Predictive Potential of Flux Balance Analysis of Saccharomyces cerevisiae Using as Optimization Function Combinations of Cell Compartmental Objectives

Background

The main objective of flux balance analysis (FBA) is to obtain quantitative predictions of metabolic fluxes of an organism, and it is necessary to use an appropriate objective function to guarantee a good estimation of those fluxes.

Methodology

In this study, the predictive performance of FBA was evaluated, using objective functions arising from the linear combination of different cellular objectives. This approach is most suitable for eukaryotic cells, owing to their multiplicity of cellular compartments. For this reason, Saccharomyces cerevisiae was used as model organism, and its metabolic network was represented using the genome-scale metabolic model iMM904. As the objective was to evaluate the predictive performance from the FBA using the kind of objective function previously described, substrate uptake and oxygen consumption were the only input data used for the FBA. Experimental information about microbial growth and exchange of metabolites with the environment was used to assess the quality of the predictions.

Conclusions

The quality of the predictions obtained with the FBA depends greatly on the knowledge of the oxygen uptake rate. For the most of studied classifications, the best predictions were obtained with “maximization of growth”, and with some combinations that include this objective. However, in the case of exponential growth with unknown oxygen exchange flux, the objective function “maximization of growth, plus minimization of NADH production in cytosol, plus minimization of NAD(P)H consumption in mitochondrion” gave much more accurate estimations of fluxes than the obtained with any other objective function explored in this study.     

Synergy between (13)C-metabolic flux analysis and flux balance analysis for understanding metabolic adaptation to anaerobiosis in E. coli

Genome-based Flux Balance Analysis (FBA) and steady-state isotopic-labeling-based Metabolic Flux Analysis (MFA) are complimentary approaches to predicting and measuring the operation and regulation of metabolic networks. Here, genome-derived models of Escherichia coli (E. coli) metabolism were used for FBA and 13C-MFA analyses of aerobic and anaerobic growths of wild-type E. coli (K-12 MG1655) cells. Validated MFA flux maps reveal that the fraction of maintenance ATP consumption in total ATP production is about 14% higher under anaerobic (51.1%) than aerobic conditions (37.2%). FBA revealed that an increased ATP utilization is consumed by ATP synthase to secrete protons from fermentation. The TCA cycle is shown to be incomplete in aerobically growing cells and submaximal growth is due to limited oxidative phosphorylation. An FBA was successful in predicting product secretion rates in aerobic culture if both glucose and oxygen uptake measurement were constrained, but the most-frequently predicted values of internal fluxes yielded from sampling the feasible space differ substantially from MFA-derived fluxes.     

Prediction of dynamic behavior of mutant strains from limited wild-type data

Metabolic engineering is the field of introducing genetic changes in organisms so as to modify their function towards synthesizing new products of high impact to society. However, engineered cells frequently have impaired growth rates thus seriously limiting the rate at which such products are made. The problem is attributable to inadequate understanding of how a metabolic network functions in a dynamic sense. Predictions of mutant strain behavior in the past have been based on steady state theories such as flux balance analysis (FBA), minimization of metabolic adjustment (MOMA), and regulatory on/off minimization (ROOM). Such predictions are restricted to product yields and cannot address productivity, which is of focal interest to applications. We demonstrate that our framework ( [Song and Ramkrishna, 2010] and [Song and Ramkrishna, 2011]), based on a “cybernetic” view of metabolic systems, makes predictions of the dynamic behavior of mutant strains of Escherichia coli from a limited amount of data obtained from the wild-type. Dynamic frameworks must necessarily address the issue of metabolic regulation, which the cybernetic approach does by postulating that metabolism is an optimal dynamic response of the organism to the environment in driving reactions towards ensuring survival. The predictions made in this paper are without parallel in the literature and lay the foundation for rational metabolic engineering.     

Comparison and analysis of objective functions in flux balance analysis

Flux balance analysis (FBA) is currently one of the most important and used techniques for estimation of metabolic reaction rates (fluxes). This mathematical approach utilizes an optimization criterion in order to select a distribution of fluxes from the feasible space delimited by the metabolic reactions and some restrictions imposed over them, assuming that cellular metabolism is in steady state. Therefore, the obtained flux distribution depends on the specific objective function used. Multiple studies have been aimed to compare distinct objective functions at given conditions, in order to determine which of those functions produces values of fluxes closer to real data when used as objective in the FBA; in other words, what is the best objective function for modeling cell metabolism at a determined environmental condition. However, these comparative studies have been designed in very dissimilar ways, and in general, several factors that can change the ideal objective function in a cellular condition have not been adequately considered. Additionally, most of them have used only one dataset for representing one condition of cell growth, and different measuring techniques have been used. For these reasons, a rigorous study on the effect of factors such as the quantity of used data, the number and type of fluxes utilized as input data, and the selected classification of growth conditions, are required in order to obtain useful conclusions for these comparative studies, allowing limiting clearly the application range on any of those results. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 30:985–991, 2014     

