k-Cone analysis: determining all candidate values for kinetic parameters on a network scale

An adaptable in silico ensemble model of the arachidonic acid cascade

Eicosanoids are a family of bioactive lipids, including derivatives of the ubiquitous fatty acid arachidonic acid (AA). The intimate involvement of eicosanoids in inflammation motivates the development of predictive in silico models for a systems-level exploration of disease mechanisms, drug development and replacement of animal models. Using an ensemble modelling strategy, we developed a computational model of the AA cascade. This approach allows the visualisation of plausible and thermodynamically feasible predictions, overcoming the limitations of fixed-parameter modelling. A quality scoring method was developed to quantify the accuracy of ensemble predictions relative to experimental data, measuring the overall uncertainty of the process. Monte Carlo ensemble modelling was used to quantify the prediction confidence levels. Model applicability was demonstrated using mass spectrometry mediator lipidomics to measure eicosanoids produced by HaCaT epidermal keratinocytes and 46BR.1N dermal fibroblasts, treated with stimuli (calcium ionophore A23187), (ultraviolet radiation, adenosine triphosphate) and a cyclooxygenase inhibitor (indomethacin). Experimentation and predictions were in good qualitative agreement, demonstrating the ability of the model to be adapted to cell types exhibiting differences in AA release and enzyme concentration profiles. The quantitative agreement between experimental and predicted outputs could be improved by expanding network topology to include additional reactions. Overall, our approach generated an adaptable, tuneable ensemble model of the AA cascade that can be tailored to represent different cell types and demonstrated that the integration of in silico and in vitro methods can facilitate a greater understanding of complex biological networks such as the AA cascade.

Robustness analysis and identification for an enzyme-catalytic complex metabolic network in batch culture

Bioconversion of glycerol to 1,3-propanediol is a promising way to mitigate the shortage of energy. To maximize the production of 1,3-propanediol, it needs to control precisely microbial fermentation process. However, it might consume lots of human and material resources when conducting experimental tests many times. In this study, a nonlinear enzyme-catalytic dynamical system is developed to describe the bioconversion process of glycerol to 1,3-propanediol, especially continuous piecewise linear functions are used as identification parameters. The existence, uniqueness and continuity of solutions are also discussed. Then, considering the fact that the concentration of intracellular substances is difficult to measure in experiments, a new quantitative definition of biological robustness is introduced as a performance index to determine the identification parameters related to intracellular substances. Meanwhile, a two-phase optimization algorithm is constructed to solve the identification model. By comparison with the experimental data, it can be found that the present nonlinear dynamical system can describe the fermentation process very well. Finally, the present nonlinear dynamical system and the corresponding optimal identification parameters might be useful in future studies on the batch culture of glycerol to 1,3-propanediol.

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

The key processes in biological and chemical systems are described by networks of chemical reactions. From molecular biology to biotechnology applications, computational models of reaction networks are used extensively to elucidate their non-linear dynamics. The model dynamics are crucially dependent on the parameter values which are often estimated from observations. Over the past decade, the interest in parameter and state estimation in models of (bio-) chemical reaction networks (BRNs) grew considerably. The related inference problems are also encountered in many other tasks including model calibration, discrimination, identifiability, and checking, and optimum experiment design, sensitivity analysis, and bifurcation analysis. The aim of this review paper is to examine the developments in literature to understand what BRN models are commonly used, and for what inference tasks and inference methods. The initial collection of about 700 documents concerning estimation problems in BRNs excluding books and textbooks in computational biology and chemistry were screened to select over 270 research papers and 20 graduate research theses. The paper selection was facilitated by text mining scripts to automate the search for relevant keywords and terms. The outcomes are presented in tables revealing the levels of interest in different inference tasks and methods for given models in the literature as well as the research trends are uncovered. Our findings indicate that many combinations of models, tasks and methods are still relatively unexplored, and there are many new research opportunities to explore combinations that have not been considered-perhaps for good reasons. The most common models of BRNs in literature involve differential equations, Markov processes, mass action kinetics, and state space representations whereas the most common tasks are the parameter inference and model identification. The most common methods in literature are Bayesian analysis, Monte Carlo sampling strategies, and model fitting to data using evolutionary algorithms. The new research problems which cannot be directly deduced from the text mining data are also discussed.

Insights into Dynamic Network States Using Metabolomic Data

Metabolomic data is the youngest of the high-throughput data types; however, it is potentially one of the most informative, as it provides a direct, quantitative biochemical phenotype. There are a number of ways in which metabolomic data can be analyzed in systems biology; however, the thermodynamic and kinetic relevance of these data cannot be overstated. Genome-scale metabolic network reconstructions provide a natural context to incorporate metabolomic data in order to provide insight into the condition-specific kinetic characteristics of metabolic networks. Herein we discuss how metabolomic data can be incorporated into constraint-based models in a flexible framework that enables scaling from small pathways to cell-scale models, while being able to accommodate coarse-grained to more detailed, allosteric interactions, all using the well-known principle of mass action.

The space of enzyme regulation in HeLa cells can be inferred from its intracellular metabolome

During the transition from a healthy state to a cancerous one, cells alter their metabolism to increase proliferation. The underlying metabolic alterations may be caused by a variety of different regulatory events on the transcriptional or post-transcriptional level whose identification contributes to the rational design of therapeutic targets. We present a mechanistic strategy capable of inferring enzymatic regulation from intracellular metabolome measurements that is independent of the actual mechanism of regulation. Here, enzyme activities are expressed by the space of all feasible kinetic constants (k-cone) such that the alteration between two phenotypes is given by their corresponding kinetic spaces. Deriving an expression for the transformation of the healthy to the cancer k-cone we identified putative regulated enzymes between the HeLa and HaCaT cell lines. We show that only a few enzymatic activities change between those two cell lines and that this regulation does not depend on gene transcription but is instead post-transcriptional. Here, we identify phosphofructokinase as the major driver of proliferation in HeLa cells and suggest an optional regulatory program, associated with oxidative stress, that affects the activity of the pentose phosphate pathway.

