Elucidation and structural analysis of conserved pools for genome-scale metabolic reconstructions

Quantifying the propagation of parametric uncertainty on flux balance analysis

Flux balance analysis (FBA) and associated techniques operating on stoichiometric genome-scale metabolic models play a central role in quantifying metabolic flows and constraining feasible phenotypes. At the heart of these methods lie two important assumptions: (i) the biomass precursors and energy requirements neither change in response to growth conditions nor environmental/genetic perturbations, and (ii) metabolite production and consumption rates are equal at all times (i.e., steady-state). Despite the stringency of these two assumptions, FBA has been shown to be surprisingly robust at predicting cellular phenotypes. In this paper, we formally assess the impact of these two assumptions on FBA results by quantifying how uncertainty in biomass reaction coefficients, and departures from steady-state due to temporal fluctuations could propagate to FBA results. In the first case, conditional sampling of parameter space is required to re-weigh the biomass reaction so as the molecular weight remains equal to 1 g mmol^-1, and in the second case, metabolite (and elemental) pool conservation must be imposed under temporally varying conditions. Results confirm the importance of enforcing the aforementioned constraints and explain the robustness of FBA biomass yield predictions.

Isolating structural errors in reaction networks in systems biology

MOTIVATION

The growing complexity of reaction-based models necessitates early detection and resolution of model errors. Considerable work has been done on the detection of mass balance errors, especially atomic mass analysis (AMA) (which compares the counts of atoms in the reactants and products) and Linear Programming analysis (which detects stoichiometric inconsistencies). This article extends model error checking to include: (i) certain structural errors in reaction networks and (ii) error isolation. First, we consider the balance of chemical structures (moieties) between reactants and products. This balance is expected in many biochemical reactions, but the imbalance of chemical structures cannot be detected if the analysis is done in units of atomic masses. Second, we improve on error isolation for stoichiometric inconsistencies by identifying a small number of reactions and/or species that cause the error. Doing so simplifies error remediation.

RESULTS

We propose two algorithms that address isolating structural errors in reaction networks. Moiety analysis finds imbalances of moieties using the same algorithm as AMA, but moiety analysis works in units of moieties instead of atomic masses. We argue for the value of checking moiety balance, and discuss two approaches to decomposing chemical species into moieties. Graphical Analysis of Mass Equivalence Sets (GAMES) provides isolation for stoichiometric inconsistencies by constructing explanations that relate errors in the structure of the reaction network to elements of the reaction network. We study the effectiveness of moiety analysis and GAMES on curated models in the BioModels repository. We have created open source codes for moiety analysis and GAMES.

AVAILABILITY AND IMPLEMENTATION

Our project is hosted at https://github.com/ModelEngineering/SBMLLint, which contains examples, documentation, source code files and build scripts used to create SBMLLint. Our source code is licensed under the MIT open source license.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Utilization of Jujube Biomass to Prepare Biochar by Pyrolysis and Activation: Characterization, Adsorption Characteristics, and Mechanisms for Nitrogen

The rapid advancement of jujube industry has produced a large amount of jujube biomass waste, requiring the development of new methods for utilization of jujube resources. Herein, medium-temperature pyrolysis is employed to produce carbon materials from jujube waste in an oxygen-free environment. Ten types of jujube biochar (JB) are prepared by modifying different pyrolysis parameters, followed by physical activation. The physicochemical properties of JB are systematically characterized, and the adsorption characteristics of JB for NO₃⁻ and NH₄⁺ are evaluated via batch adsorption experiments. Furthermore, the pyrolysis and adsorption mechanisms are discussed. The results indicate that the C content, pH, and specific surface area of JB increase with an increase in the pyrolysis temperature from 300 °C to 700 °C, whereas the O and N contents, yield, zeta potential, and total functional groups of JB decrease gradually. The pyrolysis temperature more significantly effects the biochar properties than pyrolysis time. JB affords the highest adsorption capacity for NO₃⁻ (21.17 mg·g⁻¹) and NH₄⁺ (30.57 mg·g⁻¹) at 600 °C in 2 h. The Langmuir and pseudo-second-order models suitably describe the isothermal and kinetic adsorption processes, respectively. The NO₃⁻ and NH₄⁺ adsorption mechanisms of JB may include surface adsorption, intraparticle diffusion, electrostatic interaction, and ion exchange. In addition, π–π interaction and surface complexation may also be involved in NH₄⁺ adsorption. The pyrolysis mechanism comprises the combination of hemicellulose, cellulose, and lignin decomposition involving three stages. This study is expected to provide a theoretical and practical basis for the efficient utilization of jujube biomass to develop eco-friendly biochar and nitrogenous wastewater pollution prevention.

