ETA: Robust software for determination of cell specific rates from extracellular time courses

Accurate quantification of cell specific rates and their uncertainties is of critical importance for assessing metabolic phenotypes of cultured cells. We applied two different methods of regression and error analysis to estimate specific metabolic rates from time‐course measurements obtained in exponentially growing cell cultures. Using simulated data sets to compute specific rates of growth, glucose uptake, and lactate excretion, we found that Gaussian error propagation from prime variables to the final calculated rates was the most accurate method for estimating parameter uncertainty. We incorporated this method into a MATLAB‐based software package called Extracellular Time‐Course Analysis (ETA), which automates the analysis workflow required to (i) compute cell specific metabolic rates and their uncertainties; (ii) test the goodness‐of‐fit of the experimental data to the regression model; and (iii) rapidly compare the results across multiple experiments. ETA was used to estimate the uptake or excretion rate of glucose, lactate, and 18 different amino acids in a B‐cell model of c‐Myc‐driven cancer. We found that P493‐6 cells with High Myc expression increased their specific uptake of glutamine, arginine, serine, lysine, and branched‐chain amino acids by two‐ to threefold in comparison to low Myc cells, but exhibited only modest increases in glucose uptake and lactate excretion. By making the ETA software package freely available to the scientific community, we expect that it will become an important tool for rigorous estimation of specific rates required for metabolic flux analysis and other quantitative metabolic studies. Biotechnol. Bioeng. 2013; 110: 1748–1758. © 2013 Wiley Periodicals, Inc.     

Flux balance analysis of CHO cells before and after a metabolic switch from lactate production to consumption

Mammalian cell cultures typically exhibit an energy inefficient phenotype characterized by the consumption of large quantities of glucose and the concomitant production of large quantities of lactate. Under certain conditions, mammalian cells can switch to a more energy efficient state during which lactate is consumed. Using a metabolic model derived from a mouse genome scale model we performed flux balance analysis of Chinese hamster ovary cells before and after a metabolic switch from lactate production (in the presence of glucose) to lactate consumption (after glucose depletion). Despite a residual degree of freedom after accounting for measurements, the calculated flux ranges and associated errors were narrow enough to enable investigation of metabolic changes across the metabolic switch. Surprisingly, the fluxes through the lower part of the TCA cycle from oxoglutarate to malate were very similar (around 60 µmol/gDW/h) for both phases. A detailed analysis of the energy metabolism showed that cells consuming lactate have an energy efficiency (total ATP produced per total C‐mol substrate consumed) six times greater than lactate producing cells. Biotechnol. Bioeng. 2013; 110: 660–666. © 2012 Wiley Periodicals, Inc.     

Metabolic flux analysis of HEK-293 cells in perfusion cultures for the production of adenoviral vectors

To meet increasing needs of adenovirus vectors for gene therapy programs, development of efficient and reproducible production processes is required. Perfusion cultures were employed to allow infection at greater cell concentrations. In an effort to define culture conditions resulting in enhanced productivities, experiments performed at different feed rates and infected at various cell densities were compared using metabolic flux analysis. The highest specific product yields were achieved in experiments performed at high perfusion rates and/or low cell concentrations. The intracellular flux analysis revealed that these experiments exhibited greater glycolytic fluxes, slightly higher TCA fluxes, and greater ATP production rates at the time of infection. In contrast, cultures infected at high cell density and/or low medium renewal rates were characterized by a more efficient utilization of glucose at the time of infection, but the specific product yields achieved were lower. The intracellular flux analysis provided a rational basis for the implementation of a feeding strategy that allowed successful infection at a density of 5x10(6)cells/ml.     

Altered regulation of pyruvate kinase or co-overexpression of phosphofructokinase increases glycolytic fluxes in resting Escherichia coli

