Functional states of the genome-scale Escherichia coli transcriptional regulatory system

A transcriptional regulatory network (TRN) constitutes the collection of regulatory rules that link environmental cues to the transcription state of a cell's genome. We recently proposed a matrix formalism that quantitatively represents a system of such rules (a transcriptional regulatory system [TRS]) and allows systemic characterization of TRS properties. The matrix formalism not only allows the computation of the transcription state of the genome but also the fundamental characterization of the input-output mapping that it represents. Furthermore, a key advantage of this “pseudo-stoichiometric” matrix formalism is its ability to easily integrate with existing stoichiometric matrix representations of signaling and metabolic networks. Here we demonstrate for the first time how this matrix formalism is extendable to large-scale systems by applying it to the genome-scale Escherichia coli TRS. We analyze the fundamental subspaces of the regulatory network matrix (R) to describe intrinsic properties of the TRS. We further use Monte Carlo sampling to evaluate the E. coli transcription state across a subset of all possible environments, comparing our results to published gene expression data as validation. Finally, we present novel in silico findings for the E. coli TRS, including (1) a gene expression correlation matrix delineating functional motifs; (2) sets of gene ontologies for which regulatory rules governing gene transcription are poorly understood and which may direct further experimental characterization; and (3) the appearance of a distributed TRN structure, which is in stark contrast to the more hierarchical organization of metabolic networks.

Cells are comprised of genomic information that encodes for proteins, the basic building blocks underlying all biological processes. A transcriptional regulatory system (TRS) connects a cell's environmental cues to its genome and in turn determines which genes are turned “on” in response to these cues. Consequently, TRSs control which proteins of an intracellular biochemical reaction network are present. These systems have been mathematically described, often through Boolean expressions that represent the activation or inhibition of gene transcription in response to various inputs. We recently developed a matrix formalism that extends these approaches and facilitates a quantitative representation of the Boolean logic underlying a TRS. We demonstrated on small-scale TRSs that this matrix representation is advantageous in that it facilitates the calculation of unique properties of a given TRS. Here we apply this matrix formalism to the genome-scale Escherichia coli TRS, demonstrating for the first time the predictive power of the approach at a large scale. We use the matrix-based model of E. coli transcriptional regulation to generate novel findings about the system, including new functional motifs; sets of genes whose regulation is poorly understood; and features of the TRS structure.

Proteomic and network analysis characterize stage-specific metabolism in Trypanosoma cruzi

BACKGROUND

Trypanosoma cruzi is a Kinetoplastid parasite of humans and is the cause of Chagas disease, a potentially lethal condition affecting the cardiovascular, gastrointestinal, and nervous systems of the human host. Constraint-based modeling has emerged in the last decade as a useful approach to integrating genomic and other high-throughput data sets with more traditional, experimental data acquired through decades of research and published in the literature.

RESULTS

We present a validated, constraint-based model of the core metabolism of Trypanosoma cruzi strain CL Brener. The model includes four compartments (extracellular space, cytosol, mitochondrion, glycosome), 51 transport reactions, and 93 metabolic reactions covering carbohydrate, amino acid, and energy metabolism. In addition, we make use of several replicate high-throughput proteomic data sets to specifically examine metabolism of the morphological form of T. cruzi in the insect gut (epimastigote stage).

CONCLUSION

This work demonstrates the utility of constraint-based models for integrating various sources of data (e.g., genomics, primary biochemical literature, proteomics) to generate testable hypotheses. This model represents an approach for the systematic study of T. cruzi metabolism under a wide range of conditions and perturbations, and should eventually aid in the identification of urgently needed novel chemotherapeutic targets.

