Dynamic flux balance analysis of diauxic growth in Escherichia coli

A feed-forward loop guarantees robust behavior in Escherichia coli carbohydrate uptake

MOTIVATION

In Escherichia coli, the phosphoenolpyruvate: carbohydrate phosphotransferase system acts like a sensory element which is able to measure the flux through glycolysis. Since the output of the sensor, the phosphorylated form of protein EIIA, is connected to the activity of the global transcription factor Crp, the kinetic and structural properties of the system are important for the understanding of the overall cellular behavior.

RESULTS

A family of mathematical models is presented, varying with respect to their degree of complexity (number of reactions that are taken into account, number of parameters) that show a structurally and quantitatively robust behavior. The models describe a set of experimental data that relates the output of the sensor to the specific growth rate. A central element that is responsible for the structural robustness is a feed-forward loop in the glycolysis, namely the activation of the pyruvate kinase reaction by a metabolite of the upper part of the glycolysis. The robustness is shown for variations of the measured data as well as for variations of the parameters.

AVAILABILITY

MATLAB files for model simulations are available on http://www.mpi-magdeburg.mpg.de/people/kre/robust/ A short description of the files provided on this site can be found in the Supporting information.

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

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

A procedure for the estimation over time of metabolic fluxes in scenarios where measurements are uncertain and/or insufficient

BACKGROUND

An indirect approach is usually used to estimate the metabolic fluxes of an organism: couple the available measurements with known biological constraints (e.g. stoichiometry). Typically this estimation is done under a static point of view. Therefore, the fluxes so obtained are only valid while the environmental conditions and the cell state remain stable. However, estimating the evolution over time of the metabolic fluxes is valuable to investigate the dynamic behaviour of an organism and also to monitor industrial processes. Although Metabolic Flux Analysis can be successively applied with this aim, this approach has two drawbacks: i) sometimes it cannot be used because there is a lack of measurable fluxes, and ii) the uncertainty of experimental measurements cannot be considered. The Flux Balance Analysis could be used instead, but the assumption of optimal behaviour of the organism brings other difficulties.

RESULTS

We propose a procedure to estimate the evolution of the metabolic fluxes that is structured as follows: 1) measure the concentrations of extracellular species and biomass, 2) convert this data to measured fluxes and 3) estimate the non-measured fluxes using the Flux Spectrum Approach, a variant of Metabolic Flux Analysis that overcomes the difficulties mentioned above without assuming optimal behaviour. We apply the procedure to a real problem taken from the literature: estimate the metabolic fluxes during a cultivation of CHO cells in batch mode. We show that it provides a reliable and rich estimation of the non-measured fluxes, thanks to considering measurements uncertainty and reversibility constraints. We also demonstrate that this procedure can estimate the non-measured fluxes even when there is a lack of measurable species. In addition, it offers a new method to deal with inconsistency.

CONCLUSION

This work introduces a procedure to estimate time-varying metabolic fluxes that copes with the insufficiency of measured species and with its intrinsic uncertainty. The procedure can be used as an off-line analysis of previously collected data, providing an insight into the dynamic behaviour of the organism. It can be also profitable to the on-line monitoring of a running process, mitigating the traditional lack of reliable on-line sensors in industrial environments.

Investigation of metabolic objectives in cultured hepatocytes

Using optimization based methods to predict fluxes in metabolic flux balance models has been a successful approach for some microorganisms, enabling construction of in silico models and even inference of some regulatory motifs. However, this success has not been translated to mammalian cells. The lack of knowledge about metabolic objectives in mammalian cells is a major obstacle that prevents utilization of various metabolic engineering tools and methods for tissue engineering and biomedical purposes. In this work, we investigate and identify possible metabolic objectives for hepatocytes cultured in vitro. To achieve this goal, we present a special data-mining procedure for identifying metabolic objective functions in mammalian cells. This multi-level optimization based algorithm enables identifying the major fluxes in the metabolic objective from MFA data in the absence of information about critical active constraints of the system. Further, once the objective is determined, active flux constraints can also be identified and analyzed. This information can be potentially used in a predictive manner to improve cell culture results or clinical metabolic outcomes. As a result of the application of this method, it was found that in vitro cultured hepatocytes maximize oxygen uptake, coupling of urea and TCA cycles, and synthesis of serine and urea. Selection of these fluxes as the metabolic objective enables accurate prediction of the flux distribution in the system given a limited amount of flux data; thus presenting a workable in silico model for cultured hepatocytes. It is observed that an overall homeostasis picture is also emergent in the findings.

