Regulation of gene expression in flux balance models of metabolism

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.

Integrating high-throughput and computational data elucidates bacterial networks

The flood of high-throughput biological data has led to the expectation that computational (or in silico) models can be used to direct biological discovery, enabling biologists to reconcile heterogeneous data types, find inconsistencies and systematically generate hypotheses. Such a process is fundamentally iterative, where each iteration involves making model predictions, obtaining experimental data, reconciling the predicted outcomes with experimental ones, and using discrepancies to update the in silico model. Here we have reconstructed, on the basis of information derived from literature and databases, the first integrated genome-scale computational model of a transcriptional regulatory and metabolic network. The model accounts for 1,010 genes in Escherichia coli, including 104 regulatory genes whose products together with other stimuli regulate the expression of 479 of the 906 genes in the reconstructed metabolic network. This model is able not only to predict the outcomes of high-throughput growth phenotyping and gene expression experiments, but also to indicate knowledge gaps and identify previously unknown components and interactions in the regulatory and metabolic networks. We find that a systems biology approach that combines genome-scale experimentation and computation can systematically generate hypotheses on the basis of disparate data sources.

RegulonDB (version 4.0): transcriptional regulation, operon organization and growth conditions in Escherichia coli K-12

RegulonDB is the primary database of the major international maintained curation of original literature with experimental knowledge about the elements and interactions of the network of transcriptional regulation in Escherichia coli K-12. This includes mechanistic information about operon organization and their decomposition into transcription units (TUs), promoters and their sigma type, binding sites of specific transcriptional regulators (TRs), their organization into 'regulatory phrases', active and inactive conformations of TRs, as well as terminators and ribosome binding sites. The database is complemented with clearly marked computational predictions of TUs, promoters and binding sites of TRs. The current version has been expanded to include information beyond specific mechanisms aimed at gathering different growth conditions and the associated induced and/or repressed genes. RegulonDB is now linked with Swiss-Prot, with microarray databases, and with a suite of programs to analyze and visualize microarray experiments. We provide a summary of the biological knowledge contained in RegulonDB and describe the major changes in the design of the database. RegulonDB can be accessed on the web at the URL: http://www.cifn.unam.mx/Computational_Biology/regulondb/.

Environmental conditions and transcriptional regulation inEscherichia coli: a physiological integrative approach

Bacteria develop a number of devices for sensing, responding, and adapting to different environmental conditions. Understanding within a genomic perspective how the transcriptional machinery of bacteria is modulated, as a response for changing conditions, is a major challenge for biologists. Knowledge of which genes are turned on or turned off under specific conditions is essential for our understanding of cell behavior. In this study we describe how the information pertaining to gene expression and associated growth conditions (even with very little knowledge of the associated regulatory mechanisms) is gathered from the literature and incorporated into RegulonDB, a database on transcriptional regulation and operon organization in E. coli. The link between growth conditions, signal transduction, and transcriptional regulation is modeled in the database in a simple format that highlights biological relevant information. As far as we know, there is no other database that explicitly clarifies the effect of environmental conditions on gene transcription. We discuss how this knowledge constitutes a benchmark that will impact future research aimed at integration of regulatory responses in the cell; for instance, analysis of microarrays, predicting culture behavior in biotechnological processes, and comprehension of dynamics of regulatory networks. This integrated knowledge will contribute to the future goal of modeling the behavior of E. coli as an entire cell. The RegulonDB database can be accessed on the web at the URL: http://www.cifn.unam.mx/Computational_Biology/regulondb/.

Optknock: A bilevel programming framework for identifying gene knockout strategies for microbial strain optimization

The advent of genome-scale models of metabolism has laid the foundation for the development of computational procedures for suggesting genetic manipulations that lead to overproduction. In this work, the computational OptKnock framework is introduced for suggesting gene deletion strategies leading to the overproduction of chemicals or biochemicals in E. coli. This is accomplished by ensuring that a drain towards growth resources (i.e., carbon, redox potential, and energy) must be accompanied, due to stoichiometry, by the production of a desired product. Computational results for gene deletions for succinate, lactate, and 1,3-propanediol (PDO) production are in good agreement with mutant strains published in the literature. While some of the suggested deletion strategies are straightforward and involve eliminating competing reaction pathways, many others suggest complex and nonintuitive mechanisms of compensating for the removed functionalities. Finally, the OptKnock procedure, by coupling biomass formation with chemical production, hints at a growth selection/adaptation system for indirectly evolving overproducing mutants.

