Search Results (12)

Background: When glucose molecules are metabolized by a biological cell, the molecules are constrained to flow along distinct reaction trajectories, which are defined by the cell’s underlying metabolic network. Methods: Using the computational technique of Elementary Mode Analysis, the entire set of all possible trajectories can be enumerated, effectively allowing metabolism to be viewed in a discretized space. Results: With the resulting set of Elementary Flux Modes (EMs), macroscopic fluxes, (of both mass and energy) that cross the cell envelope can be computed by a simple, linear combination of the individual EM trajectories. The challenge in this approach is that the usage probability of each EM is unknown. But, because the analytical framework we have adopted allows metabolism to be viewed in a discrete space, we can use the mathematics of statistical thermodynamics to derive the usage probabilities when the system entropy is maximized. The resulting probabilities, which obey a Boltzmann-type distribution, predict a rate structure for the metabolic network that is in remarkable agreement with experimentally measured rates of adaptively evolved E. coli strains. Conclusions: Thus, in principle, the intracellular dynamic properties of such bacteria can be predicted, using only the knowledge of the DNA sequence, to reconstruct the metabolic reaction network, and the measurement of the specific glucose uptake rate. Full article

Metabolic pathway analysis is a key method to study a metabolism in its steady state, and the concept of elementary fluxes (EFs) plays a major role in the analysis of a network in terms of non-decomposable pathways. The supports of the EFs contain in particular those of the elementary flux modes (EFMs), which are the support-minimal pathways, and EFs coincide with EFMs when the only flux constraints are given by the irreversibility of certain reactions. Practical use of both EFMs and EFs has been hampered by the combinatorial explosion of their number in large, genome-scale systems. The EFs give the possible pathways in a steady state but the real pathways are limited by biological constraints, such as thermodynamic or, more generally, kinetic constraints and regulatory constraints from the genetic network. We provide results on the mathematical structure and geometrical characterization of the solution space in the presence of such biological constraints (which is no longer a convex polyhedral cone or a convex polyhedron) and revisit the concept of EFMs and EFs in this framework. We show that most of the results depend only on very general properties of compatibility of constraints with vector signs: either sign-invariance, satisfied by regulatory constraints, or sign-monotonicity (a stronger property), satisfied by thermodynamic and kinetic constraints. We show in particular that the solution space for sign-monotone constraints is a union of particular faces of the original polyhedral cone or polyhedron and that EFs still coincide with EFMs and are just those of the original EFs that satisfy the constraint, and we show how to integrate their computation efficiently in the double description method, the most widely used method in the tools dedicated to EFs computation. We show that, for sign-invariant constraints, the situation is more complex: the solution space is a disjoint union of particular semi-open faces (i.e., without some of their own faces of lesser dimension) of the original polyhedral cone or polyhedron and, if EFs are still those of the original EFs that satisfy the constraint, their computation cannot be incrementally integrated into the double description method, and the result is not true for EFMs, that are in general strictly more numerous than those of the original EFMs that satisfy the constraint. Full article

Metabolic flux analysis is often (not to say almost always) faced with system underdeterminacy. Indeed, the linear algebraic system formed by the steady-state mass balance equations around the intracellular metabolites and the equality constraints related to the measurements of extracellular fluxes do not define a unique solution for the distribution of intracellular fluxes, but instead a set of solutions belonging to a convex polytope. Various methods have been proposed to tackle this underdeterminacy, including flux pathway analysis, flux balance analysis, flux variability analysis and sampling. These approaches are reviewed in this article and a toy example supports the discussion with illustrative numerical results. Full article

Genome-scale stoichiometric modeling methods, in particular Flux Balance Analysis (FBA) and variations thereof, are widely used to investigate cell metabolism and to optimize biotechnological processes. Given (1) a metabolic network, which can be reconstructed from an organism’s genome sequence, and (2) constraints on reaction rates, which may be based on measured nutrient uptake rates, FBA predicts which reactions maximize an objective flux, usually the production of cell components. Although FBA solutions may accurately predict the metabolic behavior of a cell, the actual flux predictions are often hard to interpret. This is especially the case for conditions with many constraints, such as for organisms growing in rich nutrient environments: it remains unclear why a certain solution was optimal. Here, we rationalize FBA solutions by explaining for which properties the optimal combination of metabolic strategies is selected. We provide a graphical formalism in which the selection of solutions can be visualized; we illustrate how this perspective provides a glimpse of the logic that underlies genome-scale modeling by applying our formalism to models of various sizes. Full article

