Ab initio prediction of thermodynamically feasible reaction directions from biochemical network stoichiometry

Analysis of the stoichiometric structure of metabolic networks provides insights into the relationships between structure, function, and regulation of metabolic systems. Based on knowledge of only reaction stoichiometry, certain aspects of network functionality and robustness can be predicted. Current theories focus on breaking a metabolic network down into non-decomposable pathways able to operate in steady state. The physics underlying these theories is based on mass balance and the laws of thermodynamics. However, due to the inherent nonlinearity of the thermodynamic constraints on metabolic fluxes, computational analysis of large-scale biochemical systems can be expensive. In this study, it is shown how the feasible reaction directions may be determined by either computing the allowable ranges under the mass-balance and thermodynamic constraints or by analyzing the stoichiometric structure of the network. The computed reaction directions translate into a set of linear constraints necessary for thermodynamic feasibility. This set of necessary linear constraints is shown to be sufficient to guarantee feasibility in certain cases, thus translating the nonlinear thermodynamic constraints to linear. We show that for a reaction network of 44 internal reactions representing energy metabolism, the computed linear inequality constraints represent necessary and sufficient conditions for thermodynamic feasibility.     

Fundamental Escherichia coli biochemical pathways for biomass and energy production: identification of reactions

Cells grow by oxidizing nutrients using a complex network of biochemical reactions. During this process new biological material is produced along with energy used for maintaining cellular organization. Because the metabolic network is highly branched, these tasks can be accomplished using a wide variety of unique reaction sequences. However, evolutionary pressures under carbon-limited growth conditions likely select organisms that utilize highly efficient pathways. Using elementary-mode analysis, we demonstrate that the metabolism of the bacterium Escherichia coli contains four unique pathways that most efficiently convert glucose and oxygen into new cells and maintenance energy under any level of oxygen limitation. Observed regulatory patterns and experimental findings suggest growing cells use these highly efficient pathways. It is predicted that five knockout mutations generate a strain that supports growth using only the most efficient reaction sequence. The analysis approach should be generally useful for predicting metabolic capabilities and efficient network designs based on only genomic information.     

Systematic analysis of conservation relations in Escherichia coli genome-scale metabolic network reveals novel growth media

A biochemical species is called producible in a constraints-based metabolic model if a feasible steady-state flux configuration exists that sustains its nonzero concentration during growth. Extreme semipositive conservation relations (ESCRs) are the simplest semipositive linear combinations of species concentrations that are invariant to all metabolic flux configurations. In this article, we outline a fundamental relationship between the ESCRs of a metabolic network and the producibility of a biochemical species under a nutrient media. We exploit this relationship in an algorithm that systematically enumerates all minimal nutrient sets that render an objective species weakly producible (i.e., producible in the absence of thermodynamic constraints) through a simple traversal of ESCRs. We apply our results to a recent genome scale model of Escherichia coli metabolism, in which we traverse the 51 anhydrous ESCRs of the metabolic network to determine all 928 minimal aqueous nutrient media that render biomass weakly producible. Applying irreversibility constraints, we find 287 of these 928 nutrient sets to be thermodynamically feasible. We also find that an additional 365 of these nutrient sets are thermodynamically feasible in the presence of oxygen. Since biomass producibility is commonly used as a surrogate for growth in genome scale metabolic models, our results represent testable hypotheses of alternate growth media derived from in silico analysis of the E. coli genome scale metabolic network.     

The Escherichia coli proteome: past, present, and future prospects.

Proteomics has emerged as an indispensable methodology for large-scale protein analysis in functional genomics. The Escherichia coli proteome has been extensively studied and is well defined in terms of biochemical, biological, and biotechnological data. Even before the entire E. coli proteome was fully elucidated, the largest available data set had been integrated to decipher regulatory circuits and metabolic pathways, providing valuable insights into global cellular physiology and the development of metabolic and cellular engineering strategies. With the recent advent of advanced proteomic technologies, the E. coli proteome has been used for the validation of new technologies and methodologies such as sample prefractionation, protein enrichment, two-dimensional gel electrophoresis, protein detection, mass spectrometry (MS), combinatorial assays with n-dimensional chromatographies and MS, and image analysis software. These important technologies will not only provide a great amount of additional information on the E. coli proteome but also synergistically contribute to other proteomic studies. Here, we review the past development and current status of E. coli proteome research in terms of its biological, biotechnological, and methodological significance and suggest future prospects.     