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

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

Optimal design of metabolic flux analysis experiments for anchorage-dependent mammalian cells using a cellular automaton model

Metabolic flux analysis (MFA) is widely used to quantify metabolic pathway activity. Typical applications involve isotopically labeled substrates, which require both metabolic and isotopic steady states for simplified data analysis. For bacterial systems, these steady states are readily achieved in chemostat cultures. However, mammalian cells are often anchorage dependent and experiments are typically conducted in batch or fed-batch systems, such as tissue culture dishes or microcarrier-containing bioreactors. Surface adherence may cause deviations from exponential growth, resulting in metabolically heterogeneous populations and a varying number of cellular "nearest neighbors" that may affect the observed metabolism. Here, we discuss different growth models suitable for deconvoluting these effects and their application to the design and optimization of MFA experiments employing surface-adherent mammalian cells. We describe a stochastic two-dimensional (2D) cellular automaton model, with empirical descriptions of cell number and non-growing cell fraction, suitable for easy application to most anchorage-dependent mammalian cell cultures. Model utility was verified by studying the impact of contact inhibition on the growth rate, specific extracellular flux rates, and isotopic labeling in lactate for MCF7 cells, a commonly studied breast cancer cell line. The model successfully defined the time over which exponential growth and a metabolically homogeneous growing cell population could be assumed. The cellular automaton model developed is shown to be a useful tool in designing optimal MFA experiments.

Hybrid semi-parametric mathematical systems: bridging the gap between systems biology and process engineering

Systems biology is an integrative science that aims at the global characterization of biological systems. Huge amounts of data regarding gene expression, proteins activity and metabolite concentrations are collected by designing systematic genetic or environmental perturbations. Then the challenge is to integrate such data in a global model in order to provide a global picture of the cell. The analysis of these data is largely dominated by nonparametric modelling tools. In contrast, classical bioprocess engineering has been primarily founded on first principles models, but it has systematically overlooked the details of the embedded biological system. The full complexity of biological systems is currently assumed by systems biology and this knowledge can now be taken by engineers to decide how to optimally design and operate their processes. This paper discusses possible methodologies for the integration of systems biology and bioprocess engineering with emphasis on applications involving animal cell cultures. At the mathematical systems level, the discussion is focused on hybrid semi-parametric systems as a way to bridge systems biology and bioprocess engineering.

Enhanced bacterial protein expression during auto-induction obtained by alteration of lac repressor dosage and medium composition

The auto-induction method of protein expression in E. coli is based on diauxic growth resulting from dynamic function of lac operon regulatory elements (lacO and LacI) in mixtures of glucose, glycerol, and lactose. The results show that successful execution of auto-induction is strongly dependent on the plasmid promoter and repressor construction, on the oxygenation state of the culture, and on the composition of the auto-induction medium. Thus expression hosts expressing high levels of LacI during aerobic growth exhibit reduced ability to effectively complete the auto-induction process. Manipulation of the promoter to decrease the expression of LacI altered the preference for lactose consumption in a manner that led to increased protein expression and partially relieved the sensitivity of the auto-induction process to the oxygenation state of the culture. Factorial design methods were used to optimize the chemically defined growth medium used for expression of two model proteins, Photinus luciferase and enhanced green fluorescent protein, including variations for production of both unlabeled and selenomethionine-labeled samples. The optimization included studies of the expression from T7 and T7-lacI promoter plasmids and from T5 phage promoter plasmids expressing two levels of LacI. Upon the basis of the analysis of over 500 independent expression results, combinations of optimized expression media and expression plasmids that gave protein yields of greater than 1000 mug/mL of expression culture were identified.

