Reaction lumping in metabolic networks for application with thermodynamic metabolic flux analysis.
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ABSTRACT:
SUBMITTER: Seep L
PROVIDER: S-EPMC8058346 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:BackgroundIn recent years, constrained optimization - usually referred to as flux balance analysis (FBA) - has become a widely applied method for the computation of stationary fluxes in large-scale metabolic networks. The striking advantage of FBA as compared to kinetic modeling is that it basically requires only knowledge of the stoichiometry of the network. On the other hand, results of FBA are to a large degree hypothetical because the method relies on plausible but hardly provable optimality principles that are thought to govern metabolic flux distributions.ResultsTo augment the reliability of FBA-based flux calculations we propose an additional side constraint which assures thermodynamic realizability, i.e. that the flux directions are consistent with the corresponding changes of Gibb's free energies. The latter depend on metabolite levels for which plausible ranges can be inferred from experimental data. Computationally, our method results in the solution of a mixed integer linear optimization problem with quadratic scoring function. An optimal flux distribution together with a metabolite profile is determined which assures thermodynamic realizability with minimal deviations of metabolite levels from their expected values. We applied our novel approach to two exemplary metabolic networks of different complexity, the metabolic core network of erythrocytes (30 reactions) and the metabolic network iJR904 of Escherichia coli (931 reactions). Our calculations show that increasing network complexity entails increasing sensitivity of predicted flux distributions to variations of standard Gibb's free energy changes and metabolite concentration ranges. We demonstrate the usefulness of our method for assessing critical concentrations of external metabolites preventing attainment of a metabolic steady state.ConclusionOur method incorporates the thermodynamic link between flux directions and metabolite concentrations into a practical computational algorithm. The weakness of conventional FBA to rely on intuitive assumptions about the reversibility of biochemical reactions is overcome. This enables the computation of reliable flux distributions even under extreme conditions of the network (e.g. enzyme inhibition, depletion of substrates or accumulation of end products) where metabolite concentrations may be drastically altered.
| S-EPMC1903363 | biostudies-literature
Project description:Motivation:Elementary flux mode (EFM) analysis allows an unbiased description of metabolic networks in terms of minimal pathways (involving a minimal set of reactions). To date, the enumeration of EFMs is impracticable in genome-scale metabolic models. In a complementary approach, we introduce the concept of a flux tope (FT), involving a maximal set of reactions (with fixed directions), which allows one to study the coordination of reaction directions in metabolic networks and opens a new way for EFM enumeration. Results:A FT is a (nontrivial) subset of the flux cone specified by fixing the directions of all reversible reactions. In a consistent metabolic network (without unused reactions), every FT contains a 'maximal pathway', carrying flux in all reactions. This decomposition of the flux cone into FTs allows the enumeration of EFMs (of individual FTs) without increasing the problem dimension by reaction splitting. To develop a mathematical framework for FT analysis, we build on the concepts of sign vectors and hyperplane arrangements. Thereby, we observe that FT analysis can be applied also to flux optimization problems involving additional (inhomogeneous) linear constraints. For the enumeration of FTs, we adapt the reverse search algorithm and provide an efficient implementation. We demonstrate that (biomass-optimal) FTs can be enumerated in genome-scale metabolic models of B.cuenoti and E.coli, and we use FTs to enumerate EFMs in models of M.genitalium and B.cuenoti. Availability and implementation:The source code is freely available at https://github.com/mpgerstl/FTA. Supplementary information:Supplementary data are available at Bioinformatics online.
| S-EPMC6330010 | biostudies-literature
Project description:MotivationRandom sampling of metabolic fluxes can provide a comprehensive description of the capabilities of a metabolic network. However, current sampling approaches do not model thermodynamics explicitly, leading to inaccurate predictions of an organism's potential or actual metabolic operations.ResultsWe present a probabilistic framework combining thermodynamic quantities with steady-state flux constraints to analyze the properties of a metabolic network. It includes methods for probabilistic metabolic optimization and for joint sampling of thermodynamic and flux spaces. Applied to a model of E. coli, we use the methods to reveal known and novel mechanisms of substrate channeling, and to accurately predict reaction directions and metabolite concentrations. Interestingly, predicted flux distributions are multimodal, leading to discrete hypotheses on E. coli's metabolic capabilities.AvailabilityPython and MATLAB packages available at https://gitlab.com/csb.ethz/pta.Supplementary informationSupplementary data are available at Bioinformatics online.
