Regulation of gene expression in flux balance models of metabolism

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.

Phenotype prediction in regulated metabolic networks

Background

Due to the growing amount of biological knowledge that is incorporated into metabolic network models, their analysis has become more and more challenging. Here, we examine the capabilities of the recently introduced chemical organization theory (OT) to ease this task. Considering only network stoichiometry, the theory allows the prediction of all potentially persistent species sets and therewith rigorously relates the structure of a network to its potential dynamics. By this, the phenotypes implied by a metabolic network can be predicted without the need for explicit knowledge of the detailed reaction kinetics.

Results

We propose an approach to deal with regulation – and especially inhibitory interactions – in chemical organization theory. One advantage of this approach is that the metabolic network and its regulation are represented in an integrated way as one reaction network. To demonstrate the feasibility of this approach we examine a model by Covert and Palsson (J Biol Chem, 277(31), 2002) of the central metabolism of E. coli that incorporates the regulation of all involved genes. Our method correctly predicts the known growth phenotypes on 16 different substrates. Without specific assumptions, organization theory correctly predicts the lethality of knockout experiments in 101 out of 116 cases. Taking into account the same model specific assumptions as in the regulatory flux balance analysis (rFBA) by Covert and Palsson, the same performance is achieved (106 correctly predicted cases). Two model specific assumptions had to be considered: first, we have to assume that secreted molecules do not influence the regulatory system, and second, that metabolites with increasing concentrations indicate a lethal state.

Conclusion

The introduced approach to model a metabolic network and its regulation in an integrated way as one reaction network makes organization analysis a universal technique to study the potential behavior of biological network models. Applying multiple methods like OT and rFBA is shown to be valuable to uncover critical assumptions and helps to improve model coherence.

The regulatory network of E. coli metabolism as a Boolean dynamical system exhibits both homeostasis and flexibility of response

Background

Elucidating the architecture and dynamics of large scale genetic regulatory networks of cells is an important goal in systems biology. We study the system level dynamical properties of the genetic network of Escherichia coli that regulates its metabolism, and show how its design leads to biologically useful cellular properties. Our study uses the database (Covert et al., Nature 2004) containing 583 genes and 96 external metabolites which describes not only the network connections but also the Boolean rule at each gene node that controls the switching on or off of the gene as a function of its inputs.

Results

We have studied how the attractors of the Boolean dynamical system constructed from this database depend on the initial condition of the genes and on various environmental conditions corresponding to buffered minimal media. We find that the system exhibits homeostasis in that its attractors, that turn out to be fixed points or low period cycles, are highly insensitive to initial conditions or perturbations of gene configurations for any given fixed environment. At the same time the attractors show a wide variation when external media are varied implying that the system mounts a highly flexible response to changed environmental conditions. The regulatory dynamics acts to enhance the cellular growth rate under changed media.

Conclusion

Our study shows that the reconstructed genetic network regulating metabolism in E. coli is hierarchical, modular, and largely acyclic, with environmental variables controlling the root of the hierarchy. This architecture makes the cell highly robust to perturbations of gene configurations as well as highly responsive to environmental changes. The twin properties of homeostasis and response flexibility are achieved by this dynamical system even though it is not close to the edge of chaos.

Reconstruction and analysis of the genetic and metabolic regulatory networks of the central metabolism of Bacillus subtilis

Background

Few genome-scale models of organisms focus on the regulatory networks and none of them integrates all known levels of regulation. In particular, the regulations involving metabolite pools are often neglected. However, metabolite pools link the metabolic to the genetic network through genetic regulations, including those involving effectors of transcription factors or riboswitches. Consequently, they play pivotal roles in the global organization of the genetic and metabolic regulatory networks.

Results

We report the manually curated reconstruction of the genetic and metabolic regulatory networks of the central metabolism of Bacillus subtilis (transcriptional, translational and post-translational regulations and modulation of enzymatic activities). We provide a systematic graphic representation of regulations of each metabolic pathway based on the central role of metabolites in regulation. We show that the complex regulatory network of B. subtilis can be decomposed as sets of locally regulated modules, which are coordinated by global regulators.

Conclusion

This work reveals the strong involvement of metabolite pools in the general regulation of the metabolic network. Breaking the metabolic network down into modules based on the control of metabolite pools reveals the functional organization of the genetic and metabolic regulatory networks of B. subtilis.

Coupling kinetic expressions and metabolic networks for predicting wine fermentations

Problematic fermentations are commonplace and cause wine industry producers substantial economic losses through wasted tank capacity and low value final products. Being able to predict such fermentations would enable enologists to take preventive actions. In this study we modeled sugar uptake kinetics and coupled them to a previously developed stoichiometric model, which describes the anaerobic metabolism of Saccharomyces cerevisiae. The resulting model was used to predict normal and slow fermentations under winemaking conditions. The effects of fermentation temperature and initial nitrogen concentration were modeled through an efficiency factor incorporated into the sugar uptake expressions. The model required few initial parameters to successfully reproduce glucose, fructose, and ethanol profiles of laboratory and industrial fermentations. Glycerol and biomass profiles were successfully predicted in nitrogen rich cultures. The time normal or slow wine fermentations needed to complete the process was predicted accurately, at different temperatures. Simulations with a model representing a genetically modified yeast fermentation, reproduced qualitatively well literature results regarding the formation of minor compounds involved in wine complexity and aroma. Therefore, the model also proves useful to explore the effects of genetic modifications on fermentation profiles.

Design and application of genome-scale reconstructed metabolic models

In this chapter, the process for the reconstruction of genome-scale metabolic networks is described, and some of the main applications of such models are illustrated. The reconstruction process can be viewed as an iterative process where information obtained from several sources is combined to construct a preliminary set of reactions and constraints. This involves steps such as genome annotation; identification of the reactions from the annotated genome sequence and available literature; determination of the reaction stoichiometry; definition of compartmentation and assignment of localization; determination of the biomass composition; measurement, calculation, or fitting of energy requirements; and definition of additional constraints. The reaction and constraint sets, after debugging, may be integrated into a stoichiometric model that can be used for simulation using tools such as Flux Balance Analysis (Section 3.8). From the flux distributions obtained, physiologic parameters such as growth yields or minimal medium components can be calculated, and their distance from similar experimental data provides a basis from where the model may need to be improved.