Thematic review series: Systems Biology Approaches to Metabolic and Cardiovascular Disorders. Network perspectives of cardiovascular metabolism

In this review, we examine cardiovascular metabolism from three different, but highly complementary, perspectives. First, from the abstract perspective of a metabolite network, composed of nodes and links. We present fundamental concepts in network theory, including emergence, to illustrate how nature has designed metabolism with a hierarchal modular scale-free topology to provide a robust system of energy delivery. Second, from the physical perspective of a modular spatially compartmentalized network. We review evidence that cardiovascular metabolism is functionally compartmentalized, such that oxidative phosphorylation, glycolysis, and glycogenolysis preferentially channel ATP to ATPases in different cellular compartments, using creatine kinase and adenylate kinase to maximize efficient energy delivery. Third, from the dynamics perspective, as a network of dynamically interactive metabolic modules capable of self-oscillation. Whereas normally, cardiac metabolism exists in a regime in which excitation-metabolism coupling closely matches energy supply and demand, we describe how under stressful conditions, the network can be pushed into a qualitatively new dynamic regime, manifested as cell-wide oscillations in ATP levels, in which the coordination between energy supply and demand is lost. We speculate how this state of "metabolic fibrillation" leads to cell death if not corrected and discuss the implications for cardioprotection.

Systems interface biology

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

Engineering challenges of BioNEMS: the integration of microfluidics, micro- and nanodevices, models and external control for systems biology

Systems biology, i.e. quantitative, postgenomic, postproteomic, dynamic, multiscale physiology, addresses in an integrative, quantitative manner the shockwave of genetic and proteomic information using computer models that may eventually have 10(6) dynamic variables with non-linear interactions. Historically, single biological measurements are made over minutes, suggesting the challenge of specifying 10(6) model parameters. Except for fluorescence and micro-electrode recordings, most cellular measurements have inadequate bandwidth to discern the time course of critical intracellular biochemical events. Micro-array expression profiles of thousands of genes cannot determine quantitative dynamic cellular signalling and metabolic variables. Major gaps must be bridged between the computational vision and experimental reality. The analysis of cellular signalling dynamics and control requires, first, micro- and nano-instruments that measure simultaneously multiple extracellular and intracellular variables with sufficient bandwidth; secondly, the ability to open existing internal control and signalling loops; thirdly, external BioMEMS micro-actuators that provide high bandwidth feedback and externally addressable intracellular nano-actuators; and, fourthly, real-time, closed-loop, single-cell control algorithms. The unravelling of the nested and coupled nature of cellular control loops requires simultaneous recording of multiple single-cell signatures. Externally controlled nano-actuators, needed to effect changes in the biochemical, mechanical and electrical environment both outside and inside the cell, will provide a major impetus for nanoscience.

Bacterial gene regulation in diauxic and non-diauxic growth

When bacteria are grown in a batch culture containing a mixture of two growth-limiting substrates, they exhibit a rich spectrum of substrate consumption patterns including diauxic growth, simultaneous consumption, and bistable growth. In previous work, we showed that a minimal model accounting only for enzyme induction and dilution captures all the substrate consumption patterns [Narang, A., 1998a. The dynamical analogy between microbial growth on mixtures of substrates and population growth of competing species. Biotechnol. Bioeng. 59, 116-121, Narang, A., 2006. Comparitive analysis of some models of gene regulation in mixed-substrate microbial growth, J. Theor. Biol. 242, 489-501]. In this work, we construct the bifurcation diagram of the minimal model, which shows the substrate consumption pattern at any given set of parameter values. The bifurcation diagram explains several general properties of mixed-substrate growth. (1) In almost all the cases of diauxic growth, the "preferred" substrate is the one that, by itself, supports a higher specific growth rate. In the literature, this property is often attributed to the optimality of regulatory mechanisms. Here, we show that the minimal model, which accounts for induction and growth only, displays the property under fairly general conditions. This suggests that the higher growth rate of the preferred substrate is an intrinsic property of the induction and dilution kinetics. It can be explained mechanistically without appealing to optimality principles. (2) The model explains the phenotypes of various mutants containing lesions in the regions encoding for the operator, repressor, and peripheral enzymes. A particularly striking phenotype is the "reversal of the diauxie" in which the wild-type and mutant strains consume the very same two substrates in opposite order. This phenotype is difficult to explain in terms of molecular mechanisms, such as inducer exclusion or CAP activation, but it turns out to be a natural consequence of the model. We show furthermore that the model is robust. The key property of the model, namely, the competitive dynamics of the enzymes, is preserved even if the model is modified to account for various regulatory mechanisms. Finally, the model has important implications for the problem of size regulation in development. It suggests that protein dilution may be the mechanism coupling patterning and growth.