Saccharomyces cerevisiae phenotypes can be predicted by using constraint-based analysis of a genome-scale reconstructed metabolic network

Full genome sequences of prokaryotic organisms have led to reconstruction of genome-scale metabolic networks and in silico computation of their integrated functions. The first genome-scale metabolic reconstruction for a eukaryotic cell, Saccharomyces cerevisiae, consisting of 1,175 metabolic reactions and 733 metabolites, has appeared. A constraint-based in silico analysis procedure was used to compute properties of the S. cerevisiae metabolic network. The computed number of ATP molecules produced per pair of electrons donated to the electron transport system (ETS) and energy-maintenance requirements were quantitatively in agreement with experimental results. Computed whole-cell functions of growth and metabolic by-product secretion in aerobic and anaerobic culture were consistent with experimental data, and thus mRNA expression profiles during metabolic shifts were computed. The computed consequences of gene knockouts on growth phenotypes were consistent with experimental observations. Thus, constraint-based analysis of a genome-scale metabolic network for the eukaryotic S. cerevisiae allows for computation of its integrated functions, producing in silico results that were consistent with observed phenotypic functions for approximately 70-80% of the conditions considered.

Data reconciliation and parameter estimation in flux-balance analysis

Flux blance analysis (FBA) has been shown to be a very effective tool to interpret and predict the metabolism of various microorganisms when the set of available measurements is not sufficient to determine the fluxes within the cell. In this methodology, an underdetermined stoichiometric model is solved using a linear programming (LP) approach. The predictions of FBA models can be improved if noisy measurements are checked for consistency, and these in turn are used to estimate model parameters. In this work, a formal methodology for data reconciliation and parameter estimation with underdetermined stoichiometric models is developed and assessed. The procedure is formulated as a nonlinear optimization problem, where the LP is transformed into a set of nonlinear constraints. However, some of these constraints violate standard regularity conditions, making the direct numerical solution very difficult. Hence, a barrier formulation is used to represent these constraints, and an iterative procedure is defined that allows solving the problem to the desired degree of convergence. This methodology is assessed using a stoichiometric yeast model. The procedure is used for data reconciliation where more reliable estimations of noisy measurements are computed. On the other hand, assuming unknown biomass composition, the procedure is applied for simultaneous data reconciliation and biomass composition estimation. In both cases it is verified that the f measurements required to get unbiased and reliable estimations is reduced if the LP approach is included as additional constraints in the optimization.

Reconstructing metabolic flux vectors from extreme pathways: defining the alpha-spectrum

The move towards genome-scale analysis of cellular functions has necessitated the development of analytical (in silico) methods to understand such large and complex biochemical reaction networks. One such method is extreme pathway analysis that uses stoichiometry and thermodynamic irreversibly to define mathematically unique, systemic metabolic pathways. These extreme pathways form the edges of a high-dimensional convex cone in the flux space that contains all the attainable steady state solutions, or flux distributions, for the metabolic network. By definition, any steady state flux distribution can be described as a nonnegative linear combination of the extreme pathways. To date, much effort has been focused on calculating, defining, and understanding these extreme pathways. However, little work has been performed to determine how these extreme pathways contribute to a given steady state flux distribution. This study represents an initial effort aimed at defining how physiological steady state solutions can be reconstructed from a network's extreme pathways. In general, there is not a unique set of nonnegative weightings on the extreme pathways that produce a given steady state flux distribution but rather a range of possible values. This range can be determined using linear optimization to maximize and minimize the weightings of a particular extreme pathway in the reconstruction, resulting in what we have termed the alpha-spectrum. The alpha-spectrum defines which extreme pathways can and cannot be included in the reconstruction of a given steady state flux distribution and to what extent they individually contribute to the reconstruction. It is shown that accounting for transcriptional regulatory constraints can considerably shrink the alpha-spectrum. The alpha-spectrum is computed and interpreted for two cases; first, optimal states of a skeleton representation of core metabolism that include transcriptional regulation, and second for human red blood cell metabolism under various physiological, non-optimal conditions.

