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.     

Reconstruction of the central carbon metabolism of Aspergillus niger.

The topology of central carbon metabolism of Aspergillus niger was identified and the metabolic network reconstructed, by integrating genomic, biochemical and physiological information available for this microorganism and other related fungi. The reconstructed network may serve as a valuable database for annotation of genes identified in future genome sequencing projects on aspergilli. Based on the metabolic reconstruction, a stoichiometric model was set up that includes 284 metabolites and 335 reactions, of which 268 represent biochemical conversions and 67 represent transport processes between the different intracellular compartments and between the cell and the extracellular medium. The stoichiometry of the metabolic reactions was used in combination with biosynthetic requirements for growth and pseudo-steady state mass balances over intracellular metabolites for the quantification of metabolic fluxes using metabolite balancing. This framework was employed to perform an in silico characterisation of the phenotypic behaviour of A. niger grown on different carbon sources. The effects on growth of single reaction deletions were assessed and essential biochemical reactions were identified for different carbon sources. Furthermore, application of the stoichiometric model for assessing the metabolic capabilities of A. niger to produce metabolites was evaluated by using succinate production as a case study.     

Genome‐derived minimal metabolic models for Escherichia coli MG1655 with estimated in vivo respiratory ATP stoichiometry

Metabolic network models describing growth of Escherichia coli on glucose, glycerol and acetate were derived from a genome scale model of E. coli. One of the uncertainties in the metabolic networks is the exact stoichiometry of energy generating and consuming processes. Accurate estimation of biomass and product yields requires correct information on the ATP stoichiometry. The unknown ATP stoichiometry parameters of the constructed E. coli network were estimated from experimental data of eight different aerobic chemostat experiments carried out with E. coli MG1655, grown at different dilution rates (0.025, 0.05, 0.1, and 0.3 h^?1) and on different carbon substrates (glucose, glycerol, and acetate). Proper estimation of the ATP stoichiometry requires proper information on the biomass composition of the organism as well as accurate assessment of net conversion rates under well‐defined conditions. For this purpose a growth rate dependent biomass composition was derived, based on measurements and literature data. After incorporation of the growth rate dependent biomass composition in a metabolic network model, an effective P/O ratio of 1.49 ± 0.26 mol of ATP/mol of O, K_X (growth dependent maintenance) of 0.46 ± 0.27 mol of ATP/C‐mol of biomass and m_ATP (growth independent maintenance) of 0.075 ± 0.015 mol of ATP/C‐mol of biomass/h were estimated using a newly developed Comprehensive Data Reconciliation (CDR) method, assuming that the three energetic parameters were independent of the growth rate and the used substrate. The resulting metabolic network model only requires the specific rate of growth, µ, as an input in order to accurately predict all other fluxes and yields. Biotechnol. Bioeng. 2010;107: 369–381. © 2010 Wiley Periodicals, Inc.     

Towards kinetic modeling of genome-scale metabolic networks without sacrificing stoichiometric,thermodynamic and physiological constraints

Mathematical modeling is an essential tool for the comprehensive understanding of cell metabolism and its interactions with the environmental and process conditions. Recent developments in the construction and analysis of stoichiometric models made it possible to define limits on steady-state metabolic behavior using flux balance analysis. However, detailed information on enzyme kinetics and enzyme regulation is needed to formulate kinetic models that can accurately capture the dynamic metabolic responses. The use of mechanistic enzyme kinetics is a difficult task due to uncertainty in the kinetic properties of enzymes. Therefore, the majority of recent works considered only mass action kinetics for reactions in metabolic networks. Herein, we applied the optimization and risk analysis of complex living entities (ORACLE) framework and constructed a large-scale mechanistic kinetic model of optimally grown Escherichia coli. We investigated the complex interplay between stoichiometry, thermodynamics, and kinetics in determining the flexibility and capabilities of metabolism. Our results indicate that enzyme saturation is a necessary consideration in modeling metabolic networks and it extends the feasible ranges of metabolic fluxes and metabolite concentrations. Our results further suggest that enzymes in metabolic networks have evolved to function at different saturation states to ensure greater flexibility and robustness of cellular metabolism.     

Network analysis of intermediary metabolism using linear optimization. I. Development of mathematical formalism.