Predicting gene essentiality using genome-scale in silico models

Genome-scale metabolic models of organisms can be reconstructed using annotated genome sequence information, well-curated databases, and primary research literature. The metabolic reaction stoichiometry and other physicochemical factors are incorporated into the model, thus imposing constraints that represent restrictions on phenotypic behavior. Based on this premise, the theoretical capabilities of the metabolic network can be assessed by using a mathematical technique known as flux balance analysis (FBA). This modeling framework, also known as the constraint-based reconstruction and analysis approach, differs from other modeling strategies because it does not attempt to predict exact network behavior. Instead, this approach uses known constraints to separate the states that a system can achieve from those that it cannot. In recent years, this strategy has been employed to probe the metabolic capabilities of a number of organisms, to generate and test experimental hypotheses, and to predict accurately metabolic phenotypes and evolutionary outcomes. This chapter introduces the constraint-based modeling approach and focuses on its application to computationally predicting gene essentiality.

Reconstruction, modeling & analysis of Halobacterium salinarum R-1 metabolism

We present a genome-scale metabolic reconstruction for the extreme halophile Halobacterium salinarum. The reconstruction represents a summary of the knowledge regarding the organism's metabolism, and has already led to new research directions and improved the existing annotation. We used the network for computational analysis and studied the aerobic growth of the organism using dynamic simulations in media with 15 available carbon and energy sources. Simulations resulted in predictions for the internal fluxes, which describe at the molecular level how the organism lives and grows. We found numerous indications that cells maximized energy production even at the cost of longer term concerns such as growth prospects. Simulations showed a very low carbon incorporation rate of only approximately 15%. All of the supplied nutrients were simultaneously degraded, unexpectedly including five which are essential. These initially surprising behaviors are likely adaptations of the organism to its natural environment where growth occurs in blooms. In addition, we also examined specific aspects of metabolism, including how each of the supplied carbon and energy sources is utilized. Finally, we investigated the consequences of the model assumptions and the network structure on the quality of the flux predictions.

Effect of weight-added regulatory networks on constraint-based metabolic models of Escherichia coli

Though the traditional flux balance analysis (FBA) has successfully predicted intracellular fluxes using stoichiometry, linear programming, and metabolic pathways, it has not automatically reflected any potential genetic effects in response to the environmental changes in the metabolic pathways. Recently, attempts have been made to impose regulatory constraints described as a binary system, such as if-then rules using Boolean logic, on the traditional FBA. Yet this binary system has limited the representation of complex interactions between transcriptional factors and target genes. In addition, it is difficult to intuitively or visually recognize changes to the interactions among stimuli, sensors/regulatory proteins, and target genes due to the properties of the if-then rule systems. Thus, in the current work, in order to improve upon the previous approaches, we have (1) determined weight values after deducing from the inequality signs of the relative strengths of interactions between sensors/regulators and target genes based on the experimental data of gene expression, (2) divided expression level into eight levels, and (3) constructed and incorporated weight-added regulatory networks using the defined symbols within the FBA. Finally, a model system with the central metabolic pathway of Escherichia coli was examined under the aerobic batch culture with glucose and acetate reutilization and the aerobic and anaerobic batch culture with glucose only to demonstrate our suggested approach.

Genome-scale analysis of Saccharomyces cerevisiae metabolism and ethanol production in fed-batch culture

A dynamic flux balance model based on a genome-scale metabolic network reconstruction is developed for in silico analysis of Saccharomyces cerevisiae metabolism and ethanol production in fed-batch culture. Metabolic engineering strategies previously identified for their enhanced steady-state biomass and/or ethanol yields are evaluated for fed-batch performance in glucose and glucose/xylose media. Dynamic analysis is shown to provide a single quantitative measure of fed-batch ethanol productivity that explicitly handles the possible tradeoff between the biomass and ethanol yields. Productivity optimization conducted to rank achievable fed-batch performance demonstrates that the genetic manipulation strategy and the fed-batch operating policy should be considered simultaneously. A library of candidate gene insertions is assembled and directly screened for their achievable ethanol productivity in fed-batch culture. A number of novel gene insertions with ethanol productivities identical to the best metabolic engineering strategies reported in previous studies are identified, thereby providing additional targets for experimental evaluation. The top performing gene insertions were substrate dependent, with the highest ranked insertions for glucose media yielding suboptimal performance in glucose/xylose media. The analysis results suggest that enhancements in biomass yield are most beneficial for the enhancement of fed-batch ethanol productivity by recombinant xylose utilizing yeast strains. We conclude that steady-state flux balance analysis is not sufficient to predict fed-batch performance and that the media, genetic manipulations, and fed-batch operating policy should be considered simultaneously to achieve optimal metabolite productivity.

Computational approaches to the topology, stability and dynamics of metabolic networks

Cellular metabolism is characterized by an intricate network of interactions between biochemical fluxes, metabolic compounds and regulatory interactions. To investigate and eventually understand the emergent global behavior arising from such networks of interaction is not possible by intuitive reasoning alone. This contribution seeks to describe recent computational approaches that aim to asses the topological and functional properties of metabolic networks. In particular, based on a recently proposed method, it is shown that it is possible to acquire a quantitative picture of the possible dynamics of metabolic systems, without assuming detailed knowledge of the underlying enzyme-kinetic rate equations and parameters. Rather, the method builds upon a statistical exploration of the comprehensive parameter space to evaluate the dynamic capabilities of a metabolic system, thus providing a first step towards the transition from topology to function of metabolic pathways. Utilizing this approach, the role of feedback mechanisms in the maintenance of stability is discussed using minimal models of cellular pathways.