Advances in flux balance analysis

Biology is going through a paradigm shift from reductionist to holistic, systems-based approaches. The complete genome sequence for a number of organisms is available and the analysis of genome sequence data is proving very useful. Thus, genome sequencing projects and bioinformatic analyses are leading to a complete 'parts catalog' of the molecular components in many organisms. The next challenge will be to reconstruct and simulate overall cellular functions based on the extensive reductionist information. Recent advances have been made in the area of flux balance analysis, a mathematical modeling approach often utilized by metabolic engineers to quantitatively simulate microbial metabolism.

H. influenzae Consortium: integrative study of H. influenzae-human interactions

Developments in high-throughput analysis tools coupled with integrative computational techniques have enabled biological studies to reach new levels. The ability to correlate large volumes of diverse data types into cohesive models of organism function has spawned a new systematic approach to biological investigation. The creation of a new consortium has been proposed to investigate a single organism utilizing these comprehensive approaches. The Haemophilus influenzae Consortium (HIC) would be comprised of five laboratories, each providing separate and complementary areas of expertise in the study of Haemophilus influenzae (HI). The 5-year study proposes to develop coherent models of HI, both as a stand-alone organism, and more importantly, as a human pathogen. Studies in growth condition specificity followed by genomic, metabolic, and proteomic experimentation will be combined and integrated through computational and experimental analyses to form dynamic and predictive models of HI and its responses. Data from the HIC will allow greater understanding of cellular behavior, pathogen-host interactions, bacterial infection, and provide future scientific endeavors with a template for studies of other pathogens.

Constraints-based models: regulation of gene expression reduces the steady-state solution space

Constraints-based models have been effectively used to analyse, interpret, and predict the function of reconstructed genome-scale metabolic models. The first generation of these models used "hard" non-adjustable constraints associated with network connectivity, irreversibility of metabolic reactions, and maximal flux capacities. These constraints restrict the allowable behaviors of a network to a convex mathematical solution space whose edges are extreme pathways that can be used to characterize the optimal performance of a network under a stated performance criterion. The development of a second generation of constraints-based models by incorporating constraints associated with regulation of gene expression was described in a companion paper published in this journal, using flux-balance analysis to generate time courses of growth and by-product secretion using a skeleton representation of core metabolism. The imposition of these additional restrictions prevents the use of a subset of the extreme pathways that are derived from the "hard" constraints, thus reducing the solution space and restricting allowable network functions. Here, we examine the reduction of the solution space due to regulatory constraints using extreme pathway analysis. The imposition of environmental conditions and regulatory mechanisms sharply reduces the number of active extreme pathways. This approach is demonstrated for the skeleton system mentioned above, which has 80 extreme pathways. As regulatory constraints are applied to the system, the number of feasible extreme pathways is reduced to between 26 and 2 extreme pathways, a reduction of between 67.5 and 97.5%. The method developed here provides a way to interpret how regulatory mechanisms are used to constrain network functions and produce a small range of physiologically meaningful behaviors from all allowable network functions.

Genome-scale microbial in silico models: the constraints-based approach

Genome sequencing and annotation has enabled the reconstruction of genome-scale metabolic networks. The phenotypic functions that these networks allow for can be defined and studied using constraints-based models and in silico simulation. Several useful predictions have been obtained from such in silico models, including substrate preference, consequences of gene deletions, optimal growth patterns, outcomes of adaptive evolution and shifts in expression profiles. The success rate of these predictions is typically in the order of 70-90% depending on the organism studied and the type of prediction being made. These results are useful as a basis for iterative model building and for several practical applications.

Two approaches for metabolic pathway analysis?