Advances in metabolic modeling of oleaginous microalgae

Production of biofuels and bioenergy precursors by phototrophic microorganisms, such as microalgae and cyanobacteria, is a promising alternative to conventional fuels obtained from non-renewable resources. Several species of microalgae have been investigated as potential candidates for the production of biofuels, for the most part due to their exceptional metabolic capability to accumulate large quantities of lipids. Constraint-based modeling, a systems biology approach that accurately predicts the metabolic phenotype of phototrophs, has been deployed to identify suitable culture conditions as well as to explore genetic enhancement strategies for bioproduction. Core metabolic models were employed to gain insight into the central carbon metabolism in photosynthetic microorganisms. More recently, comprehensive genome-scale models, including organelle-specific information at high resolution, have been developed to gain new insight into the metabolism of phototrophic cell factories. Here, we review the current state of the art of constraint-based modeling and computational method development and discuss how advanced models led to increased prediction accuracy and thus improved lipid production in microalgae.

Predicting Dynamic Metabolic Demands in the Photosynthetic Eukaryote Chlorella vulgaris

Phototrophic organisms exhibit a highly dynamic proteome, adapting their biomass composition in response to diurnal light/dark cycles and nutrient availability. Here, we used experimentally determined biomass compositions over the course of growth to determine and constrain the biomass objective function (BOF) in a genome-scale metabolic model of Chlorella vulgaris UTEX 395 over time. Changes in the BOF, which encompasses all metabolites necessary to produce biomass, influence the state of the metabolic network thus directly affecting predictions. Simulations using dynamic BOFs predicted distinct proteome demands during heterotrophic or photoautotrophic growth. Model-driven analysis of extracellular nitrogen concentrations and predicted nitrogen uptake rates revealed an intracellular nitrogen pool, which contains 38% of the total nitrogen provided in the medium for photoautotrophic and 13% for heterotrophic growth. Agreement between flux and gene expression trends was determined by statistical comparison. Accordance between predicted flux trends and gene expression trends was found for 65% of multisubunit enzymes and 75% of allosteric reactions. Reactions with the highest agreement between simulations and experimental data were associated with energy metabolism, terpenoid biosynthesis, fatty acids, nucleotides, and amino acid metabolism. Furthermore, predicted flux distributions at each time point were compared with gene expression data to gain new insights into intracellular compartmentalization, specifically for transporters. A total of 103 genes related to internal transport reactions were identified and added to the updated model of C. vulgaris, iCZ946, thus increasing our knowledgebase by 10% for this model green alga.

Identification of Conserved Moieties in Metabolic Networks by Graph Theoretical Analysis of Atom Transition Networks

Conserved moieties are groups of atoms that remain intact in all reactions of a metabolic network. Identification of conserved moieties gives insight into the structure and function of metabolic networks and facilitates metabolic modelling. All moiety conservation relations can be represented as nonnegative integer vectors in the left null space of the stoichiometric matrix corresponding to a biochemical network. Algorithms exist to compute such vectors based only on reaction stoichiometry but their computational complexity has limited their application to relatively small metabolic networks. Moreover, the vectors returned by existing algorithms do not, in general, represent conservation of a specific moiety with a defined atomic structure. Here, we show that identification of conserved moieties requires data on reaction atom mappings in addition to stoichiometry. We present a novel method to identify conserved moieties in metabolic networks by graph theoretical analysis of their underlying atom transition networks. Our method returns the exact group of atoms belonging to each conserved moiety as well as the corresponding vector in the left null space of the stoichiometric matrix. It can be implemented as a pipeline of polynomial time algorithms. Our implementation completes in under five minutes on a metabolic network with more than 4,000 mass balanced reactions. The scalability of the method enables extension of existing applications for moiety conservation relations to genome-scale metabolic networks. We also give examples of new applications made possible by elucidating the atomic structure of conserved moieties.