A scalable algorithm to explore the Gibbs energy landscape of genome-scale metabolic networks

The integration of various types of genomic data into predictive models of biological networks is one of the main challenges currently faced by computational biology. Constraint-based models in particular play a key role in the attempt to obtain a quantitative understanding of cellular metabolism at genome scale. In essence, their goal is to frame the metabolic capabilities of an organism based on minimal assumptions that describe the steady states of the underlying reaction network via suitable stoichiometric constraints, specifically mass balance and energy balance (i.e. thermodynamic feasibility). The implementation of these requirements to generate viable configurations of reaction fluxes and/or to test given flux profiles for thermodynamic feasibility can however prove to be computationally intensive. We propose here a fast and scalable stoichiometry-based method to explore the Gibbs energy landscape of a biochemical network at steady state. The method is applied to the problem of reconstructing the Gibbs energy landscape underlying metabolic activity in the human red blood cell, and to that of identifying and removing thermodynamically infeasible reaction cycles in the Escherichia coli metabolic network (iAF1260). In the former case, we produce consistent predictions for chemical potentials (or log-concentrations) of intracellular metabolites; in the latter, we identify a restricted set of loops (23 in total) in the periplasmic and cytoplasmic core as the origin of thermodynamic infeasibility in a large sample (10(6)) of flux configurations generated randomly and compatibly with the prior information available on reaction reversibility.     

Assessment of the metabolic capabilities of Haemophilus influenzae Rd through a genome-scale pathway analysis

The annotated full DNA sequence is becoming available for a growing number of organisms. This information along with additional biochemical and strain-specific data can be used to define metabolic genotypes and reconstruct cellular metabolic networks. The first free-living organism for which the entire genomic sequence was established was Haemophilus influenzae. Its metabolic network is reconstructed herein and contains 461 reactions operating on 367 intracellular and 84 extracellular metabolites. With the metabolic reaction network established, it becomes necessary to determine its underlying pathway structure as defined by the set of extreme pathways. The H. influenzae metabolic network was subdivided into six subsystems and the extreme pathways determined for each subsystem based on stoichiometric, thermodynamic, and systems-specific constraints. Positive linear combinations of these pathways can be taken to determine the extreme pathways for the complete system. Since these pathways span the capabilities of the full system, they could be used to address a number of important physiological questions. First, they were used to reconcile and curate the sequence annotation by identifying reactions whose function was not supported in any of the extreme pathways. Second, they were used to predict gene products that should be co-regulated and perhaps co-expressed. Third, they were used to determine the composition of the minimal substrate requirements needed to support the production of 51 required metabolic products such as amino acids, nucleotides, phospholipids, etc. Fourth, sets of critical gene deletions from core metabolism were determined in the presence of the minimal substrate conditions and in more complete conditions reflecting the environmental niche of H. influenzae in the human host. In the former case, 11 genes were determined to be critical while six remained critical under the latter conditions. This study represents an important milestone in theoretical biology, namely the establishment of the first extreme pathway structure of a whole genome.     

Thermodynamically based profiling of drug metabolism and drug-drug metabolic interactions: a case study of acetaminophen and ethanol toxic interaction

Drug-drug metabolic interactions can result in unwanted side effects, including reduced drug efficacy and formation of toxic metabolic intermediates. In this work, thermodynamic constraints on non-equilibrium metabolite concentrations are used to reveal the biochemical interactions between the metabolic pathways of ethanol and acetaminophen (N-acetyl-p-aminophenol), two drugs known to interact unfavorably. It is known that many reactions of these pathways are coupled to the central energy metabolic reactions through a number of metabolites and the cellular redox potential. Based on these observations, a metabolic network model has been constructed and a database of thermodynamic properties for all participating metabolites and reactions has been compiled. Constraint-based computational analysis of the feasible metabolite concentrations reveals that the non-toxic pathways for APAP metabolism and the pathway for detoxifying N-acetyl-p-benzoquinoneimine (NAPQI) are inhibited by network interactions with ethanol metabolism. These results point to the potential utility of thermodynamically based profiling of metabolic network interactions in screening of drug candidates and analysis of potential toxicity.     