Introduction to systems biology

The developments in the molecular biosciences have made possible a shift to combined molecular and system-level approaches to biological research under the name of Systems Biology. It integrates many types of molecular knowledge, which can best be achieved by the synergistic use of models and experimental data. Many different types of modeling approaches are useful depending on the amount and quality of the molecular data available and the purpose of the model. Analysis of such models and the structure of molecular networks have led to the discovery of principles of cell functioning overarching single species. Two main approaches of systems biology can be distinguished. Top-down systems biology is a method to characterize cells using system-wide data originating from the Omics in combination with modeling. Those models are often phenomenological but serve to discover new insights into the molecular network under study. Bottom-up systems biology does not start with data but with a detailed model of a molecular network on the basis of its molecular properties. In this approach, molecular networks can be quantitatively studied leading to predictive models that can be applied in drug design and optimization of product formation in bioengineering. In this chapter we introduce analysis of molecular network by use of models, the two approaches to systems biology, and we shall discuss a number of examples of recent successes in systems biology.

Selective control of the apoptosis signaling network in heterogeneous cell populations

BACKGROUND

Selective control in a population is the ability to control a member of the population while leaving the other members relatively unaffected. The concept of selective control is developed using cell death or apoptosis in heterogeneous cell populations as an example. Control of apoptosis is essential in a variety of therapeutic environments, including cancer where cancer cell death is a desired outcome and Alzheimer's disease where neuron survival is the desired outcome. However, in both cases these responses must occur with minimal response in other cells exposed to treatment; that is, the response must be selective.

METHODOLOGY AND PRINCIPAL FINDINGS

Apoptosis signaling in heterogeneous cells is described by an ensemble of gene networks with identical topology but different link strengths. Selective control depends on the statistics of signaling in the ensemble of networks, and we analyze the effects of superposition, non-linearity and feedback on these statistics. Parallel pathways promote normal statistics while series pathways promote skew distributions, which in the most extreme cases become log-normal. We also show that feedback and non-linearity can produce bimodal signaling statistics, as can discreteness and non-linearity. Two methods for optimizing selective control are presented. The first is an exhaustive search method and the second is a linear programming based approach. Though control of a single gene in the signaling network yields little selectivity, control of a few genes typically yields higher levels of selectivity. The statistics of gene combinations susceptible to selective control in heterogeneous apoptosis networks is studied and is used to identify general control strategies.

CONCLUSIONS AND SIGNIFICANCE

We have explored two methods for the study of selectivity in cell populations. The first is an exhaustive search method limited to three node perturbations. The second is an effective linear model, based on interpolation of single node sensitivity, in which the selective combinations can be found by linear programming optimization. We found that selectivity is promoted by acting on the least sensitive nodes in the case of weak populations, while selective control of robust populations is optimized through perturbations of more sensitive nodes. High throughput experiments with heterogeneous cell lines could be designed in an analogous manner, with the further possibility of incorporating the selectivity optimization process into a closed-loop control system.

A genome-scale computational study of the interplay between transcriptional regulation and metabolism

This paper presents a new method, steady-state regulatory flux balance analysis (SR-FBA), for predicting gene expression and metabolic fluxes in a large-scale integrated metabolic–regulatory model. Using SR-FBA to study the metabolism of Escherichia coli, we quantify the extent to which the different levels of metabolic and transcriptional regulatory constraints determine metabolic behavior: metabolic constraints determine the flux activity state of 45–51% of metabolic genes, depending on the growth media, whereas transcription regulation determines the flux activity state of 13–20% of the genes. A considerable number of 36 genes are redundantly expressed, that is, they are expressed even though the fluxes of their associated reactions are zero, indicating that they are not optimally tuned for cellular flux demands. The undetermined state of the remaining ∼30% of the genes suggests that they may represent metabolic variability within a given growth medium. Overall, SR-FBA enables one to address a host of new questions concerning the interplay between regulation and metabolism.

Quantifying the metabolic capabilities of engineered Zymomonas mobilis using linear programming analysis

Background

The need for discovery of alternative, renewable, environmentally friendly energy sources and the development of cost-efficient, "clean" methods for their conversion into higher fuels becomes imperative. Ethanol, whose significance as fuel has dramatically increased in the last decade, can be produced from hexoses and pentoses through microbial fermentation. Importantly, plant biomass, if appropriately and effectively decomposed, is a potential inexpensive and highly renewable source of the hexose and pentose mixture. Recently, the engineered (to also catabolize pentoses) anaerobic bacterium Zymomonas mobilis has been widely discussed among the most promising microorganisms for the microbial production of ethanol fuel. However, Z. mobilis genome having been fully sequenced in 2005, there is still a small number of published studies of its in vivo physiology and limited use of the metabolic engineering experimental and computational toolboxes to understand its metabolic pathway interconnectivity and regulation towards the optimization of its hexose and pentose fermentation into ethanol.

Results

In this paper, we reconstructed the metabolic network of the engineered Z. mobilis to a level that it could be modelled using the metabolic engineering methodologies. We then used linear programming (LP) analysis and identified the Z. mobilis metabolic boundaries with respect to various biological objectives, these boundaries being determined only by Z. mobilis network's stoichiometric connectivity. This study revealed the essential for bacterial growth reactions and elucidated the association between the metabolic pathways, especially regarding main product and byproduct formation. More specifically, the study indicated that ethanol and biomass production depend directly on anaerobic respiration stoichiometry and activity. Thus, enhanced understanding and improved means for analyzing anaerobic respiration and redox potential in vivo are needed to yield further conclusions for potential genetic targets that may lead to optimized Z. mobilis strains.

Conclusion

Applying LP to study the Z. mobilis physiology enabled the identification of the main factors influencing the accomplishment of certain biological objectives due to metabolic network connectivity only. This first-level metabolic analysis model forms the basis for the incorporation of more complex regulatory mechanisms and the formation of more realistic models for the accurate simulation of the in vivo Z. mobilis physiology.