Computational prediction of essential metabolic genes using constraint-based approaches

In this chapter, we describe the application of constraint-based modeling to predict the impact of gene deletions on a metabolic phenotype. The metabolic reactions taking place inside cells form large networks, which have been reconstructed at a genome-scale for several organisms at increasing levels of detail. By integrating mathematical modeling techniques with biochemical principles, constraint-based approaches enable predictions of metabolite fluxes and growth under specific environmental conditions or for genetically modified microorganisms. Similar to the experimental knockout of a gene, predicting the essentiality of a metabolic gene for a phenotype further allows to generate hypotheses on its biological function and design of genetic engineering strategies for biotechnological applications. Here, we summarize the principles of constraint-based approaches and provide a detailed description of the procedure to predict the essentiality of metabolic genes with respect to a specific metabolic function. We exemplify the approach by predicting the essentiality of reactions in the citric acid cycle for the production of glucose from fatty acids.

Predictive sulfur metabolism - a field in flux

The key role of sulfur metabolites in response to biotic and abiotic stress in plants, as well as their importance in diet and health has led to a significant interest and effort in trying to understand and manipulate the production of relevant compounds. Metabolic engineering utilizes a set of theoretical tools to help rationally design modifications that enhance the production of a desired metabolite. Such approaches have proven their value in bacterial systems, however, the paucity of success stories to date in plants, suggests that challenges remain. Here, we review the most commonly used methods for understanding metabolic flux, focusing on the sulfur assimilatory pathway. We highlight known issues with both experimental and theoretical approaches, as well as presenting recent methods for integrating different modeling strategies, and progress toward an understanding of flux at the whole plant level.

Kinetic models in industrial biotechnology - Improving cell factory performance

An increasing number of industrial bioprocesses capitalize on living cells by using them as cell factories that convert sugars into chemicals. These processes range from the production of bulk chemicals in yeasts and bacteria to the synthesis of therapeutic proteins in mammalian cell lines. One of the tools in the continuous search for improved performance of such production systems is the development and application of mathematical models. To be of value for industrial biotechnology, mathematical models should be able to assist in the rational design of cell factory properties or in the production processes in which they are utilized. Kinetic models are particularly suitable towards this end because they are capable of representing the complex biochemistry of cells in a more complete way compared to most other types of models. They can, at least in principle, be used to in detail understand, predict, and evaluate the effects of adding, removing, or modifying molecular components of a cell factory and for supporting the design of the bioreactor or fermentation process. However, several challenges still remain before kinetic modeling will reach the degree of maturity required for routine application in industry. Here we review the current status of kinetic cell factory modeling. Emphasis is on modeling methodology concepts, including model network structure, kinetic rate expressions, parameter estimation, optimization methods, identifiability analysis, model reduction, and model validation, but several applications of kinetic models for the improvement of cell factories are also discussed.

k-OptForce: integrating kinetics with flux balance analysis for strain design

Computational strain design protocols aim at the system-wide identification of intervention strategies for the enhanced production of biochemicals in microorganisms. Existing approaches relying solely on stoichiometry and rudimentary constraint-based regulation overlook the effects of metabolite concentrations and substrate-level enzyme regulation while identifying metabolic interventions. In this paper, we introduce k-OptForce, which integrates the available kinetic descriptions of metabolic steps with stoichiometric models to sharpen the prediction of intervention strategies for improving the bio-production of a chemical of interest. It enables identification of a minimal set of interventions comprised of both enzymatic parameter changes (for reactions with available kinetics) and reaction flux changes (for reactions with only stoichiometric information). Application of k-OptForce to the overproduction of L-serine in E. coli and triacetic acid lactone (TAL) in S. cerevisiae revealed that the identified interventions tend to cause less dramatic rearrangements of the flux distribution so as not to violate concentration bounds. In some cases the incorporation of kinetic information leads to the need for additional interventions as kinetic expressions render stoichiometry-only derived interventions infeasible by violating concentration bounds, whereas in other cases the kinetic expressions impart flux changes that favor the overproduction of the target product thereby requiring fewer direct interventions. A sensitivity analysis on metabolite concentrations shows that the required number of interventions can be significantly affected by changing the imposed bounds on metabolite concentrations. Furthermore, k-OptForce was capable of finding non-intuitive interventions aiming at alleviating the substrate-level inhibition of key enzymes in order to enhance the flux towards the product of interest, which cannot be captured by stoichiometry-alone analysis. This study paves the way for the integrated analysis of kinetic and stoichiometric models and enables elucidating system-wide metabolic interventions while capturing regulatory and kinetic effects.

