distributions; and (iii) the algorithms for statistical analysis of the estimated parameters and fluxes, which use the covariance matrix evaluation, as well as Monte Carlo simulations. An example of using this tool for the analysis of (13)C distribution in the metabolites of glucose degradation pathways has demonstrated the evaluation of optimal set of parameters and fluxes consistent with the experimental pattern, their range and statistical significance, and also the advantages of using dynamic rather than the usual steady-state method of analysis. AVAILABILITY: Software is available free from http://www.bq.ub.es/bioqint/selivanov.htm

MOTIVATION: Addition of labeled substrates and the measurement of the subsequent distribution of the labels in isotopomers in reaction networks provide a unique method for assessing metabolic fluxes in whole cells. However, owing to insufficiency of information, attempts to quantify the fluxes often yield multiple possible sets of solutions that are consistent with a given experimental pattern of isotopomers. In the study of the pentose phosphate pathways, the need to consider isotope exchange reactions of transketolase (TK) and transaldolase (TA) (which in past analyses have often been ignored) magnifies this problem; but accounting for the interrelation between the fluxes known from biochemical studies and kinetic modeling solves it. The mathematical relationships between kinetic and equilibrium constants restrict the domain of estimated fluxes to the ones compatible not only with a given set of experimental data, but also with other biochemical information. METHOD: We present software that integrates kinetic modeling with isotopomer distribution analysis. It solves the ordinary differential equations for total concentrations (accounting for the kinetic mechanisms) as well as for all isotopomers in glycolysis and the pentose phosphate pathway (PPP). In the PPP the fluxes created in the TK and TA reactions are expressed through unitary rate constants. The algorithms that account for all the kinetic and equilbrium constant constraints are integrated with the previously developed algorithms, which have been further optimized. The most time-consuming calculations were programmed directly in assembly language; this gave an order of magnitude decrease in the computation time, thus allowing analysis of more complex systems. The software was developed as C-code linked to a program written in Mathematica (Wolfram Research, Champaign, IL), and also as a C++ program independent from Mathematica. RESULTS: Implementing constraints imposed by kinetic and equilibrium constants in the isotopomer distribution analysis in the data from the cancer cells eliminated estimates of fluxes that were inconsistent with the kinetic mechanisms of TK and TA. Fluxes measured experimentally in cells can be used to estimate better the kinetics of TK and TA as they operate in situ. Thus, our approach of integrating various methods for in situ flux analysis opens up the possibility of designing new types of experiments to probe metabolic interrelationships, including the incorporation of additional biochemical information. AVAILABILITY: Software is available freely at: http://www.bq.ub.es/bioqint/selivanov.htm CONTACT: [email protected]

MOTIVATION: Analysis of the conversion of (13)C glucose within the metabolic network allows the evaluation of the biochemical fluxes in interconnecting metabolic pathways. Such analyses require solving hundreds of equations with respect to individual isotopomer concentrations, and this assumes applying special software even for constructing the equations. The algorithm, proposed by others could be improved. METHOD: A C-code linked to the program written in Mathematica (Wolfram Research Inc.), constructs and solves differential equations for all isotopomer concentrations, using the general enzyme characteristics (K(m), equilibrium constant, etc.). This code uses innovative algorithm of determination for the isotopomers-products, thus essentially decreasing the computation time. Feasible metabolic fluxes are provided by the parameters of enzyme kinetics found from the data fitting. RESULTS: The software effectively evaluates metabolic fluxes based on the measured isotopomer distribution, as was illustrated by the analysis of glycolysis and pentose phosphate cycle. The mechanism of transketolase and transaldolase catalysis was shown to induce a specific kind of isotopomer re-distribution, which, despite the significance of its effect, usually is not taken into account. AVAILABILITY: The software could be freely downloaded from the site: http://bq.ub.es/bioqint/label_distribution/.