Characterization of metabolism in the Fe(III)-reducing organism Geobacter sulfurreducens by constraint-based modeling.

Geobacter sulfurreducens is a well-studied representative of the Geobacteraceae, which play a critical role in organic matter oxidation coupled to Fe(III) reduction, bioremediation of groundwater contaminated with organics or metals, and electricity production from waste organic matter. In order to investigate G. sulfurreducens central metabolism and electron transport, a metabolic model which integrated genome-based predictions with available genetic and physiological data was developed via the constraint-based modeling approach. Evaluation of the rates of proton production and consumption in the extracellular and cytoplasmic compartments revealed that energy conservation with extracellular electron acceptors, such as Fe(III), was limited relative to that associated with intracellular acceptors. This limitation was attributed to lack of cytoplasmic proton consumption during reduction of extracellular electron acceptors. Model-based analysis of the metabolic cost of producing an extracellular electron shuttle to promote electron transfer to insoluble Fe(III) oxides demonstrated why Geobacter species, which do not produce shuttles, have an energetic advantage over shuttle-producing Fe(III) reducers in subsurface environments. In silico analysis also revealed that the metabolic network of G. sulfurreducens could synthesize amino acids more efficiently than that of Escherichia coli due to the presence of a pyruvate-ferredoxin oxidoreductase, which catalyzes synthesis of pyruvate from acetate and carbon dioxide in a single step. In silico phenotypic analysis of deletion mutants demonstrated the capability of the model to explore the flexibility of G. sulfurreducens central metabolism and correctly predict mutant phenotypes. These results demonstrate that iterative modeling coupled with experimentation can accelerate the understanding of the physiology of poorly studied but environmentally relevant organisms and may help optimize their practical applications.

The effects of alternate optimal solutions in constraint-based genome-scale metabolic models.

Genome-scale constraint-based models of several organisms have now been constructed and are being used for model driven research. A key issue that may arise in the use of such models is the existence of alternate optimal solutions wherein the same maximal objective (e.g., growth rate) can be achieved through different flux distributions. Herein, we investigate the effects that alternate optimal solutions may have on the predicted range of flux values calculated using currently practiced linear (LP) and quadratic programming (QP) methods. An efficient LP-based strategy is described to calculate the range of flux variability that can be present in order to achieve optimal as well as suboptimal objective states. Sample results are provided for growth predictions of E. coli using glucose, acetate, and lactate as carbon substrates. These results demonstrate the extent of flux variability to be highly dependent on environmental conditions and network composition. In addition we examined the impact of alternate optima for growth under gene knockout conditions as calculated using QP-based methods. It was observed that calculations using QP-based methods can show significant variation in growth rate if the flux variability among alternate optima is high. The underlying biological significance and general source of such flux variability is further investigated through the identification of redundancies in the network (equivalent reaction sets) that lead to alternate solutions. Collectively, these results illustrate the variability inherent in metabolic flux distributions and the possible implications of this heterogeneity for constraint-based modeling approaches. These methods also provide an efficient and robust method to calculate the range of flux distributions that can be derived from quantitative fermentation data.

Regulation of gene expression in flux balance models of metabolism.

Genome-scale metabolic networks can now be reconstructed based on annotated genomic data augmented with biochemical and physiological information about the organism. Mathematical analysis can be performed to assess the capabilities of these reconstructed networks. The constraints-based framework, with flux balance analysis (FBA), has been used successfully to predict time course of growth and by-product secretion, effects of mutation and knock-outs, and gene expression profiles. However, FBA leads to incorrect predictions in situations where regulatory effects are a dominant influence on the behavior of the organism. Thus, there is a need to include regulatory events within FBA to broaden its scope and predictive capabilities. Here we represent transcriptional regulatory events as time-dependent constraints on the capabilities of a reconstructed metabolic network to further constrain the space of possible network functions. Using a simplified metabolic/regulatory network, growth is simulated under various conditions to illustrate systemic effects such as catabolite repression, the aerobic/anaerobic diauxic shift and amino acid biosynthesis pathway repression. The incorporation of transcriptional regulatory events in FBA enables us to interpret, analyse and predict the effects of transcriptional regulation on cellular metabolism at the systemic level.

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.

GRASP-DNA: a web application to screen prokaryotic genomes for specific DNA-binding sites and repeat motifs.

The ability to control multiple genes at the transcriptional level often relies on the existence of short stretches of well-defined DNA sequences, to which regulatory proteins and transcription factors bind. In this article we present a freely accessible web-based application (GRASP-DNA), that can be used to screen prokaryotic genomes for putative DNA-binding sites of a particular transcription factor or DNA-binding molecule. This application utilizes existing theories, such as information and statistical-mechanical theories, for the calculation of positive weight matrices generated from block aligned binding sites. Using these position weight matrices entire prokaryotic genomes are screened to identify sites that display a high level of sequence similarity to existing binding sites. This application can be used in combination with high-throughput technologies for gene expression analysis and binding site characterization to assist in the elucidation of global regulatory networks.

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.

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.

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.

Metabolic pathway analysis: basic concepts and scientific applications in the post-genomic era.

This article reviews the relatively short history of metabolic pathway analysis. Computer-aided algorithms for the synthesis of metabolic pathways are discussed. Important algebraic concepts used in pathway analysis, such as null space and convex cone, are explained. It is demonstrated how these concepts can be translated into meaningful metabolic concepts. For example, it is shown that the simplest vectors spanning the region of all admissible fluxes in stationary states, for which the term elementary flux modes was coined, correspond to fundamental pathways in the system. The concepts are illustrated with the help of a reaction scheme representing the glyoxylate cycle and adjacent reactions of aspartate and glutamate synthesis. The interrelations between pathway analysis and metabolic control theory are outlined. Promising applications for genome annotation and for biotechnological purposes are discussed. Armed with a better understanding of the architecture of cellular metabolism and the enormous amount of genomic data available today, biochemists and biotechnologists will be able to draw the entire metabolic map of a cell and redesign it by rational and directed metabolic engineering.

The underlying pathway structure of biochemical reaction networks.

Bioinformatics is yielding extensive, and in some cases complete, genetic and biochemical information about individual cell types and cellular processes, providing the composition of living cells and the molecular structure of its components. These components together perform integrated cellular functions that now need to be analyzed. In particular, the functional definition of biochemical pathways and their role in the context of the whole cell is lacking. In this study, we show how the mass balance constraints that govern the function of biochemical reaction networks lead to the translation of this problem into the realm of linear algebra. The functional capabilities of biochemical reaction networks, and thus the choices that cells can make, are reflected in the null space of their stoichiometric matrix. The null space is spanned by a finite number of basis vectors. We present an algorithm for the synthesis of a set of basis vectors for spanning the null space of the stoichiometric matrix, in which these basis vectors represent the underlying biochemical pathways that are fundamental to the corresponding biochemical reaction network. In other words, all possible flux distributions achievable by a defined set of biochemical reactions are represented by a linear combination of these basis pathways. These basis pathways thus represent the underlying pathway structure of the defined biochemical reaction network. This development is significant from a fundamental and conceptual standpoint because it yields a holistic definition of biochemical pathways in contrast to definitions that have arisen from the historical development of our knowledge about biochemical processes. Additionally, this new conceptual framework will be important in defining, characterizing, and studying biochemical pathways from the rapidly growing information on cellular function.