Towards kinetic modeling of genome-scale metabolic networks without sacrificing stoichiometric, thermodynamic and physiological constraints

Mathematical modeling is an essential tool for the comprehensive understanding of cell metabolism and its interactions with the environmental and process conditions. Recent developments in the construction and analysis of stoichiometric models made it possible to define limits on steady-state metabolic behavior using flux balance analysis. However, detailed information on enzyme kinetics and enzyme regulation is needed to formulate kinetic models that can accurately capture the dynamic metabolic responses. The use of mechanistic enzyme kinetics is a difficult task due to uncertainty in the kinetic properties of enzymes. Therefore, the majority of recent works considered only mass action kinetics for reactions in metabolic networks. Herein, we applied the optimization and risk analysis of complex living entities (ORACLE) framework and constructed a large-scale mechanistic kinetic model of optimally grown Escherichia coli. We investigated the complex interplay between stoichiometry, thermodynamics, and kinetics in determining the flexibility and capabilities of metabolism. Our results indicate that enzyme saturation is a necessary consideration in modeling metabolic networks and it extends the feasible ranges of metabolic fluxes and metabolite concentrations. Our results further suggest that enzymes in metabolic networks have evolved to function at different saturation states to ensure greater flexibility and robustness of cellular metabolism.

Characterizing the relationship between steady state and response using analytical expressions for the steady states of mass action models

The steady states of cells affect their response to perturbation. Indeed, diagnostic markers for predicting the response to therapeutic perturbation are often based on steady state measurements. In spite of this, no method exists to systematically characterize the relationship between steady state and response. Mathematical models are established tools for studying cellular responses, but characterizing their relationship to the steady state requires that it have a parametric, or analytical, expression. For some models, this expression can be derived by the King-Altman method. However, King-Altman requires that no substrate act as an enzyme, and is therefore not applicable to most models of signal transduction. For this reason we developed py-substitution, a simple but general method for deriving analytical expressions for the steady states of mass action models. Where the King-Altman method is applicable, we show that py-substitution yields an equivalent expression, and at comparable efficiency. We use py-substitution to study the relationship between steady state and sensitivity to the anti-cancer drug candidate, dulanermin (recombinant human TRAIL). First, we use py-substitution to derive an analytical expression for the steady state of a published model of TRAIL-induced apoptosis. Next, we show that the amount of TRAIL required for cell death is sensitive to the steady state concentrations of procaspase 8 and its negative regulator, Bar, but not the other procaspase molecules. This suggests that activation of caspase 8 is a critical point in the death decision process. Finally, we show that changes in the threshold at which TRAIL results in cell death is not always equivalent to changes in the time of death, as is commonly assumed. Our work demonstrates that an analytical expression is a powerful tool for identifying steady state determinants of the cellular response to perturbation. All code is available at http://signalingsystems.ucsd.edu/models-and-code/ or as supplementary material accompanying this paper.

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

Background

Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization.

Results

Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity.

Conclusions

Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

Gaussian graphical modeling reconstructs pathway reactions from high-throughput metabolomics data

Background

With the advent of high-throughput targeted metabolic profiling techniques, the question of how to interpret and analyze the resulting vast amount of data becomes more and more important. In this work we address the reconstruction of metabolic reactions from cross-sectional metabolomics data, that is without the requirement for time-resolved measurements or specific system perturbations. Previous studies in this area mainly focused on Pearson correlation coefficients, which however are generally incapable of distinguishing between direct and indirect metabolic interactions.

Results

In our new approach we propose the application of a Gaussian graphical model (GGM), an undirected probabilistic graphical model estimating the conditional dependence between variables. GGMs are based on partial correlation coefficients, that is pairwise Pearson correlation coefficients conditioned against the correlation with all other metabolites. We first demonstrate the general validity of the method and its advantages over regular correlation networks with computer-simulated reaction systems. Then we estimate a GGM on data from a large human population cohort, covering 1020 fasting blood serum samples with 151 quantified metabolites. The GGM is much sparser than the correlation network, shows a modular structure with respect to metabolite classes, and is stable to the choice of samples in the data set. On the example of human fatty acid metabolism, we demonstrate for the first time that high partial correlation coefficients generally correspond to known metabolic reactions. This feature is evaluated both manually by investigating specific pairs of high-scoring metabolites, and then systematically on a literature-curated model of fatty acid synthesis and degradation. Our method detects many known reactions along with possibly novel pathway interactions, representing candidates for further experimental examination.

Conclusions

In summary, we demonstrate strong signatures of intracellular pathways in blood serum data, and provide a valuable tool for the unbiased reconstruction of metabolic reactions from large-scale metabolomics data sets.

Ensemble modeling of hepatic fatty acid metabolism with a synthetic glyoxylate shunt

The liver plays a central role in maintaining whole body metabolic and energy homeostasis by consuming and producing glucose and fatty acids. Glucose and fatty acids compete for hepatic substrate oxidation with regulation ensuring glucose is oxidized preferentially. Increasing fatty acid oxidation is expected to decrease lipid storage in the liver and avoid lipid-induced insulin-resistance. To increase hepatic lipid oxidation in the presence of glucose, we previously engineered a synthetic glyoxylate shunt into human hepatocyte cultures and a mouse model and showed that this synthetic pathway increases free fatty acid beta-oxidation and confers resistance to diet-induced obesity in the mouse model. Here we used ensemble modeling to decipher the effects of perturbations to the hepatic metabolic network on fatty acid oxidation and glucose uptake. Despite sampling of kinetic parameters using the most fundamental elementary reaction models, the models based on current metabolic regulation did not readily describe the phenotype generated by glyoxylate shunt expression. Although not conclusive, this initial negative result prompted us to probe unknown regulations, and malate was identified as inhibitor of hexokinase 2 expression either through direct or indirect actions. This regulation allows the explanation of observed phenotypes (increased fatty acid degradation and decreased glucose consumption). Moreover, the result is a function of pyruvate-carboxylase, mitochondrial pyruvate transporter, citrate transporter protein, and citrate synthase activities. Some subsets of these flux ratios predict increases in fatty acid and decreases in glucose uptake after glyoxylate expression, whereas others predict no change. Altogether, this work defines the possible biochemical space where the synthetic shunt will produce the desired phenotype and demonstrates the efficacy of ensemble modeling for synthetic pathway design.

