Basic and applied uses of genome‐scale metabolic network reconstructions of Escherichia coli

The genome‐scale model (GEM) of metabolism in the bacterium Escherichia coli K‐12 has been in development for over a decade and is now in wide use. GEM‐enabled studies of E. coli have been primarily focused on six applications: (1) metabolic engineering, (2) model‐driven discovery, (3) prediction of cellular phenotypes, (4) analysis of biological network properties, (5) studies of evolutionary processes, and (6) models of interspecies interactions. In this review, we provide an overview of these applications along with a critical assessment of their successes and limitations, and a perspective on likely future developments in the field. Taken together, the studies performed over the past decade have established a genome‐scale mechanistic understanding of genotype–phenotype relationships in E. coli metabolism that forms the basis for similar efforts for other microbial species. Future challenges include the expansion of GEMs by integrating additional cellular processes beyond metabolism, the identification of key constraints based on emerging data types, and the development of computational methods able to handle such large‐scale network models with sufficient accuracy.     

Modeling of uncertainties in biochemical reactions

Mathematical modeling is an indispensable tool for research and development in biotechnology and bioengineering. The formulation of kinetic models of biochemical networks depends on knowledge of the kinetic properties of the enzymes of the individual reactions. However, kinetic data acquired from experimental observations bring along uncertainties due to various experimental conditions and measurement methods. In this contribution, we propose a novel way to model the uncertainty in the enzyme kinetics and to predict quantitatively the responses of metabolic reactions to the changes in enzyme activities under uncertainty. The proposed methodology accounts explicitly for mechanistic properties of enzymes and physico‐chemical and thermodynamic constraints, and is based on formalism from systems theory and metabolic control analysis. We achieve this by observing that kinetic responses of metabolic reactions depend: (i) on the distribution of the enzymes among their free form and all reactive states; (ii) on the equilibrium displacements of the overall reaction and that of the individual enzymatic steps; and (iii) on the net fluxes through the enzyme. Relying on this observation, we develop a novel, efficient Monte Carlo sampling procedure to generate all states within a metabolic reaction that satisfy imposed constrains. Thus, we derive the statistics of the expected responses of the metabolic reactions to changes in enzyme levels and activities, in the levels of metabolites, and in the values of the kinetic parameters. We present aspects of the proposed framework through an example of the fundamental three‐step reversible enzymatic reaction mechanism. We demonstrate that the equilibrium displacements of the individual enzymatic steps have an important influence on kinetic responses of the enzyme. Furthermore, we derive the conditions that must be satisfied by a reversible three‐step enzymatic reaction operating far away from the equilibrium in order to respond to changes in metabolite levels according to the irreversible Michelis–Menten kinetics. The efficient sampling procedure allows easy, scalable, implementation of this methodology to modeling of large‐scale biochemical networks. Biotechnol. Bioeng. 2011;108: 413–423. © 2010 Wiley Periodicals, Inc.     

Process model comparison and transferability across bioreactor scales and modes of operation for a mammalian cell bioprocess

A Monod kinetic model, logistic equation model, and statistical regression model were developed for a Chinese hamster ovary cell bioprocess operated under three different modes of operation (batch, bolus fed‐batch, and continuous fed‐batch) and grown on two different bioreactor scales (3 L bench‐top and 15 L pilot‐scale). The Monod kinetic model was developed for all modes of operation under study and predicted cell density, glucose glutamine, lactate, and ammonia concentrations well for the bioprocess. However, it was computationally demanding due to the large number of parameters necessary to produce a good model fit. The transferability of the Monod kinetic model structure and parameter set across bioreactor scales and modes of operation was investigated and a parameter sensitivity analysis performed. The experimentally determined parameters had the greatest influence on model performance. They changed with scale and mode of operation, but were easily calculated. The remaining parameters, which were fitted using a differential evolutionary algorithm, were not as crucial. Logistic equation and statistical regression models were investigated as alternatives to the Monod kinetic model. They were less computationally intensive to develop due to the absence of a large parameter set. However, modeling of the nutrient and metabolite concentrations proved to be troublesome due to the logistic equation model structure and the inability of both models to incorporate a feed. The complexity, computational load, and effort required for model development has to be balanced with the necessary level of model sophistication when choosing which model type to develop for a particular application. © 2012 American Institute of Chemical Engineers Biotechnol. Prog., 2013     

Towards Kinetic Modeling of Global Metabolic Networks: Methylobacterium extorquens AM1 Growth as Validation

