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.     

What CHO is made of: Variations in the biomass composition of Chinese hamster ovary cell lines

BackgroundCell line-specific, genome-scale metabolic models enable rigorous and systematic in silico investigation of cellular metabolism. Such models have recently become available for Chinese hamster ovary (CHO) cells. However, a key ingredient, namely an experimentally validated biomass function that summarizes the cellular composition, was so far missing. Here, we close this gap by providing extensive experimental data on the biomass composition of 13 parental and producer CHO cell lines under various conditions.ResultsWe report total protein, lipid, DNA, RNA and carbohydrate content, cell dry mass, and detailed protein and lipid composition. Furthermore, we present meticulous data on exchange rates between cells and environment and provide detailed experimental protocols on how to determine all of the above. The biomass composition is converted into cell line- and condition-specific biomass functions for use in cell line-specific, genome-scale metabolic models of CHO. Finally, flux balance analysis (FBA) is used to demonstrate consistency between in silico predictions and experimental analysis.ConclusionsOur study reveals a strong variability of the total protein content and cell dry mass across cell lines. However, the relative amino acid composition is independent of the cell line and condition and thus needs not be explicitly measured for each new cell line. In contrast, the lipid composition is strongly influenced by the growth media and thus will have to be determined in each case. These cell line-specific variations in biomass composition have a small impact on growth rate predictions with FBA, as inaccuracies in the predictions are rather dominated by inaccuracies in the exchange rate spectra. Cell-specific biomass variations only become important if the experimental errors in the exchange rate spectra drop below twenty percent.     

Predicting Growth Conditions from Internal Metabolic Fluxes in an In-Silico Model of E. coli

A widely studied problem in systems biology is to predict bacterial phenotype from growth conditions, using mechanistic models such as flux balance analysis (FBA). However, the inverse prediction of growth conditions from phenotype is rarely considered. Here we develop a computational framework to carry out this inverse prediction on a computational model of bacterial metabolism. We use FBA to calculate bacterial phenotypes from growth conditions in E. coli, and then we assess how accurately we can predict the original growth conditions from the phenotypes. Prediction is carried out via regularized multinomial regression. Our analysis provides several important physiological and statistical insights. First, we show that by analyzing metabolic end products we can consistently predict growth conditions. Second, prediction is reliable even in the presence of small amounts of impurities. Third, flux through a relatively small number of reactions per growth source (∼10) is sufficient for accurate prediction. Fourth, combining the predictions from two separate models, one trained only on carbon sources and one only on nitrogen sources, performs better than models trained to perform joint prediction. Finally, that separate predictions perform better than a more sophisticated joint prediction scheme suggests that carbon and nitrogen utilization pathways, despite jointly affecting cellular growth, may be fairly decoupled in terms of their dependence on specific assortments of molecular precursors.     

Quantifying the propagation of parametric uncertainty on flux balance analysis

Flux balance analysis (FBA) and associated techniques operating on stoichiometric genome-scale metabolic models play a central role in quantifying metabolic flows and constraining feasible phenotypes. At the heart of these methods lie two important assumptions: (i) the biomass precursors and energy requirements neither change in response to growth conditions nor environmental/genetic perturbations, and (ii) metabolite production and consumption rates are equal at all times (i.e., steady-state). Despite the stringency of these two assumptions, FBA has been shown to be surprisingly robust at predicting cellular phenotypes. In this paper, we formally assess the impact of these two assumptions on FBA results by quantifying how uncertainty in biomass reaction coefficients, and departures from steady-state due to temporal fluctuations could propagate to FBA results. In the first case, conditional sampling of parameter space is required to re-weigh the biomass reaction so as the molecular weight remains equal to 1 g mmol⁻¹, and in the second case, metabolite (and elemental) pool conservation must be imposed under temporally varying conditions. Results confirm the importance of enforcing the aforementioned constraints and explain the robustness of FBA biomass yield predictions.     

