A novel algorithm to calculate elementary modes: Analysis of Campylobacter jejuni metabolism.

We describe a novel algorithm, 'LPEM', that given a steady-state flux vector from a (possibly genome-scale) metabolic model, decomposes that vector into a set of weighted elementary modes such that the sum of these elementary modes is equal to the original flux vector. We apply the algorithm to a genome scale metabolic model of the human pathogen Campylobacter jejuni. This organism is unusual in that it has an absolute growth requirement for oxygen, despite being able to operate the electron transport chain anaerobically. We conclude that (1) Microaerophilly in C. jejuni can be explained by the dependence of pyridoxine 5'-phosphate oxidase for the synthesis of pyridoxal 5'- phosphate (the biologically active form of vitamin B6), (2) The LPEM algorithm is capable of determining the elementary modes of a linear programming solution describing the simultaneous production of 51 biomass precursors, (3) Elementary modes for the production of individual biomass precursors are significantly more complex when all others are produced simultaneously than those for the same product in isolation and (4) The sum of elementary modes for the production of all precursors in isolation requires a greater number of reactions and overall total flux than the simultaneous production of all precursors.

EFMlrs: a Python package for elementary flux mode enumeration via lexicographic reverse search.

BACKGROUND: Elementary flux mode (EFM) analysis is a well-established, yet computationally challenging approach to characterize metabolic networks. Standard algorithms require huge amounts of memory and lack scalability which limits their application to single servers and consequently limits a comprehensive analysis to medium-scale networks. Recently, Avis et al. developed mplrs-a parallel version of the lexicographic reverse search (lrs) algorithm, which, in principle, enables an EFM analysis on high-performance computing environments (Avis and Jordan. mplrs: a scalable parallel vertex/facet enumeration code. arXiv:1511.06487 , 2017). Here we test its applicability for EFM enumeration. RESULTS: We developed EFMlrs, a Python package that gives users access to the enumeration capabilities of mplrs. EFMlrs uses COBRApy to process metabolic models from sbml files, performs loss-free compressions of the stoichiometric matrix, and generates suitable inputs for mplrs as well as efmtool, providing support not only for our proposed new method for EFM enumeration but also for already established tools. By leveraging COBRApy, EFMlrs also allows the application of additional reaction boundaries and seamlessly integrates into existing workflows. CONCLUSION: We show that due to mplrs's properties, the algorithm is perfectly suited for high-performance computing (HPC) and thus offers new possibilities for the unbiased analysis of substantially larger metabolic models via EFM analyses. EFMlrs is an open-source program that comes together with a designated workflow and can be easily installed via pip.

Topological Analysis of the Carbon-Concentrating CETCH Cycle and a Photorespiratory Bypass Reveals Boosted CO2-Sequestration by Plants.

Synthetically designed alternative photorespiratory pathways increase the biomass of tobacco and rice plants. Likewise, some in planta-tested synthetic carbon-concentrating cycles (CCCs) hold promise to increase plant biomass while diminishing atmospheric carbon dioxide burden. Taking these individual contributions into account, we hypothesize that the integration of bypasses and CCCs will further increase plant productivity. To test this in silico, we reconstructed a metabolic model by integrating photorespiration and photosynthesis with the synthetically designed alternative pathway 3 (AP3) enzymes and transporters. We calculated fluxes of the native plant system and those of AP3 combined with the inhibition of the glycolate/glycerate transporter by using the YANAsquare package. The activity values corresponding to each enzyme in photosynthesis, photorespiration, and for synthetically designed alternative pathways were estimated. Next, we modeled the effect of the crotonyl-CoA/ethylmalonyl-CoA/hydroxybutyryl-CoA cycle (CETCH), which is a set of natural and synthetically designed enzymes that fix CO2 manifold more than the native Calvin-Benson-Bassham (CBB) cycle. We compared estimated fluxes across various pathways in the native model and under an introduced CETCH cycle. Moreover, we combined CETCH and AP3-w/plgg1RNAi, and calculated the fluxes. We anticipate higher carbon dioxide-harvesting potential in plants with an AP3 bypass and CETCH-AP3 combination. We discuss the in vivo implementation of these strategies for the improvement of C3 plants and in natural high carbon harvesters.

Speeding up the core algorithm for the dual calculation of minimal cut sets in large metabolic networks.