SIMPLE: a sequential immunoperoxidase labeling and erasing method

The ability to simultaneously visualize expression of multiple antigens in cells and tissues can provide powerful insights into cellular and organismal biology. However, standard methods are limited to the use of just two or three simultaneous probes and have not been widely adopted for routine use in paraffin-embedded tissue. We have developed a novel approach called sequential immunoperoxidase labeling and erasing (SIMPLE) that enables the simultaneous visualization of at least five markers within a single tissue section. Utilizing the alcohol-soluble peroxidase substrate 3-amino-9-ethylcarbazole, combined with a rapid non-destructive method for antibody-antigen dissociation, we demonstrate the ability to erase the results of a single immunohistochemical stain while preserving tissue antigenicity for repeated rounds of labeling. SIMPLE is greatly facilitated by the use of a whole-slide scanner, which can capture the results of each sequential stain without any information loss.

A scalable systems analysis approach for regulated metabolic networks

High-throughput data such as genome sequencing and genome expression profiling have enabled the reconstruction of cellular networks. These networks have been represented in computational frameworks that can be used to make testable predictions concerning phenotypes under a variety of experimental conditions and multiple molecular perturbations. This presentation will detail several recent advances in the analysis of these networks as well as provide an outlook of remaining challenges.

Flux balance analysis: interrogating genome-scale metabolic networks

Flux balance analysis (FBA) is a computational method to analyze reconstructions of biochemical networks. FBA requires the formulation of a biochemical network in a precise mathematical framework called a stoichiometric matrix. An objective function is defined (e.g., growth rate) toward which the system is assumed to be optimized. In this chapter, we present the methodology, theory, and common pitfalls of the application of FBA.

Genome-scale reconstruction and analysis of the Pseudomonas putida KT2440 metabolic network facilitates applications in biotechnology

A cornerstone of biotechnology is the use of microorganisms for the efficient production of chemicals and the elimination of harmful waste. Pseudomonas putida is an archetype of such microbes due to its metabolic versatility, stress resistance, amenability to genetic modifications, and vast potential for environmental and industrial applications. To address both the elucidation of the metabolic wiring in P. putida and its uses in biocatalysis, in particular for the production of non-growth-related biochemicals, we developed and present here a genome-scale constraint-based model of the metabolism of P. putida KT2440. Network reconstruction and flux balance analysis (FBA) enabled definition of the structure of the metabolic network, identification of knowledge gaps, and pin-pointing of essential metabolic functions, facilitating thereby the refinement of gene annotations. FBA and flux variability analysis were used to analyze the properties, potential, and limits of the model. These analyses allowed identification, under various conditions, of key features of metabolism such as growth yield, resource distribution, network robustness, and gene essentiality. The model was validated with data from continuous cell cultures, high-throughput phenotyping data, ¹³C-measurement of internal flux distributions, and specifically generated knock-out mutants. Auxotrophy was correctly predicted in 75% of the cases. These systematic analyses revealed that the metabolic network structure is the main factor determining the accuracy of predictions, whereas biomass composition has negligible influence. Finally, we drew on the model to devise metabolic engineering strategies to improve production of polyhydroxyalkanoates, a class of biotechnologically useful compounds whose synthesis is not coupled to cell survival. The solidly validated model yields valuable insights into genotype–phenotype relationships and provides a sound framework to explore this versatile bacterium and to capitalize on its vast biotechnological potential.

The pseudomonads include a diverse set of bacteria whose metabolic versatility and genetic plasticity have enabled their survival in a broad range of environments. Many members of this family are able to either degrade toxic compounds or to efficiently produce high value compounds and are therefore of interest for both bioremediation and bulk chemical production. To better understand the growth and metabolism of these bacteria, we developed a large-scale mathematical model of the metabolism of Pseudomonas putida, a representative of the industrially relevant pseudomonads. The model was initially expanded and validated with substrate utilization data and carbon-tracking data. Next, the model was used to identify key features of metabolism such as growth yield, internal distribution of resources, and network robustness. We then used the model to predict novel strategies for the production of precursors for bioplastics of medical and industrial relevance. Such an integrated computational and experimental approach can be used to study its metabolism and to explore the potential of other industrially and environmentally important microorganisms.