Mass action stoichiometric simulation models: incorporating kinetics and regulation into stoichiometric models

The ability to characterize biological dynamics is important for understanding the integrated molecular processes that underlie normal and abnormal cellular states. The availability of metabolomic data, in addition to new developments in the formal description of dynamic states of networks, has enabled a new data integration approach for building large-scale kinetic networks. We show that dynamic network models can be constructed in a scalable manner using metabolomic data mapped onto stoichiometric models, resulting in mass action stoichiometric simulation (MASS) models. Enzymes and their various functional states are represented explicitly as compounds, or nodes in a stoichiometric network, within this formalism. Analyses and simulations of MASS models explicitly show that regulatory enzymes can control dynamic states of networks in part by binding numerous metabolites at multiple sites. Thus, network functional states are reflected in the fractional states of a regulatory enzyme, such as the fraction of the total enzyme concentration that is in a catalytically active versus inactive state. The feasible construction of MASS models represents a practical means to increase the size, scope, and predictive capabilities of dynamic network models in cell and molecular biology.

BiGG: a Biochemical Genetic and Genomic knowledgebase of large scale metabolic reconstructions

BACKGROUND

Genome-scale metabolic reconstructions under the Constraint Based Reconstruction and Analysis (COBRA) framework are valuable tools for analyzing the metabolic capabilities of organisms and interpreting experimental data. As the number of such reconstructions and analysis methods increases, there is a greater need for data uniformity and ease of distribution and use.

DESCRIPTION

We describe BiGG, a knowledgebase of Biochemically, Genetically and Genomically structured genome-scale metabolic network reconstructions. BiGG integrates several published genome-scale metabolic networks into one resource with standard nomenclature which allows components to be compared across different organisms. BiGG can be used to browse model content, visualize metabolic pathway maps, and export SBML files of the models for further analysis by external software packages. Users may follow links from BiGG to several external databases to obtain additional information on genes, proteins, reactions, metabolites and citations of interest.

CONCLUSIONS

BiGG addresses a need in the systems biology community to have access to high quality curated metabolic models and reconstructions. It is freely available for academic use at http://bigg.ucsd.edu.

Integrated stoichiometric, thermodynamic and kinetic modelling of steady state metabolism

The quantitative analysis of biochemical reactions and metabolites is at frontier of biological sciences. The recent availability of high-throughput technology data sets in biology has paved the way for new modelling approaches at various levels of complexity including the metabolome of a cell or an organism. Understanding the metabolism of a single cell and multi-cell organism will provide the knowledge for the rational design of growth conditions to produce commercially valuable reagents in biotechnology. Here, we demonstrate how equations representing steady state mass conservation, energy conservation, the second law of thermodynamics, and reversible enzyme kinetics can be formulated as a single system of linear equalities and inequalities, in addition to linear equalities on exponential variables. Even though the feasible set is non-convex, the reformulation is exact and amenable to large-scale numerical analysis, a prerequisite for computationally feasible genome scale modelling. Integrating flux, concentration and kinetic variables in a unified constraint-based formulation is aimed at increasing the quantitative predictive capacity of flux balance analysis. Incorporation of experimental and theoretical bounds on thermodynamic and kinetic variables ensures that the predicted steady state fluxes are both thermodynamically and biochemically feasible. The resulting in silico predictions are tested against fluxomic data for central metabolism in Escherichia coli and compare favourably with in silico prediction by flux balance analysis.

An integrated model of eicosanoid metabolism and signaling based on lipidomics flux analysis

There is increasing evidence for a major and critical involvement of lipids in signal transduction and cellular trafficking, and this has motivated large-scale studies on lipid pathways. The Lipid Metabolites and Pathways Strategy consortium is actively investigating lipid metabolism in mammalian cells and has made available time-course data on various lipids in response to treatment with KDO(2)-lipid A (a lipopolysaccharide analog) of macrophage RAW 264.7 cells. The lipids known as eicosanoids play an important role in inflammation. We have reconstructed an integrated network of eicosanoid metabolism and signaling based on the KEGG pathway database and the literature and have developed a kinetic model. A matrix-based approach was used to estimate the rate constants from experimental data and these were further refined using generalized constrained nonlinear optimization. The resulting model fits the experimental data well for all species, and simulated enzyme activities were similar to their literature values. The quantitative model for eicosanoid metabolism that we have developed can be used to design experimental studies utilizing genetic and pharmacological perturbations to probe fluxes in lipid pathways.

Filling kinetic gaps: dynamic modeling of metabolism where detailed kinetic information is lacking

BACKGROUND

Integrative analysis between dynamical modeling of metabolic networks and data obtained from high throughput technology represents a worthy effort toward a holistic understanding of the link among phenotype and dynamical response. Even though the theoretical foundation for modeling metabolic network has been extensively treated elsewhere, the lack of kinetic information has limited the analysis in most of the cases. To overcome this constraint, we present and illustrate a new statistical approach that has two purposes: integrate high throughput data and survey the general dynamical mechanisms emerging for a slightly perturbed metabolic network.

METHODOLOGY/PRINCIPAL FINDINGS

This paper presents a statistic framework capable to study how and how fast the metabolites participating in a perturbed metabolic network reach a steady-state. Instead of requiring accurate kinetic information, this approach uses high throughput metabolome technology to define a feasible kinetic library, which constitutes the base for identifying, statistical and dynamical properties during the relaxation. For the sake of illustration we have applied this approach to the human Red blood cell metabolism (hRBC) and its capacity to predict temporal phenomena was evaluated. Remarkable, the main dynamical properties obtained from a detailed kinetic model in hRBC were recovered by our statistical approach. Furthermore, robust properties in time scale and metabolite organization were identify and one concluded that they are a consequence of the combined performance of redundancies and variability in metabolite participation.