| S-EPMC8479673 | biostudies-literature
Project description:BackgroundChemical reaction networks provide an abstraction scheme for a broad range of models in biology and ecology. The two common means for simulating these networks are the deterministic and the stochastic approaches. The traditional deterministic approach, based on differential equations, enjoys a rich set of analysis techniques, including a treatment of reaction fluxes. However, the discrete stochastic simulations, which provide advantages in some cases, lack a quantitative treatment of network fluxes.ResultsWe describe a method for flux analysis of chemical reaction networks, where flux is given by the flow of species between reactions in stochastic simulations of the network. Extending discrete event simulation algorithms, our method constructs several data structures, and thereby reveals a variety of statistics about resource creation and consumption during the simulation. We use these structures to quantify the causal interdependence and relative importance of the reactions at arbitrary time intervals with respect to the network fluxes. This allows us to construct reduced networks that have the same flux-behavior, and compare these networks, also with respect to their time series. We demonstrate our approach on an extended example based on a published ODE model of the same network, that is, Rho GTP-binding proteins, and on other models from biology and ecology.ConclusionsWe provide a fully stochastic treatment of flux analysis. As in deterministic analysis, our method delivers the network behavior in terms of species transformations. Moreover, our stochastic analysis can be applied, not only at steady state, but at arbitrary time intervals, and used to identify the flow of specific species between specific reactions. Our cases study of Rho GTP-binding proteins reveals the role played by the cyclic reverse fluxes in tuning the behavior of this network.
| S-EPMC3878955 | biostudies-literature
Project description:Thermodynamic analysis of metabolic networks has recently generated increasing interest for its ability to add constraints on metabolic network operation, and to combine metabolic fluxes and metabolite measurements in a mechanistic manner. Concepts for the calculation of the change in Gibbs energy of biochemical reactions have long been established. However, a concept for incorporation of cross-membrane transport in these calculations is still missing, although the theory for calculating thermodynamic properties of transport processes is long known. Here, we have developed two equivalent equations to calculate the change in Gibbs energy of combined transport and reaction processes based on two different ways of treating biochemical thermodynamics. We illustrate the need for these equations by showing that in some cases there is a significant difference between the proposed correct calculation and using an approximative method. With the developed equations, thermodynamic analysis of metabolic networks spanning over multiple physical compartments can now be correctly described.
| S-EPMC2980713 | biostudies-literature
Project description:BackgroundWith the advent of genomic technology, the size of metabolic networks that are subject to analysis is growing. A common task when analyzing metabolic networks is to find all possible steady state regimes. There are several technical issues that have to be addressed when analyzing large metabolic networks including accumulation of numerical errors and presentation of the solution to the researcher. One way to resolve those technical issues is to analyze the network using symbolic methods. The aim of this paper is to develop a routine that symbolically finds the steady state solutions of large metabolic networks.ResultsA symbolic Gauss-Jordan elimination routine was developed for analyzing large metabolic networks. This routine was tested by finding the steady state solutions for a number of curated stoichiometric matrices with the largest having about 4000 reactions. The routine was able to find the solution with a computational time similar to the time used by a numerical singular value decomposition routine. As an advantage of symbolic solution, a set of independent fluxes can be suggested by the researcher leading to the formation of a desired flux basis describing the steady state solution of the network. These independent fluxes can be constrained using experimental data. We demonstrate the application of constraints by calculating a flux distribution for the central metabolic and amino acid biosynthesis pathways of yeast.ConclusionsWe were able to find symbolic solutions for the steady state flux distribution of large metabolic networks. The ability to choose a flux basis was found to be useful in the constraint process and provides a strong argument for using symbolic Gauss-Jordan elimination in place of singular value decomposition.
| S-EPMC3130677 | biostudies-literature
Project description:In pursuit of establishing a realistic metabolic phenotypic space, the reversibility of reactions is thermodynamically constrained in modern metabolic networks. The reversibility constraints follow from heuristic thermodynamic poise approximations that take anticipated cellular metabolite concentration ranges into account. Because constraints reduce the feasible space, draft metabolic network reconstructions may need more extensive reconciliation, and a larger number of genes may become essential. Notwithstanding ubiquitous application, the effect of reversibility constraints on the predictive capabilities of metabolic networks has not been investigated in detail. Instead, work has focused on the implementation and validation of the thermodynamic poise calculation itself. With the advance of fast linear programming-based network reconciliation, the effects of reversibility constraints on network reconciliation and gene essentiality predictions have become feasible and are the subject of this study. Networks with thermodynamically informed reversibility constraints outperformed gene essentiality predictions compared to networks that were constrained with randomly shuffled constraints. Unconstrained networks predicted gene essentiality as accurately as thermodynamically constrained networks, but predicted substantially fewer essential genes. Networks that were reconciled with sequence similarity data and strongly enforced reversibility constraints outperformed all other networks. We conclude that metabolic network analysis confirmed the validity of the thermodynamic constraints, and that thermodynamic poise information is actionable during network reconciliation.
