Jeremy S. Edwards

In silico predictions of Escherichia coli metabolic capabilities are consistent with experimental data

A significant goal in the post-genome era is to relate the annotated genome sequence to the physiological functions of a cell. Working from the annotated genome sequence, as well as biochemical and physiological information, it is possible to reconstruct complete metabolic networks. Furthermore, computational methods have been developed to interpret and predict the optimal performance of a metabolic network under a range of growth conditions. We have tested the hypothesis that Escherichia coli uses its metabolism to grow at a maximal rate using the E. coli MG1655 metabolic reconstruction. Based on this hypothesis, we formulated experiments that describe the quantitative relationship between a primary carbon source (acetate or succinate) uptake rate, oxygen uptake rate, and maximal cellular growth rate. We found that the experimental data were consistent with the stated hypothesis, namely that the E. coli metabolic network is optimized to maximize growth under the experimental conditions considered. This study thus demonstrates how the combination of in silico and experimental biology can be used to obtain a quantitative genotype–phenotype relationship for metabolism in bacterial cells.

Escherichia coli K-12 undergoes adaptive evolution to achieve in silico predicted optimal growth

Annotated genome sequences can be used to reconstruct whole-cell metabolic networks. These metabolic networks can be modelled and analysed (computed) to study complex biological functions. In particular, constraints-based in silico models have been used to calculate optimal growth rates on common carbon substrates, and the results were found to be consistent with experimental data under many but not all conditions. Optimal biological functions are acquired through an evolutionary process. Thus, incorrect predictions of in silico models based on optimal performance criteria may be due to incomplete adaptive evolution under the conditions examined. Escherichia coli K-12 MG1655 grows sub-optimally on glycerol as the sole carbon source. Here we show that when placed under growth selection pressure, the growth rate of E. coli on glycerol reproducibly evolved over 40 days, or about 700 generations, from a sub-optimal value to the optimal growth rate predicted from a whole-cell in silico model. These results open the possibility of using adaptive evolution of entire metabolic networks to realize metabolic states that have been determined a priori based on in silico analysis.

Dynamic Flux Balance Analysis of Diauxic Growth in Escherichia coli

Flux Balance Analysis (FBA) has been used in the past to analyze microbial metabolic networks. Typically, FBA is used to study the metabolic flux at a particular steady state of the system. However, there are many situations where the reprogramming of the metabolic network is important. Therefore, the dynamics of these metabolic networks have to be studied. In this paper, we have extended FBA to account for dynamics and present two different formulations for dynamic FBA. These two approaches were used in the analysis of diauxic growth in Escherichia coli. Dynamic FBA was used to simulate the batch growth of E. coli on glucose, and the predictions were found to qualitatively match experimental data. The dynamic FBA formalism was also used to study the sensitivity to the objective function. It was found that an instantaneous objective function resulted in better predictions than a terminal-type objective function. The constraints that govern the growth at different phases in the batch culture were also identified. Therefore, dynamic FBA provides a framework for analyzing the transience of metabolism due to metabolic reprogramming and for obtaining insights for the design of metabolic networks.

Genome-Scale Metabolic Model of Helicobacter pylori 26695

A genome-scale metabolic model of Helicobacter pylori 26695 was constructed from genome sequence annotation, biochemical, and physiological data. This represents an in silico model largely derived from genomic information for an organism for which there is substantially less biochemical information available relative to previously modeled organisms such as Escherichia coli. The reconstructed metabolic network contains 388 enzymatic and transport reactions and accounts for 291 open reading frames. Within the paradigm of constraint-based modeling, extreme-pathway analysis and flux balance analysis were used to explore the metabolic capabilities of the in silico model. General network properties were analyzed and compared to similar results previously generated for Haemophilus influenzae. A minimal medium required by the model to generate required biomass constituents was calculated, indicating the requirement of eight amino acids, six of which correspond to essential human amino acids. In addition a list of potential substrates capable of fulfilling the bulk carbon requirements of H. pylori were identified. A deletion study was performed wherein reactions and associated genes in central metabolism were deleted and their effects were simulated under a variety of substrate availability conditions, yielding a number of reactions that are deemed essential. Deletion results were compared to recently published in vitro essentiality determinations for 17 genes. The in silico model accurately predicted 10 of 17 deletion cases, with partial support for additional cases. Collectively, the results presented herein suggest an effective strategy of combining in silico modeling with experimental technologies to enhance biological discovery for less characterized organisms and their genomes.

Systems properties of the Haemophilus influenzae Rd metabolic genotype.

Haemophilus influenzae Rd was the first free-living organism for which the complete genomic sequence was established. The annotated sequence and known biochemical information was used to define the H. influenzae Rd metabolic genotype. This genotype contains 488 metabolic reactions operating on 343 metabolites. The stoichiometric matrix was used to determine the systems characteristics of the metabolic genotype and to assess the metabolic capabilities of H. influenzae. The need to balance cofactor and biosynthetic precursor production during growth on mixed substrates led to the definition of six different optimal metabolic phenotypes arising from the same metabolic genotype, each with different constraining features. The effects of variations in the metabolic genotype were also studied, and it was shown that theH. influenzae Rd metabolic genotype contains redundant functions under defined conditions. We thus show that the synthesis ofin silico metabolic genotypes from annotated genome sequences is possible and that systems analysis methods are available that can be used to analyze and interpret phenotypic behavior of such genotypes.

Metabolic modeling of microbial strains in silico

The large volume of genome-scale data that is being produced and made available in databases on the World Wide Web is demanding the development of integrated mathematical models of cellular processes. The analysis of reconstructed metabolic networks as systems leads to the development of an in silico or computer representation of collections of cellular metabolic constituents, their interactions and their integrated function as a whole. The use of quantitative analysis methods to generate testable hypotheses and drive experimentation at a whole-genome level signals the advent of a systemic modeling approach to cellular and molecular biology.

Metabolic flux balance analysis and the in silico analysis of Escherichia coli K-12 gene deletions

BackgroundGenome 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 silico representations 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.ResultsHerein, we have utilized FBA to interpret and analyze the metabolic capabilities of Escherichia coli. We have computationally mapped the metabolic capabilities of E. coli using FBA and examined the optimal utilization of the E. coli metabolic pathways as a function of environmental variables. We have used an in silico analysis to identify seven gene products of central metabolism (glycolysis, pentose phosphate pathway, TCA cycle, electron transport system) essential for aerobic growth of E. coli on 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 silico isogenic strains.ConclusionsWe found that computational models of E. coli metabolism based on physicochemical constraints can be used to interpret mutant behavior. These in silica results lead to a further understanding of the complex genotype-phenotype relation.Supplementary information: http://gcrg.ucsd.edu/supplementary_data/DeletionAnalysis/main.htm

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

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

Toward Metabolic Phenomics: Analysis of Genomic Data Using Flux Balances

Small genome sequencing and annotations are leading to the definition of metabolic genotypes in an increasing number of organisms. Proteomics is beginning to give insights into the use of the metabolic genotype under given growth conditions. These data sets give the basis for systemically studying the genotype−phenotype relationship. Methods of systems science need to be employed to analyze, interpret, and predict this complex relationship. These endeavors will lead to the development of a new field, tentatively named phenomics. This article illustrates how the metabolic characteristics of annotated small genomes can be analyzed using flux balance analysis (FBA). A general algorithm for the formulation of in silico metabolic genotypes is described. Illustrative analyses of the in silico Escherichia coli K‐12 metabolic genotypes are used to show how FBA can be used to study the capabilities of this strain.

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.