Elementary Flux Modes (EFMs) provide a rigorous basis to systematically characterize the steady state, cellular phenotypes, as well as metabolic network robustness and fragility. However, the number of EFMs typically grows exponentially with the size of the metabolic network, leading to excessive computational demands, and unfortunately, a large fraction of these EFMs are not biologically feasible due to system constraints. This combinatorial explosion often prevents the complete analysis of genome-scale metabolic models. Traditionally, EFMs are computed by the double description method, an efficient algorithm based on matrix calculation; however, only a few constraints can be integrated into this computation. They must be monotonic with regard to the set inclusion of the supports; otherwise, they must be treated in post-processing and thus do not save computational time. We present aspefm, a hybrid computational tool based on Answer Set Programming (ASP) and Linear Programming (LP) that permits the computation of EFMs while implementing many different types of constraints. We apply our methodology to the Escherichia coli core model, which contains $226\times {10}^6$ EFMs. In considering transcriptional and environmental regulation, thermodynamic constraints, and resource usage considerations, the solution space is reduced to 1118 EFMs that can be computed directly with aspefm. The solution set, for E. coli growth on O₂ gradients spanning fully aerobic to anaerobic, can be further reduced to four optimal EFMs using post-processing and Pareto front analysis. Full article

Structural analysis of constraint-based metabolic network models attempts to find the network’s properties by searching for subsets of suitable modes or Elementary Flux Modes (EFMs). One useful approach is based on Linear Program (LP) techniques, which introduce an objective function to convert the stoichiometric and thermodynamic constraints into a linear program (LP), using additional constraints to generate different nontrivial modes. This work introduces FLFS-FC (Fixed Length Function Sampling with Flux Coupling), a new approach to increase the efficiency of generation of large sets of different EFMs for the network. FLFS-FC is based on the importance of the length of the objective functions used in the associated LP problem and the imposition of additional negative constraints. Our proposal overrides some of the known drawbacks associated with the EFM extraction, such as the appearance of unfeasible problems or multiple repeated solutions arising from different LP problems. Full article

Substrate availability plays a key role in dictating metabolic strategies. Most microorganisms consume carbon/energy sources in a sequential, preferential order. The presented study investigates metabolic strategies of Alicyclobacillus acidocaldarius, a thermoacidophilic bacterium that has been shown to co-utilize glucose and xylose, as well as degrade phenolic compounds. An existing metabolic model was expanded to include phenol degradation and was analyzed with both metabolic pathway and constraint-based analysis methods. Elementary flux mode analysis was used in conjunction with resource allocation theory to investigate ecologically optimal metabolic pathways for different carbon substrate combinations. Additionally, a dynamic version of flux balance analysis was used to generate time-resolved simulations of growth on phenol and xylose. Results showed that availability of xylose along with glucose did not predict enhanced growth efficiency beyond that of glucose alone, but did predict some differences in pathway utilization and byproduct profiles. In contrast, addition of phenol as a co-substrate with xylose predicted lower growth efficiency. Dynamic simulations predicted co-consumption of xylose and phenol in a similar pattern as previously reported experiments. Altogether, this work serves as a case study for combining both elementary flux mode and flux balance analyses to probe unique metabolic features, and also demonstrates the versatility of A. acidocaldarius for lignocellulosic biomass processing applications. Full article

Elementary Flux Modes (EFMs) are a tool for constraint-based modeling and metabolic network analysis. However, systematic and automated visualization of EFMs, capable of integrating various data types is still a challenge. In this study, we developed an extension for the widely adopted COBRA Toolbox, EFMviz, for analysis and graphical visualization of EFMs as networks of reactions, metabolites and genes. The analysis workflow offers a platform for EFM visualization to improve EFM interpretability by connecting COBRA toolbox with the network analysis and visualization software Cytoscape. The biological applicability of EFMviz is demonstrated in two use cases on medium (Escherichia coli, iAF1260) and large (human, Recon 2.2) genome-scale metabolic models. EFMviz is open-source and integrated into COBRA Toolbox. The analysis workflows used for the two use cases are detailed in the two tutorials provided with EFMviz along with the data used in this study. Full article