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.     

The Ability of Flux Balance Analysis to Predict Evolution of Central Metabolism Scales with the Initial Distance to the Optimum

The most powerful genome-scale framework to model metabolism, flux balance analysis (FBA), is an evolutionary optimality model. It hypothesizes selection upon a proposed optimality criterion in order to predict the set of internal fluxes that would maximize fitness. Here we present a direct test of the optimality assumption underlying FBA by comparing the central metabolic fluxes predicted by multiple criteria to changes measurable by a ¹³C-labeling method for experimentally-evolved strains. We considered datasets for three Escherichia coli evolution experiments that varied in their length, consistency of environment, and initial optimality. For ten populations that were evolved for 50,000 generations in glucose minimal medium, we observed modest changes in relative fluxes that led to small, but significant decreases in optimality and increased the distance to the predicted optimal flux distribution. In contrast, seven populations evolved on the poor substrate lactate for 900 generations collectively became more optimal and had flux distributions that moved toward predictions. For three pairs of central metabolic knockouts evolved on glucose for 600–800 generations, there was a balance between cases where optimality and flux patterns moved toward or away from FBA predictions. Despite this variation in predictability of changes in central metabolism, two generalities emerged. First, improved growth largely derived from evolved increases in the rate of substrate use. Second, FBA predictions bore out well for the two experiments initiated with ancestors with relatively sub-optimal yield, whereas those begun already quite optimal tended to move somewhat away from predictions. These findings suggest that the tradeoff between rate and yield is surprisingly modest. The observed positive correlation between rate and yield when adaptation initiated further from the optimum resulted in the ability of FBA to use stoichiometric constraints to predict the evolution of metabolism despite selection for rate.     

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     

A mathematical model for cell separation technique of centrifugal elutriation

A mathematical model for the cell separation technique of centrifugal elutriation is developed. The model simulates both steady and non-steady-state operation of the elutriator. The model can be used to predict the required set of flow rates of elutriating liquid necessary to fractionate a cell culture, the required time of sampling before steady state is achieved, and the range of cell size/cell density combinations contained in any fraction. The model predictions were verified experimentally. Variations in cell density and cell size due to the suspending environment have a significant effect on the accuracy (although not the trends) of the model predictions. Quantification of these variations will lead to significantly more accurate model predictions. An enhanced separation method was developed using the model, to yield finer separation of a cell culture than previously possible. The use of the centrifugal elutriator may now be given a firm theoretical basis, with the quality of separation understood in terms of the basic theory of operation.     

Dynamic flux balance analysis of diauxic growth in Escherichia coli

Flux Balance Analysis (FBA) has been used in the past to analyze microbial metabolic networks. Typically, FBA is used to study the metabolic flux at a particular steady state of the system. However, there are many situations where the reprogramming of the metabolic network is important. Therefore, the dynamics of these metabolic networks have to be studied. In this paper, we have extended FBA to account for dynamics and present two different formulations for dynamic FBA. These two approaches were used in the analysis of diauxic growth in Escherichia coli. Dynamic FBA was used to simulate the batch growth of E. coli on glucose, and the predictions were found to qualitatively match experimental data. The dynamic FBA formalism was also used to study the sensitivity to the objective function. It was found that an instantaneous objective function resulted in better predictions than a terminal-type objective function. The constraints that govern the growth at different phases in the batch culture were also identified. Therefore, dynamic FBA provides a framework for analyzing the transience of metabolism due to metabolic reprogramming and for obtaining insights for the design of metabolic networks.     

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.     