CONCLUSIONS/SIGNIFICANCE

In this work we present an approach that integrates high throughput metabolome data to define the dynamic behavior of a slightly perturbed metabolic network where kinetic information is lacking. Having information of metabolite concentrations at steady-state, this method has significant relevance due its potential scope to analyze others genome scale metabolic reconstructions. Thus, I expect this approach will significantly contribute to explore the relationship between dynamic and physiology in other metabolic reconstructions, particularly those whose kinetic information is practically nulls. For instances, I envisage that this approach can be useful in genomic medicine or pharmacogenomics, where the estimation of time scales and the identification of metabolite organization may be crucial to characterize and identify (dis)functional stages.

Decomposing complex reaction networks using random sampling, principal component analysis and basis rotation

Background

Metabolism and its regulation constitute a large fraction of the molecular activity within cells. The control of cellular metabolic state is mediated by numerous molecular mechanisms, which in effect position the metabolic network flux state at specific locations within a mathematically-definable steady-state flux space. Post-translational regulation constitutes a large class of these mechanisms, and decades of research indicate that achieving a network flux state through post-translational metabolic regulation is both a complex and complicated regulatory problem. No analysis method for the objective, top-down assessment of such regulation problems in large biochemical networks has been presented and demonstrated.

Results

We show that the use of Monte Carlo sampling of the steady-state flux space of a cell-scale metabolic system in conjunction with Principal Component Analysis and eigenvector rotation results in a low-dimensional and biochemically interpretable decomposition of the steady flux states of the system. This decomposition comes in the form of a low number of small reaction sets whose flux variability accounts for nearly all of the flux variability in the entire system. This result indicates an underlying simplicity and implies that the regulation of a relatively low number of reaction sets can essentially determine the flux state of the entire network in the given growth environment.

Conclusion

We demonstrate how our top-down analysis of networks can be used to determine key regulatory requirements independent of specific parameters and mechanisms. Our approach complements the reductionist approach to elucidation of regulatory mechanisms and facilitates the development of our understanding of global regulatory strategies in biological networks.

Steady-state kinetic modeling constrains cellular resting states and dynamic behavior

A defining characteristic of living cells is the ability to respond dynamically to external stimuli while maintaining homeostasis under resting conditions. Capturing both of these features in a single kinetic model is difficult because the model must be able to reproduce both behaviors using the same set of molecular components. Here, we show how combining small, well-defined steady-state networks provides an efficient means of constructing large-scale kinetic models that exhibit realistic resting and dynamic behaviors. By requiring each kinetic module to be homeostatic (at steady state under resting conditions), the method proceeds by (i) computing steady-state solutions to a system of ordinary differential equations for each module, (ii) applying principal component analysis to each set of solutions to capture the steady-state solution space of each module network, and (iii) combining optimal search directions from all modules to form a global steady-state space that is searched for accurate simulation of the time-dependent behavior of the whole system upon perturbation. Importantly, this stepwise approach retains the nonlinear rate expressions that govern each reaction in the system and enforces constraints on the range of allowable concentration states for the full-scale model. These constraints not only reduce the computational cost of fitting experimental time-series data but can also provide insight into limitations on system concentrations and architecture. To demonstrate application of the method, we show how small kinetic perturbations in a modular model of platelet P2Y₁ signaling can cause widespread compensatory effects on cellular resting states.

Cells respond to extracellular signals through a complex coordination of interacting molecular components. Computational models can serve as powerful tools for prediction and analysis of signaling systems, but constructing large models typically requires extensive experimental datasets and computation. To facilitate the construction of complex signaling models, we present a strategy in which the models are built in a stepwise fashion, beginning with small “resting” networks that are combined to form larger models with complex time-dependent behaviors. Interestingly, we found that only a minor fraction of potential model configurations were compatible with resting behavior in an example signaling system. These reduced sets of configurations were used to limit the search for more complicated solutions that also captured the dynamic behavior of the system. Using an example model constructed by this approach, we show how a cell's resting behavior adjusts to changes in the kinetic rate processes of the system. This strategy offers a general and biologically intuitive framework for building large-scale kinetic models of steady-state cellular systems and their dynamics.

Genome-scale models of bacterial metabolism: reconstruction and applications

Genome-scale metabolic models bridge the gap between genome-derived biochemical information and metabolic phenotypes in a principled manner, providing a solid interpretative framework for experimental data related to metabolic states, and enabling simple in silico experiments with whole-cell metabolism. Models have been reconstructed for almost 20 bacterial species, so far mainly through expert curation efforts integrating information from the literature with genome annotation. A wide variety of computational methods exploiting metabolic models have been developed and applied to bacteria, yielding valuable insights into bacterial metabolism and evolution, and providing a sound basis for computer-assisted design in metabolic engineering. Recent advances in computational systems biology and high-throughput experimental technologies pave the way for the systematic reconstruction of metabolic models from genomes of new species, and a corresponding expansion of the scope of their applications. In this review, we provide an introduction to the key ideas of metabolic modeling, survey the methods, and resources that enable model reconstruction and refinement, and chart applications to the investigation of global properties of metabolic systems, the interpretation of experimental results, and the re-engineering of their biochemical capabilities.