Robustness analysis of the Escherichia coli metabolic network

Genomic, biochemical, and strain-specific data can be assembled to define an in silico representation of the metabolic network for a select group of single cellular organisms. Flux-balance analysis and phenotypic phase planes derived therefrom have been developed and applied to analyze the metabolic capabilities and characteristics of Escherichia coli K-12. These analyses have shown the existence of seven essential reactions in the central metabolic pathways (glycolysis, pentose phosphate pathway, tricarboxylic acid cycle) for the growth in glucose minimal media. The corresponding seven gene products can be grouped into three categories: (1) pentose phosphate pathway genes, (2) three-carbon glycolytic genes, and (3) tricarboxylic acid cycle genes. Here we develop a procedure that calculates the sensitivity of optimal cellular growth to altered flux levels of these essential gene products. The results indicate that the E. coli metabolic network is robust with respect to the flux levels of these enzymes. The metabolic flux in the transketolase and the tricarboxylic acid cycle reactions can be reduced to 15% and 19%, respectively, of the optimal value without significantly influencing the optimal growth flux. The metabolic network also exhibited robustness with respect to the ribose-5-phosphate isomerase, and the ribose-5-phosephate isomerase flux was reduced to 28% of the optimal value without significantly effecting the optimal growth flux. The metabolic network exhibited limited robustness to the three-carbon glycolytic fluxes both increased and decreased. The development presented another dimension to the use of FBA to study the capabilities of metabolic networks.     

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     

HEPNet: A Knowledge Base Model of Human Energy Pool Network for Predicting the Energy Availability Status of an Individual

HEPNet is an electronic representation of metabolic reactions occurring within human cellular organization focusing on inflow and outflow of the energy currency ATP, GTP and other energy associated moieties. The backbone of HEPNet consists of primary bio-molecules such as carbohydrates, proteins and fats which ultimately constitute the chief source for the synthesis and obliteration of energy currencies in a cell. A series of biochemical pathways and reactions constituting the catabolism and anabolism of various metabolites are portrayed through cellular compartmentalization. The depicted pathways function synchronously toward an overarching goal of producing ATP and other energy associated moieties to bring into play a variety of cellular functions. HEPNet is manually curated with raw data from experiments and is also connected to KEGG and Reactome databases. This model has been validated by simulating it with physiological states like fasting, starvation, exercise and disease conditions like glycaemia, uremia and dihydrolipoamide dehydrogenase deficiency (DLDD). The results clearly indicate that ATP is the master regulator under different metabolic conditions and physiological states. The results also highlight that energy currencies play a minor role. However, the moiety creatine phosphate has a unique character, since it is a ready-made source of phosphoryl groups for the rapid synthesis of ATP from ADP. HEPNet provides a framework for further expanding the network diverse age groups of both the sexes, followed by the understanding of energetics in more complex metabolic pathways that are related to human disorders.     

Theory for the systemic definition of metabolic pathways and their use in interpreting metabolic function from a pathway-oriented perspective

Cellular metabolism is most often described and interpreted in terms of the biochemical reactions that make up the metabolic network. Genomics is providing near complete information regarding the genes/gene products participating in cellular metabolism for a growing number of organisms. As the true functional units of metabolic systems are its pathways, the time has arrived to define metabolic pathways in the context of whole-cell metabolism for the analysis of the structural design and capabilities of the metabolic network. In this study, we present the theoretical foundations for the identification of the unique set of systemically independent biochemical pathways, termed extreme pathways, based on system stochiometry and limited thermodynamics. These pathways represent the edges of the steady-state flux cone derived from convex analysis, and they can be used to represent any flux distribution achievable by the metabolic network. An algorithm is presented to determine the set of extreme pathways for a system of any complexity and a classification scheme is introduced for the characterization of these pathways. The property of systemic independence is discussed along with its implications for issues related to metabolic regulation and the evolution of cellular metabolic networks. The underlying pathway structure that is determined from the set of extreme pathways now provides us with the ability to analyse, interpret, and perhaps predict metabolic function from a pathway-based perspective in addition to the traditional reaction-based perspective. The algorithm and classification scheme developed can be used to describe the pathway structure in annotated genomes to explore the capabilities of an organism.     

Graph-theoretical identification of pathways for biochemical reactions

A rigorous method for identifying biochemical reaction or metabolic pathways through its systematic synthesis has been established. The current method for synthesizing networks of metabolic pathways follows the general framework of a highly exacting combinatorial method. The method is capable of generating not only all combinatorially independent, feasible reaction networks only once, but also those combinations of independent pathways. A case study involving the conversion of glucose to pyruvate with 14 elementary reactions illustrates the efficiency and efficacy of the method. All the results have been obtained with a PC (Pentium-III 550 MHz, 256 MB RAM) within 1 s.     

