Group contribution method for thermodynamic analysis of complex metabolic networks

A new, to our knowledge, group contribution method based on the group contribution method of Mavrovouniotis is introduced for estimating the standard Gibbs free energy of formation (Δ_fG′°) and reaction (Δ_rG′°) in biochemical systems. Gibbs free energy contribution values were estimated for 74 distinct molecular substructures and 11 interaction factors using multiple linear regression against a training set of 645 reactions and 224 compounds. The standard error for the fitted values was 1.90 kcal/mol. Cross-validation analysis was utilized to determine the accuracy of the methodology in estimating Δ_rG′° and Δ_fG′° for reactions and compounds not included in the training set, and based on the results of the cross-validation, the standard error involved in these estimations is 2.22 kcal/mol. This group contribution method is demonstrated to be capable of estimating Δ_rG′° and Δ_fG′° for the majority of the biochemical compounds and reactions found in the iJR904 and iAF1260 genome-scale metabolic models of Escherichia coli and in the Kyoto Encyclopedia of Genes and Genomes and University of Minnesota Biocatalysis and Biodegradation Database. A web-based implementation of this new group contribution method is available free at http://sparta.chem-eng.northwestern.edu/cgi-bin/GCM/WebGCM.cgi.     

A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks

A set of linear pathways often does not capture the full range of behaviors of a metabolic network. The concept of 'elementary flux modes' provides a mathematical tool to define and comprehensively describe all metabolic routes that are both stoichiometrically and thermodynamically feasible for a group of enzymes. We have used this concept to analyze the interplay between the pentose phosphate pathway (PPP) and glycolysis. The set of elementary modes for this system involves conventional glycolysis, a futile cycle, all the modes of PPP function described in biochemistry textbooks, and additional modes that are a priori equally entitled to pathway status. Applications include maximizing product yield in amino acid and antibiotic synthesis, reconstruction and consistency checks of metabolism from genome data, analysis of enzyme deficiencies, and drug target identification in metabolic networks.     

细胞代谢复杂网络研究进展

复杂网络理论为细胞代谢网络研究提供了新的工具,基于复杂网络理论的细胞代谢网络研究可称细胞代谢复杂网络研究．先简要介绍了细胞代谢复杂网络的研究背景;随后详细总结和论述了细胞代谢复杂网络在建模、分析和控制三个方面的研究现状;再进一步指出了细胞代谢复杂网络在建模、分析和控制这三个方面研究中所存在的一些问题．为细胞代谢复杂网络领域的研究指出了一些有意义的方向,具有一定的参考价值。     

Exploring the diversity of complex metabolic networks

MOTIVATION: Metabolism, the network of chemical reactions that make life possible, is one of the most complex processes in nature. We describe here the development of a computational approach for the identification of every possible biochemical reaction from a given set of enzyme reaction rules that allows the de novo synthesis of metabolic pathways composed of these reactions, and the evaluation of these novel pathways with respect to their thermodynamic properties. RESULTS: We applied this framework to the analysis of the aromatic amino acid pathways and discovered almost 75,000 novel biochemical routes from chorismate to phenylalanine, more than 350,000 from chorismate to tyrosine, but only 13 from chorismate to tryptophan. Thermodynamic analysis of these pathways suggests that the native pathways are thermodynamically more favorable than the alternative possible pathways. The pathways generated involve compounds that exist in biological databases, as well as compounds that exist in chemical databases and novel compounds, suggesting novel biochemical routes for these compounds and the existence of biochemical compounds that remain to be discovered or synthesized through enzyme and pathway engineering. AVAILABILITY: Framework will be available via web interface at http://systemsbiology.northwestern.edu/BNICE (site under construction). CONTACT: vassily@northwestern.edu or broadbelt@northwestern.edu SUPPLEMENTARY INFORMATION: http://systemsbiology.northwestern.edu/BNICE/publications.     

Use of randomized sampling for analysis of metabolic networks

Genome-scale metabolic network reconstructions in microorganisms have been formulated and studied for about 8 years. The constraint-based approach has shown great promise in analyzing the systemic properties of these network reconstructions. Notably, constraint-based models have been used successfully to predict the phenotypic effects of knock-outs and for metabolic engineering. The inherent uncertainty in both parameters and variables of large-scale models is significant and is well suited to study by Monte Carlo sampling of the solution space. These techniques have been applied extensively to the reaction rate (flux) space of networks, with more recent work focusing on dynamic/kinetic properties. Monte Carlo sampling as an analysis tool has many advantages, including the ability to work with missing data, the ability to apply post-processing techniques, and the ability to quantify uncertainty and to optimize experiments to reduce uncertainty. We present an overview of this emerging area of research in systems biology.     

Consistency analysis of metabolic correlation networks

Background  

Metabolic correlation networks are derived from the covariance of metabolites in replicates of metabolomics experiments. They constitute an interesting intermediate between topology (i.e. the system's architecture defined by the set of reactions between metabolites) and dynamics (i.e. the metabolic concentrations observed as fluctuations around steady-state values in the metabolic network).     