Dynamic analysis of optimality in myocardial energy metabolism under normal and ischemic conditions

To better understand the dynamic regulation of optimality in metabolic networks under perturbed conditions, we reconstruct the energetic-metabolic network in mammalian myocardia using dynamic flux balance analysis (DFBA). Additionally, we modified the optimal objective from the maximization of ATP production to the minimal fluctuation of the profile of metabolite concentration under ischemic conditions, extending the hypothesis of original minimization of metabolic adjustment to create a composite modeling approach called M-DFBA. The simulation results are more consistent with experimental data than are those of the DFBA model, particularly the retentive predominant contribution of fatty acid to oxidative ATP synthesis, the exact mechanism of which has not been elucidated and seems to be unpredictable by the DFBA model. These results suggest that the systemic states of metabolic networks do not always remain optimal, but may become suboptimal when a transient perturbation occurs. This finding supports the relevance of our hypothesis and could contribute to the further exploration of the underlying mechanism of dynamic regulation in metabolic networks.

Hybrid dynamic/static method for large-scale simulation of metabolism

Background

Many computer studies have employed either dynamic simulation or metabolic flux analysis (MFA) to predict the behaviour of biochemical pathways. Dynamic simulation determines the time evolution of pathway properties in response to environmental changes, whereas MFA provides only a snapshot of pathway properties within a particular set of environmental conditions. However, owing to the large amount of kinetic data required for dynamic simulation, MFA, which requires less information, has been used to manipulate large-scale pathways to determine metabolic outcomes.

Results

Here we describe a simulation method based on cooperation between kinetics-based dynamic models and MFA-based static models. This hybrid method enables quasi-dynamic simulations of large-scale metabolic pathways, while drastically reducing the number of kinetics assays needed for dynamic simulations. The dynamic behaviour of metabolic pathways predicted by our method is almost identical to that determined by dynamic kinetic simulation.

Conclusion

The discrepancies between the dynamic and the hybrid models were sufficiently small to prove that an MFA-based static module is capable of performing dynamic simulations as accurately as kinetic models. Our hybrid method reduces the number of biochemical experiments required for dynamic models of large-scale metabolic pathways by replacing suitable enzyme reactions with a static module.

Iterative approach to model identification of biological networks

BACKGROUND

Recent advances in molecular biology techniques provide an opportunity for developing detailed mathematical models of biological processes. An iterative scheme is introduced for model identification using available system knowledge and experimental measurements.

RESULTS

The scheme includes a state regulator algorithm that provides estimates of all system unknowns (concentrations of the system components and the reaction rates of their inter-conversion). The full system information is used for estimation of the model parameters. An optimal experiment design using the parameter identifiability and D-optimality criteria is formulated to provide "rich" experimental data for maximizing the accuracy of the parameter estimates in subsequent iterations. The importance of model identifiability tests for optimal measurement selection is also considered. The iterative scheme is tested on a model for the caspase function in apoptosis where it is demonstrated that model accuracy improves with each iteration. Optimal experiment design was determined to be critical for model identification.

CONCLUSION

The proposed algorithm has general application to modeling a wide range of cellular processes, which include gene regulation networks, signal transduction and metabolic networks.