Glycolytic fluxes in resting Escherichia coli were enhanced by overexpression of heterologous pyruvate kinases (Pyk) from Bacillus stearothermophilus and Zymomonas mobilis, but not homologous Pyk. Compared to the control, an increase of 10% in specific glucose consumption and of 15% in specific ethanol production rates was found in anaerobic resting cells, expressing the heterologous Pyks, that were harvested from exponentially growing aerobic cultures. A further increase in glycolytic flux was achieved by simultaneous overexpression of E. coli phosphofructokinase (Pfk) and Pyk with specific glucose consumption and ethanol production rates of 25% and 35% greater, respectively, than the control. Fluxes to lactate were not significantly affected, contrary to previous observations with resting cells harvested from anaerobically growing cultures. To correlate the physiology of resting cells with the physiology of cells prior to harvest, we determined the relevant growth parameters from aerobic and anaerobic precultures. We conclude that glycolytic fluxes in E. coli with submaximal (aerobic) metabolic activity can be increased by overexpression of pyruvate kinases which do not require allosteric activation or co-overexpression with Pfk. However, such improvements require more extensive engineering in E. coli with near maximal (anaerobic) metabolic activity.     

Elucidating the role of copper in CHO cell energy metabolism using 13C metabolic flux analysis

¹³C‐metabolic flux analysis was used to understand copper deficiency‐related restructuring of energy metabolism, which leads to excessive lactate production in recombinant protein‐producing CHO cells. Stationary‐phase labeling experiments with U‐¹³C glucose were conducted on CHO cells grown under high and limiting copper in 3 L fed‐batch bioreactors. The resultant labeling patterns of soluble metabolites were measured by GC‐MS and used to estimate metabolic fluxes in the central carbon metabolism pathways using OpenFlux. Fluxes were evaluated 300 times from stoichiometrically feasible random guess values and their confidence intervals calculated by Monte Carlo simulations. Results from metabolic flux analysis exhibited significant carbon redistribution throughout the metabolic network in cells under Cu deficiency. Specifically, glycolytic fluxes increased (25%–79% relative to glucose uptake) whereas fluxes through the TCA and pentose phosphate pathway (PPP) were lower (15%–23% and 74%, respectively) compared with the Cu‐containing condition. Furthermore, under Cu deficiency, 33% of the flux entering TCA via the pyruvate node was redirected to lactate and malate production. Based on these results, we hypothesize that Cu deficiency disrupts the electron transport chain causing ATP deficiency, redox imbalance, and oxidative stress, which in turn drive copper‐deficient CHO cells to produce energy via aerobic glycolysis, which is associated with excessive lactate production, rather than the more efficient route of oxidative phosphorylation. © 2015 American Institute of Chemical Engineers Biotechnol. Prog., 31:1179–1186, 2015     

The metabolic network of Lactococcus lactis: distribution of (14)C-labeled substrates between catabolic and anabolic pathways

Lactococcus lactis NCDO 2118 was grown in a simple synthetic medium containing only six essential amino acids and glucose as carbon substrates to determine qualitatively and quantitatively the carbon fluxes into the metabolic network. The specific rates of substrate consumption, product formation, and biomass synthesis, calculated during the exponential growth phase, represented the carbon fluxes within the catabolic and anabolic pathways. The macromolecular composition of the biomass was measured to distribute the global anabolic flux into the specific anabolic pathways. Finally, the distribution of radiolabeled substrates, both into the excreted fermentation end products and into the different macromolecular fractions of biomass, was monitored. The classical end products of lactic acid metabolism (lactate, formate, and acetate) were labeled with glucose, which did not label other excreted products, and to a lesser extent with serine, which was deaminated to pyruvate and represented approximately 10% of the pyruvate flux. Other minor products, keto and hydroxy acids, were produced from glutamate and branched-chain amino acids via deamination and subsequent decarboxylation and/or reduction. Glucose labeled all biomass fractions and accounted for 66% of the cellular carbon, although this represented only 5% of the consumed glucose.     

The propagation of errors in long-term measurements of land-atmosphere fluxes of carbon and water

For surface fluxes of carbon dioxide, the net daily flux is the sum of daytime and nighttime fluxes of approximately the same magnitude and opposite direction. The net flux is therefore significantly smaller than the individual flux measurements and error assessment is critical in determining whether a surface is a net source or sink of carbon dioxide. For carbon dioxide flux measurements, it is an occasional misconception that the net flux is measured as the difference between the net upward and downward fluxes (i.e. a small difference between large terms). This is not the case. The net flux is the sum of individual (half-hourly or hourly) flux measurements, each with an associated error term. The question of errors and uncertainties in long-term flux measurements of carbon and water is addressed by first considering the potential for errors in flux measuring systems in general and thus errors which are relevant to a wide range of timescales of measurement. We also focus exclusively on flux measurements made by the micrometeorological method of eddy covariance. Errors can loosely be divided into random errors and systematic errors, although in reality any particular error may be a combination of both types. Systematic errors can be fully systematic errors (errors that apply on all of the daily cycle) or selectively systematic errors (errors that apply to only part of the daily cycle), which have very different effects. Random errors may also be full or selective, but these do not differ substantially in their properties. We describe an error analysis in which these three different types of error are applied to a long-term dataset to discover how errors may propagate through long-term data and which can be used to estimate the range of uncertainty in the reported sink strength of the particular ecosystem studied.     