Structural and functional analysis of cellular networks with CellNetAnalyzer

Background

Mathematical modelling of cellular networks is an integral part of Systems Biology and requires appropriate software tools. An important class of methods in Systems Biology deals with structural or topological (parameter-free) analysis of cellular networks. So far, software tools providing such methods for both mass-flow (metabolic) as well as signal-flow (signalling and regulatory) networks are lacking.

Results

Herein we introduce CellNetAnalyzer, a toolbox for MATLAB facilitating, in an interactive and visual manner, a comprehensive structural analysis of metabolic, signalling and regulatory networks. The particular strengths of CellNetAnalyzer are methods for functional network analysis, i.e. for characterising functional states, for detecting functional dependencies, for identifying intervention strategies, or for giving qualitative predictions on the effects of perturbations. CellNetAnalyzer extends its predecessor FluxAnalyzer (originally developed for metabolic network and pathway analysis) by a new modelling framework for examining signal-flow networks. Two of the novel methods implemented in CellNetAnalyzer are discussed in more detail regarding algorithmic issues and applications: the computation and analysis (i) of shortest positive and shortest negative paths and circuits in interaction graphs and (ii) of minimal intervention sets in logical networks.

Conclusion

CellNetAnalyzer provides a single suite to perform structural and qualitative analysis of both mass-flow- and signal-flow-based cellular networks in a user-friendly environment. It provides a large toolbox with various, partially unique, functions and algorithms for functional network analysis.CellNetAnalyzer is freely available for academic use.

Toward whole cell modeling and simulation: comprehensive functional genomics through the constraint-based approach

The increasing availability of various system-level, or so-called 'omics', datasets, in concert with existing data from the primary research literature, is facilitating the development of genome-scale metabolic models for many organisms. By incorporating the metabolic reaction stoichiometry as well as other physicochemical properties into systemic network reconstructions, these models account for the constraints that restrict an organism's phenotypic behavior. Accordingly, unlike many contemporary modeling strategies, this constraint-based modeling approach does not attempt to predict network behavior exactly; rather, it seeks to clearly distinguish those network states that a system can achieve from those that it cannot. A variety of analytical tools have been designed and developed to probe these models, thus enabling studies that investigate the metabolic capabilities of a number of organisms, that generate and test experimental hypotheses, and that predict accurately metabolic phenotypes and evolutionary outcomes. This chapter introduces the concepts that underlie the constraint-based modeling approach, and describes several of its applications with an emphasis on those potentially relevant to the drug development field. In addition, while this chapter focuses on the primary application of the constraint-based approach to date, namely in modeling metabolic networks, the latter sections of the chapter discuss its relatively recent application to modeling other cellular systems. Finally, the chapter concludes with an assessment of future directions focusing on the efforts that will be required to utilize the constraint-based approach in generating a holistic model of a viable organism.

Integration of omics data: how well does it work for bacteria?

In the current omics era, innovative high-throughput technologies allow measuring temporal and conditional changes at various cellular levels. Although individual analysis of each of these omics data undoubtedly results into interesting findings, it is only by integrating them that gaining a global insight into cellular behaviour can be aimed at. A systems approach thus is predicated on data integration. However, because of the complexity of biological systems and the specificities of the data-generating technologies (noisiness, heterogeneity, etc.), integrating omics data in an attempt to reconstruct signalling networks is not trivial. Developing its methodologies constitutes a major research challenge. Besides for their intrinsic value towards health care, environment and industry, prokaryotes are ideal model systems to further develop these methods because of their lower regulatory complexity compared with eukaryotes, and the ease with which they can be manipulated. Several successful examples outlined in this review already show the potential of the systems approach for both fundamental and industrial applications, which would be time-consuming or impossible to develop solely through traditional reductionist approaches.

From in vivo to in silico biology and back

The massive acquisition of data in molecular and cellular biology has led to the renaissance of an old topic: simulations of biological systems. Simulations, increasingly paired with experiments, are being successfully and routinely used by computational biologists to understand and predict the quantitative behaviour of complex systems, and to drive new experiments. Nevertheless, many experimentalists still consider simulations an esoteric discipline only for initiates. Suspicion towards simulations should dissipate as the limitations and advantages of their application are better appreciated, opening the door to their permanent adoption in everyday research.

Systems interface biology

The field of systems biology has attracted the attention of biologists, engineers, mathematicians, physicists, chemists and others in an endeavour to create systems-level understanding of complex biological networks. In particular, systems engineering methods are finding unique opportunities in characterizing the rich behaviour exhibited by biological systems. In the same manner, these new classes of biological problems are motivating novel developments in theoretical systems approaches. Hence, the interface between systems and biology is of mutual benefit to both disciplines.

Experimental and computational assessment of conditionally essential genes in Escherichia coli

Genome-wide gene essentiality data sets are becoming available for Escherichia coli, but these data sets have yet to be analyzed in the context of a genome scale model. Here, we present an integrative model-driven analysis of the Keio E. coli mutant collection screened in this study on glycerol-supplemented minimal medium. Out of 3,888 single-deletion mutants tested, 119 mutants were unable to grow on glycerol minimal medium. These conditionally essential genes were then evaluated using a genome scale metabolic and transcriptional-regulatory model of E. coli, and it was found that the model made the correct prediction in approximately 91% of the cases. The discrepancies between model predictions and experimental results were analyzed in detail to indicate where model improvements could be made or where the current literature lacks an explanation for the observed phenotypes. The identified set of essential genes and their model-based analysis indicates that our current understanding of the roles these essential genes play is relatively clear and complete. Furthermore, by analyzing the data set in terms of metabolic subsystems across multiple genomes, we can project which metabolic pathways are likely to play equally important roles in other organisms. Overall, this work establishes a paradigm that will drive model enhancement while simultaneously generating hypotheses that will ultimately lead to a better understanding of the organism.

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.

A joint model of regulatory and metabolic networks

Background

Gene regulation and metabolic reactions are two primary activities of life. Although many works have been dedicated to study each system, the coupling between them is less well understood. To bridge this gap, we propose a joint model of gene regulation and metabolic reactions.