Here we report a systematic method for constructing a large scale kinetic metabolic model and its initial application to the modeling of central metabolism of Methylobacterium extorquens AM1, a methylotrophic and environmental important bacterium. Its central metabolic network includes formaldehyde metabolism, serine cycle, citric acid cycle, pentose phosphate pathway, gluconeogensis, PHB synthesis and acetyl-CoA conversion pathway, respiration and energy metabolism. Through a systematic and consistent procedure of finding a set of parameters in the physiological range we overcome an outstanding difficulty in large scale kinetic modeling: the requirement for a massive number of enzymatic reaction parameters. We are able to construct the kinetic model based on general biological considerations and incomplete experimental kinetic parameters. Our method consists of the following major steps: 1) using a generic enzymatic rate equation to reduce the number of enzymatic parameters to a minimum set while still preserving their characteristics; 2) using a set of steady state fluxes and metabolite concentrations in the physiological range as the expected output steady state fluxes and metabolite concentrations for the kinetic model to restrict the parametric space of enzymatic reactions; 3) choosing enzyme constants K’s and K’eqs optimized for reactions under physiological concentrations, if their experimental values are unknown; 4) for models which do not cover the entire metabolic network of the organisms, designing a dynamical exchange for the coupling between the metabolism represented in the model and the rest not included.     

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

The absence of comprehensive measured kinetic values and the observed inconsistency in the available in vitro kinetic data has hindered the formulation of network-scale kinetic models of biochemical reaction networks. To meet this challenge we present an approach to construct a convex space, termed the k-cone, which contains all the allowable numerical values of the kinetic constants in large-scale biochemical networks. The definition of the k-cone relies on the incorporation of in vivo concentration data and a simplified approach to represent enzyme kinetics within an established constraint-based modeling approach. The k-cone approach was implemented to define the allowable combination of numerical values for a full kinetic model of human red blood cell metabolism and to study its correlated kinetic parameters. The k-cone approach can be used to determine consistency between in vitro measured kinetic values and in vivo concentration and flux measurements when used in a network-scale kinetic model. k-Cone analysis was successful in determining whether in vitro measured kinetic values used in the reconstruction of a kinetic-based model of Saccharomyces cerevisiae central metabolism could reproduce in vivo measurements. Further, the k-cone can be used to determine which numerical values of in vitro measured parameters are required to be changed in a kinetic model if in vivo measured values are not reproduced. k-Cone analysis could identify what minimum number of in vitro determined kinetic parameters needed to be adjusted in the S. cerevisiae model to be consistent with the in vivo data. Applying the k-cone analysis a priori to kinetic model development may reduce the time and effort involved in model building and parameter adjustment. With the recent developments in high-throughput profiling of metabolite concentrations at a whole-cell scale and advances in metabolomics technologies, the k-cone approach presented here may hold the promise for kinetic characterization of metabolic networks as well as other biological functions at a whole-cell level.     

Review of advanced physical and data-driven models for dynamic bioprocess simulation: Case study of algae–bacteria consortium wastewater treatment

Microorganism production and remediation processes are of critical importance to the next generation of sustainable industries. Undertaking mathematical treatment of dynamic biosystems operating at any spatial or temporal scale is essential to guarantee their performance and safety. However, constructing physical models remains a challenge due to the extreme complexity of process biological mechanisms. Data-driven models also encounter severe limitations because datasets from large-scale bioprocesses are often scarce without complete information and on a restricted operational space. To fill this gap, the current research compares the performance of advanced physical and data-driven models for dynamic bioprocess simulations subject to incomplete and scarce datasets, which to the best of our knowledge has never been addressed before. In specific, kinetic models were constructed by integrating different classic models, and state-of-the-art hyperparameter selection frameworks were developed to design artificial neural networks and Gaussian process regression models. An algae–bacteria consortium wastewater treatment process was selected to test the accuracy of these modeling strategies, as it is one of the most sophisticated biosystems due to the intricate mutualistic and competitive interactions. Based on the current results and available data, a heuristic model selection procedure is provided. This study paves the way to facilitate future bioprocess modeling.     

A survey on methods for modeling and analyzing integrated biological networks

Understanding how cellular systems build up integrated responses to their dynamically changing environment is one of the open questions in Systems Biology. Despite their intertwinement, signaling networks, gene regulation and metabolism have been frequently modeled independently in the context of well-defined subsystems. For this purpose, several mathematical formalisms have been developed according to the features of each particular network under study. Nonetheless, a deeper understanding of cellular behavior requires the integration of these various systems into a model capable of capturing how they operate as an ensemble. With the recent advances in the "omics" technologies, more data is becoming available and, thus, recent efforts have been driven toward this integrated modeling approach. We herein review and discuss methodological frameworks currently available for modeling and analyzing integrated biological networks, in particular metabolic, gene regulatory and signaling networks. These include network-based methods and Chemical Organization Theory, Flux-Balance Analysis and its extensions, logical discrete modeling, Petri Nets, traditional kinetic modeling, Hybrid Systems and stochastic models. Comparisons are also established regarding data requirements, scalability with network size and computational burden. The methods are illustrated with successful case studies in large-scale genome models and in particular subsystems of various organisms.     