Genome-scale model for Clostridium acetobutylicum: Part II. Development of specific proton flux states and numerically determined sub-systems

A regulated genome-scale model for Clostridium acetobutylicum ATCC 824 was developed based on its metabolic network reconstruction. To aid model convergence and limit the number of flux-vector possible solutions (the size of the phenotypic solution space), modeling strategies were developed to impose a new type of constraint at the endo-exo-metabolome interface. This constraint is termed the specific proton flux state, and its use enabled accurate prediction of the extracellular medium pH during vegetative growth of batch cultures. The specific proton flux refers to the influx or efflux of free protons (per unit biomass) across the cell membrane. A specific proton flux state encompasses a defined range of specific proton fluxes and includes all metabolic flux distributions resulting in a specific proton flux within this range. Effective simulation of time-course batch fermentation required the use of independent flux balance solutions from an optimum set of specific proton flux states. Using a real-coded genetic algorithm to optimize temporal bounds of specific proton flux states, we show that six separate specific proton flux states are required to model vegetative-growth metabolism and accurately predict the extracellular medium pH. Further, we define the apparent proton flux stoichiometry per weak acids efflux and show that this value decreases from approximately 3.5 mol of protons secreted per mole of weak acids at the start of the culture to approximately 0 at the end of vegetative growth. Calculations revealed that when specific weak acids production is maximized in vegetative growth, the net proton exchange between the cell and environment occurs primarily through weak acids efflux (apparent proton flux stoichiometry is 1). However, proton efflux through cation channels during the early stages of acidogenesis was found to be significant. We have also developed the concept of numerically determined sub-systems of genome-scale metabolic networks here as a sub-network with a one-dimensional null space basis set. A numerically determined sub-system was constructed in the genome-scale metabolic network to study the flux magnitudes and directions of acetylornithine transaminase, alanine racemase, and D-alanine transaminase. These results were then used to establish additional constraints for the genome-scale model.

Use of randomized sampling for analysis of metabolic networks

Genome-scale metabolic network reconstructions in microorganisms have been formulated and studied for about 8 years. The constraint-based approach has shown great promise in analyzing the systemic properties of these network reconstructions. Notably, constraint-based models have been used successfully to predict the phenotypic effects of knock-outs and for metabolic engineering. The inherent uncertainty in both parameters and variables of large-scale models is significant and is well suited to study by Monte Carlo sampling of the solution space. These techniques have been applied extensively to the reaction rate (flux) space of networks, with more recent work focusing on dynamic/kinetic properties. Monte Carlo sampling as an analysis tool has many advantages, including the ability to work with missing data, the ability to apply post-processing techniques, and the ability to quantify uncertainty and to optimize experiments to reduce uncertainty. We present an overview of this emerging area of research in systems biology.

Ensemble modeling of metabolic networks

Complete modeling of metabolic networks is desirable, but it is difficult to accomplish because of the lack of kinetics. As a step toward this goal, we have developed an approach to build an ensemble of dynamic models that reach the same steady state. The models in the ensemble are based on the same mechanistic framework at the elementary reaction level, including known regulations, and span the space of all kinetics allowable by thermodynamics. This ensemble allows for the examination of possible phenotypes of the network upon perturbations, such as changes in enzyme expression levels. The size of the ensemble is reduced by acquiring data for such perturbation phenotypes. If the mechanistic framework is approximately accurate, the ensemble converges to a smaller set of models and becomes more predictive. This approach bypasses the need for detailed characterization of kinetic parameters and arrives at a set of models that describes relevant phenotypes upon enzyme perturbations.

Top-down analysis of temporal hierarchy in biochemical reaction networks

The study of dynamic functions of large-scale biological networks has intensified in recent years. A critical component in developing an understanding of such dynamics involves the study of their hierarchical organization. We investigate the temporal hierarchy in biochemical reaction networks focusing on: (1) the elucidation of the existence of “pools” (i.e., aggregate variables) formed from component concentrations and (2) the determination of their composition and interactions over different time scales. To date the identification of such pools without prior knowledge of their composition has been a challenge. A new approach is developed for the algorithmic identification of pool formation using correlations between elements of the modal matrix that correspond to a pair of concentrations and how such correlations form over the hierarchy of time scales. The analysis elucidates a temporal hierarchy of events that range from chemical equilibration events to the formation of physiologically meaningful pools, culminating in a network-scale (dynamic) structure–(physiological) function relationship. This method is validated on a model of human red blood cell metabolism and further applied to kinetic models of yeast glycolysis and human folate metabolism, enabling the simplification of these models. The understanding of temporal hierarchy and the formation of dynamic aggregates on different time scales is foundational to the study of network dynamics and has relevance in multiple areas ranging from bacterial strain design and metabolic engineering to the understanding of disease processes in humans.

Cellular metabolism describes the complex web of biochemical transformations that are necessary to build the structural components, to convert nutrients into “usable energy” by the cell, and to degrade or excrete the by-products. A critical aspect toward understanding metabolism is the set of dynamic interactions between metabolites, some of which occur very quickly while others occur more slowly. To develop a “systems” understanding of how networks operate dynamically we need to identify the different processes that occur on different time scales. When one moves from very fast time scales to slower ones, certain components in the network move in concert and pool together. We develop a method to elucidate the time scale hierarchy of a network and to simplify its structure by identifying these pools. This is applied to dynamic models of metabolism for the human red blood cell, human folate metabolism, and yeast glycolysis. It was possible to simplify the structure of these networks into biologically meaningful groups of variables. Because dynamics play important roles in normal and abnormal function in biology, it is expected that this work will contribute to an area of great relevance for human disease and engineering applications.