Error propagation in constraint-based modeling of Chinese hamster ovary cells

Chinese hamster ovary (CHO) cells are the most popular mammalian cell factories for the production of glycosylated biopharmaceuticals. To further increase titer and productivity and ensure product quality, rational system-level engineering strategies based on constraint-based metabolic modeling, such as flux balance analysis (FBA), have gained strong interest. However, the quality of FBA predictions depends on the accuracy of the experimental input data, especially on the exchange rates of extracellular metabolites. Yet, it is not standard practice to devote sufficient attention to the accurate determination of these rates. In this work, we investigated to what degree the sampling frequency during a batch culture and the measurement errors of metabolite concentrations influence the accuracy of the calculated exchange rates and further, how this error then propagates into FBA predictions of growth rates. We determined that accurate measurements of essential amino acids with low uptake rates are crucial for the accuracy of FBA predictions, followed by a sufficient number of analyzed time points. We observed that the measured difference in growth rates of two cell lines can only be reliably predicted when both high measurement accuracy and sampling frequency are ensured.     

Simulating Serial-Target Antibacterial Drug Synergies Using Flux Balance Analysis

Flux balance analysis (FBA) is an increasingly useful approach for modeling the behavior of metabolic systems. However, standard FBA modeling of genetic knockouts cannot predict drug combination synergies observed between serial metabolic targets, even though such synergies give rise to some of the most widely used antibiotic treatments. Here we extend FBA modeling to simulate responses to chemical inhibitors at varying concentrations, by diverting enzymatic flux to a waste reaction. This flux diversion yields very similar qualitative predictions to prior methods for single target activity. However, we find very different predictions for combinations, where flux diversion, which mimics the kinetics of competitive metabolic inhibitors, can explain serial target synergies between metabolic enzyme inhibitors that we confirmed in Escherichia coli cultures. FBA flux diversion opens the possibility for more accurate genome-scale predictions of drug synergies, which can be used to suggest treatments for infections and other diseases.     

Understanding the Adaptive Growth Strategy of Lactobacillus plantarum by In Silico Optimisation

In the study of metabolic networks, optimization techniques are often used to predict flux distributions, and hence, metabolic phenotype. Flux balance analysis in particular has been successful in predicting metabolic phenotypes. However, an inherent limitation of a stoichiometric approach such as flux balance analysis is that it can predict only flux distributions that result in maximal yields. Hence, previous attempts to use FBA to predict metabolic fluxes in Lactobacillus plantarum failed, as this lactic acid bacterium produces lactate, even under glucose-limited chemostat conditions, where FBA predicted mixed acid fermentation as an alternative pathway leading to a higher yield. In this study we tested, however, whether long-term adaptation on an unusual and poor carbon source (for this bacterium) would select for mutants with optimal biomass yields. We have therefore adapted Lactobacillus plantarum to grow well on glycerol as its main growth substrate. After prolonged serial dilutions, the growth yield and corresponding fluxes were compared to in silico predictions. Surprisingly, the organism still produced mainly lactate, which was corroborated by FBA to indeed be optimal. To understand these results, constraint-based elementary flux mode analysis was developed that predicted 3 out of 2669 possible flux modes to be optimal under the experimental conditions. These optimal pathways corresponded very closely to the experimentally observed fluxes and explained lactate formation as the result of competition for oxygen by the other flux modes. Hence, these results provide thorough understanding of adaptive evolution, allowing in silico predictions of the resulting flux states, provided that the selective growth conditions favor yield optimization as the winning strategy.     

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.     

Estimating Metabolic Fluxes Using a Maximum Network Flexibility Paradigm

MotivationGenome-scale metabolic networks can be modeled in a constraint-based fashion. Reaction stoichiometry combined with flux capacity constraints determine the space of allowable reaction rates. This space is often large and a central challenge in metabolic modeling is finding the biologically most relevant flux distributions. A widely used method is flux balance analysis (FBA), which optimizes a biologically relevant objective such as growth or ATP production. Although FBA has proven to be highly useful for predicting growth and byproduct secretion, it cannot predict the intracellular fluxes under all environmental conditions. Therefore, alternative strategies have been developed to select flux distributions that are in agreement with experimental “omics” data, or by incorporating experimental flux measurements. The latter, unfortunately can only be applied to a limited set of reactions and is currently not feasible at the genome-scale. On the other hand, it has been observed that micro-organisms favor a suboptimal growth rate, possibly in exchange for a more “flexible” metabolic network. Instead of dedicating the internal network state to an optimal growth rate in one condition, a suboptimal growth rate is used, that allows for an easier switch to other nutrient sources. A small decrease in growth rate is exchanged for a relatively large gain in metabolic capability to adapt to changing environmental conditions.ResultsHere, we propose Maximum Metabolic Flexibility (MMF) a computational method that utilizes this observation to find the most probable intracellular flux distributions. By mapping measured flux data from central metabolism to the genome-scale models of Escherichia coli and Saccharomyces cerevisiae we show that i) indeed, most of the measured fluxes agree with a high adaptability of the network, ii) this result can be used to further reduce the space of feasible solutions iii) this reduced space improves the quantitative predictions made by FBA and contains a significantly larger fraction of the measured fluxes compared to the flux space that was reduced by a uniform sampling approach and iv) MMF can be used to select reactions in the network that contribute most to the steady-state flux space. Constraining the selected reactions improves the quantitative predictions of FBA considerably more than adding an equal amount of flux constraints, selected using a more naïve approach. Our method can be applied to any cell type without requiring prior information.AvailabilityMMF is freely available as a MATLAB plugin at: http://cs.ru.nl/~wmegchel/mmf.     