Replicators are fundamental to the origin of life and evolvability. Biology exhibits homochirality: only one of two enantiomers is used in proteins and nucleic acids. Thermodynamic studies of chemical replicators able to lead to homochirality shed valuable light on the origin of homochirality and life in conformity with the underlying mechanisms and constraints. In line with this framework, enantioselective hypercyclic replicators may lead to spontaneous mirror symmetry breaking (SMSB) without the need for additional heterochiral inhibition reactions, which can be an obstacle for the emergence of evolutionary selection properties. We analyze the entropy production of a two-replicator system subject to homochiral cross-catalysis which can undergo SMSB in an open-flow reactor. The entropy exchange with the environment is provided by the input and output matter flows, and is essential for balancing the entropy production at the non-equilibrium stationary states. The partial entropy contributions, associated with the individual elementary flux modes, as defined by stoichiometric network analysis (SNA), describe how the system’s internal currents evolve, maintaining the balance between entropy production and exchange, while minimizing the entropy production after the symmetry breaking transition. We validate the General Evolution Criterion, stating that the change in the chemical affinities proceeds in a way as to lower the value of the entropy production. Full article

FluxVisualizer (Version 1.0, 2017, freely available at https://fluxvisualizer.ibgc.cnrs.fr) is a software to visualize fluxes values on a scalable vector graphic (SVG) representation of a metabolic network by colouring or increasing the width of reaction arrows of the SVG file. FluxVisualizer does not aim to draw metabolic networks but to use a customer’s SVG file allowing him to exploit his representation standards with a minimum of constraints. FluxVisualizer is especially suitable for small to medium size metabolic networks, where a visual representation of the fluxes makes sense. The flux distribution can either be an elementary flux mode (EFM), a flux balance analysis (FBA) result or any other flux distribution. It allows the automatic visualization of a series of pathways of the same network as is needed for a set of EFMs. The software is coded in python3 and provides a graphical user interface (GUI) and an application programming interface (API). All functionalities of the program can be used from the API and the GUI and allows advanced users to add their own functionalities. The software is able to work with various formats of flux distributions (Metatool, CellNetAnalyzer, COPASI and FAME export files) as well as with Excel files. This simple software can save a lot of time when evaluating fluxes simulations on a metabolic network. Full article

Computational representations of metabolism are increasingly common in medical, environmental, and bioprocess applications. Cellular growth is often an important output of computational biology analyses, and therefore, accurate measurement of biomass constituents is critical for relevant model predictions. There is a distinct lack of detailed macromolecular measurement protocols, including comparisons to alternative assays and methodologies, as well as tools to convert the experimental data into biochemical reactions for computational biology applications. Herein is compiled a concise literature review regarding methods for five major cellular macromolecules (carbohydrate, DNA, lipid, protein, and RNA) with a step-by-step protocol for a select method provided for each macromolecule. Additionally, each method was tested on three different bacterial species, and recommendations for troubleshooting and testing new species are given. The macromolecular composition measurements were used to construct biomass synthesis reactions with appropriate quality control metrics such as elemental balancing for common computational biology methods, including flux balance analysis and elementary flux mode analysis. Finally, it was demonstrated that biomass composition can substantially affect fundamental model predictions. The effects of biomass composition on in silico predictions were quantified here for biomass yield on electron donor, biomass yield on electron acceptor, biomass yield on nitrogen, and biomass degree of reduction, as well as the calculation of growth associated maintenance energy; these parameters varied up to 7%, 70%, 35%, 12%, and 40%, respectively, between the reference biomass composition and ten test biomass compositions. The current work furthers the computational biology community by reviewing literature regarding a variety of common analytical measurements, developing detailed procedures, testing the methods in the laboratory, and applying the results to metabolic models, all in one publicly available resource. Full article

Metabolic acclimation to photosynthesis-associated stresses was examined in the thermophilic cyanobacterium Thermosynechococcus elongatus BP-1 using integrated computational and photobioreactor analyses. A genome-enabled metabolic model, complete with measured biomass composition, was analyzed using ecological resource allocation theory to predict and interpret metabolic acclimation to irradiance, O₂, and nutrient stresses. Reduced growth efficiency, shifts in photosystem utilization, changes in photorespiration strategies, and differing byproduct secretion patterns were predicted to occur along culturing stress gradients. These predictions were compared with photobioreactor physiological data and previously published transcriptomic data and found to be highly consistent with observations, providing a systems-based rationale for the culture phenotypes. The analysis also indicated that cyanobacterial stress acclimation strategies created niches for heterotrophic organisms and that heterotrophic activity could enhance cyanobacterial stress tolerance by removing inhibitory metabolic byproducts. This study provides mechanistic insight into stress acclimation strategies in photoautotrophs and establishes a framework for predicting, designing, and engineering both axenic and photoautotrophic-heterotrophic systems as a function of controllable parameters. Full article