Analysis of metabolic networks using linear optimization theory allows one to quantify and understand the limitations imposed on the cell by its metabolic stoichiometry, and to understand how the flux through each pathway influences the overall behavior of metabolism. A stoichiometric matrix accounting for the major pathways involved in energy and mass transformations in the cell was used in our analysis. The auxiliary parameters of linear optimization, the so-called shadow prices, identify the intermediates and cofactors that cause the growth to be limited on each nutrient. This formalism was used to examine how well the cell balances its needs for carbon, nitrogen, and energy during growth on different substrates. The relative values of glucose and glutamine as nutrients were compared by varying the ratio of rates of glucose to glutamine uptakes, and calculating the maximum growth rate. The optimum value of this ratio is between 2-7, similar to experimentally observed ratios. The theoretical maximum growth rate was calculated for growth on each amino acid, and the amino acids catabolized directly to glutamate were found to be the optimal nutrients. The importance of each reaction in the network can be examined both by selectively limiting the flux through the reaction, and by the value of the reduced cost for that reaction. Some reactions, such as malic enzyme and glutamate dehydrogenase, may be inhibited or deleted with little or no adverse effect on the calculated cell growth rate.     

Hybrid dynamic modeling of Escherichia coli central metabolic network combining Michaelis–Menten and approximate kinetic equations

The construction of dynamic metabolic models at reaction network level requires the use of mechanistic enzymatic rate equations that comprise a large number of parameters. The lack of knowledge on these equations and the difficulty in the experimental identification of their associated parameters, represent nowadays the limiting factor in the construction of such models. In this study, we compare four alternative modeling approaches based on Michaelis–Menten kinetics for the bi-molecular reactions and different types of simplified rate equations for the remaining reactions (generalized mass action, convenience kinetics, lin-log and power-law). Using the mechanistic model for Escherichia coli central carbon metabolism as a benchmark, we investigate the alternative modeling approaches through comparative simulations analyses. The good dynamic behavior and the powerful predictive capabilities obtained using the hybrid model composed of Michaelis–Menten and the approximate lin-log kinetics indicate that this is a possible suitable approach to model complex large-scale networks where the exact rate laws are unknown.     

Timing and Variability of Galactose Metabolic Gene Activation Depend on the Rate of Environmental Change

Modulation of gene network activity allows cells to respond to changes in environmental conditions. For example, the galactose utilization network in Saccharomyces cerevisiae is activated by the presence of galactose but repressed by glucose. If both sugars are present, the yeast will first metabolize glucose, depleting it from the extracellular environment. Upon depletion of glucose, the genes encoding galactose metabolic proteins will activate. Here, we show that the rate at which glucose levels are depleted determines the timing and variability of galactose gene activation. Paradoxically, we find that Gal1p, an enzyme needed for galactose metabolism, accumulates more quickly if glucose is depleted slowly rather than taken away quickly. Furthermore, the variability of induction times in individual cells depends non-monotonically on the rate of glucose depletion and exhibits a minimum at intermediate depletion rates. Our mathematical modeling suggests that the dynamics of the metabolic transition from glucose to galactose are responsible for the variability in galactose gene activation. These findings demonstrate that environmental dynamics can determine the phenotypic outcome at both the single-cell and population levels.     

Enumeration of minimal stoichiometric precursor sets in metabolic networks

Background

What an organism needs at least from its environment to produce a set of metabolites, e.g. target(s) of interest and/or biomass, has been called a minimal precursor set. Early approaches to enumerate all minimal precursor sets took into account only the topology of the metabolic network (topological precursor sets). Due to cycles and the stoichiometric values of the reactions, it is often not possible to produce the target(s) from a topological precursor set in the sense that there is no feasible flux. Although considering the stoichiometry makes the problem harder, it enables to obtain biologically reasonable precursor sets that we call stoichiometric. Recently a method to enumerate all minimal stoichiometric precursor sets was proposed in the literature. The relationship between topological and stoichiometric precursor sets had however not yet been studied.

Results

Such relationship between topological and stoichiometric precursor sets is highlighted. We also present two algorithms that enumerate all minimal stoichiometric precursor sets. The first one is of theoretical interest only and is based on the above mentioned relationship. The second approach solves a series of mixed integer linear programming problems. We compared the computed minimal precursor sets to experimentally obtained growth media of several Escherichia coli strains using genome-scale metabolic networks.

Conclusions

The results show that the second approach efficiently enumerates minimal precursor sets taking stoichiometry into account, and allows for broad in silico studies of strains or species interactions that may help to understand e.g. pathotype and niche-specific metabolic capabilities. sasita is written in Java, uses cplex as LP solver and can be downloaded together with all networks and input files used in this paper at http://sasita.gforge.inria.fr/.