Escher-FBA: a web application for interactive flux balance analysis

Background

Flux balance analysis (FBA) is a widely-used method for analyzing metabolic networks. However, most existing tools that implement FBA require downloading software and writing code. Furthermore, FBA generates predictions for metabolic networks with thousands of components, so meaningful changes in FBA solutions can be difficult to identify. These challenges make it difficult for beginners to learn how FBA works.

Results

To meet this need, we present Escher-FBA, a web application for interactive FBA simulations within a pathway visualization. Escher-FBA allows users to set flux bounds, knock out reactions, change objective functions, upload metabolic models, and generate high-quality figures without downloading software or writing code. We provide detailed instructions on how to use Escher-FBA to replicate several FBA simulations that generate real scientific hypotheses.

Conclusions

We designed Escher-FBA to be as intuitive as possible so that users can quickly and easily understand the core concepts of FBA. The web application can be accessed at https://sbrg.github.io/escher-fba.

     

Integrating flux balance analysis into kinetic models to decipher the dynamic metabolism of Shewanella oneidensis MR-1

Shewanella oneidensis MR-1 sequentially utilizes lactate and its waste products (pyruvate and acetate) during batch culture. To decipher MR-1 metabolism, we integrated genome-scale flux balance analysis (FBA) into a multiple-substrate Monod model to perform the dynamic flux balance analysis (dFBA). The dFBA employed a static optimization approach (SOA) by dividing the batch time into small intervals (i.e., ～400 mini-FBAs), then the Monod model provided time-dependent inflow/outflow fluxes to constrain the mini-FBAs to profile the pseudo-steady-state fluxes in each time interval. The mini-FBAs used a dual-objective function (a weighted combination of "maximizing growth rate" and "minimizing overall flux") to capture trade-offs between optimal growth and minimal enzyme usage. By fitting the experimental data, a bi-level optimization of dFBA revealed that the optimal weight in the dual-objective function was time-dependent: the objective function was constant in the early growth stage, while the functional weight of minimal enzyme usage increased significantly when lactate became scarce. The dFBA profiled biologically meaningful dynamic MR-1 metabolisms: 1. the oxidative TCA cycle fluxes increased initially and then decreased in the late growth stage; 2. fluxes in the pentose phosphate pathway and gluconeogenesis were stable in the exponential growth period; and 3. the glyoxylate shunt was up-regulated when acetate became the main carbon source for MR-1 growth.     

Effect of amino acid supplementation on titer and glycosylation distribution in hybridoma cell cultures—Systems biology‐based interpretation using genome‐scale metabolic flux balance model and multivariate data analysis

Genome‐scale flux balance analysis (FBA) is a powerful systems biology tool to characterize intracellular reaction fluxes during cell cultures. FBA estimates intracellular reaction rates by optimizing an objective function, subject to the constraints of a metabolic model and media uptake/excretion rates. A dynamic extension to FBA, dynamic flux balance analysis (DFBA), can calculate intracellular reaction fluxes as they change during cell cultures. In a previous study by Read et al. (2013), a series of informed amino acid supplementation experiments were performed on twelve parallel murine hybridoma cell cultures, and this data was leveraged for further analysis (Read et al., Biotechnol Prog. 2013;29:745–753). In order to understand the effects of media changes on the model murine hybridoma cell line, a systems biology approach is applied in the current study. Dynamic flux balance analysis was performed using a genome‐scale mouse metabolic model, and multivariate data analysis was used for interpretation. The calculated reaction fluxes were examined using partial least squares and partial least squares discriminant analysis. The results indicate media supplementation increases product yield because it raises nutrient levels extending the growth phase, and the increased cell density allows for greater culture performance. At the same time, the directed supplementation does not change the overall metabolism of the cells. This supports the conclusion that product quality, as measured by glycoform assays, remains unchanged because the metabolism remains in a similar state. Additionally, the DFBA shows that metabolic state varies more at the beginning of the culture but less by the middle of the growth phase, possibly due to stress on the cells during inoculation. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:1163–1173, 2016     