Metabolic pathway analysis is becoming increasingly important for assessing inherent network properties in (reconstructed) biochemical reaction networks. Of the two most promising concepts for pathway analysis, one relies on elementary flux modes and the other on extreme pathways. These concepts are closely related because extreme pathways are a subset of elementary modes. Here, the common features, differences and applicability of these concepts are discussed. Assessing metabolic systems by the set of extreme pathways can, in general, give misleading results owing to the exclusion of possibly important routes. However, in certain network topologies, the sets of elementary modes and extreme pathways coincide. This is quite often the case in realistic applications. In our opinion, the unification of both approaches into one common framework for metabolic pathway analysis is necessary and achievable.

Sequence-based analysis of metabolic demands for protein synthesis in prokaryotes

Constraints-based models for microbial metabolism can currently be constructed on a genome-scale. These models do not account for RNA and protein synthesis. A scalable formalism to describe translation and transcription that can be integrated with the existing metabolic models is thus needed. Here, we developed such a formalism. The fundamental protein synthesis network described by this formalism was analysed via extreme pathway and flux balance analyses. The protein synthesis network exhibited one extreme pathway per messenger RNA synthesized and one extreme pathway per protein synthesized. The key parameters in this network included promoter strengths, messenger RNA half-lives, and the availability of nucleotide triphosphates, amino acids, RNA polymerase, and active ribosomes. Given these parameters, we were able to calculate a cell's material and energy expenditures for protein synthesis using a flux balance approach. The framework provided herein can subsequently be integrated with genome-scale metabolic models, providing a sequence-based accounting of the metabolic demands resulting from RNA and protein polymerization.

An ensemble method for identifying regulatory circuits with special reference to the qa gene cluster of Neurospora crassa

A chemical reaction network for the regulation of the quinic acid (qa) gene cluster of Neurospora crassa is proposed. An efficient Monte Carlo method for walking through the parameter space of possible chemical reaction networks is developed to identify an ensemble of deterministic kinetics models with rate constants consistent with RNA and protein profiling data. This method was successful in identifying a model ensemble fitting available RNA profiling data on the qa gene cluster.

Transcriptional regulation in constraints-based metabolic models of Escherichia coli

Full genome sequences enable the construction of genome-scale in silico models of complex cellular functions. Genome-scale constraints-based models of Escherichia coli metabolism have been constructed and used to successfully interpret and predict cellular behavior under a range of conditions. These previous models do not account for regulation of gene transcription and thus cannot accurately predict some organism functions. Here we present an in silico model of the central E. coli metabolism that accounts for regulation of gene expression. This model accounts for 149 genes, the products of which include 16 regulatory proteins and 73 enzymes. These enzymes catalyze 113 reactions, 45 of which are controlled by transcriptional regulation. The combined metabolic/regulatory model can predict the ability of mutant E. coli strains to grow on defined media as well as time courses of cell growth, substrate uptake, metabolic by-product secretion, and qualitative gene expression under various conditions, as indicated by comparison with experimental data under a variety of environmental conditions. The in silico model may also be used to interpret dynamic behaviors observed in cell cultures. This combined metabolic/regulatory model is thus an important step toward the goal of synthesizing genome-scale models that accurately represent E. coli behavior.

Extreme pathway analysis of human red blood cell metabolism

The development of high-throughput technologies and the resulting large-scale data sets have necessitated a systems approach to the analysis of metabolic networks. One way to approach the issue of complex metabolic function is through the calculation and interpretation of extreme pathways. Extreme pathways are a mathematically defined set of generating vectors that describe the conical steady-state solution space for flux distributions through an entire metabolic network. Herein, the extreme pathways of the well-characterized human red blood cell metabolic network were calculated and interpreted in a biochemical and physiological context. These extreme pathways were divided into groups based on such criteria as their cofactor and by-product production, and carbon inputs including those that 1) convert glucose to pyruvate; 2) interchange pyruvate and lactate; 3) produce 2,3-diphosphoglycerate that binds to hemoglobin; 4) convert inosine to pyruvate; 5) induce a change in the total adenosine pool; and 6) dissipate ATP. Additionally, results from a full kinetic model of red blood cell metabolism were predicted based solely on an interpretation of the extreme pathway structure. The extreme pathways for the red blood cell thus give a concise representation of red blood cell metabolism and a way to interpret its metabolic physiology.