Results

We integrate regulatory and metabolic networks by adding links specifying the feedback control from the substrates of metabolic reactions to enzyme gene expressions. We adopt two alternative approaches to build those links: inferring the links between metabolites and transcription factors to fit the data or explicitly encoding the general hypotheses of feedback control as links between metabolites and enzyme expressions. A perturbation data is explained by paths in the joint network if the predicted response along the paths is consistent with the observed response. The consistency requirement for explaining the perturbation data imposes constraints on the attributes in the network such as the functions of links and the activities of paths. We build a probabilistic graphical model over the attributes to specify these constraints, and apply an inference algorithm to identify the attribute values which optimally explain the data. The inferred models allow us to 1) identify the feedback links between metabolites and regulators and their functions, 2) identify the active paths responsible for relaying perturbation effects, 3) computationally test the general hypotheses pertaining to the feedback control of enzyme expressions, 4) evaluate the advantage of an integrated model over separate systems.

Conclusion

The modeling results provide insight about the mechanisms of the coupling between the two systems and possible "design rules" pertaining to enzyme gene regulation. The model can be used to investigate the less well-probed systems and generate consistent hypotheses and predictions for further validation.

Iterative reconstruction of transcriptional regulatory networks: an algorithmic approach

The number of complete, publicly available genome sequences is now greater than 200, and this number is expected to rapidly grow in the near future as metagenomic and environmental sequencing efforts escalate and the cost of sequencing drops. In order to make use of this data for understanding particular organisms and for discerning general principles about how organisms function, it will be necessary to reconstruct their various biochemical reaction networks. Principal among these will be transcriptional regulatory networks. Given the physical and logical complexity of these networks, the various sources of (often noisy) data that can be utilized for their elucidation, the monetary costs involved, and the huge number of potential experiments (~10¹²) that can be performed, experiment design algorithms will be necessary for synthesizing the various computational and experimental data to maximize the efficiency of regulatory network reconstruction. This paper presents an algorithm for experimental design to systematically and efficiently reconstruct transcriptional regulatory networks. It is meant to be applied iteratively in conjunction with an experimental laboratory component. The algorithm is presented here in the context of reconstructing transcriptional regulation for metabolism in Escherichia coli, and, through a retrospective analysis with previously performed experiments, we show that the produced experiment designs conform to how a human would design experiments. The algorithm is able to utilize probability estimates based on a wide range of computational and experimental sources to suggest experiments with the highest potential of discovering the greatest amount of new regulatory knowledge.

In recent years, the exploration of life has been bolstered through the advent of whole genome sequencing. This new data source significantly enables the reconstruction of genome-scale metabolic networks. After a metabolic reconstruction, it will be necessary to discover the genetic control mechanisms that operate within an organism. Transcriptional regulatory network (TRN) reconstruction is costly both in terms of time and money, so it is critical that the reconstruction efforts be made as efficient as possible. Experiments must be designed so that the most new regulatory knowledge is discovered in each experiment. The huge number of possible experiments (~10¹²) and the vast amount of heterogeneous data available for designing experiments overwhelms the human ability to assimilate. The authors have developed an algorithm that utilizes a mathematical model of a reconstructed metabolic network integrated with a partially reconstructed TRN to identify the experiment designs with the highest potential of yielding the most new regulatory knowledge. The authors show that the produced experiment designs are similar to those a human expert would produce, and that the algorithm has a facility to incorporate any relevant data source to design such experiments.

Yeast systems biology to unravel the network of life

Systems biology focuses on obtaining a quantitative description of complete biological systems, even complete cellular function. In this way, it will be possible to perform computer-guided design of novel drugs, advanced therapies for treatment of complex diseases, and to perform in silico design of advanced cell factories for production of fuels, chemicals, food ingredients and pharmaceuticals. The yeast Saccharomyces cerevisiae represents an excellent model system; the density of biological information available on this organism allows it to serve as a eukaryotic model for studying human diseases. Furthermore, it serves as an industrial workhorse for production of a wide range of chemicals and pharmaceuticals. Systems biology involves the combination of novel experimental techniques from different disciplines as well as functional genomics, bioinformatics and mathematical modelling, and hence no single laboratory has access to all the necessary competences. For this reason the Yeast Systems Biology Network (YSBN) has been established. YSBN will coordinate research efforts in yeast systems biology and, through the recently obtained EU funding for a Coordination Action, it will be possible to set appropriate guidelines, establish an appropriate infrastructure for the network and organize courses, meetings and conferences that will consolidate the network and promote systems biology. This paper discusses the impacts of systems biology and how YSBN may play a role in the future development of the field.

Integrated analysis of regulatory and metabolic networks reveals novel regulatory mechanisms in Saccharomyces cerevisiae

We describe the use of model-driven analysis of multiple data types relevant to transcriptional regulation of metabolism to discover novel regulatory mechanisms in Saccharomyces cerevisiae. We have reconstructed the nutrient-controlled transcriptional regulatory network controlling metabolism in S. cerevisiae consisting of 55 transcription factors regulating 750 metabolic genes, based on information in the primary literature. This reconstructed regulatory network coupled with an existing genome-scale metabolic network model allows in silico prediction of growth phenotypes of regulatory gene deletions as well as gene expression profiles. We compared model predictions of gene expression changes in response to genetic and environmental perturbations to experimental data to identify potential novel targets for transcription factors. We then identified regulatory cascades connecting transcription factors to the potential targets through a systematic model expansion strategy using published genome-wide chromatin immunoprecipitation and binding-site-motif data sets. Finally, we show the ability of an integrated metabolic and regulatory network model to predict growth phenotypes of transcription factor knockout strains. These studies illustrate the potential of model-driven data integration to systematically discover novel components and interactions in regulatory and metabolic networks in eukaryotic cells.