     

The Carbon Assimilation Network in Escherichia coli Is Densely Connected and Largely Sign-Determined by Directions of Metabolic Fluxes

Gene regulatory networks consist of direct interactions but also include indirect interactions mediated by metabolites and signaling molecules. We describe how these indirect interactions can be derived from a model of the underlying biochemical reaction network, using weak time-scale assumptions in combination with sensitivity criteria from metabolic control analysis. We apply this approach to a model of the carbon assimilation network in Escherichia coli. Our results show that the derived gene regulatory network is densely connected, contrary to what is usually assumed. Moreover, the network is largely sign-determined, meaning that the signs of the indirect interactions are fixed by the flux directions of biochemical reactions, independently of specific parameter values and rate laws. An inversion of the fluxes following a change in growth conditions may affect the signs of the indirect interactions though. This leads to a feedback structure that is at the same time robust to changes in the kinetic properties of enzymes and that has the flexibility to accommodate radical changes in the environment.     

Structural analysis of metabolic networks based on flux centrality

Metabolic reactions are fundamental to living organisms, and a large number of reactions simultaneously occur at a given time in living cells transforming diverse metabolites into each other. There has been an ongoing debate on how to classify metabolites with respect to their importance for metabolic performance, usually based on the analysis of topological properties of genome scale metabolic networks. However, none of these studies have accounted quantitatively for flux in metabolic networks, thus lacking an important component of a cell’s biochemistry.We therefore analyzed a genome scale metabolic network of Escherichia coli by comparing growth under 19 different growth conditions, using flux balance analysis and weighted network centrality investigation. With this novel concept of flux centrality we generated metabolite rankings for each particular growth condition. In contrast to the results of conventional analysis of genome scale metabolic networks, different metabolites were top-ranking dependent on the growth condition. At the same time, several metabolites were consistently among the high ranking ones. Those are associated with pathways that have been described by biochemists as the most central part of metabolism, such as glycolysis, tricarboxylic acid cycle and pentose phosphate pathway. The values for the average path length of the analyzed metabolite networks were between 10.5 and 12.6, supporting recent findings that the metabolic network of E. coli is not a small-world network.     

Novel approach to engineer strains for simultaneous sugar utilization

Use of lignocellulosic biomass as a second generation feedstock in the biofuels industry is a pressing challenge. Among other difficulties in using lignocellulosic biomass, one major challenge is the optimal utilization of both 6-carbon (glucose) and 5-carbon (xylose) sugars by industrial microorganisms. Most industrial microorganisms preferentially utilize glucose over xylose owing to the regulatory phenomenon of carbon catabolite repression (CCR). Microorganisms that can co-utilize glucose and xylose are of considerable interest to the biofuels industry due to their ability to simplify the fermentation processes. However, elimination of CCR in microorganisms is challenging due to the multiple coordinating mechanisms involved. We report a novel algorithm, SIMUP, which finds metabolic engineering strategies to force co-utilization of two sugars, without targeting the regulatory pathways of CCR. Mutants of Escherichia coli based on SIMUP algorithm showed predicted growth phenotypes and co-utilized glucose and xylose; however, consumed the sugars slower than the wild-type. Some solutions identified by the algorithm were based on stoichiometric imbalance and were not obvious from the metabolic network topology. Furthermore, sequencing studies on the genes involved in CCR showed that the mechanism for co-utilization of the sugars could be different from previously known mechanisms.     

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.     

Metabolic flux balance analysis and the in silicoanalysis of Escherichia coliK-12 gene deletions

Background

Genome sequencing and bioinformatics are producing detailed lists of the molecular components contained in many prokaryotic organisms. From this 'parts catalogue' of a microbial cell, in silicorepresentations of integrated metabolic functions can be constructed and analyzed using flux balance analysis (FBA). FBA is particularly well-suited to study metabolic networks based on genomic, biochemical, and strain specific information.

Results

Herein, we have utilized FBA to interpret and analyze the metabolic capabilities of Escherichia coli. We have computationally mapped the metabolic capabilities of E. coliusing FBA and examined the optimal utilization of the E. colimetabolic pathways as a function of environmental variables. We have used an in silicoanalysis to identify seven gene products of central metabolism (glycolysis, pentose phosphate pathway, TCA cycle, electron transport system) essential for aerobic growth of E. colion glucose minimal media, and 15 gene products essential for anaerobic growth on glucose minimal media. The in silico tpi ^-, zwf, and pta ^-mutant strains were examined in more detail by mapping the capabilities of these in silicoisogenic strains.

Conclusions

We found that computational models of E. colimetabolism based on physicochemical constraints can be used to interpret mutant behavior. These in silicaresults lead to a further understanding of the complex genotype-phenotype relation. Supplementary information: 10.1186/1471-2105-1-1     

Network-level analysis of metabolic regulation in the human red blood cell using random sampling and singular value decomposition

Background  

Extreme pathways (ExPas) have been shown to be valuable for studying the functions and capabilities of metabolic networks through characterization of the null space of the stoichiometric matrix (S). Singular value decomposition (SVD) of the ExPa matrix P has previously been used to characterize the metabolic regulatory problem in the human red blood cell (hRBC) from a network perspective. The calculation of ExPas is NP-hard, and for genome-scale networks the computation of ExPas has proven to be infeasible. Therefore an alternative approach is needed to reveal regulatory properties of steady state solution spaces of genome-scale stoichiometric matrices.     