Conserved moieties are transferred between metabolites in internal reactions of a metabolic network but are not synthesised, degraded or exchanged with the environment. The total amount of a conserved moiety in the metabolic network is therefore constant over time. Metabolites that share a conserved moiety have interdependent concentrations because their total amount is constant. Identification of conserved moieties results in a concise description of all concentration dependencies in a metabolic network. The problem of identifying conserved moieties has previously been formulated in terms of the stoichiometry of metabolic reactions. Methods based on this formulation are computationally intractable for large networks. We show that reaction stoichiometry alone gives insufficient information to identify conserved moieties. By first incorporating additional data on the fate of atoms in metabolic reactions, we developed and implemented a computationally tractable algorithm to identify conserved moieties and their atomic structure.

Quorum-Sensing Synchronization of Synthetic Toggle Switches: A Design Based on Monotone Dynamical Systems Theory

Synthetic constructs in biotechnology, biocomputing, and modern gene therapy interventions are often based on plasmids or transfected circuits which implement some form of “on-off” switch. For example, the expression of a protein used for therapeutic purposes might be triggered by the recognition of a specific combination of inducers (e.g., antigens), and memory of this event should be maintained across a cell population until a specific stimulus commands a coordinated shut-off. The robustness of such a design is hampered by molecular (“intrinsic”) or environmental (“extrinsic”) noise, which may lead to spontaneous changes of state in a subset of the population and is reflected in the bimodality of protein expression, as measured for example using flow cytometry. In this context, a “majority-vote” correction circuit, which brings deviant cells back into the required state, is highly desirable, and quorum-sensing has been suggested as a way for cells to broadcast their states to the population as a whole so as to facilitate consensus. In this paper, we propose what we believe is the first such a design that has mathematically guaranteed properties of stability and auto-correction under certain conditions. Our approach is guided by concepts and theory from the field of “monotone” dynamical systems developed by M. Hirsch, H. Smith, and others. We benchmark our design by comparing it to an existing design which has been the subject of experimental and theoretical studies, illustrating its superiority in stability and self-correction of synchronization errors. Our stability analysis, based on dynamical systems theory, guarantees global convergence to steady states, ruling out unpredictable (“chaotic”) behaviors and even sustained oscillations in the limit of convergence. These results are valid no matter what are the values of parameters, and are based only on the wiring diagram. The theory is complemented by extensive computational bifurcation analysis, performed for a biochemically-detailed and biologically-relevant model that we developed. Another novel feature of our approach is that our theorems on exponential stability of steady states for homogeneous or mixed populations are valid independently of the number N of cells in the population, which is usually very large (N ≫ 1) and unknown. We prove that the exponential stability depends on relative proportions of each type of state only. While monotone systems theory has been used previously for systems biology analysis, the current work illustrates its power for synthetic biology design, and thus has wider significance well beyond the application to the important problem of coordination of toggle switches.

For the last decade, outstanding progress has been made, and considerable practical experience has accumulated, in the construction of elementary genetic circuits that perform various tasks, such as memory storage and logical operations, in response to both exogenous and endogenous stimuli. Using modern molecular “plug-and-play” technologies, various (re-)programmable cellular populations can be engineered, and they can be combined into more complex cellular systems. Among all engineered synthetic circuits, a toggle, a robust bistable switch leading to a binary response dynamics, is the simplest basic synthetic biology device, analogous to the “flip-flop” or latch in electronic design, and it plays a key role in biotechnology, biocomputing, and proposed gene therapies. However, despite many remarkable properties of the existing toggle designs, they must be tightly controlled in order to avoid spontaneous switching between different expression states (loss of long-term memory) or even the breakdown of stability through the generation of stable oscillations. To address this concrete challenge, we have developed a new design for quorum-sensing synthetic toggles, based on monotone dynamical systems theory. Our design is endowed with strong theoretical guarantees that completely exclude unpredictable chaotic behaviors in the limit of convergence, as well as undesired stable oscillations, and leads to robust consensus states.