Metabolic engineering in the -omics era: elucidating and modulating regulatory networks

The importance of regulatory control in metabolic processes is widely acknowledged, and several enquiries (both local and global) are being made in understanding regulation at various levels of the metabolic hierarchy. The wealth of biological information has enabled identifying the individual components (genes, proteins, and metabolites) of a biological system, and we are now in a position to understand the interactions between these components. Since phenotype is the net result of these interactions, it is immensely important to elucidate them not only for an integrated understanding of physiology, but also for practical applications of using biological systems as cell factories. We present some of the recent "-omics" approaches that have expanded our understanding of regulation at the gene, protein, and metabolite level, followed by analysis of the impact of this progress on the advancement of metabolic engineering. Although this review is by no means exhaustive, we attempt to convey our ideology that combining global information from various levels of metabolic hierarchy is absolutely essential in understanding and subsequently predicting the relationship between changes in gene expression and the resulting phenotype. The ultimate aim of this review is to provide metabolic engineers with an overview of recent advances in complementary aspects of regulation at the gene, protein, and metabolite level and those involved in fundamental research with potential hurdles in the path to implementing their discoveries in practical applications.

Systematic analysis of conservation relations in Escherichia coli genome-scale metabolic network reveals novel growth media

A biochemical species is called producible in a constraints-based metabolic model if a feasible steady-state flux configuration exists that sustains its nonzero concentration during growth. Extreme semipositive conservation relations (ESCRs) are the simplest semipositive linear combinations of species concentrations that are invariant to all metabolic flux configurations. In this article, we outline a fundamental relationship between the ESCRs of a metabolic network and the producibility of a biochemical species under a nutrient media. We exploit this relationship in an algorithm that systematically enumerates all minimal nutrient sets that render an objective species weakly producible (i.e., producible in the absence of thermodynamic constraints) through a simple traversal of ESCRs. We apply our results to a recent genome scale model of Escherichia coli metabolism, in which we traverse the 51 anhydrous ESCRs of the metabolic network to determine all 928 minimal aqueous nutrient media that render biomass weakly producible. Applying irreversibility constraints, we find 287 of these 928 nutrient sets to be thermodynamically feasible. We also find that an additional 365 of these nutrient sets are thermodynamically feasible in the presence of oxygen. Since biomass producibility is commonly used as a surrogate for growth in genome scale metabolic models, our results represent testable hypotheses of alternate growth media derived from in silico analysis of the E. coli genome scale metabolic network.

The global transcriptional regulatory network for metabolism in Escherichia coli exhibits few dominant functional states

A principal aim of systems biology is to develop in silico models of whole cells or cellular processes that explain and predict observable cellular phenotypes. Here, we use a model of a genome-scale reconstruction of the integrated metabolic and transcriptional regulatory networks for Escherichia coli, composed of 1,010 gene products, to assess the properties of all functional states computed in 15,580 different growth environments. The set of all functional states of the integrated network exhibits a discernable structure that can be visualized in 3-dimensional space, showing that the transcriptional regulatory network governing metabolism in E. coli responds primarily to the available electron acceptor and the presence of glucose as the carbon source. This result is consistent with recently published experimental data. The observation that a complex network composed of 1,010 genes is organized to achieve few dominant modes demonstrates the utility of the systems approach for consolidating large amounts of genome-scale molecular information about a genome and its regulation to elucidate an organism's preferred environments and functional capabilities.

Use of constraint-based modeling for the prediction and validation of antimicrobial targets

The overall process of antimicrobial drug discovery and development seems simple, to cure infectious disease by identifying suitable antibiotic drugs. However, this goal has been difficult to fulfill in recent years. Despite the promise of the high-throughput innovations sparked by the genomics revolution, discovery, and development of new antibiotics has lagged in recent years exacerbating the already serious problem of evolution of antibiotic resistance. Therefore, both new antimicrobials are desperately needed as are improvements to speed up or improve nearly all steps in the process of discovering novel antibiotics and bringing these to clinical use. Another product of the genomic revolution is the modeling of metabolism using computational methodologies. Genomic-scale networks of metabolic reactions based on stoichiometry, thermodynamics and other physico-chemical constraints that emulate microbial metabolism have been developed into valuable research tools in metabolic engineering and other fields. This constraint-based modeling is predictive in identifying critical reactions, metabolites, and genes in metabolism. This is extremely useful in determining and rationalizing cellular metabolic requirements. In turn, these methods can be used to predict potential metabolic targets for antimicrobial research especially if used to increase the confidence in prioritization of metabolic targets. The many different capacities of constraint-based modeling also enable prediction of cellular response to specific inhibitors such as antibiotics and this may, ultimately find a role in drug discovery and development. Herein, we describe the principles of metabolic modeling and how they might initially be applied to antimicrobial research.

Development of a software tool for in silico simulation of Escherichia coli using a visual programming environment

This study describes the development of a software tool, EcoSim, to assist users in implementing quantitative in silico simulation easily. It consists of four parts: extracellular environment and constraints setting mode, table for optimal metabolic flux distribution and chart for changes of substrate concentration, dynamic flux distribution viewer and dynamic hierarchical regulatory network viewer. Representation of a hierarchical regulatory network was constructed with defined modeling symbols and weight in the central Escherichia coli metabolism. All programming procedures for EcoSim were accomplished in a visual programming environment (LabVIEW). To illustrate quantitative in silico simulation with EcoSim, this program was performed on E. coli using glucose and acetate as carbon sources. The simulation results were in agreement with the experimental data obtained from the literature. EcoSim can be used to assist biologists and engineers in predicting and interpreting dynamic behaviors of E. coli under a variety of environmental conditions.