Sloppiness, robustness, and evolvability in systems biology

The functioning of many biochemical networks is often robust-remarkably stable under changes in external conditions and internal reaction parameters. Much recent work on robustness and evolvability has focused on the structure of neutral spaces, in which system behavior remains invariant to mutations. Recently we have shown that the collective behavior of multiparameter models is most often sloppy: insensitive to changes except along a few 'stiff' combinations of parameters, with an enormous sloppy neutral subspace. Robustness is often assumed to be an emergent evolved property, but the sloppiness natural to biochemical networks offers an alternative nonadaptive explanation. Conversely, ideas developed to study evolvability in robust systems can be usefully extended to characterize sloppy systems.

Optimization in computational systems biology

Optimization aims to make a system or design as effective or functional as possible. Mathematical optimization methods are widely used in engineering, economics and science. This commentary is focused on applications of mathematical optimization in computational systems biology. Examples are given where optimization methods are used for topics ranging from model building and optimal experimental design to metabolic engineering and synthetic biology. Finally, several perspectives for future research are outlined.

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.

Extraction of elementary rate constants from global network analysis of E. coli central metabolism

Background

As computational performance steadily increases, so does interest in extending one-particle-per-molecule models to larger physiological problems. Such models however require elementary rate constants to calculate time-dependent rate coefficients under physiological conditions. Unfortunately, even when in vivo kinetic data is available, it is often in the form of aggregated rate laws (ARL) that do not specify the required elementary rate constants corresponding to mass-action rate laws (MRL). There is therefore a need to develop a method which is capable of automatically transforming ARL kinetic information into more detailed MRL rate constants.

Results

By incorporating proteomic data related to enzyme abundance into an MRL modelling framework, here we present an efficient method operating at a global network level for extracting elementary rate constants from experiment-based aggregated rate law (ARL) models. The method combines two techniques that can be used to overcome the difficult properties in parameterization. The first, a hybrid MRL/ARL modelling technique, is used to divide the parameter estimation problem into sub-problems, so that the parameters of the mass action rate laws for each enzyme are estimated in separate steps. This reduces the number of parameters that have to be optimized simultaneously. The second, a hybrid algebraic-numerical simulation and optimization approach, is used to render some rate constants identifiable, as well as to greatly narrow the bounds of the other rate constants that remain unidentifiable. This is done by incorporating equality constraints derived from the King-Altman and Cleland method into the simulated annealing algorithm. We apply these two techniques to estimate the rate constants of a model of E. coli glycolytic pathways. The simulation and statistical results show that our innovative method performs well in dealing with the issues of high computation cost, stiffness, local minima and uncertainty inherent with large-scale non-convex nonlinear MRL models.

Conclusion

In short, this new hybrid method can ensure the proper solution of a challenging parameter estimation problem of nonlinear dynamic MRL systems, while keeping the computational effort reasonable. Moreover, the work provides us with some optimism that physiological models at the particle scale can be rooted on a firm foundation of parameters generated in the macroscopic regime on an experimental basis. Thus, the proposed method should have applications to multi-scale modelling of the real biological systems allowing for enzyme intermediates, stochastic and spatial effects inside a cell.

Formulating genome-scale kinetic models in the post-genome era

The biological community is now awash in high-throughput data sets and is grappling with the challenge of integrating disparate data sets. Such integration has taken the form of statistical analysis of large data sets, or through the bottom-up reconstruction of reaction networks. While progress has been made with statistical and structural methods, large-scale systems have remained refractory to dynamic model building by traditional approaches. The availability of annotated genomes enabled the reconstruction of genome-scale networks, and now the availability of high-throughput metabolomic and fluxomic data along with thermodynamic information opens the possibility to build genome-scale kinetic models. We describe here a framework for building and analyzing such models. The mathematical analysis challenges are reflected in four foundational properties, (i) the decomposition of the Jacobian matrix into chemical, kinetic and thermodynamic information, (ii) the structural similarity between the stoichiometric matrix and the transpose of the gradient matrix, (iii) the duality transformations enabling either fluxes or concentrations to serve as the independent variables and (iv) the timescale hierarchy in biological networks. Recognition and appreciation of these properties highlight notable and challenging new in silico analysis issues.

Universally sloppy parameter sensitivities in systems biology models

Quantitative computational models play an increasingly important role in modern biology. Such models typically involve many free parameters, and assigning their values is often a substantial obstacle to model development. Directly measuring in vivo biochemical parameters is difficult, and collectively fitting them to other experimental data often yields large parameter uncertainties. Nevertheless, in earlier work we showed in a growth-factor-signaling model that collective fitting could yield well-constrained predictions, even when it left individual parameters very poorly constrained. We also showed that the model had a "sloppy" spectrum of parameter sensitivities, with eigenvalues roughly evenly distributed over many decades. Here we use a collection of models from the literature to test whether such sloppy spectra are common in systems biology. Strikingly, we find that every model we examine has a sloppy spectrum of sensitivities. We also test several consequences of this sloppiness for building predictive models. In particular, sloppiness suggests that collective fits to even large amounts of ideal time-series data will often leave many parameters poorly constrained. Tests over our model collection are consistent with this suggestion. This difficulty with collective fits may seem to argue for direct parameter measurements, but sloppiness also implies that such measurements must be formidably precise and complete to usefully constrain many model predictions. We confirm this implication in our growth-factor-signaling model. Our results suggest that sloppy sensitivity spectra are universal in systems biology models. The prevalence of sloppiness highlights the power of collective fits and suggests that modelers should focus on predictions rather than on parameters.