Optimizing performance of semi‐continuous cell culture in an ambr15™ microbioreactor using dynamic flux balance modeling

The ambr bioreactors are single‐use microbioreactors for cell line development and process optimization. With operating conditions for large‐scale biopharmaceutical production properly scaled down, microbioreactors such as the ambr15? can potentially be used to predict the effect of process changes such as modified media or different cell lines. While there have been some recent studies evaluating the ambr15? technology as a scale‐down model for fed‐batch operations, little has been reported for semi‐continuous or continuous operation. Gassing rates and dilution rates in the ambr15? were varied in this study to attempt to replicate performance of a perfusion process at the 5 L scale. At both scales, changes to metabolite production and consumption, and cell growth rate and therapeutic protein production were measured. Conditions were identified in the ambr15? bioreactor that produced metabolic shifts and specific metabolic and protein production rates that are characteristic of the corresponding 5 L perfusion process. A dynamic flux balance (DFB) model was employed to understand and predict the metabolic changes observed. The DFB model predicted trends observed experimentally, including lower specific glucose consumption and a switch from lactate production to consumption when dissolved CO₂ was maintained at higher levels in the broth. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 34:420–431, 2018     

Metabolic and morphological differences between rapidly proliferating cancerous and normal breast epithelial cells

The metabolic and morphological characteristics of two human epithelial breast cell populations--MCF7 cells, a cancerous cell line, and 48R human mammary epithelial cells (48R HMECs), a noncancerous, finite lifespan cell strain--were compared at identical growth rates. Both cell types were induced to grow rapidly in nutrient-rich media containing 13C-labeled glucose, and the isotopic enrichment of cellular metabolites was quantified to calculate metabolic fluxes in key pathways. Despite their similar growth rates, the cells exhibited distinctly different metabolic and morphological profiles. MCF7 cells have an 80% smaller exposed surface area and contain 26% less protein per cell than the 48R cells. Surprisingly, rapidly proliferating 48R cells exhibited a 225% higher per-cell glucose consumption rate, a 250% higher per-cell lactate production rate, and a nearly identical per-cell glutamine consumption rate relative to the cancer cell line. However, when fluxes were considered on the basis of exposed area, the cancer cells were observed to have higher glucose, lactate, and glutamine fluxes, demonstrating superior transport capabilities per unit area of cell membrane. MCF7 cells also consumed amino acids at rates much higher than are generally required for protein synthesis, whereas 48R cells generally did not. Pentose phosphate pathway activity was higher in MCF7 cells, and the flux of glutamine to glutamate was less reversible. Energy efficiency was significantly higher in MCF7 cells, as a result of a combination of their smaller size and greater reliance on the TCA cycle than the 48R cells. These observations support evolutionary models of cancer cell metabolism and suggest targets for metabolic drugs in metastatic breast cancers.     

Metabolic analysis of the synthesis of high levels of intracellular human SOD in Saccharomyces cerevisiae rhSOD 2060 411 SGA122