Novel pathway compendium analysis elucidates mechanism of pro-angiogenic synthetic small molecule

MOTIVATION

Computational techniques have been applied to experimental datasets to identify drug mode-of-action. A shortcoming of existing approaches is the requirement of large reference databases of compound expression profiles. Here, we developed a new pathway-based compendium analysis that couples multi-timepoint, controlled microarray data for a single compound with systems-based network analysis to elucidate drug mechanism more efficiently.

RESULTS

We applied this approach to a transcriptional regulatory footprint of phthalimide neovascular factor 1 (PNF1)-a novel synthetic small molecule that exhibits significant in vitro endothelial potency-spanning 1-48 h post-supplementation in human micro-vascular endothelial cells (HMVEC) to comprehensively interrogate PNF1 effects. We concluded that PNF1 first induces tumor necrosis factor-alpha (TNF-alpha) signaling pathway function which in turn affects transforming growth factor-beta (TGF-beta) signaling. These results are consistent with our previous observations of PNF1-directed TGF-beta signaling at 24 h, including differential regulation of TGF-beta-induced matrix metalloproteinase 14 (MMP14/MT1-MMP) which is implicated in angiogenesis. Ultimately, we illustrate how our pathway-based compendium analysis more efficiently generates hypotheses for compound mechanism than existing techniques.

Dynamic analysis of integrated signaling, metabolic, and regulatory networks

Extracellular cues affect signaling, metabolic, and regulatory processes to elicit cellular responses. Although intracellular signaling, metabolic, and regulatory networks are highly integrated, previous analyses have largely focused on independent processes (e.g., metabolism) without considering the interplay that exists among them. However, there is evidence that many diseases arise from multifunctional components with roles throughout signaling, metabolic, and regulatory networks. Therefore, in this study, we propose a flux balance analysis (FBA)–based strategy, referred to as integrated dynamic FBA (idFBA), that dynamically simulates cellular phenotypes arising from integrated networks. The idFBA framework requires an integrated stoichiometric reconstruction of signaling, metabolic, and regulatory processes. It assumes quasi-steady-state conditions for “fast” reactions and incorporates “slow” reactions into the stoichiometric formalism in a time-delayed manner. To assess the efficacy of idFBA, we developed a prototypic integrated system comprising signaling, metabolic, and regulatory processes with network features characteristic of actual systems and incorporating kinetic parameters based on typical time scales observed in literature. idFBA was applied to the prototypic system, which was evaluated for different environments and gene regulatory rules. In addition, we applied the idFBA framework in a similar manner to a representative module of the single-cell eukaryotic organism Saccharomyces cerevisiae. Ultimately, idFBA facilitated quantitative, dynamic analysis of systemic effects of extracellular cues on cellular phenotypes and generated comparable time-course predictions when contrasted with an equivalent kinetic model. Since idFBA solves a linear programming problem and does not require an exhaustive list of detailed kinetic parameters, it may be efficiently scaled to integrated intracellular systems that incorporate signaling, metabolic, and regulatory processes at the genome scale, such as the S. cerevisiae system presented here.

Cellular systems comprise many diverse components and component interactions spanning signal transduction, transcriptional regulation, and metabolism. Although signaling, metabolic, and regulatory activities are often investigated independently of one another, there is growing evidence that considerable interplay occurs among them, and that the malfunctioning of this interplay is associated with disease. The computational analysis of integrated networks has been challenging because of the varying time scales involved as well as the sheer magnitude of such systems (e.g., the numbers of rate constants involved). To this end, we developed a novel computational framework called integrated dynamic flux balance analysis (idFBA) that generates quantitative, dynamic predictions of species concentrations spanning signaling, regulatory, and metabolic processes. idFBA extends an existing approach called flux balance analysis (FBA) in that it couples “fast” and “slow” reactions, thereby facilitating the study of whole-cell phenotypes and not just sub-cellular network properties. We applied this framework to a prototypic integrated system derived from literature as well as a representative integrated yeast module (the high-osmolarity glycerol [HOG] pathway) and generated time-course predictions that matched with available experimental data. By extending this framework to larger-scale systems, phenotypic profiles of whole-cell systems could be attained expeditiously.