Thermodynamics-based metabolic flux analysis

A new form of metabolic flux analysis (MFA) called thermodynamics-based metabolic flux analysis (TMFA) is introduced with the capability of generating thermodynamically feasible flux and metabolite activity profiles on a genome scale. TMFA involves the use of a set of linear thermodynamic constraints in addition to the mass balance constraints typically used in MFA. TMFA produces flux distributions that do not contain any thermodynamically infeasible reactions or pathways, and it provides information about the free energy change of reactions and the range of metabolite activities in addition to reaction fluxes. TMFA is applied to study the thermodynamically feasible ranges for the fluxes and the Gibbs free energy change, Delta(r)G', of the reactions and the activities of the metabolites in the genome-scale metabolic model of Escherichia coli developed by Palsson and co-workers. In the TMFA of the genome scale model, the metabolite activities and reaction Delta(r)G' are able to achieve a wide range of values at optimal growth. The reaction dihydroorotase is identified as a possible thermodynamic bottleneck in E. coli metabolism with a Delta(r)G' constrained close to zero while numerous reactions are identified throughout metabolism for which Delta(r)G' is always highly negative regardless of metabolite concentrations. As it has been proposed previously, these reactions with exclusively negative Delta(r)G' might be candidates for cell regulation, and we find that a significant number of these reactions appear to be the first steps in the linear portion of numerous biosynthesis pathways. The thermodynamically feasible ranges for the concentration ratios ATP/ADP, NAD(P)/NAD(P)H, and H(extracellular)(+)/H(intracellular)(+) are also determined and found to encompass the values observed experimentally in every case. Further, we find that the NAD/NADH and NADP/NADPH ratios maintained in the cell are close to the minimum feasible ratio and maximum feasible ratio, respectively.

Parameter estimate of signal transduction pathways

BACKGROUND

The "inverse" problem is related to the determination of unknown causes on the bases of the observation of their effects. This is the opposite of the corresponding "direct" problem, which relates to the prediction of the effects generated by a complete description of some agencies. The solution of an inverse problem entails the construction of a mathematical model and takes the moves from a number of experimental data. In this respect, inverse problems are often ill-conditioned as the amount of experimental conditions available are often insufficient to unambiguously solve the mathematical model. Several approaches to solving inverse problems are possible, both computational and experimental, some of which are mentioned in this article. In this work, we will describe in details the attempt to solve an inverse problem which arose in the study of an intracellular signaling pathway.

RESULTS

Using the Genetic Algorithm to find the sub-optimal solution to the optimization problem, we have estimated a set of unknown parameters describing a kinetic model of a signaling pathway in the neuronal cell. The model is composed of mass action ordinary differential equations, where the kinetic parameters describe protein-protein interactions, protein synthesis and degradation. The algorithm has been implemented on a parallel platform. Several potential solutions of the problem have been computed, each solution being a set of model parameters. A sub-set of parameters has been selected on the basis on their small coefficient of variation across the ensemble of solutions.

CONCLUSION

Despite the lack of sufficiently reliable and homogeneous experimental data, the genetic algorithm approach has allowed to estimate the approximate value of a number of model parameters in a kinetic model of a signaling pathway: these parameters have been assessed to be relevant for the reproduction of the available experimental data.

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.

Theodor Bücher Lecture. Metabolomics, modelling and machine learning in systems biology - towards an understanding of the languages of cells. Delivered on 3 July 2005 at the 30th FEBS Congress and the 9th IUBMB conference in Budapest

The newly emerging field of systems biology involves a judicious interplay between high-throughput 'wet' experimentation, computational modelling and technology development, coupled to the world of ideas and theory. This interplay involves iterative cycles, such that systems biology is not at all confined to hypothesis-dependent studies, with intelligent, principled, hypothesis-generating studies being of high importance and consequently very far from aimless fishing expeditions. I seek to illustrate each of these facets. Novel technology development in metabolomics can increase substantially the dynamic range and number of metabolites that one can detect, and these can be exploited as disease markers and in the consequent and principled generation of hypotheses that are consistent with the data and achieve this in a value-free manner. Much of classical biochemistry and signalling pathway analysis has concentrated on the analyses of changes in the concentrations of intermediates, with 'local' equations - such as that of Michaelis and Menten v=(Vmax x S)/(S+K m) - that describe individual steps being based solely on the instantaneous values of these concentrations. Recent work using single cells (that are not subject to the intellectually unsupportable averaging of the variable displayed by heterogeneous cells possessing nonlinear kinetics) has led to the recognition that some protein signalling pathways may encode their signals not (just) as concentrations (AM or amplitude-modulated in a radio analogy) but via changes in the dynamics of those concentrations (the signals are FM or frequency-modulated). This contributes in principle to a straightforward solution of the crosstalk problem, leads to a profound reassessment of how to understand the downstream effects of dynamic changes in the concentrations of elements in these pathways, and stresses the role of signal processing (and not merely the intermediates) in biological signalling. It is this signal processing that lies at the heart of understanding the languages of cells. The resolution of many of the modern and postgenomic problems of biochemistry requires the development of a myriad of new technologies (and maybe a new culture), and thus regular input from the physical sciences, engineering, mathematics and computer science. One solution, that we are adopting in the Manchester Interdisciplinary Biocentre (http://www.mib.ac.uk/) and the Manchester Centre for Integrative Systems Biology (http://www.mcisb.org/), is thus to colocate individuals with the necessary combinations of skills. Novel disciplines that require such an integrative approach continue to emerge. These include fields such as chemical genomics, synthetic biology, distributed computational environments for biological data and modelling, single cell diagnostics/bionanotechnology, and computational linguistics/text mining.

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.