From Enzyme Kinetics to Metabolic Network Modeling – Visualization Tool for Enhanced Kinetic Analysis of Biochemical Network Models

Model‐based analysis of enzyme kinetics allows the determination of optimal conditions for their use in biocatalysis. For biotransformations or fermentative approaches the modeling of metabolic pathways or complex metabolic networks is necessary to obtain model‐based predictions of steps which limit product formation within the network. To set up adequate kinetic models, relevant mechanistic information about enzyme properties is required and can be taken from in vitro studies with isolated enzymes or from in vivo investigations using stimulus‐response experiments which provide a lot of kinetic information about the metabolic network. But with increasing number of reaction steps and regulatory interdependencies in the network structure the amount of simulation data dramatically increases and the simulation results from the dynamic models become difficult to analyze and interpret. Demonstrated for an Escherichia coli model of the central carbon metabolism, methods for visualization and animation of simulation data were applied and extended to facilitate model analysis and biological interpretation. The dynamic metabolite pool and metabolic flux changes were visualized simultaneously by a software tool. In addition, a new quantification method for enzyme activation/inhibition was proposed, and this information was implemented in the metabolic visualization.     

Modeling changes in biomass composition during microwave‐based alkali pretreatment of switchgrass

This study used two different approaches to model changes in biomass composition during microwave‐based pretreatment of switchgrass: kinetic modeling using a time‐dependent rate coefficient, and a Mamdani‐type fuzzy inference system. In both modeling approaches, the dielectric loss tangent of the alkali reagent and pretreatment time were used as predictors for changes in amounts of lignin, cellulose, and xylan during the pretreatment. Training and testing data sets for development and validation of the models were obtained from pretreatment experiments conducted using 1–3% w/v NaOH (sodium hydroxide) and pretreatment times ranging from 5 to 20 min. The kinetic modeling approach for lignin and xylan gave comparable results for training and testing data sets, and the differences between the predictions and experimental values were within 2%. The kinetic modeling approach for cellulose was not as effective, and the differences were within 5–7%. The time‐dependent rate coefficients of the kinetic models estimated from experimental data were consistent with the heterogeneity of individual biomass components. The Mamdani‐type fuzzy inference was shown to be an effective approach to model the pretreatment process and yielded predictions with less than 2% deviation from the experimental values for lignin and with less than 3% deviation from the experimental values for cellulose and xylan. The entropies of the fuzzy outputs from the Mamdani‐type fuzzy inference system were calculated to quantify the uncertainty associated with the predictions. Results indicate that there is no significant difference between the entropies associated with the predictions for lignin, cellulose, and xylan. It is anticipated that these models could be used in process simulations of bioethanol production from lignocellulosic materials. Biotechnol. Bioeng. 2010;105: 88–97. © 2009 Wiley Periodicals, Inc.     

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.     

A kinetic model of Escherichia coli core metabolism satisfying multiple sets of mutant flux data

In contrast to stoichiometric-based models, the development of large-scale kinetic models of metabolism has been hindered by the challenge of identifying kinetic parameter values and kinetic rate laws applicable to a wide range of environmental and/or genetic perturbations. The recently introduced ensemble modeling (EM) procedure provides a promising remedy to address these challenges by decomposing metabolic reactions into elementary reaction steps and incorporating all phenotypic observations, upon perturbation, in its model parameterization scheme. Here, we present a kinetic model of Escherichia coli core metabolism that satisfies the fluxomic data for wild-type and seven mutant strains by making use of the EM concepts. This model encompasses 138 reactions, 93 metabolites and 60 substrate-level regulatory interactions accounting for glycolysis/gluconeogenesis, pentose phosphate pathway, TCA cycle, major pyruvate metabolism, anaplerotic reactions and a number of reactions in other parts of the metabolism. Parameterization is performed using a formal optimization approach that minimizes the discrepancies between model predictions and flux measurements. The predicted fluxes by the model are within the uncertainty range of experimental flux data for 78% of the reactions (with measured fluxes) for both the wild-type and seven mutant strains. The remaining flux predictions are mostly within three standard deviations of reported ranges. Converting the EM-based parameters into a Michaelis–Menten equivalent formalism revealed that 35% of K_m and 77% of k_cat parameters are within uncertainty range of the literature-reported values. The predicted metabolite concentrations by the model are also within uncertainty ranges of metabolomic data for 68% of the metabolites. A leave-one-out cross-validation test to evaluate the flux prediction performance of the model showed that metabolic fluxes for the mutants located in the proximity of mutations used for training the model can be predicted more accurately. The constructed model and the parameterization procedure presented in this study pave the way for the construction of larger-scale kinetic models with more narrowly distributed parameter values as new metabolomic/fluxomic data sets are becoming available for E. coli and other organisms.     