The synthesis of human superoxide dismutase (SOD) in batch cultures of a Saccharomyces cerevisiae strain using a glucose-limited minimal medium was studied through metabolic flux analysis. A stoichiometric model was built, which included 78 reactions, according to metabolic pathways operative in these strains during respirofermentative and oxidative metabolism. It allowed calculation of the distribution of metabolic fluxes during diauxic growth on glucose and ethanol. Fermentation profiles and metabolic fluxes were analyzed at different phases of diauxic growth for the recombinant strain (P+) and for its wild type (P-). The synthesis of SOD by the strain P+ resulted in a decrease in specific growth rate of 34 and 54% (growth on glucose and ethanol respectively) in comparison to the wild type. Both strains exhibited similar flux of glucose consumption and ethanol synthesis but important differences in carbon distribution with biomass/substrate yields and ATP production 50% higher in P-. A higher contribution of fermentative metabolism, with 64% of the energy produced at the phosphorylation level, was observed during SOD production. The flux of precursors to amino acids and nucleotides was higher in the recombinant strain, in agreement with the higher total RNA and protein levels. Lower specific growth rates in strain P+ appear to be related to the decrease in the rate of synthesis of nonrecombinant protein, as well as a decrease in the activities of the pentose phosphate (PP) pathway and TCA cycle. A very different way of entry into the stationary phase was observed for each strain: in the wild-type strain most metabolic fluxes decreased and fluxes related to energy reserve synthesis increased, while in the P+ strain the flux of 22 reactions (including PP pathway and amino acids biosynthesis) related to SOD production increased their fluxes. Changes in SOD production rates at different physiological states appear to be related to the differences in building blocks availability between respirofermentative and oxidative metabolism. Using the present expression system, ideal conditions for SOD synthesis are represented by either active growth during respirofermentative metabolism or transition from a growing to a nongrowing state. An increase in SOD flux could be achieved using an expression system nonassociated to growth and potentially eliminating part of the metabolic burden.     

Metabolic flux analysis of Shewanella spp. reveals evolutionary robustness in central carbon metabolism

Shewanella spp. are a group of facultative anaerobic bacteria widely distributed in marine and freshwater environments. In this study, we profiled the central metabolic fluxes of eight recently sequenced Shewanella species grown under the same condition in minimal medium with [3‐¹³C] lactate. Although the tested Shewanella species had slightly different growth rates (0.23–0.29 h^?1) and produced different amounts of acetate and pyruvate during early exponential growth (pseudo‐steady state), the relative intracellular metabolic flux distributions were remarkably similar. This result indicates that Shewanella species share similar regulation in regard to central carbon metabolic fluxes under steady growth conditions: the maintenance of metabolic robustness is not only evident in a single species under genetic perturbations (Fischer and Sauer, 2005; Nat Genet 37(6):636–640), but also observed through evolutionary related microbial species. This remarkable conservation of relative flux profiles through phylogenetic differences prompts us to introduce the concept of metabotype as an alternative scheme to classify microbial fluxomics. On the other hand, Shewanella spp. display flexibility in the relative flux profiles when switching their metabolism from consuming lactate to consuming pyruvate and acetate. Biotechnol. Bioeng. 2009;102: 1161–1169. © 2008 Wiley Periodicals, Inc.     

Metabolic flux analysis of CHO cells in perfusion culture by metabolite balancing and 2D [13C, 1H] COSY NMR spectroscopy

The physiological state of CHO cells in perfusion culture was quantified by determining fluxes through the bioreaction network using ¹³C glucose and 2D-NMR spectroscopy. CHO cells were cultivated in a 2.5 L perfusion bioreactor with glucose and glutamine as the primary carbon and energy sources. The reactor was inoculated at a cell density of 8×10⁶ cells/mL and operated at ～10×10⁶ cells/mL using unlabeled glucose for the first 13 days. The second phase lasted 12 days and the medium consisted of 10% [U-¹³C]glucose, 40% labeled [1-¹³C]glucose with the balance unlabeled. After the culture attained isotopic steady state, biomass samples from the last 3 days of cultivation were considered representative and used for flux estimation. They were hydrolyzed and analyzed by 2D [¹³C, ¹H] COSY measurements using the heteronuclear single quantum correlation sequence with gradients for artifacts suppression. Metabolic fluxes were determined using the 13C-Flux software package by minimizing the residuals between the experimental and the simulated NMR data. Normalized residuals exhibited a Gaussian distribution indicating good model fit to experimental data. The glucose consumption rate was 5-fold higher than that of glutamine with 41% of glucose channeled through the pentose phosphate pathway. The fluxes at the pyruvate branch point were almost equally distributed between lactate and the TCA cycle (55% and 45%, respectively). The anaplerotic conversion of pyruvate to oxaloacetate by pyruvate carboxylase accounted for 10% of the pyruvate flux with the remaining 90% entering the TCA cycle through acetyl-CoA. The conversion of malate to pyruvate catalyzed by the malic enzyme was 70% higher than that for the anaplerotic reaction catalyzed by pyruvate carboxylase. Most amino acid catabolic and biosynthetic fluxes were significantly lower than the glycolytic and TCA cycle fluxes. Metabolic flux data from NMR analysis validated a simplified model where metabolite balancing was used for flux estimation. In this reduced flux space, estimates from these two methods were in good agreement. This simplified model can routinely be used in bioprocess development experiments to estimate metabolic fluxes with much reduced analytical investment. The high resolution flux information from 2D-NMR spectroscopy coupled with the capability to validate a simplified metabolite balancing based model for routine use make ¹³C-isotopomer analysis an attractive bioprocess development tool for mammalian cell cultures.     