Systems analysis of metabolism in the pathogenic trypanosomatid Leishmania major

Systems analyses have facilitated the characterization of metabolic networks of several organisms. We have reconstructed the metabolic network of Leishmania major, a poorly characterized organism that causes cutaneous leishmaniasis in mammalian hosts. This network reconstruction accounts for 560 genes, 1112 reactions, 1101 metabolites and 8 unique subcellular localizations. Using a systems-based approach, we hypothesized a comprehensive set of lethal single and double gene deletions, some of which were validated using published data with approximately 70% accuracy. Additionally, we generated hypothetical annotations to dozens of previously uncharacterized genes in the L. major genome and proposed a minimal medium for growth. We further demonstrated the utility of a network reconstruction with two proof-of-concept examples that yielded insight into robustness of the network in the presence of enzymatic inhibitors and delineation of promastigote/amastigote stage-specific metabolism. This reconstruction and the associated network analyses of L. major is the first of its kind for a protozoan. It can serve as a tool for clarifying discrepancies between data sources, generating hypotheses that can be experimentally validated and identifying ideal therapeutic targets.

Predicting biological system objectives de novo from internal state measurements

Background

Optimization theory has been applied to complex biological systems to interrogate network properties and develop and refine metabolic engineering strategies. For example, methods are emerging to engineer cells to optimally produce byproducts of commercial value, such as bioethanol, as well as molecular compounds for disease therapy. Flux balance analysis (FBA) is an optimization framework that aids in this interrogation by generating predictions of optimal flux distributions in cellular networks. Critical features of FBA are the definition of a biologically relevant objective function (e.g., maximizing the rate of synthesis of biomass, a unit of measurement of cellular growth) and the subsequent application of linear programming (LP) to identify fluxes through a reaction network. Despite the success of FBA, a central remaining challenge is the definition of a network objective with biological meaning.

Results

We present a novel method called Biological Objective Solution Search (BOSS) for the inference of an objective function of a biological system from its underlying network stoichiometry as well as experimentally-measured state variables. Specifically, BOSS identifies a system objective by defining a putative stoichiometric "objective reaction," adding this reaction to the existing set of stoichiometric constraints arising from known interactions within a network, and maximizing the putative objective reaction via LP, all the while minimizing the difference between the resultant in silico flux distribution and available experimental (e.g., isotopomer) flux data. This new approach allows for discovery of objectives with previously unknown stoichiometry, thus extending the biological relevance from earlier methods. We verify our approach on the well-characterized central metabolic network of Saccharomyces cerevisiae.

Conclusion

We illustrate how BOSS offers insight into the functional organization of biochemical networks, facilitating the interrogation of cellular design principles and development of cellular engineering applications. Furthermore, we describe how growth is the best-fit objective function for the yeast metabolic network given experimentally-measured fluxes.

Mechanistic exploration of phthalimide neovascular factor 1 using network analysis tools

Neovascularization is essential for the survival and successful integration of most engineering tissues after implantation in vivo. The objective of this study was to elucidate possible mechanisms of phthalimide neovascular factor 1 (PNF1), a new synthetic small molecule proposed for therapeutic induction of angiogenesis. Complementary deoxyribonucleic acid microarray analysis was used to identify 568 transcripts in human microvascular endothelial cells (HMVECs) that were significantly regulated after 24-h stimulation with 30 muM of PNF1, previously known as SC-3-149. Network analysis tools were used to identify genetic networks of the global biological processes involved in PNF1 stimulation and to describe known molecular and cellular functions that the drug regulated most highly. Examination of the most significantly perturbed networks identified gene products associated with transforming growth factor-beta (TGF-beta), which has many known effects on angiogenesis, and related signal transduction pathways. These include molecules integral to the thrombospondin, plasminogen, fibroblast growth factor, epidermal growth factor, ephrin, Rho, and Ras signaling pathways that are essential to endothelial function. Moreover, real-time reverse-transcriptase polymerase chain reaction (RT-PCR) of select genes showed significant increases in TGF-beta-associated receptors endoglin and beta glycan. These experiments provide important insight into the pro-angiogenic mechanism of PNF1, namely, TGF-beta-associated signaling pathways, and may ultimately offer new molecular targets for directed drug discovery.