Cryptococcus neoformans gene expression during murine macrophage infection

The fungal pathogen Cryptococcus neoformans survives phagocytosis by macrophages and proliferates within, ultimately establishing latent infection as a facultative intracellular pathogen that can escape macrophage control to cause disseminated disease. This process is hypothesized to be important for C. neoformans pathogenesis; however, it is poorly understood how C. neoformans adapts to and overcomes the hostile intracellular environment of the macrophage. Using DNA microarray technology, we have investigated the transcriptional response of C. neoformans to phagocytosis by murine macrophages. The expression profiles of several genes were verified using quantitative reverse transcription-PCR and a green fluorescent protein reporter strain. Multiple membrane transporters for hexoses, amino acids, and iron were up-regulated, as well as genes involved in responses to oxidative stress. Genes involved in autophagy, peroxisome function, and lipid metabolism were also induced. Interestingly, almost the entire mating type locus displayed increased expression 24 h after internalization, suggesting an intrinsic connection between infection and the MAT locus. Genes in the Gpa1-cyclic AMP-protein kinase A pathway were also up-regulated. Both gpa1 and pka1 mutants were found to be compromised in macrophage infection, confirming the important role of this virulence pathway. A large proportion of the repressed genes are involved in ribosome-related functions, rRNA processing, and translation initiation/elongation, implicating a reduction in translation as a central response to phagocytosis. In summary, this gene expression profile allows us to interpret the adaptation of C. neoformans to the intracellular infection process and informs the search for genes encoding novel virulence attributes.

Computational design of reduced metabolic networks

Cellular functions are based on thousands of chemical reactions and transport processes, most of them being catalysed and regulated by specific proteins. Systematic gene knockouts have provided evidence that this complex reaction network possesses considerable redundancy, that is, alternative routes exist along which signals and metabolic fluxes may be directed to accomplish an identical output behaviour. This property is of particular importance in cases where parts of the reaction network are transiently or permanently impaired, for example, due to an infection or genetic alterations. Here we present a computational concept to determine enzyme-reduced metabolic networks that are still sufficient to accomplish a given set of cellular functions. Our approach consists of defining an objective function that expresses the compromise that has to be made between successive reduction of the network by omission of enzymes and its decreasing thermodynamic and kinetic feasibility. Optimisation of this objective function results in a linear mixed-integer program. With increasing weight given to the reduction of the number of enzymes, the total flux in the network increases and some of the reactions have to proceed in thermodynamically unfavourable directions. The approach was applied to two metabolic schemes: the energy and redox metabolism of red blood cells and the carbon metabolism of Methylobacterium extorquens. For these two example networks, we determined various variants of reduced networks differing in the number and types of disabled enzymes and disconnected reactions. Using a comprehensive kinetic model of the erythrocyte metabolism, we assess the kinetic feasibility of enzyme-reduced subnetworks. The number of enzymes predicted to be indispensable amounts to 14 (out of 28) for the erythrocyte scheme and 13 (out of 77) for the bacterium scheme, the largest group of enzymes predicted to be simultaneously dispensable amounts to 3 and 37 for these two systems. Our approach might contribute to identifying potential target enzymes for rational drug design, to rationalising gene-expression profiles of metabolic enzymes and to designing synthetic networks with highly specialised metabolic functions.

Kinetic constraints for formation of steady states in biochemical networks

The constraint-based analysis has emerged as a useful tool for analysis of biochemical networks. This work introduces the concept of kinetic constraints. It is shown that maximal reaction rates are appropriate constraints only for isolated enzymatic reactions. For biochemical networks, it is revealed that constraints for formation of a steady state require specific relationships between maximal reaction rates of all enzymes. The constraints for a branched network are significantly different from those for a cyclic network. Moreover, the constraints do not require Michaelis-Menten constants for most enzymes, and they only require the constants for the enzymes at the branching or cyclic point. Reversibility of reactions at system boundary or branching point may significantly impact on kinetic constraints. When enzymes are regulated, regulations may impose severe kinetic constraints for the formation of steady states. As the complexity of a network increases, kinetic constraints become more severe. In addition, it is demonstrated that kinetic constraints for networks with co-regulation can be analyzed using the approach. In general, co-regulation enhances the constraints and therefore larger fluctuations in fluxes can be accommodated in the networks with co-regulation. As a first example of the application, we derive the kinetic constraints for an actual network that describes sucrose accumulation in the sugar cane culm, and confirm their validity using numerical simulations.

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.

Surviving heat shock: control strategies for robustness and performance

Molecular biology studies the cause-and-effect relationships among microscopic processes initiated by individual molecules within a cell and observes their macroscopic phenotypic effects on cells and organisms. These studies provide a wealth of information about the underlying networks and pathways responsible for the basic functionality and robustness of biological systems. At the same time, these studies create exciting opportunities for the development of quantitative and predictive models that connect the mechanism to its phenotype then examine various modular structures and the range of their dynamical behavior. The use of such models enables a deeper understanding of the design principles underlying biological organization and makes their reverse engineering and manipulation both possible and tractable The heat shock response presents an interesting mechanism where such an endeavor is possible. Using a model of heat shock, we extract the design motifs in the system and justify their existence in terms of various performance objectives. We also offer a modular decomposition that parallels that of traditional engineering control architectures.

Genome-scale models of microbial cells: evaluating the consequences of constraints

Microbial cells operate under governing constraints that limit their range of possible functions. With the availability of annotated genome sequences, it has become possible to reconstruct genome-scale biochemical reaction networks for microorganisms. The imposition of governing constraints on a reconstructed biochemical network leads to the definition of achievable cellular functions. In recent years, a substantial and growing toolbox of computational analysis methods has been developed to study the characteristics and capabilities of microorganisms using a constraint-based reconstruction and analysis (COBRA) approach. This approach provides a biochemically and genetically consistent framework for the generation of hypotheses and the testing of functions of microbial cells.