Computational design of reduced metabolic networks

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

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

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

Use of genome-scale microbial models for metabolic engineering

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

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

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

The effects of alternate optimal solutions in constraint-based genome-scale metabolic models

Genome-scale constraint-based models of several organisms have now been constructed and are being used for model driven research. A key issue that may arise in the use of such models is the existence of alternate optimal solutions wherein the same maximal objective (e.g., growth rate) can be achieved through different flux distributions. Herein, we investigate the effects that alternate optimal solutions may have on the predicted range of flux values calculated using currently practiced linear (LP) and quadratic programming (QP) methods. An efficient LP-based strategy is described to calculate the range of flux variability that can be present in order to achieve optimal as well as suboptimal objective states. Sample results are provided for growth predictions of E. coli using glucose, acetate, and lactate as carbon substrates. These results demonstrate the extent of flux variability to be highly dependent on environmental conditions and network composition. In addition we examined the impact of alternate optima for growth under gene knockout conditions as calculated using QP-based methods. It was observed that calculations using QP-based methods can show significant variation in growth rate if the flux variability among alternate optima is high. The underlying biological significance and general source of such flux variability is further investigated through the identification of redundancies in the network (equivalent reaction sets) that lead to alternate solutions. Collectively, these results illustrate the variability inherent in metabolic flux distributions and the possible implications of this heterogeneity for constraint-based modeling approaches. These methods also provide an efficient and robust method to calculate the range of flux distributions that can be derived from quantitative fermentation data.

Identifying constraints that govern cell behavior: a key to converting conceptual to computational models in biology?

Cells must abide by a number of constraints. The environmental constrains of cellular behavior and physicochemical limitations affect cellular processes. To regulate and adapt their functions, cells impose constraints on themselves. Enumerating, understanding, and applying these constraints leads to a constraints-based modeling formalism that has been helpful in converting conceptual models to computational models in biology. The continued success of the constraints-based approach depends upon identification and incorporation of new constraints to more accurately define cellular capabilities. This review considers constraints in terms of environmental, physicochemical, and self-imposed regulatory and evolutionary constraints with the purpose of refining current constraints-based models of cell phenotype.

Description and interpretation of adaptive evolution of Escherichia coli K-12 MG1655 by using a genome-scale in silico metabolic model

Genome-scale in silico metabolic networks of Escherichia coli have been reconstructed. By using a constraint-based in silico model of a reconstructed network, the range of phenotypes exhibited by E. coli under different growth conditions can be computed, and optimal growth phenotypes can be predicted. We hypothesized that the end point of adaptive evolution of E. coli could be accurately described a priori by our in silico model since adaptive evolution should lead to an optimal phenotype. Adaptive evolution of E. coli during prolonged exponential growth was performed with M9 minimal medium supplemented with 2 g of alpha-ketoglutarate per liter, 2 g of lactate per liter, or 2 g of pyruvate per liter at both 30 and 37 degrees C, which produced seven distinct strains. The growth rates, substrate uptake rates, oxygen uptake rates, by-product secretion patterns, and growth rates on alternative substrates were measured for each strain as a function of evolutionary time. Three major conclusions were drawn from the experimental results. First, adaptive evolution leads to a phenotype characterized by maximized growth rates that may not correspond to the highest biomass yield. Second, metabolic phenotypes resulting from adaptive evolution can be described and predicted computationally. Third, adaptive evolution on a single substrate leads to changes in growth characteristics on other substrates that could signify parallel or opposing growth objectives. Together, the results show that genome-scale in silico metabolic models can describe the end point of adaptive evolution a priori and can be used to gain insight into the adaptive evolutionary process for E. coli.

Advances in flux balance analysis

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

Bioreactor state estimation and control

Advanced control methods have been effectively employed for industrial chemical processing for decades. Only recently, however, have model-based strategies been implemented for biological processes. Some notable advances include the enhancement of metabolic flux models to describe the dynamic behavior observed in biochemical reactors. The combination of more than one type of model in a hybrid form was shown to perform well for bioprocess control applications.

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

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