Flux Imbalance Analysis and the Sensitivity of Cellular Growth to Changes in Metabolite Pools

Stoichiometric models of metabolism, such as flux balance analysis (FBA), are classically applied to predicting steady state rates - or fluxes - of metabolic reactions in genome-scale metabolic networks. Here we revisit the central assumption of FBA, i.e. that intracellular metabolites are at steady state, and show that deviations from flux balance (i.e. flux imbalances) are informative of some features of in vivo metabolite concentrations. Mathematically, the sensitivity of FBA to these flux imbalances is captured by a native feature of linear optimization, the dual problem, and its corresponding variables, known as shadow prices. First, using recently published data on chemostat growth of Saccharomyces cerevisae under different nutrient limitations, we show that shadow prices anticorrelate with experimentally measured degrees of growth limitation of intracellular metabolites. We next hypothesize that metabolites which are limiting for growth (and thus have very negative shadow price) cannot vary dramatically in an uncontrolled way, and must respond rapidly to perturbations. Using a collection of published datasets monitoring the time-dependent metabolomic response of Escherichia coli to carbon and nitrogen perturbations, we test this hypothesis and find that metabolites with negative shadow price indeed show lower temporal variation following a perturbation than metabolites with zero shadow price. Finally, we illustrate the broader applicability of flux imbalance analysis to other constraint-based methods. In particular, we explore the biological significance of shadow prices in a constraint-based method for integrating gene expression data with a stoichiometric model. In this case, shadow prices point to metabolites that should rise or drop in concentration in order to increase consistency between flux predictions and gene expression data. In general, these results suggest that the sensitivity of metabolic optima to violations of the steady state constraints carries biologically significant information on the processes that control intracellular metabolites in the cell.     

Scoring function accuracy for membrane protein structure prediction

We perform a systematic examination of the ability of several different high-resolution, atomic-detail scoring functions to discriminate native conformations of loops in membrane proteins from non-native but physically reasonable, or "decoy," conformations. Decoys constructed from changing a loop conformation while keeping the remainder of the protein fixed are a challenging test of energy function accuracy. Nevertheless, the best of the energy functions we examined recognized the native structure as lowest in energy around half the time, and consistently chose it as a low-energy structure. This suggests that the best of present energy functions, even without a representation of the lipid bilayer, are of sufficient accuracy to give reasonable confidence in predictions of membrane protein structure. We also constructed homology models for each structure, using other known structures in the same protein family as templates. Homology models were constructed using several scoring functions and modeling programs, but with a comparable sampling effort for each procedure. Our results indicate that the quality of sequence alignment is probably the most important factor in model accuracy for sequence identity from 20-40%; one can expect a reasonably accurate model for membrane proteins when sequence identity is greater than 30%, in agreement with previous studies. Most errors are localized in loop regions, which tend to be found outside the lipid bilayer. For the most discriminative energy functions, it appears that errors are most likely due to lack of sufficient sampling, although it should be stressed that present energy functions are still far from perfectly reliable.     

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.     

Genome-Scale Metabolic Network Validation of Shewanella oneidensis Using Transposon Insertion Frequency Analysis

Transposon mutagenesis, in combination with parallel sequencing, is becoming a powerful tool for en-masse mutant analysis. A probability generating function was used to explain observed miniHimar transposon insertion patterns, and gene essentiality calls were made by transposon insertion frequency analysis (TIFA). TIFA incorporated the observed genome and sequence motif bias of the miniHimar transposon. The gene essentiality calls were compared to: 1) previous genome-wide direct gene-essentiality assignments; and, 2) flux balance analysis (FBA) predictions from an existing genome-scale metabolic model of Shewanella oneidensis MR-1. A three-way comparison between FBA, TIFA, and the direct essentiality calls was made to validate the TIFA approach. The refinement in the interpretation of observed transposon insertions demonstrated that genes without insertions are not necessarily essential, and that genes that contain insertions are not always nonessential. The TIFA calls were in reasonable agreement with direct essentiality calls for S. oneidensis, but agreed more closely with E. coli essentiality calls for orthologs. The TIFA gene essentiality calls were in good agreement with the MR-1 FBA essentiality predictions, and the agreement between TIFA and FBA predictions was substantially better than between the FBA and the direct gene essentiality predictions.     