Genome-scale in silico models of E. coli have multiple equivalent phenotypic states: assessment of correlated reaction subsets that comprise network states

The constraint-based analysis of genome-scale metabolic and regulatory networks has been successful in predicting phenotypes and useful for analyzing high-throughput data sets. Within this modeling framework, linear optimization has been used to study genome-scale metabolic models, resulting in the enumeration of single optimal solutions describing the best use of the network to support growth. Here mixed-integer linear programming was used to calculate and study a subset of the alternate optimal solutions for a genome-scale metabolic model of Escherichia coli (iJR904) under a wide variety of environmental conditions. Analysis of the calculated sets of optimal solutions found that: (1) only a small subset of reactions in the network have variable fluxes across optima; (2) sets of reactions that are always used together in optimal solutions, correlated reaction sets, showed moderate agreement with the currently known transcriptional regulatory structure in E. coli and available expression data, and (3) reactions that are used under certain environmental conditions can provide clues about network regulatory needs. In addition, calculation of suboptimal flux distributions, using flux variability analysis, identified reactions which are used under significantly more environmental conditions suboptimally than optimally. Together these results demonstrate the utilization of reactions in genome-scale models under a variety of different growth conditions.

Integration of gene expression data into genome-scale metabolic models

A framework for integration of transcriptome data into stoichiometric metabolic models to obtain improved flux predictions is presented. The key idea is to exploit the regulatory information in the expression data to give additional constraints on the metabolic fluxes in the model. Measurements of gene expression from chemostat and batch cultures of Saccharomyces cerevisiae were combined with a recently developed genome-scale model, and the computed metabolic flux distributions were compared to experimental values from carbon labeling experiments and metabolic network analysis. The integration of expression data resulted in improved predictions of metabolic behavior in batch cultures, enabling quantitative predictions of exchange fluxes as well as qualitative estimations of changes in intracellular fluxes. A critical discussion of correlation between gene expression and metabolic fluxes is given.

The Systems Biology of Glycosylation

Glycosylation can have a profound influence on the function of a variety of eukaryotic cells. In particular, it can affect signal transduction and cell-cell communication properties and thus shape critical cell decisions, including the regulation of differentiation and apoptosis. Regulation of glycosylation has multiple layers of complexity, both structural and functional, which make its experimental and theoretical analysis difficult to perform and interpret. Novel research methodologies provided by systems biology can help to address many outstanding issues and integrate glycosylation with other metabolic and cell regulation processes. Here we review the toolbox available for biochemical systems analysis of glycosylation.

Use of genome-scale microbial models for metabolic engineering

Metabolic engineering serves as an integrated approach to design new cell factories by providing rational design procedures and valuable mathematical and experimental tools. Mathematical models have an important role for phenotypic analysis, but can also be used for the design of optimal metabolic network structures. The major challenge for metabolic engineering in the post-genomic era is to broaden its design methodologies to incorporate genome-scale biological data. Genome-scale stoichiometric models of microorganisms represent a first step in this direction.

Reconstruction of microbial transcriptional regulatory networks

Although metabolic networks can be readily reconstructed through comparative genomics, the reconstruction of regulatory networks has been hindered by the relatively low level of evolutionary conservation of their molecular components. Recent developments in experimental techniques have allowed the generation of vast amounts of data related to regulatory networks. This data together with literature-derived knowledge has opened the way for genome-scale reconstruction of transcriptional regulatory networks. Large-scale regulatory network reconstructions can be converted to in silico models that allow systematic analysis of network behavior in response to changes in environmental conditions. These models can further be combined with genome-scale metabolic models to build integrated models of cellular function including both metabolism and its regulation.

Monte Carlo sampling can be used to determine the size and shape of the steady-state flux space

Constraint-based modeling results in a convex polytope that defines a solution space containing all possible steady-state flux distributions. The properties of this polytope have been studied extensively using linear programming to find the optimal flux distribution under various optimality conditions and convex analysis to define its extreme pathways (edges) and elementary modes. The work presented herein further studies the steady-state flux space by defining its hyper-volume. In low dimensions (i.e. for small sample networks), exact volume calculation algorithms were used. However, due to the #P-hard nature of the vertex enumeration and volume calculation problem in high dimensions, random Monte Carlo sampling was used to characterize the relative size of the solution space of the human red blood cell metabolic network. Distributions of the steady-state flux levels for each reaction in the metabolic network were generated to show the range of flux values for each reaction in the polytope. These results give insight into the shape of the high-dimensional solution space. The value of measuring uptake and secretion rates in shrinking the steady-state flux solution space is illustrated through singular value decomposition of the randomly sampled points. The V(max) of various reactions in the network are varied to determine the sensitivity of the solution space to the maximum capacity constraints. The methods developed in this study are suitable for testing the implication of additional constraints on a metabolic network system and can be used to explore the effects of single nucleotide polymorphisms (SNPs) on network capabilities.

Characterization of the cellular uptake and metabolic conversion of acetylated N-acetylmannosamine (ManNAc) analogues to sialic acids

"Sialic acid engineering" refers to the strategy where cell surface carbohydrates are modified by the biosynthetic incorporation of metabolic intermediates, such as non-natural N-acetylmannosamine (ManNAc) analogues, into cellular glycoconjugates. While this technology has promising research, biomedical, and biotechnological applications due to its ability to endow the cell surface with novel physical and chemical properties, its adoption on a large scale is hindered by the inefficient metabolic utilization of ManNAc analogues. We address this limitation by proposing the use of acetylated ManNAc analogues for sialic acid engineering applications. In this paper, the metabolic flux of these "second-generation" compounds into a cell, and, subsequently, into the target sialic acid biosynthetic pathway is characterized in detail. We show that acetylated ManNAc analogues are metabolized up to 900-fold more efficiently than their natural counterparts. The acetylated compounds, however, decrease cell viability under certain culture conditions. To determine if these toxic side effects can be avoided, we developed an assay to measure the cellular uptake of acetylated ManNAc from the culture medium and its subsequent flux into sialic acid biosynthetic pathway. This assay shows that the majority ( > 80%) of acetylated ManNAc is stored in a cellular "reservoir" capable of safely sequestering this analogue. These results provide conditions that, from a practical perspective, enable the acetylated analogues to be used safely and efficaciously and therefore offer a general strategy to facilitate metabolic substrate-based carbohydrate engineering efforts. In addition, these results provide fundamental new insights into the metabolic processing of non-natural monosaccharides.