Hierarchical analysis of dependency in metabolic networks

MOTIVATION: Elucidation of metabolic networks for an increasing number of organisms reveals that even small networks can contain thousands of reactions and chemical species. The intimate connectivity between components complicates their decomposition into biologically meaningful sub-networks. Moreover, traditional higher-order representations of metabolic networks as metabolic pathways, suffers from the lack of rigorous definition, yielding pathways of disparate content and size. RESULTS: We introduce a hierarchical representation that emphasizes the gross organization of metabolic networks in largely independent pathways and sub-systems at several levels of independence. The approach highlights the coupling of different pathways and the shared compounds responsible for those couplings. By assessing our results on Escherichia coli (E.coli metabolic reactions, Genetic Circuits Research Group, University of California, San Diego, http://gcrg.ucsd.edu/organisms/ecoli.html, 'model v 1.01. reactions') against accepted biochemical annotations, we provide the first systematic synopsis of an organism's metabolism. Comparison with operons of E.coli shows that low-level clusters are reflected in genome organization and gene regulation. AVAILABILITY: Source code, data sets and supplementary information are available at http://www.mas.ecp.fr/labo/equipe/gagneur/hierarchy/hierarchy.html     

Combining pathway analysis with flux balance analysis for the comprehensive study of metabolic systems

The elucidation of organism-scale metabolic networks necessitates the development of integrative methods to analyze and interpret the systemic properties of cellular metabolism. A shift in emphasis from single metabolic reactions to systemically defined pathways is one consequence of such an integrative analysis of metabolic systems. The constraints of systemic stoichiometry, and limited thermodynamics have led to the definition of the flux space within the context of convex analysis. The flux space of the metabolic system, containing all allowable flux distributions, is constrained to a convex polyhedral cone in a high-dimensional space. From metabolic pathway analysis, the edges of the high-dimensional flux cone are vectors that correspond to systemically defined "extreme pathways" spanning the capabilities of the system. The addition of maximum flux capacities of individual metabolic reactions serves to further constrain the flux space and has led to the development of flux balance analysis using linear optimization to calculate optimal flux distributions. Here we provide the precise theoretical connections between pathway analysis and flux balance analysis allowing for their combined application to study integrated metabolic function. Shifts in metabolic behavior are calculated using linear optimization and are then interpreted using the extreme pathways to demonstrate the concept of pathway utilization. Changes to the reaction network, such as the removal of a reaction, can lead to the generation of suboptimal phenotypes that can be directly attributed to the loss of pathway function and capabilities. Optimal growth phenotypes are calculated as a function of environmental variables, such as the availability of substrate and oxygen, leading to the definition of phenotypic phase planes. It is illustrated how optimality properties of the computed flux distributions can be interpreted in terms of the extreme pathways. Together these developments are applied to an example network and to core metabolism of Escherichia coli demonstrating the connections between the extreme pathways, optimal flux distributions, and phenotypic phase planes. The consequences of changing environmental and internal conditions of the network are examined for growth on glucose and succinate in the face of a variety of gene deletions. The convergence of the calculation of optimal phenotypes through linear programming and the definition of extreme pathways establishes a different perspective for the understanding of how a defined metabolic network is best used under different environmental and internal conditions or, in other words, a pathway basis for the interpretation of the metabolic reaction norm.     

Insights into plant metabolic networks from steady-state metabolic flux analysis

Steady-state metabolic flux analysis (MFA) is an experimental approach that allows the measurement of multiple fluxes in the core network of primary carbon metabolism. It is based on isotopic labelling experiments, and although well established in the analysis of micro-organisms, and some mammalian systems, the extension of the method to plant cells has been challenging because of the extensive subcellular compartmentation of the metabolic network. Despite this difficulty there has been substantial progress in developing robust protocols for the analysis of heterotrophic plant metabolism by steady-state MFA, and flux maps have now been published that reflect the metabolic phenotypes of excised root tips, developing embryos and cotyledons, hairy root cultures, and cell suspensions under a variety of physiological conditions. There has been a steady improvement in the quality, extent and statistical reliability of these analyses, and new information is emerging on the performance of the plant metabolic network and the contributions of specific pathways.     

Combinatorial complexity of pathway analysis in metabolic networks

Elementary flux mode analysis is a promising approach for a pathway-oriented perspective of metabolic networks. However, in larger networks it is hampered by the combinatorial explosion of possible routes. In this work we give some estimations on the combinatorial complexity including theoretical upper bounds for the number of elementary flux modes in a network of a given size. In a case study, we computed the elementary modes in the central metabolism of Escherichia coli while utilizing four different substrates. Interestingly, although the number of modes occurring in this complex network can exceed half a million, it is still far below the upper bound. Hence, to a certain extent, pathway analysis of central catabolism is feasible to assess network properties such as flexibility and functionality.     

Optimization strategies for metabolic networks

Background  

The increasing availability of models and data for metabolic networks poses new challenges in what concerns optimization for biological systems. Due to the high level of complexity and uncertainty associated to these networks the suggested models often lack detail and liability, required to determine the proper optimization strategies. A possible approach to overcome this limitation is the combination of both kinetic and stoichiometric models. In this paper three control optimization methods, with different levels of complexity and assuming various degrees of process information, are presented and their results compared using a prototype network.     