Increased activity of the non-regulated enzymes fructose-1,6-bisphosphate aldolase and triosephosphate isomerase in Anabaena sp. strain PCC 7120 increases photosynthetic yield

Non-regulated enzymes in the Calvin cycle are generally presumed to be less important for the regulation of photosynthetic yield. Here, to investigate the relationship between the activity of non-regulated enzymes and photosynthetic yield, two non-regulated enzymes in the Calvin cycle—a rice cytosolic fructose-1,6-bisphosphate aldolase (FBA) and a spinach chloroplast triosephosphate isomerase (TPI)—were cloned and co-expressed in cells of the cyanobacterium Anabaena sp. strain PCC 7120. The activity of FBA and TPI and the photosynthetic yield reflected by photosynthetic O₂ evolution and cell dry weight were measured and compared between wild-type and transgenic cells. Our results demonstrated that the activity of FBA and TPI were increased in transgenic cells relative to wild-type cells, and that activity was further increased in a transgenic strain harboring two sets of FBA-TPI tandem genes relative to cells containing one copy of the FBA-TPI tandem gene. The increased activity of FBA and TPI in Anabaena sp. strain PCC 7120 increased photosynthetic yield, with increased activity levels correlating closely with the degree of changes in photosynthetic yield. This implies that the photosynthetic yield is limited by the activity of the non-regulated enzymes FBA and TPI, and that the endogenous activity of non-regulated enzymes is not sufficient to increase photosynthetic yield. We discuss the various roles of FBA and TPI, and regulated and non-regulated enzymes, in modulating photosynthetic yield. W. Ma and L. Wei contributed equally to this work.     

Accuracy and sensitivity of residual DNA detection by QPCR is not predicted by target copy number

A major issue in the use of mammalian cell culture in biopharmaceutical manufacturing is the removal of process related impurities, such as residual host cell DNA, during the product purification process. To ensure that sufficient DNA removal is achieved during purification, it is essential to have an accurate and sensitive assay for host cell DNA. The quantitative polymerase chain reaction (QPCR) is widely used for this purpose; however, the extent to which the choice of QPCR gene target can have an impact on final results requires further understanding. In the present study, we examined the relationship between the genomic copy number of eight different Chinese Hamster ovary (CHO) gene targets and the sensitivity and accuracy afforded by those targets in a residual host cell DNA QPCR assay. We also evaluated the use of each gene target for accurate measurement of residual DNA clearance using in-process purification samples from two CHO production cell lines. Our results revealed a correlation between gene target abundance and the potential sensitivity for use in a QPCR assay. However, we found that higher copy number gene targets do not provide the highest measurement or reveal the largest clearance of residual host cell DNA from purification samples. These findings suggest that different DNA sequences may clear or degrade at differential rates and highlight unexpected considerations that must be made in the choice of QPCR gene target when designing QPCR assays.     

Evaluating a non-destructive method for calibrating tree biomass equations derived from tree branching architecture

Key message

Functional branch analysis (FBA) is a promising non-destructive method that can produce accurate tree biomass equations when applied to trees which exhibit fractal branching architecture.

Abstract

Functional branch analysis (FBA) is a promising non-destructive alternative to the standard destructive method of tree biomass equation development. In FBA, a theoretical model of tree branching architecture is calibrated with measurements of tree stems and branches to estimate the coefficients of the biomass equation. In this study, species-specific and mixed-species tree biomass equations were derived from destructive sampling of trees in Western Kenya and compared to tree biomass equations derived non-destructively from FBA. The results indicated that the non-destructive FBA method can produce biomass equations that are similar to, but less accurate than, those derived from standard methods. FBA biomass prediction bias was attributed to the fact that real trees diverged from fractal branching architecture due to highly variable length–diameter relationships of stems and branches and inaccurate scaling relationships for the lengths of tree crowns and trunks assumed under the FBA model.