Multiscale computational analysis of Xenopus laevis morphogenesis reveals key insights of systems-level behavior

Background

Tissue morphogenesis is a complex process whereby tissue structures self-assemble by the aggregate behaviors of independently acting cells responding to both intracellular and extracellular cues in their environment. During embryonic development, morphogenesis is particularly important for organizing cells into tissues, and although key regulatory events of this process are well studied in isolation, a number of important systems-level questions remain unanswered. This is due, in part, to a lack of integrative tools that enable the coupling of biological phenomena across spatial and temporal scales. Here, we present a new computational framework that integrates intracellular signaling information with multi-cell behaviors in the context of a spatially heterogeneous tissue environment.

Results

We have developed a computational simulation of mesendoderm migration in the Xenopus laevis explant model, which is a well studied biological model of tissue morphogenesis that recapitulates many features of this process during development in humans. The simulation couples, via a JAVA interface, an ordinary differential equation-based mass action kinetics model to compute intracellular Wnt/β-catenin signaling with an agent-based model of mesendoderm migration across a fibronectin extracellular matrix substrate. The emergent cell behaviors in the simulation suggest the following properties of the system: maintaining the integrity of cell-to-cell contact signals is necessary for preventing fractionation of cells as they move, contact with the Fn substrate and the existence of a Fn gradient provides an extracellular feedback loop that governs migration speed, the incorporation of polarity signals is required for cells to migrate in the same direction, and a delicate balance of integrin and cadherin interactions is needed to reproduce experimentally observed migratory behaviors.

Conclusion

Our computational framework couples two different spatial scales in biology: intracellular with multicellular. In our simulation, events at one scale have quantitative and dynamic impact on events at the other scale. This integration enables the testing and identification of key systems-level hypotheses regarding how signaling proteins affect overall tissue-level behavior during morphogenesis in an experimentally verifiable system. Applications of this approach extend to the study of tissue patterning processes that occur during adulthood and disease, such as tumorgenesis and atherogenesis.

Matrix formalism to describe functional states of transcriptional regulatory systems

Complex regulatory networks control the transcription state of a genome. These transcriptional regulatory networks (TRNs) have been mathematically described using a Boolean formalism, in which the state of a gene is represented as either transcribed or not transcribed in response to regulatory signals. The Boolean formalism results in a series of regulatory rules for the individual genes of a TRN that in turn can be used to link environmental cues to the transcription state of a genome, thereby forming a complete transcriptional regulatory system (TRS). Herein, we develop a formalism that represents such a set of regulatory rules in a matrix form. Matrix formalism allows for the systemic characterization of the properties of a TRS and facilitates the computation of the transcriptional state of the genome under any given set of environmental conditions. Additionally, it provides a means to incorporate mechanistic detail of a TRS as it becomes available. In this study, the regulatory network matrix, R, for a prototypic TRS is characterized and the fundamental subspaces of this matrix are described. We illustrate how the matrix representation of a TRS coupled with its environment (R*) allows for a sampling of all possible expression states of a given network, and furthermore, how the fundamental subspaces of the matrix provide a way to study key TRS features and may assist in experimental design.