Identifying all moiety conservation laws in genome-scale metabolic networks

The stoichiometry of a metabolic network gives rise to a set of conservation laws for the aggregate level of specific pools of metabolites, which, on one hand, pose dynamical constraints that cross-link the variations of metabolite concentrations and, on the other, provide key insight into a cell's metabolic production capabilities. When the conserved quantity identifies with a chemical moiety, extracting all such conservation laws from the stoichiometry amounts to finding all non-negative integer solutions of a linear system, a programming problem known to be NP-hard. We present an efficient strategy to compute the complete set of integer conservation laws of a genome-scale stoichiometric matrix, also providing a certificate for correctness and maximality of the solution. Our method is deployed for the analysis of moiety conservation relationships in two large-scale reconstructions of the metabolism of the bacterium E. coli, in six tissue-specific human metabolic networks, and, finally, in the human reactome as a whole, revealing that bacterial metabolism could be evolutionarily designed to cover broader production spectra than human metabolism. Convergence to the full set of moiety conservation laws in each case is achieved in extremely reduced computing times. In addition, we uncover a scaling relation that links the size of the independent pool basis to the number of metabolites, for which we present an analytical explanation.

Integration of metabolic databases for the reconstruction of genome-scale metabolic networks

BACKGROUND

Genome-scale metabolic reconstructions have been recognised as a valuable tool for a variety of applications ranging from metabolic engineering to evolutionary studies. However, the reconstruction of such networks remains an arduous process requiring a high level of human intervention. This process is further complicated by occurrences of missing or conflicting information and the absence of common annotation standards between different data sources.

RESULTS

In this article, we report a semi-automated methodology aimed at streamlining the process of metabolic network reconstruction by enabling the integration of different genome-wide databases of metabolic reactions. We present results obtained by applying this methodology to the metabolic network of the plant Arabidopsis thaliana. A systematic comparison of compounds and reactions between two genome-wide databases allowed us to obtain a high-quality core consensus reconstruction, which was validated for stoichiometric consistency. A lower level of consensus led to a larger reconstruction, which has a lower quality standard but provides a baseline for further manual curation.

CONCLUSION

This semi-automated methodology may be applied to other organisms and help to streamline the process of genome-scale network reconstruction in order to accelerate the transfer of such models to applications.

Use of genome-scale metabolic models for understanding microbial physiology

The exploitation of microorganisms in industrial, medical, food and environmental biotechnology requires a comprehensive understanding of their physiology. The availability of genome sequences and accumulation of high-throughput data allows gaining understanding of microbial physiology at the systems level, and genome-scale metabolic models represent a valuable framework for integrative analysis of metabolism of microorganisms. Genome-scale metabolic models are reconstructed based on a combination of genome sequence information and detailed biochemical information, and these reconstructed models can be used for analyzing and simulating the operation of metabolism in response to different stimuli. Here we discuss the requirement for having detailed physiological insight in order to exploit microorganisms for production of fuels, chemicals and pharmaceuticals. We further describe the reconstruction process of genome-scale metabolic models and different algorithms that can be used to apply these models to gain improved insight into microbial physiology.