Quasi-multiparameter sensitivity measure for robustness analysis of complex biochemical networks

Robustness is the ability to resume reliable operation in the face of different types of perturbations. Analysis of how network structure achieves robustness enables one to understand and design cellular systems. It is typically true that all parameters simultaneously differ from their nominal values in vivo, but there have been few intelligible measures to estimate the robustness of a system's function to the uncertainty of all parameters.We propose a numerical and fast measure of a robust property to the uncertainty of all kinetic parameters, named quasi-multiparameter sensitivity (QMPS), which is defined as the sum of the squared magnitudes of single-parameter sensitivities. Despite its plain idea, it has hardly been employed in analysis of biological models. While QMPS is theoretically derived as a linear model, QMPS can be consistent with the expected variance simulated by the widely used Monte Carlo method in nonlinear biological models, when relatively small perturbations are given. To demonstrate the feasibility of QMPS, it is employed for numerical comparison to analyze the mechanism of how specific regulations generate robustness in typical biological models.QMPS characterizes the robustness much faster than the Monte Carlo method, thereby enabling the extensive search of a large parameter space to perform the numerical comparison between alternative or competing models. It provides a theoretical or quantitative insight to an understanding of how specific network structures are related to robustness. In circadian oscillators, a negative feedback loop with multiple phosphorylations is demonstrated to play a critical role in generating robust cycles to the uncertainty of multiple parameters.     

Modulation of nutrient precursors for controlling metabolic inhibitors by genome-scale flux balance analysis

Therapeutic protein productivity and glycosylation pattern highly rely on cell metabolism. Cell culture medium composition and feeding strategy are critical to regulate cell metabolism. In this study, the relationship between toxic metabolic inhibitors and their nutrient precursors was explored to identify the critical medium components toward cell growth and generation of metabolic by-products. Generic CHO metabolic model was tailored and integrated with CHO fed-batch metabolomic data to obtain a cell line- and process-specific model. Flux balance analysis study was conducted on toxic metabolites cytidine monophosphate, guanosine monophosphate and n-acetylputrescine—all of which were previously reported to generate from endogenous cell metabolism—by mapping them to a compartmentalized carbon utilization network. Using this approach, the study projected high level of inhibitory metabolites accumulation when comparing three industrially relevant fed-batch feeding conditions one against another, from which the results were validated via a dose-dependent amino acids spiking study. In the end, a medium optimization design was employed to lower the amount of supplemented nutrients, of which improvements in critical process performance were realized at 40% increase in peak viable cell density (VCD), 15% increase in integral VCD, and 37% increase in growth rate. Tight control of toxic by-products was also achieved, as the study measured decreased inhibitory metabolites accumulation across all conditions. Overall, the study successfully presented a digital twin approach to investigate the intertwined relationship between supplemented medium constituents and downstream toxic metabolites generated through host cell metabolism, further elucidating different control strategies capable of improving cellular phenotypes and regulating toxic inhibitors.     

Including metabolite concentrations into flux balance analysis: thermodynamic realizability as a constraint on flux distributions in metabolic networks

Background  

In 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.     

CONTROL: software for the analysis of the control of metabolic networks

The program CONTROL is based on metabolic control theory anduses the method developed by Reder (1988). In this theory, twosets of parameters are defined in the vicinity of a steady-state:the elasticity coefficients which describe the local behaviourof the isolated enzymes, and the control coefficients whichexpress the response of the whole metabolic network to perturbationsat a given step. The theory shows that relationships exist betweenthe control coefficients (summation relationships or structuralrelationships) and also between the two types of coefficients(control and elasticity coefficients: connectivity relationships).The program CONTROL is divided into two parts (sub-menus). Thefirst one calculates all the control coefficients (flux andconcentrations) of a metabolic network from the elasticity coefficients.Using the second menu, the symbolic relationships are obtainedbetween the control coefficients (summation relationships) andbetween the control coefficients and the elasticity coefficients(connectivity relationships). These two sub-menus can be appliedindependently to any metabolic network (to date limited to 19steps and 19 metabolites).     

Finding elementary flux modes in metabolic networks based on flux balance analysis and flux coupling analysis: application to the analysis of Escherichia coli metabolism

Elementary modes (EMs) are steady-state metabolic flux vectors with minimal set of active reactions. Each EM corresponds to a metabolic pathway. Therefore, studying EMs is helpful for analyzing the production of biotechnologically important metabolites. However, memory requirements for computing EMs may hamper their applicability as, in most genome-scale metabolic models, no EM can be computed due to running out of memory. In this study, we present a method for computing randomly sampled EMs. In this approach, a network reduction algorithm is used for EM computation, which is based on flux balance-based methods. We show that this approach can be used to recover the EMs in the medium- and genome-scale metabolic network models, while the EMs are sampled in an unbiased way. The applicability of such results is shown by computing “estimated” control-effective flux values in Escherichia coli metabolic network.