Shewanella oneidensis MR-1 fluxome under various oxygen conditions

The central metabolic fluxes of Shewanella oneidensis MR-1 were examined under carbon-limited (aerobic) and oxygen-limited (microaerobic) chemostat conditions, using 13C-labeled lactate as the sole carbon source. The carbon labeling patterns of key amino acids in biomass were probed using both gas chromatography-mass spectrometry (GC-MS) and 13C nuclear magnetic resonance (NMR). Based on the genome annotation, a metabolic pathway model was constructed to quantify the central metabolic flux distributions. The model showed that the tricarboxylic acid (TCA) cycle is the major carbon metabolism route under both conditions. The Entner-Doudoroff and pentose phosphate pathways were utilized primarily for biomass synthesis (with a flux below 5% of the lactate uptake rate). The anaplerotic reactions (pyruvate to malate and oxaloacetate to phosphoenolpyruvate) and the glyoxylate shunt were active. Under carbon-limited conditions, a substantial amount (9% of the lactate uptake rate) of carbon entered the highly reversible serine metabolic pathway. Under microaerobic conditions, fluxes through the TCA cycle decreased and acetate production increased compared to what was found for carbon-limited conditions, and the flux from glyoxylate to glycine (serine-glyoxylate aminotransferase) became measurable. Although the flux distributions under aerobic, microaerobic, and shake flask culture conditions were different, the relative flux ratios for some central metabolic reactions did not differ significantly (in particular, between the shake flask and aerobic-chemostat groups). Hence, the central metabolism of S. oneidensis appears to be robust to environmental changes. Our study also demonstrates the merit of coupling GC-MS with 13C NMR for metabolic flux analysis to reduce the use of 13C-labeled substrates and to obtain more-accurate flux values.     

Comparative metabolic analysis of lactate for CHO cells in glucose and galactose

t-PA producing CHO cells have been shown to undergo a metabolic shift when the culture medium is supplemented with a mixture of glucose and galactose. This metabolic change is characterized by the reincorporation of lactate and its use as an additional carbon source. The aim of this work is to understand lactate metabolism. To do so, Chinese hamster ovary cells were grown in batch cultures in four different conditions consisting in different combinations of glucose and galactose. In experiments supplemented with glucose, only lactate production was observed. Cultures with glucose and galactose consumed glucose first and produced lactate at the same time, after glucose depletion galactose consumption began and lactate uptake was observed. Comparison of the metabolic state of cells with and without the shift by metabolic flux analysis show that the metabolic fluxes distribution changes mostly in the reactions involving pyruvate metabolism. When not enough pyruvate is being produced for cells to support their energy requirements, lactate dehydrogenase complex changes the direction of the reaction yielding pyruvate to feed the TCA cycle. The slow change from high fluxes during glucose consumption to low fluxes in galactose consumption generates intracellular conditions that allow the influx of lactate. Lactate consumption is possible in cell cultures supplemented with glucose and galactose due to the low rates at which galactose is consumed. Evidence suggests that an excessive production and accumulation of pyruvate during glucose consumption leads to lactate production and accumulation inside the cell. Other internal conditions such as a decrease in internal pH, forces the flow of lactate outside the cell. After metabolic shift the intracellular pool of pyruvate, lactate and H⁺ drops permitting the reversal of the monocarboxylate transporter direction, therefore leading to lactate uptake. Metabolic analysis comparing glucose and galactose consumption indicates that after metabolic shift not enough pyruvate is produced to supply energy metabolism and lactate is used for pyruvate synthesis. In addition, MFA indicates that most carbon consumed during low carbon flux is directed towards maintaining energy metabolism.     