The use of network analyses for elucidating mechanisms in cardiovascular disease

Systems biology offers the potential to provide new insights into our understanding of the pathogenesis of complex diseases such as atherosclerosis. It seeks to comprehend the system properties of the non-linear interactions of the multiple biomolecular components that characterize a living organism. An important component of this research approach is identifying the biological networks that connect the differing elements of a system and in the process describe the characteristics that define a shift in equilibrium from a healthy to a diseased state. The utility of this method becomes clear when applied to multifactorial diseases with complex etiologies such as inflammatory-related diseases, herein exemplified by cardiovascular disease. In this study, the application of network theory to systems biology is described in detail and an example is provided using data from a clinical biobank database of carotid endarterectomies from the Karolinska University Hospital (Biobank of Karolinska Endarterectomies, BiKE). Data from 47 microarrays were examined using a combination of Bioconductor modules and the Cytoscape resource with several associated plugins to analyze the transcriptomics data and create a combined gene association and correlation network of atherosclerosis. The methodology and workflow are described in detail, with a total of 43 genes found to be differentially expressed on a gender-specific basis, of which 15 were not directly linked to the sex chromosomes. In particular, the APOC1 gene was 2.1-fold down-regulated in plaques in women relative to men and was selected for further analysis based upon a purported role in cardiovascular disease. The resulting network was identified as a scale-free network that contained specific sub-networks related to immune function and lipid biosynthesis. These sub-networks link atherosclerotic-related genes to other genes that may not have previously known roles in disease etiology and only evidence small alterations, which are challenging to find by statistical and comparison-based methods. A number of Gene Ontology (GO), BioCarta and KEGG pathways involved in the atherosclerotic process were identified in the constructed sub-network, with 19 GO pathways related to APOC1 of which 'phospholipid efflux' evidenced the strongest association. The utility and functionality of network analysis and the different Cytoscape plugins employed are discussed. Lastly, the applications of these methods to cardiovascular disease are discussed with focus on the current limitations and future visions of this emerging field.

Model reduction of multiscale chemical langevin equations: a numerical case study

Two very important characteristics of biological reaction networks need to be considered carefully when modeling these systems. First, models must account for the inherent probabilistic nature of systems far from the thermodynamic limit. Often, biological systems cannot be modeled with traditional continuous-deterministic models. Second, models must take into consideration the disparate spectrum of time scales observed in biological phenomena, such as slow transcription events and fast dimerization reactions. In the last decade, significant efforts have been expended on the development of stochastic chemical kinetics models to capture the dynamics of biomolecular systems, and on the development of robust multiscale algorithms, able to handle stiffness. In this paper, the focus is on the dynamics of reaction sets governed by stiff chemical Langevin equations, i.e., stiff stochastic differential equations. These are particularly challenging systems to model, requiring prohibitively small integration step sizes. We describe and illustrate the application of a semianalytical reduction framework for chemical Langevin equations that results in significant gains in computational cost.

Systems biology approaches and pathway tools for investigating cardiovascular disease

Systems biology aims to understand the nonlinear interactions of multiple biomolecular components that characterize a living organism. One important aspect of systems biology approaches is to identify the biological pathways or networks that connect the differing elements of a system, and examine how they evolve with temporal and environmental changes. The utility of this method becomes clear when applied to multifactorial diseases with complex etiologies, such as inflammatory-related diseases, herein exemplified by atherosclerosis. In this paper, the initial studies in this discipline are reviewed and examined within the context of the development of the field. In addition, several different software tools are briefly described and a novel application for the KEGG database suite called KegArray is presented. This tool is designed for mapping the results of high-throughput omics studies, including transcriptomics, proteomics and metabolomics data, onto interactive KEGG metabolic pathways. The utility of KegArray is demonstrated using a combined transcriptomics and lipidomics dataset from a published study designed to examine the potential of cholesterol in the diet to influence the inflammatory component in the development of atherosclerosis. These data were mapped onto the KEGG PATHWAY database, with a low cholesterol diet affecting 60 distinct biochemical pathways and a high cholesterol exposure affecting 76 biochemical pathways. A total of 77 pathways were differentially affected between low and high cholesterol diets. The KEGG pathways "Biosynthesis of unsaturated fatty acids" and "Sphingolipid metabolism" evidenced multiple changes in gene/lipid levels between low and high cholesterol treatment, and are discussed in detail. Taken together, this paper provides a brief introduction to systems biology and the applications of pathway mapping to the study of cardiovascular disease, as well as a summary of available tools. Current limitations and future visions of this emerging field are discussed, with the conclusion that combining knowledge from biological pathways and high-throughput omics data will move clinical medicine one step further to individualize medical diagnosis and treatment.