Complex regulatory networks control the transcription state of a genome that defines the components of a biochemical network. These transcriptional regulatory networks have been mathematically described. The purpose of many such mathematical models is to allow for the prediction of gene expression under a variety of environmental conditions. However, to date, quantitative models have been limited in scope due to a paucity of relevant data, and models of larger networks have been limited in their quantitative predictive power. Herein, Gianchandani and colleagues present a formalism that represents regulatory rules in a matrix form which attempts to address these issues. This matrix formalism allows for the systemic characterization of the properties of a transcriptional regulatory system and facilitates the computation of the transcriptional state of the corresponding genome under any given set of environmental conditions. Additionally, it provides a means to incorporate mechanistic detail of a transcriptional regulatory system as it becomes available. The authors illustrate how this matrix representation allows for a sampling of all possible expression states of a given network and provides a way to study key features. They also present how it may assist in experimental design to interrogate genome-scale cellular networks.

Flux balance analysis in the era of metabolomics

Flux balance analysis (FBA) has emerged as an effective means to analyse biological networks in a quantitative manner. Much progress has been made on the extension of FBA to incorporate a priori biological knowledge, provide more practical descriptions of observed cell behaviours, and predict the outcome of network perturbations. Metabolomics is independently advancing as a set of high-throughput data acquisition tools providing dynamic profiles of metabolites in an unbiased manner. These data sets are neither yet sufficiently comprehensive nor accurate enough for generating large-scale kinetic models. Thus, there is a pressing need to develop quantitative techniques that can make use of the emerging data and embrace the associated uncertainties. This article reviews recent advances in FBA to meet this need and discusses the utility of FBA as a complement to metabolomics and the expected synergy as a result of combining these two techniques.

Systems analyses characterize integrated functions of biochemical networks

Metabolic, regulatory and signaling pathways have been characterized in detail over the past century. As the amount of genomic, proteomic and metabolic data has increased, and the mathematical and analytical capabilities of interrogating these data have advanced, the overlapping roles of pathway constituents have been described. These developments reflect the truly integrated nature of subcellular biochemical networks. Systems analyses, including the reconstruction of stoichiometric networks, provide a key set of tools for quantifying overlap among the metabolic, regulatory and signaling functions of network components. Accounting for this integration is crucial for accurately describing the function of biochemical networks.

Reconstruction of cellular signalling networks and analysis of their properties

The study of cellular signalling over the past 20 years and the advent of high-throughput technologies are enabling the reconstruction of large-scale signalling networks. After careful reconstruction of signalling networks, their properties must be described within an integrative framework that accounts for the complexity of the cellular signalling network and that is amenable to quantitative modelling.

Hierarchical thinking in network biology: the unbiased modularization of biochemical networks

As reconstructed biochemical reaction networks continue to grow in size and scope, there is a growing need to describe the functional modules within them. Such modules facilitate the study of biological processes by deconstructing complex biological networks into conceptually simple entities. The definition of network modules is often based on intuitive reasoning. As an alternative, methods are being developed for defining biochemical network modules in an unbiased fashion. These unbiased network modules are mathematically derived from the structure of the whole network under consideration.

The JAK-STAT signaling network in the human B-cell: an extreme signaling pathway analysis

Large-scale models of signaling networks are beginning to be reconstructed and corresponding analysis frameworks are being developed. Herein, a reconstruction of the JAK-STAT signaling system in the human B-cell is described and a scalable framework for its network analysis is presented. This approach is called extreme signaling pathway analysis and involves the description of network properties with systemically independent basis vectors called extreme pathways. From the extreme signaling pathways, emergent systems properties of the JAK-STAT signaling network have been characterized, including 1), a mathematical definition of network crosstalk; 2), an analysis of redundancy in signaling inputs and outputs; 3), a study of reaction participation in the network; and 4), a delineation of 85 correlated reaction sets, or systemic signaling modules. This study is the first such analysis of an actual biological signaling system. Extreme signaling pathway analysis is a topologically based approach and assumes a balanced use of the signaling network. As large-scale reconstructions of signaling networks emerge, such scalable analyses will lead to a description of the fundamental systems properties of signal transduction networks.