Influence of medium exchange schedules on metabolic, growth, and GM-CSF secretion rates of genetically engineered NIH-3T3 cells.

The metabolic and secretory characteristics of NIH-3T3 fibroblasts transfected with a cDNA encoding human granulocyte-macrophage colony stimulating factor (GM-CSF) were examined as a function of the culture medium exchange schedule. The rates of glucose and glutamine consumption and of lactate and ammonia production were measured over exchange schedules ranging from complete medium replacement weekly (1/week) to complete medium replacement daily (7/week). All measured metabolic rates increased with increased medium exchange rates and accelerated sharply between exchange rates of 3.5/week and 7/week. The lactate/glucose and ammonia/glutamine yield coefficients, however, remained invariant at about 1.9 and 1.0 mol/mol, respectively, under all medium perfusion conditions. A shift-up in medium perfusion rates from 3.5/week to 7/week resulted in increased metabolic rates that resembled those observed in the cultures that were exchanged at the 7/week rate throughout, showing that the metabolic rates could be directly controlled by the perfusion rate. Differential regulation of medium versus serum perfusion demonstrated that increased NIH-3T3 cell metabolism was directly proportional to the serum flux to which the cells were exposed. Thus a limiting serum component is responsible for the altered metabolic and growth rates. The GM-CSF production by the transfected 3T3 cells was stable but exhibited substantial transient increases during periods of cell proliferation, demonstrating that the secretion of transfected gene products can be highly modulated even when the cDNA is driven from a constitutive promoter. These studies show that the metabolic and secretory behavior of genetically engineered cells is influenced by the medium exchange schedule.     

Metabolic analysis of Escherichia coli in the presence and absence of the carboxylating enzymes phosphoenolpyruvate carboxylase and pyruvate carboxylase

Fermentation patterns of Escherichia coli with and without the phosphoenolpyruvate carboxylase (PPC) and pyruvate carboxylase (PYC) enzymes were compared under anaerobic conditions with glucose as a carbon source. Time profiles of glucose and fermentation product concentrations were determined and used to calculate metabolic fluxes through central carbon pathways during exponential cell growth. The presence of the Rhizobium etli pyc gene in E. coli (JCL1242/pTrc99A-pyc) restored the succinate producing ability of E. coli ppc null mutants (JCL1242), with PYC competing favorably with both pyruvate formate lyase and lactate dehydrogenase. Succinate formation was slightly greater by JCL1242/pTrc99A-pyc than by cells which overproduced PPC (JCL1242/pPC201, ppc(+)), even though PPC activity in cell extracts of JCL1242/pPC201 (ppc(+)) was 40-fold greater than PYC activity in extracts of JCL1242/pTrc99a-pyc. Flux calculations indicate that during anaerobic metabolism the pyc(+) strain had a 34% greater specific glucose consumption rate, a 37% greater specific rate of ATP formation, and a 6% greater specific growth rate compared to the ppc(+) strain. In light of the important position of pyruvate at the juncture of NADH-generating pathways and NADH-dissimilating branches, the results show that when PPC or PYC is expressed, the metabolic network adapts by altering the flux to lactate and the molar ratio of ethanol to acetate formation.     

Combining mechanistic and data‐driven approaches to gain process knowledge on the control of the metabolic shift to lactate uptake in a fed‐batch CHO process

A growing body of knowledge is available on the cellular regulation of overflow metabolism in mammalian hosts of recombinant protein production. However, to develop strategies to control the regulation of overflow metabolism in cell culture processes, the effect of process parameters on metabolism has to be well understood. In this study, we investigated the effect of pH and temperature shift timing on lactate metabolism in a fed‐batch Chinese hamster ovary (CHO) process by using a Design of Experiments (DoE) approach. The metabolic switch to lactate consumption was controlled in a broad range by the proper timing of pH and temperature shifts. To extract process knowledge from the large experimental dataset, we proposed a novel methodological concept and demonstrated its usefulness with the analysis of lactate metabolism. Time‐resolved metabolic flux analysis and PLS‐R VIP were combined to assess the correlation of lactate metabolism and the activity of the major intracellular pathways. Whereas the switch to lactate uptake was mainly triggered by the decrease in the glycolytic flux, lactate uptake was correlated to TCA activity in the last days of the cultivation. These metabolic interactions were visualized on simple mechanistic plots to facilitate the interpretation of the results. Taken together, the combination of knowledge‐based mechanistic modeling and data‐driven multivariate analysis delivered valuable insights into the metabolic control of lactate production and has proven to be a powerful tool for the analysis of large metabolic datasets. © 2015 American Institute of Chemical Engineers Biotechnol. Prog., 31:1657–1668, 2015     