Identifying essential genes in Escherichia coli from a metabolic optimization principle

Understanding the organization of reaction fluxes in cellular metabolism from the stoichiometry and the topology of the underlying biochemical network is a central issue in systems biology. In this task, it is important to devise reasonable approximation schemes that rely on the stoichiometric data only, because full-scale kinetic approaches are computationally affordable only for small networks (e.g., red blood cells, approximately 50 reactions). Methods commonly used are based on finding the stationary flux configurations that satisfy mass-balance conditions for metabolites, often coupling them to local optimization rules (e.g., maximization of biomass production) to reduce the size of the solution space to a single point. Such methods have been widely applied and have proven able to reproduce experimental findings for relatively simple organisms in specific conditions. Here, we define and study a constraint-based model of cellular metabolism where neither mass balance nor flux stationarity are postulated and where the relevant flux configurations optimize the global growth of the system. In the case of Escherichia coli, steady flux states are recovered as solutions, although mass-balance conditions are violated for some metabolites, implying a nonzero net production of the latter. Such solutions furthermore turn out to provide the correct statistics of fluxes for the bacterium E. coli in different environments and compare well with the available experimental evidence on individual fluxes. Conserved metabolic pools play a key role in determining growth rate and flux variability. Finally, we are able to connect phenomenological gene essentiality with "frozen" fluxes (i.e., fluxes with smaller allowed variability) in E. coli metabolism.

Incorporating genome-wide DNA sequence information into a dynamic whole-cell model of Escherichia coli: application to DNA replication

The advent of thousands of annotated genomes, detailed metabolic reconstructions and databases within the flourishing field of systems biology necessitates the development of functionally complete computer models of whole cells and cellular systems. Such models would realistically describe fundamental properties of living systems such as growth, division and chromosome replication. This will inevitably bridge bioinformatic technologies with ongoing mathematical modelling efforts and would allow for in silico prediction of important dynamic physiological events. To demonstrate a potential for the anticipated merger of bioinformatic genome-wide data with a whole-cell computer model, the authors present here an updated version of a dynamic model of Escherichia coli, including a module that correctly describes the initiation and control of DNA replication by nucleoprotein DnaA-ATP molecules. Specifically, a rigorous mathematical approach used to explicitly include the genome-wide distribution of DnaA-binding sites on the replicating chromosome into a computer model of a bacterial cell is discussed. A new simple deterministic approximation of the complex stochastic process of DNA replication initiation is also provided. It is shown for the first time that reasonable assumptions about the mechanism of DNA replication initiation can be implemented in a deterministic whole-cell model to make predictions about the timing of chromosome replication. Furthermore, it is proposed that a large increase in the concentration of DnaA-binding boxes will result in a decreased steady-state growth rate in E. coli.

Genome-scale models of bacterial metabolism: reconstruction and applications

Genome-scale metabolic models bridge the gap between genome-derived biochemical information and metabolic phenotypes in a principled manner, providing a solid interpretative framework for experimental data related to metabolic states, and enabling simple in silico experiments with whole-cell metabolism. Models have been reconstructed for almost 20 bacterial species, so far mainly through expert curation efforts integrating information from the literature with genome annotation. A wide variety of computational methods exploiting metabolic models have been developed and applied to bacteria, yielding valuable insights into bacterial metabolism and evolution, and providing a sound basis for computer-assisted design in metabolic engineering. Recent advances in computational systems biology and high-throughput experimental technologies pave the way for the systematic reconstruction of metabolic models from genomes of new species, and a corresponding expansion of the scope of their applications. In this review, we provide an introduction to the key ideas of metabolic modeling, survey the methods, and resources that enable model reconstruction and refinement, and chart applications to the investigation of global properties of metabolic systems, the interpretation of experimental results, and the re-engineering of their biochemical capabilities.