BACKGROUND: The concept of minimal cut sets (MCS) has become an important mathematical framework for analyzing and (re)designing metabolic networks. However, the calculation of MCS in genome-scale metabolic models is a complex computational problem. The development of duality-based algorithms in the last years allowed the enumeration of thousands of MCS in genome-scale networks by solving mixed-integer linear problems (MILP). A recent advancement in this field was the introduction of the MCS2 approach. In contrast to the Farkas-lemma-based dual system used in earlier studies, the MCS2 approach employs a more condensed representation of the dual system based on the nullspace of the stoichiometric matrix, which, due to its reduced dimension, holds promise to further enhance MCS computations. RESULTS: In this work, we introduce several new variants and modifications of duality-based MCS algorithms and benchmark their effects on the overall performance. As one major result, we generalize the original MCS2 approach (which was limited to blocking the operation of certain target reactions) to the most general case of MCS computations with arbitrary target and desired regions. Building upon these developments, we introduce a new MILP variant which allows maximal flexibility in the formulation of MCS problems and fully leverages the reduced size of the nullspace-based dual system. With a comprehensive set of benchmarks, we show that the MILP with the nullspace-based dual system outperforms the MILP with the Farkas-lemma-based dual system speeding up MCS computation with an averaged factor of approximately 2.5. We furthermore present several simplifications in the formulation of constraints, mainly related to binary variables, which further enhance the performance of MCS-related MILP. However, the benchmarks also reveal that some highly condensed formulations of constraints, especially on reversible reactions, may lead to worse behavior when compared to variants with a larger number of (more explicit) constraints and involved variables. CONCLUSIONS: Our results further enhance the algorithmic toolbox for MCS calculations and are of general importance for theoretical developments as well as for practical applications of the MCS framework.

Application of dynamic metabolic flux analysis for process modeling: Robust flux estimation with regularization, confidence bounds, and selection of elementary modes.

In macroscopic dynamic models of fermentation processes, elementary modes (EM) derived from metabolic networks are often used to describe the reaction stoichiometry in a simplified manner and to build predictive models by parameterizing kinetic rate equations for the EM. In this procedure, the selection of a set of EM is a key step which is followed by an estimation of their reaction rates and of the associated confidence bounds. In this paper, we present a method for the computation of reaction rates of cellular reactions and EM as well as an algorithm for the selection of EM for process modeling. The method is based on the dynamic metabolic flux analysis (DMFA) proposed by Leighty and Antoniewicz (2011, Metab Eng, 13(6), 745-755) with additional constraints, regularization and analysis of uncertainty. Instead of using estimated uptake or secretion rates, concentration measurements are used directly to avoid an amplification of measurement errors by numerical differentiation. It is shown that the regularized DMFA for EM method is significantly more robust against measurement noise than methods using estimated rates. The confidence intervals for the estimated reaction rates are obtained by bootstrapping. For the selection of a set of EM for a given st oichiometric model, the DMFA for EM method is combined with a multiobjective genetic algorithm. The method is applied to real data from a CHO fed-batch process. From measurements of six fed-batch experiments, 10 EM were identified as the smallest subset of EM based upon which the data can be described sufficiently accurately by a dynamic model. The estimated EM reaction rates and their confidence intervals at different process conditions provide useful information for the kinetic modeling and subsequent process optimization.

Stoichiometric analysis of the energetics and metabolic impact of photorespiration in C3 plants.

Analysis of the impact of photorespiration on plant metabolism is usually based on manual inspection of small network diagrams. Here we create a structural metabolic model that contains the reactions that participate in photorespiration in the plastid, peroxisome, mitochondrion and cytosol, and the metabolite exchanges between them. This model was subjected to elementary flux modes analysis, a technique that enumerates all the component, minimal pathways of a network. Any feasible photorespiratory metabolism in the plant will be some combination of the elementary flux modes (EFMs) that contain the Rubisco oxygenase reaction. Amongst the EFMs we obtained was the classic photorespiratory cycle, but there were also modes that involve photorespiration coupled with mitochondrial metabolism and ATP production, the glutathione-ascorbate cycle and nitrate reduction to ammonia. The modes analysis demonstrated the underlying basis of the metabolic linkages with photorespiration that have been inferred experimentally. The set of reactions common to all the elementary modes showed good agreement with the gene products of mutants that have been reported to have a defective phenotype in photorespiratory conditions. Finally, the set of modes provided a formal demonstration that photorespiration itself does not impact on the CO2 :O2 ratio (assimilation quotient), except in those modes associated with concomitant nitrate reduction.

Use of CellNetAnalyzer in biotechnology and metabolic engineering.

Mathematical models of the cellular metabolism have become an essential tool for the optimization of biotechnological processes. They help to obtain a systemic understanding of the metabolic processes in the used microorganisms and to find suitable genetic modifications maximizing the production performance. In particular, methods of stoichiometric and constraint-based modeling are frequently used in the context of metabolic and bioprocess engineering. Since metabolic networks can be complex and comprise hundreds or even thousands of metabolites and reactions, dedicated software tools are required for an efficient analysis. One such software suite is CellNetAnalyzer, a MATLAB package providing, among others, various methods for analyzing stoichiometric and constraint-based metabolic models. CellNetAnalyzer can be used via command-line based operations or via a graphical user interface with embedded network visualizations. Herein we will present key functionalities of CellNetAnalyzer for applications in biotechnology and metabolic engineering and thereby review constraint-based modeling techniques such as metabolic flux analysis, flux balance analysis, flux variability analysis, metabolic pathway analysis (elementary flux modes) and methods for computational strain design.