Predicting metabolic biomarkers of human inborn errors of metabolism

Early diagnosis of inborn errors of metabolism is commonly performed through biofluid metabolomics, which detects specific metabolic biomarkers whose concentration is altered due to genomic mutations. The identification of new biomarkers is of major importance to biomedical research and is usually performed through data mining of metabolomic data. After the recent publication of the genome‐scale network model of human metabolism, we present a novel computational approach for systematically predicting metabolic biomarkers in stochiometric metabolic models. Applying the method to predict biomarkers for disruptions of red‐blood cell metabolism demonstrates a marked correlation with altered metabolic concentrations inferred through kinetic model simulations. Applying the method to the genome‐scale human model reveals a set of 233 metabolites whose concentration is predicted to be either elevated or reduced as a result of 176 possible dysfunctional enzymes. The method's predictions are shown to significantly correlate with known disease biomarkers and to predict many novel potential biomarkers. Using this method to prioritize metabolite measurement experiments to identify new biomarkers can provide an order of a 10‐fold increase in biomarker detection performance.     

Thermodynamic Constraints in Kinetic Modeling: Thermodynamic‐Kinetic Modeling in Comparison to Other Approaches

Kinetic models of reaction networks may easily violate the laws of thermodynamics and the principle of detailed balance. In large network models, the constraints that are imposed by these laws are particularly difficult to address. This hinders modeling of biochemical reaction networks. Thermodynamic‐kinetic modeling is a method that provides a thermodynamically sound and formally appealing way for deriving dynamic model equations of reaction systems. State variables of this approach are thermokinetic potentials that describe the ability of compounds to drive a reaction. A compound has a parameter called capacity, which is the ratio of its concentration and thermokinetic potential. A reaction is described by its resistance which is the ratio of the thermokinetic driving force and flux. In these aspects, the formalism is similar to the modeling formalism for electrical networks and an analogous graphical representation is possible. The thermodynamic‐kinetic modeling formalism is equivalent to the traditional kinetic modeling formalism with the exception that it is not possible to build thermodynamically infeasible models. Here, the thermodynamic‐kinetic modeling formalism is reviewed, compared to other approaches, and some of its advantages are worked out. In contrast to other approaches, thermodynamic‐kinetic modeling does not rely on an explicit enumeration of stoichiometric cycles. It is capable of describing rate laws far from equilibrium. Further, the parameterization by capacities and resistances is particularly intuitive and powerful.     

Strategies for dealing with incomplete information in the modeling of molecular interaction networks

Modelers of molecular interaction networks encounter the paradoxical situation that while large amounts of data are available, these are often insufficient for the formulation and analysis of mathematical models describing the network dynamics. In particular, information on the reaction mechanisms and numerical values of kinetic parameters are usually not available for all but a few well-studied model systems. In this article we review two strategies that have been proposed for dealing with incomplete information in the study of molecular interaction networks: parameter sensitivity analysis and model simplification. These strategies are based on the biologically justified intuition that essential properties of the system dynamics are robust against moderate changes in the value of kinetic parameters or even in the rate laws describing the interactions. Although advanced measurement techniques can be expected to relieve the problem of incomplete information to some extent, the strategies discussed in this article will retain their interest as tools providing an initial characterization of essential properties of the network dynamics.     

A robust methodology for kinetic model parameter estimation for biocatalytic reactions

Effective estimation of parameters in biocatalytic reaction kinetic expressions are very important when building process models to enable evaluation of process technology options and alternative biocatalysts. The kinetic models used to describe enzyme‐catalyzed reactions generally include several parameters, which are strongly correlated with each other. State‐of‐the‐art methodologies such as nonlinear regression (using progress curves) or graphical analysis (using initial rate data, for example, the Lineweaver‐Burke plot, Hanes plot or Dixon plot) often incorporate errors in the estimates and rarely lead to globally optimized parameter values. In this article, a robust methodology to estimate parameters for biocatalytic reaction kinetic expressions is proposed. The methodology determines the parameters in a systematic manner by exploiting the best features of several of the current approaches. The parameter estimation problem is decomposed into five hierarchical steps, where the solution of each of the steps becomes the input for the subsequent step to achieve the final model with the corresponding regressed parameters. The model is further used for validating its performance and determining the correlation of the parameters. The final model with the fitted parameters is able to describe both initial rate and dynamic experiments. Application of the methodology is illustrated with a case study using the ω‐transaminase catalyzed synthesis of 1‐phenylethylamine from acetophenone and 2‐propylamine. © 2012 American Institute of Chemical Engineers Biotechnol. Prog., 2012