Genome-scale model for Clostridium acetobutylicum: Part I. Metabolic network resolution and analysis

A genome-scale metabolic network reconstruction for Clostridium acetobutylicum (ATCC 824) was carried out using a new semi-automated reverse engineering algorithm. The network consists of 422 intracellular metabolites involved in 552 reactions and includes 80 membrane transport reactions. The metabolic network illustrates the reliance of clostridia on the urea cycle, intracellular L-glutamate solute pools, and the acetylornithine transaminase for amino acid biosynthesis from the 2-oxoglutarate precursor. The semi-automated reverse engineering algorithm identified discrepancies in reaction network databases that are major obstacles for fully automated network-building algorithms. The proposed semi-automated approach allowed for the conservation of unique clostridial metabolic pathways, such as an incomplete TCA cycle. A thermodynamic analysis was used to determine the physiological conditions under which proposed pathways (e.g., reverse partial TCA cycle and reverse arginine biosynthesis pathway) are feasible. The reconstructed metabolic network was used to create a genome-scale model that correctly characterized the butyrate kinase knock-out and the asolventogenic M5 pSOL1 megaplasmid degenerate strains. Systematic gene knock-out simulations were performed to identify a set of genes encoding clostridial enzymes essential for growth in silico.

The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli

The number and scope of methods developed to interrogate and use metabolic network reconstructions has significantly expanded over the past 15 years. In particular, Escherichia coli metabolic network reconstruction has reached the genome scale and been utilized to address a broad spectrum of basic and practical applications in five main categories: metabolic engineering, model-directed discovery, interpretations of phenotypic screens, analysis of network properties and studies of evolutionary processes. Spurred on by these accomplishments, the field is expected to move forward and further broaden the scope and content of network reconstructions, develop new and novel in silico analysis tools, and expand in adaptation to uses of proximal and distal causation in biology. Taken together, these efforts will solidify a mechanistic genotype-phenotype relationship for microbial metabolism.

The implications of human metabolic network topology for disease comorbidity

Most diseases are the consequence of the breakdown of cellular processes, but the relationships among genetic/epigenetic defects, the molecular interaction networks underlying them, and the disease phenotypes remain poorly understood. To gain insights into such relationships, here we constructed a bipartite human disease association network in which nodes are diseases and two diseases are linked if mutated enzymes associated with them catalyze adjacent metabolic reactions. We find that connected disease pairs display higher correlated reaction flux rate, corresponding enzyme-encoding gene coexpression, and higher comorbidity than those that have no metabolic link between them. Furthermore, the more connected a disease is to other diseases, the higher is its prevalence and associated mortality rate. The network topology-based approach also helps to uncover potential mechanisms that contribute to their shared pathophysiology. Thus, the structure and modeled function of the human metabolic network can provide insights into disease comorbidity, with potentially important consequences for disease diagnosis and prevention.

An inflammatory arthritis-associated metabolite biomarker pattern revealed by 1H NMR spectroscopy

Rheumatoid arthritis, a debilitating, systemic inflammatory joint disease, is likely accompanied by alterations in circulating metabolites. Here, an 1H NMR spectroscopy-based metabolomics approach was developed to establish a metabolic 'biomarker pattern' in a model of rheumatoid arthritis, the K/BxN transgenic mouse. Sera obtained from arthritic K/BxN mice (N = 15) and a control population (N = 19) having the same genetic background, but lacking the arthritogenic T-cell receptor KRN transgene, were compared by 1H NMR spectroscopy. A unique method was developed by combining technologies such as ultrafiltration to remove proteins from serum samples, quantitative 'targeted profiling' of known metabolites, pseudo-quantitative profiling of unknown resonances, a supervised O-PLS-DA pattern recognition analysis, and a metabolic-pathway based network analysis for interpretation of results. In total, 88 spectral features were profiled (59 metabolites and 28 unknown resonances). A highly significant subset of 18 spectral features (15 known compounds and 3 unknown resonances) was identified (p = 0.00075 using MANOVA) that we term a 'metabolic bioprofile'. We identified metabolites relating to nucleic acid, amino acid, and fatty acid metabolism, as well as lipolysis, reactive oxygen species generation, and methylation. Pathway analysis suggested a shift from metabolites involved in numerous reactions (hub-metabolites) toward intermediates and metabolic endpoints associated with arthritis. The results attest to the metabolic complexity of systemic inflammation and to the power of the experimental approach for identifying a wide variety of disease-associated marker candidates. The diagnostic and prognostic implications of monitoring a spectrum of metabolic events simultaneously using serum samples is discussed with respect to the potential for individualized medicine.