Comparison of network-based pathway analysis methods

Network-based definitions of biochemical pathways have emerged in recent years. These pathway definitions insist on the balanced use of a whole network of biochemical reactions. Two such related definitions, elementary modes and extreme pathways, have generated novel hypotheses regarding biochemical network function. The relationship between these two approaches can be illustrated by comparing and contrasting the elementary modes and extreme pathways of previously published metabolic reconstructions of the human red blood cell (RBC) and the human pathogen Helicobacter pylori. Descriptions of network properties generated by using these two approaches in the analysis of realistic metabolic networks need careful interpretation.

Topological analysis of mass-balanced signaling networks: a framework to obtain network properties including crosstalk

Signal transduction networks have only been studied at a small scale because large-scale reconstructions and suitable in silico analysis methods have not been available. Since reconstructions of large signaling networks are progressing well there is now a need to develop a framework for analysing structural properties of signaling networks. One such framework is presented here, one that is based on systemically independent pathways and a mass-balanced representation of signaling events. This approach was applied to a prototypic signaling network and it allowed for: (1) a systemic analysis of all possible input/output relationships, (2) a quantitative evaluation of network crosstalk, or the interconnectivity of systemically independent pathways, (3) a measure of the redundancy in the signaling network, (4) the participation of reactions in signaling pathways, and (5) the calculation of correlated reaction sets. These properties emerge from network structure and can only be derived and studied within a defined mathematical framework. The calculations presented are the first of their kind for a signaling network, while similar analysis has been extensively performed for prototypic and genome-scale metabolic networks. This approach does not yet account for dynamic concentration profiles. Due to the scalability of the stoichiometric formalism used, the results presented for the prototypic signaling network can be obtained for large signaling networks once their reconstruction is completed.

Network-based analysis of metabolic regulation in the human red blood cell

Reconstruction of cell-scale metabolic networks is now possible. A description of allowable metabolic network functions can be obtained using extreme pathways, which are the convex basis vectors of the solution space containing all steady state flux distributions. However, only a portion of these allowable network functions are physiologically possible due to kinetic and regulatory constraints. Methods are now needed that enable us to take a defined metabolic network and deduce candidate regulatory structures that control the selection of these physiologically relevant states. One such approach is the singular value decomposition (SVD) of extreme pathway matrices (P), which allows for the characterization of steady state solution spaces. Eigenpathways, which are the left singular vectors from the SVD of P, can be described and categorized by their biochemical function. SVD of P for the human red blood cell showed that the first five eigenpathways, out of a total of 23, effectively characterize all the relevant physiological states of red blood cell metabolism calculated with a detailed kinetic model. Thus, with five degrees of freedom the magnitude and nature of the regulatory needs are defined. Additionally, the dominant features of these first five eigenpathways described key metabolic splits that are indeed regulated in the human red blood cell. The extreme pathway matrix is derived directly from network topology and only knowledge of Vmax values is needed to reach these conclusions. Thus, we have implemented a network-based analysis of regulation that complements the study of individual regulatory events. This topological approach may provide candidate regulatory structures for metabolic networks with known stoichiometry but poorly characterized regulation.

Metabolic pathways in the post-genome era

Metabolic pathways are a central paradigm in biology. Historically, they have been defined on the basis of their step-by-step discovery. However, the genome-scale metabolic networks now being reconstructed from annotation of genome sequences demand new network-based definitions of pathways to facilitate analysis of their capabilities and functions, such as metabolic versatility and robustness, and optimal growth rates. This demand has led to the development of a new mathematically based analysis of complex, metabolic networks that enumerates all their unique pathways that take into account all requirements for cofactors and byproducts. Applications include the design of engineered biological systems, the generation of testable hypotheses regarding network structure and function, and the elucidation of properties that can not be described by simple descriptions of individual components (such as product yield, network robustness, correlated reactions and predictions of minimal media). Recently, these properties have also been studied in genome-scale networks. Thus, network-based pathways are emerging as an important paradigm for analysis of biological systems.