| S-EPMC5549646 | biostudies-other
Project description:Elementary flux modes (EFMs) are non-decomposable steady-state pathways in metabolic networks. They characterize phenotypes, quantify robustness or identify engineering targets. An EFM analysis (EFMA) is currently restricted to medium-scale models, as the number of EFMs explodes with the network's size. However, many topologically feasible EFMs are biologically irrelevant. We present thermodynamic EFMA (tEFMA), which calculates only the small(er) subset of thermodynamically feasible EFMs. We integrate network embedded thermodynamics into EFMA and show that we can use the metabolome to identify and remove thermodynamically infeasible EFMs during an EFMA without losing biologically relevant EFMs. Calculating only the thermodynamically feasible EFMs strongly reduces memory consumption and program runtime, allowing the analysis of larger networks. We apply tEFMA to study the central carbon metabolism of E. coli and find that up to 80% of its EFMs are thermodynamically infeasible. Moreover, we identify glutamate dehydrogenase as a bottleneck, when E. coli is grown on glucose and explain its inactivity as a consequence of network embedded thermodynamics. We implemented tEFMA as a Java package which is available for download at https://github.com/mpgerstl/tEFMA.
| S-EPMC4354105 | biostudies-literature
Project description:BackgroundGeobacter sulfurreducens is a member of the Geobacter species, which are capable of oxidation of organic waste coupled to the reduction of heavy metals and electrode with applications in bioremediation and bioenergy generation. While the metabolism of this organism has been studied through the development of a stoichiometry based genome-scale metabolic model, the associated regulatory network has not yet been well studied. In this manuscript, we report on the implementation of a thermodynamics based metabolic flux model for Geobacter sulfurreducens. We use this updated model to identify reactions that are subject to regulatory control in the metabolic network of G. sulfurreducens using thermodynamic variability analysis.FindingsAs a first step, we have validated the regulatory sites and bottleneck reactions predicted by the thermodynamic flux analysis in E. coli by evaluating the expression ranges of the corresponding genes. We then identified ten reactions in the metabolic network of G. sulfurreducens that are predicted to be candidates for regulation. We then compared the free energy ranges for these reactions with the corresponding gene expression fold changes under conditions of different environmental and genetic perturbations and show that the model predictions of regulation are consistent with data. In addition, we also identify reactions that operate close to equilibrium and show that the experimentally determined exchange coefficient (a measure of reversibility) is significant for these reactions.ConclusionsApplication of the thermodynamic constraints resulted in identification of potential bottleneck reactions not only from the central metabolism but also from the nucleotide and amino acid subsystems, thereby showing the highly coupled nature of the thermodynamic constraints. In addition, thermodynamic variability analysis serves as a valuable tool in estimating the ranges of DeltarG' of every reaction in the model leading to the prediction of regulatory sites in the metabolic network, thereby characterizing the regulatory network in both a model organism such as E. coli as well as a non model organism such as G. sulfurreducens.
| S-EPMC2873351 | biostudies-literature
Project description:Cells adapt their metabolic fluxes in response to changes in the environment. We present a framework for the systematic construction of flux-based graphs derived from organism-wide metabolic networks. Our graphs encode the directionality of metabolic flows via edges that represent the flow of metabolites from source to target reactions. The methodology can be applied in the absence of a specific biological context by modelling fluxes probabilistically, or can be tailored to different environmental conditions by incorporating flux distributions computed through constraint-based approaches such as Flux Balance Analysis. We illustrate our approach on the central carbon metabolism of Escherichia coli and on a metabolic model of human hepatocytes. The flux-dependent graphs under various environmental conditions and genetic perturbations exhibit systemic changes in their topological and community structure, which capture the re-routing of metabolic flows and the varying importance of specific reactions and pathways. By integrating constraint-based models and tools from network science, our framework allows the study of context-specific metabolic responses at a system level beyond standard pathway descriptions.
| S-EPMC6092364 | biostudies-literature