A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information

An updated genome-scale reconstruction of the metabolic network in Escherichia coli K-12 MG1655 is presented. This updated metabolic reconstruction includes: (1) an alignment with the latest genome annotation and the metabolic content of EcoCyc leading to the inclusion of the activities of 1260 ORFs, (2) characterization and quantification of the biomass components and maintenance requirements associated with growth of E. coli and (3) thermodynamic information for the included chemical reactions. The conversion of this metabolic network reconstruction into an in silico model is detailed. A new step in the metabolic reconstruction process, termed thermodynamic consistency analysis, is introduced, in which reactions were checked for consistency with thermodynamic reversibility estimates. Applications demonstrating the capabilities of the genome-scale metabolic model to predict high-throughput experimental growth and gene deletion phenotypic screens are presented. The increased scope and computational capability using this new reconstruction is expected to broaden the spectrum of both basic biology and applied systems biology studies of E. coli metabolism.

Sensitivity and control analysis of periodically forced reaction networks using the Green's function method

A general sensitivity and control analysis of periodically forced reaction networks with respect to small perturbations in arbitrary network parameters is presented. A well-known property of sensitivity coefficients for periodic processes in dynamical systems is that the coefficients generally become unbounded as time tends to infinity. To circumvent this conceptual obstacle, a relative time or phase variable is introduced so that the periodic sensitivity coefficients can be calculated. By employing the Green's function method, the sensitivity coefficients can be defined using integral control operators that relate small perturbations in the network's parameters and forcing frequency to variations in the metabolite concentrations and reaction fluxes. The properties of such operators do not depend on a particular parameter perturbation and are described by the summation and connectivity relationships within a control-matrix operator equation. The aim of this paper is to derive such a general control-matrix operator equation for periodically forced reaction networks, including metabolic pathways. To illustrate the general method, the two limiting cases of high and low forcing frequency are considered. We also discuss a practically important case where enzyme activities and forcing frequency are modulated simultaneously. We demonstrate the developed framework by calculating the sensitivity and control coefficients for a simple two reaction pathway where enzyme activities enter reaction rates linearly and specifically.

Metabolite coupling in genome-scale metabolic networks

Background

Biochemically detailed stoichiometric matrices have now been reconstructed for various bacteria, yeast, and for the human cardiac mitochondrion based on genomic and proteomic data. These networks have been manually curated based on legacy data and elementally and charge balanced. Comparative analysis of these well curated networks is now possible. Pairs of metabolites often appear together in several network reactions, linking them topologically. This co-occurrence of pairs of metabolites in metabolic reactions is termed herein "metabolite coupling." These metabolite pairs can be directly computed from the stoichiometric matrix, S. Metabolite coupling is derived from the matrix ŜŜ^T, whose off-diagonal elements indicate the number of reactions in which any two metabolites participate together, where Ŝ is the binary form of S.

Results

Metabolite coupling in the studied networks was found to be dominated by a relatively small group of highly interacting pairs of metabolites. As would be expected, metabolites with high individual metabolite connectivity also tended to be those with the highest metabolite coupling, as the most connected metabolites couple more often. For metabolite pairs that are not highly coupled, we show that the number of reactions a pair of metabolites shares across a metabolic network closely approximates a line on a log-log scale. We also show that the preferential coupling of two metabolites with each other is spread across the spectrum of metabolites and is not unique to the most connected metabolites. We provide a measure for determining which metabolite pairs couple more often than would be expected based on their individual connectivity in the network and show that these metabolites often derive their principal biological functions from existing in pairs. Thus, analysis of metabolite coupling provides information beyond that which is found from studying the individual connectivity of individual metabolites.

Conclusion

The coupling of metabolites is an important topological property of metabolic networks. By computing coupling quantitatively for the first time in genome-scale metabolic networks, we provide insight into the basic structure of these networks.

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.