A principal components method constrained by elementary flux modes: analysis of flux data sets.

BACKGROUND: Non-negative linear combinations of elementary flux modes (EMs) describe all feasible reaction flux distributions for a given metabolic network under the quasi steady state assumption. However, only a small subset of EMs contribute to the physiological state of a given cell. RESULTS: In this paper, a method is proposed that identifies the subset of EMs that best explain the physiological state captured in reaction flux data, referred to as principal EMs (PEMs), given a pre-specified universe of EM candidates. The method avoids the evaluation of all possible combinations of EMs by using a branch and bound approach which is computationally very efficient. The performance of the method is assessed using simulated and experimental data of Pichia pastoris and experimental fluxome data of Saccharomyces cerevisiae. The proposed method is benchmarked against principal component analysis (PCA), commonly used to study the structure of metabolic flux data sets. CONCLUSIONS: The overall results show that the proposed method is computationally very effective in identifying the subset of PEMs within a large set of EM candidates (cases with ~100 and ~1000 EMs were studied). In contrast to the principal components in PCA, the identified PEMs have a biological meaning enabling identification of the key active pathways in a cell as well as the conditions under which the pathways are activated. This method clearly outperforms PCA in the interpretability of flux data providing additional insights into the underlying regulatory mechanisms.

Metabolic flux prediction in cancer cells with altered substrate uptake.

Proliferating cells, such as cancer cells, are known to have an unusual metabolism, characterized by an increased rate of glycolysis and amino acid metabolism. Our understanding of this phenomenon is limited but could potentially be used in order to develop new therapies. Computational modelling techniques, such as flux balance analysis (FBA), have been used to predict fluxes in various cell types, but remain of limited use to explain the unusual metabolic shifts and altered substrate uptake in human cancer cells. We implemented a new flux prediction method based on elementary modes (EMs) and structural flux (StruF) analysis and tested them against experimentally measured flux data obtained from (13)C-labelling in a cancer cell line. We assessed the quality of predictions using different objective functions along with different techniques in normalizing a metabolic network with more than one substrate input. Results show a good correlation between predicted and experimental values and indicate that the choice of cellular objective critically affects the quality of predictions. In particular, lactate gives an excellent correlation and correctly predicts the high flux through glycolysis, matching the observed characteristics of cancer cells. In contrast with FBA, which requires a priori definition of all uptake rates, often hard to measure, atomic StruFs (aStruFs) are able to predict uptake rates of multiple substrates.

Modelling metabolism of the diatom Phaeodactylum tricornutum.

Marine diatoms have potential as a biotechnological production platform, especially for lipid-derived products, including biofuels. Here we introduce some features of diatom metabolism, particularly with respect to photosynthesis, photorespiration and lipid synthesis and their differences relative to other photosynthetic eukaryotes. Since structural metabolic modelling of other photosynthetic organisms has been shown to be capable of representing their metabolic capabilities realistically, we briefly review the main approaches to this type of modelling. We then propose that genome-scale modelling of the diatom Phaeodactylum tricornutum, in response to varying light intensity, could uncover the novel aspects of the metabolic potential of this organism.

Lysine overproducing Corynebacterium glutamicum is characterized by a robust linear combination of two optimal phenotypic states.

A homoserine auxotroph strain of Corynebacterium glutamicum accumulates storage compound trehalose with lysine when limited by growth. Industrially lysine is produced from C. glutamicum through aspartate biosynthetic pathway, where enzymatic activity of aspartate kinase is allosterically controlled by the concerted feedback inhibition of threonine plus lysine. Ample threonine in the medium supports growth and inhibits lysine production (phenotype-I) and its complete absence leads to inhibition of growth in addition to accumulating lysine and trehalose (phenotype-II). In this work, we demonstrate that as threonine concentration becomes limiting, metabolic state of the cell shifts from maximizing growth (phenotype-I) to maximizing trehalose phenotype (phenotype-II) in a highly sensitive manner (with a Hill coefficient of 4). Trehalose formation was linked to lysine production through stoichiometry of the network. The study demonstrated that the net flux of the population was a linear combination of the two optimal phenotypic states, requiring only two experimental measurements to evaluate the flux distribution. The property of linear combination of two extreme phenotypes was robust for various medium conditions including varying batch time, initial glucose concentrations and medium osmolality.