Effects of alkalosis on muscle ions at rest and with intense exercise

The effects of metabolic and respiratory alkalosis (MALK and RALK) on intracellular strong ion concentrations ([ion]i) and muscle to blood ion fluxes were examined at rest and during 5 min of intense, intermittent tetanic stimulation in the isolated, perfused rat hindlimb. Compared with the control (C), perfusion of resting skeletal muscle during MALK and RALK significantly increased [Cl-]i and [Na+]i, and RALK significantly lowered [K+]i; these changes, however, did not affect initial hindlimb force production. In both resting and stimulated muscle, the intracellular ion changes corresponded to appropriate perfusate to muscle ion fluxes. At rest, changes in slow-twitch soleus were greater than in fast-twitch white gastrocnemius (WG), but stimulation-induced changes in [Lac]i and [K+]i were greater in WG. At the end of stimulation [K+]i and [Mg2+]i had decreased less in MALK than in C and RALK, particularly in plantaris and WG muscles. Compared with C, the muscle to perfusate flux of Lac- increased by 37% in MALK and 27% in RALK. This was associated with significantly less Lac- accumulation in all muscles in MALK than in RALK, which, in turn, had significantly less lactate than C. Lactate efflux from contracting skeletal muscle was significantly correlated with an uptake of Cl- by muscle. It is concluded that extracellular alkalosis alters skeletal muscle intracellular ionic composition and increases Lac- efflux from skeletal muscle. In agreement with other studies, lactate release appears to occur by both ionic and molecular transport processes. Alkalosis had no apparent effect on muscle performance with this preparation.     

Determination of confidence intervals of metabolic fluxes estimated from stable isotope measurements

Metabolic fluxes, estimated from stable isotope studies, provide a key to quantifying physiology in fields ranging from metabolic engineering to the analysis of human metabolic diseases. A serious drawback of the flux estimation method in current use is that it does not produce confidence limits for the estimated fluxes. Without this information it is difficult to interpret flux results and expand the physiological significance of flux studies. To address this shortcoming we derived analytical expressions of flux sensitivities with respect to isotope measurements and measurement errors. These tools allow the determination of local statistical properties of fluxes and relative importance of measurements. Furthermore, we developed an efficient algorithm to determine accurate flux confidence intervals and demonstrated that confidence intervals obtained with this method closely approximate true flux uncertainty. In contrast, confidence intervals approximated from local estimates of standard deviations are inappropriate due to inherent system nonlinearities. We applied these methods to analyze the statistical significance and confidence of estimated gluconeogenesis fluxes from human studies with [U-13C]glucose as tracer and found true limits for flux estimation in specific human isotopic protocols.     

Optimal selection of metabolic fluxes for in vivo measurement. I. Development of mathematical methods.

The measurement of uptake and secretion rates is often not sufficient to allow the calculation of all internal metabolic fluxes. Measurements of internal fluxes are needed and these additional measurements are used in conjunction with mass-balance equations to calculate the complete metabolic flux map. A method is presented that identifies the fluxes that should be selected for experimental measurement, and the fluxes that can be computed using the mass-balance equations. The criterion for selecting internal metabolic fluxes for measurement is that the values of the computed fluxes should have low sensitivity to experimental error in the measured fluxes. A condition number indicating the upper bound on this sensitivity, is calculated based on stoichiometry alone. The actual sensitivity is dependent on both the flux measurements and the error in flux measurements, as well as the stoichiometry. If approximate physiologic ranges of fluxes are known a realistic sensitivity can be computed. The exact sensitivity cannot be calculated since the experimental error is usually unknown. The most probable value of the actual sensitivity for a given selection of measured fluxes is estimated by selecting a large number of representative error vectors and calculating the actual sensitivity for each of these. A frequency distribution of actual sensitivities is thus obtained giving a representative range of actual sensitivities for a particular experimental situation.