Dynamic metabolic engineering for increasing bioprocess productivity

Yield and productivity are critical for the economics and viability of a bioprocess. In metabolic engineering, the main objective is the increase of a target metabolite production through genetic engineering. However, genetic manipulations usually result in lower productivity due to growth impairment. Previously, it has been shown that the dynamic control of metabolic fluxes can increase the amount of product formed in an anaerobic batch fermentation of Escherichia coli. In order to apply this control strategy, the genetic toggle switch is used to manipulate key fluxes of the metabolic network. We have designed and analyzed an integrated computational model for the dynamic control of gene expression. This controller, when coupled to the metabolism of E. coli, resulted in increased bioprocess productivity.     

FASIMU: flexible software for flux-balance computation series in large metabolic networks

Background  

Flux-balance analysis based on linear optimization is widely used to compute metabolic fluxes in large metabolic networks and gains increasingly importance in network curation and structural analysis. Thus, a computational tool flexible enough to realize a wide variety of FBA algorithms and able to handle batch series of flux-balance optimizations is of great benefit.     

Dynamic metagenome-scale metabolic modeling of a yogurt bacterial community

Genome-scale metabolic models and flux balance analysis (FBA) have been extensively used for modeling and designing bacterial fermentation. However, FBA-based metabolic models that accurately simulate the dynamics of coculture are still rare, especially for lactic acid bacteria used in yogurt fermentation. To investigate metabolic interactions in yogurt starter culture of Streptococcus thermophilus and Lactobacillus delbrueckii subsp. bulgaricus, this study built a dynamic metagenome-scale metabolic model which integrated constrained proteome allocation. The accuracy of the model was evaluated by comparing predicted bacterial growth, consumption of lactose and production of lactic acid with reference experimental data. The model was then used to predict the impact of different initial bacterial inoculation ratios on acidification. The dynamic simulation demonstrated the mutual dependence of S. thermophilus and L. d. bulgaricus during the yogurt fermentation process. As the first dynamic metabolic model of the yogurt bacterial community, it provided a foundation for the computer-aided process design and control of the production of fermented dairy products.     

Metabolic reconstruction and modeling of nitrogen fixation in Rhizobium etli

Rhizobiaceas are bacteria that fix nitrogen during symbiosis with plants. This symbiotic relationship is crucial for the nitrogen cycle, and understanding symbiotic mechanisms is a scientific challenge with direct applications in agronomy and plant development. Rhizobium etli is a bacteria which provides legumes with ammonia (among other chemical compounds), thereby stimulating plant growth. A genome-scale approach, integrating the biochemical information available for R. etli, constitutes an important step toward understanding the symbiotic relationship and its possible improvement. In this work we present a genome-scale metabolic reconstruction (iOR363) for R. etli CFN42, which includes 387 metabolic and transport reactions across 26 metabolic pathways. This model was used to analyze the physiological capabilities of R. etli during stages of nitrogen fixation. To study the physiological capacities in silico, an objective function was formulated to simulate symbiotic nitrogen fixation. Flux balance analysis (FBA) was performed, and the predicted active metabolic pathways agreed qualitatively with experimental observations. In addition, predictions for the effects of gene deletions during nitrogen fixation in Rhizobia in silico also agreed with reported experimental data. Overall, we present some evidence supporting that FBA of the reconstructed metabolic network for R. etli provides results that are in agreement with physiological observations. Thus, as for other organisms, the reconstructed genome-scale metabolic network provides an important framework which allows us to compare model predictions with experimental measurements and eventually generate hypotheses on ways to improve nitrogen fixation.     

Capturing the essence of a metabolic network: A flux balance analysis approach

As genome-scale metabolic reconstructions emerge, tools to manage their size and complexity will be increasingly important. Flux balance analysis (FBA) is a constraint-based approach widely used to study the metabolic capabilities of cellular or subcellular systems. FBA problems are highly underdetermined and many different phenotypes can satisfy any set of constraints through which the metabolic system is represented.Two of the main concerns in FBA are exploring the space of solutions for a given metabolic network and finding a specific phenotype which is representative for a given task such as maximal growth rate. Here, we introduce a recursive algorithm suitable for overcoming both of these concerns. The method proposed is able to find the alternate optimal patterns of active reactions of an FBA problem and identify the minimal subnetwork able to perform a specific task as optimally as the whole.Our method represents an alternative to and an extension of other approaches conceived for exploring the space of solutions of an FBA problem. It may also be particularly helpful in defining a scaffold of reactions upon which to build up a dynamic model, when the important pathways of the system have not yet been well-defined.