Prediction of Rate‐Limiting Reactions for Growth‐Associated Production Using a Constraint‐Based Approach

Identification of a rate‐limiting step in pathways is a key challenge in metabolic engineering. Although the prediction of rate‐limiting steps using a kinetic model is a powerful approach, there are several technical hurdles for developing a kinetic model. In this study, an in silico screening algorithm of key enzyme for metabolic engineering is developed to identify the possible rate‐limiting reactions for the growth‐coupled target production using a stoichiometric model without any experimental data and kinetic parameters. In this method, for each reaction, an upper‐bound flux constraint is imposed and the target production is predicted by linear programming. When the constraint decreases the target production at the optimal growth state, the reaction is thought to be a possible rate‐limiting step. For validation, this method is applied to the production of succinate or 1,4‐butanediol (1,4‐BDO) in Escherichia coli, in which the experimental engineering for eliminating rate‐limiting steps has been previously reported. In succinate production from glycerol, nine reactions including phosphoenolpyruvate carboxylase are predicted as the rate‐limiting steps. In 1,4‐BDO production from glucose, eight reactions including pyruvate dehydrogenase are predicted as the rate‐limiting steps. These predictions include experimentally identified rate‐limiting steps, which would contribute to metabolic engineering as a practical tool for screening candidates of rate‐limiting reactions.     

Complete genome sequence,metabolic model construction and phenotypic characterization of Geobacillus LC300, an extremely thermophilic,fast growing,xylose-utilizing bacterium

We have isolated a new extremely thermophilic fast-growing Geobacillus strain that can efficiently utilize xylose, glucose, mannose and galactose for cell growth. When grown aerobically at 72 °C, Geobacillus LC300 has a growth rate of 2.15 h⁻¹ on glucose and 1.52 h⁻¹ on xylose (doubling time less than 30 min). The corresponding specific glucose and xylose utilization rates are 5.55 g/g/h and 5.24 g/g/h, respectively. As such, Geobacillus LC300 grows 3-times faster than E. coli on glucose and xylose, and has a specific xylose utilization rate that is 3-times higher than the best metabolically engineered organism to date. To gain more insight into the metabolism of Geobacillus LC300 its genome was sequenced using PacBio׳s RS II single-molecule real-time (SMRT) sequencing platform and annotated using the RAST server. Based on the genome annotation and the measured biomass composition a core metabolic network model was constructed. To further demonstrate the biotechnological potential of this organism, Geobacillus LC300 was grown to high cell-densities in a fed-batch culture, where cells maintained a high xylose utilization rate under low dissolved oxygen concentrations. All of these characteristics make Geobacillus LC300 an attractive host for future metabolic engineering and biotechnology applications.     

Basic concepts and principles of stoichiometric modeling of metabolic networks

Metabolic networks supply the energy and building blocks for cell growth and maintenance. Cells continuously rewire their metabolic networks in response to changes in environmental conditions to sustain fitness. Studies of the systemic properties of metabolic networks give insight into metabolic plasticity and robustness, and the ability of organisms to cope with different environments. Constraint-based stoichiometric modeling of metabolic networks has become an indispensable tool for such studies. Herein, we review the basic theoretical underpinnings of constraint-based stoichiometric modeling of metabolic networks. Basic concepts, such as stoichiometry, chemical moiety conservation, flux modes, flux balance analysis, and flux solution spaces, are explained with simple, illustrative examples. We emphasize the mathematical definitions and their network topological interpretations.     

Chemostat cultures of yeasts, continuous culture fundamentals and simple unstructured mathematical models.

Fundamental aspects of chemostat cultures are reviewed. Using yeast cultures as examples, it is shown that steady states in chemostats may be predicted quantitatively by combining the correct number of unstructured kinetic models with expressions for existing stoichiometric constraints. The necessary number of such kinetic models corresponds to the number of limiting substrates and increases with the number of different metabolic pathways available to the strain. This is demonstrated by an experimental comparison of yeast growth limited by glucose alone for which metabolism is oxidative, and growth doubly limited by both glucose and oxygen, which occurs according to an oxido-reductive metabolism. The steady state data for such experiments can in principle be predicted based on a minimal amount of information by a simple stoichiometric model. It represents the overall stoichiometry of growth by a superposition of a fully oxidative and a fully reductive growth reaction and uses the concept of "aerobicity" to characterize the relative importance of the two reactions.