Protein interaction networks in bacteria

The complement of expressed cellular proteins - the proteome - is organized into functional, structured networks of protein interactions that mediate assembly of molecular machines and dynamic cellular pathways. Recent studies reveal the biological roles of protein interactions in bacteriophage T7 and Helicobacter pylori, and new methods allow to compare and to predict interaction networks in other species. Smaller scale networks provide biological insights into DNA replication and chromosome dynamics in Bacillus subtilis and Archeoglobus fulgidus, and into the assembly of multiprotein complexes such as the type IV secretion system of Agrobacterium tumefaciens, and the cell division machinery of Escherichia coli. Genome-wide interaction networks in several species are needed to obtain a biologically meaningful view of the higher order organization of the proteome in bacteria.     

Systemic metabolic reactions are obtained by singular value decomposition of genome-scale stoichiometric matrices

Genome-scale metabolic networks can be reconstructed. The systemic biochemical properties of these networks can now be studied. Here, genome-scale reconstructed metabolic networks were analysed using singular value decomposition (SVD). All the individual biochemical conversions contained in a reconstructed metabolic network are described by a stoichiometric matrix (S). SVD of S led to the definition of the underlying modes that characterize the overall biochemical conversions that take place in a network and rank-ordered their importance. The modes were shown to correspond to systemic biochemical reactions and they could be used to identify the groups and clusters of individual biochemical reactions that drive them. Comparative analysis of the Escherichia coli, Haemophilus influenzae, and Helicobacter pylori genome-scale metabolic networks showed that the four dominant modes in all three networks correspond to: (1) the conversion of ATP to ADP, (2) redox metabolism of NADP, (3) proton-motive force, and (4) inorganic phosphate metabolism. The sets of individual metabolic reactions deriving these systemic conversions, however, differed among the three organisms. Thus, we can now define systemic metabolic reactions, or eigen-reactions, for the study of systems biology of metabolism and have a basis for comparing the overall properties of genome-specific metabolic networks.     

Modular decomposition of metabolic reaction networks based on flux analysis and pathway projection

MOTIVATION: The rational decomposition of biochemical networks into sub-structures has emerged as a useful approach to study the design of these complex systems. A biochemical network is characterized by an inhomogeneous connectivity distribution, which gives rise to several organizational features, including modularity. To what extent the connectivity-based modules reflect the functional organization of the network remains to be further explored. In this work, we examine the influence of physiological perturbations on the modular organization of cellular metabolism. RESULTS: Modules were characterized for two model systems, liver and adipocyte primary metabolism, by applying an algorithm for top-down partition of directed graphs with non-uniform edge weights. The weights were set by the engagement of the corresponding reactions as expressed by the flux distribution. For the base case of the fasted rat liver, three modules were found, carrying out the following biochemical transformations: ketone body production, glucose synthesis and transamination. This basic organization was further modified when different flux distributions were applied that describe the liver's metabolic response to whole body inflammation. For the fully mature adipocyte, only a single module was observed, integrating all of the major pathways needed for lipid storage. Weaker levels of integration between the pathways were found for the early stages of adipocyte differentiation. Our results underscore the inhomogeneous distribution of both connectivity and connection strengths, and suggest that global activity data such as the flux distribution can be used to study the organizational flexibility of cellular metabolism. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Thermodynamics of stoichiometric biochemical networks in living systems far from equilibrium

The principles of thermodynamics apply to both equilibrium and nonequilibrium biochemical systems. The mathematical machinery of the classic thermodynamics, however, mainly applies to systems in equilibrium. We introduce a thermodynamic formalism for the study of metabolic biochemical reaction (open, nonlinear) networks in both time-dependent and time-independent nonequilibrium states. Classical concepts in equilibrium thermodynamics-enthalpy, entropy, and Gibbs free energy of biochemical reaction systems-are generalized to nonequilibrium settings. Chemical motive force, heat dissipation rate, and entropy production (creation) rate, key concepts in nonequilibrium systems, are introduced. Dynamic equations for the thermodynamic quantities are presented in terms of the key observables of a biochemical network: stoichiometric matrix Q, reaction fluxes J, and chemical potentials of species mu without evoking empirical rate laws. Energy conservation and the Second Law are established for steady-state and dynamic biochemical networks. The theory provides the physiochemical basis for analyzing large-scale metabolic networks in living organisms.