Rapid sampling for analysis of in vivo kinetics using the BioScope: a system for continuous-pulse experiments

In this article we present a novel device, the BioScope, which allows elucidation of in vivo kinetics of microbial metabolism via perturbation experiments. The perturbations are carried out according to the continuous-flow method. The BioScope consists of oxygen permeable silicon tubing, connected to the fermentor, through which the broth flows at constant velocity. The tubing has a special geometry (serpentine channel) to ensure plug flow. After leaving the fermentor, the broth is mixed with a small flow of perturbing agent. This represents the start of the perturbation. The broth is sampled at different locations along the tubing, corresponding to different incubation times. The maximal incubation time is 69 s; the minimally possible time interval between the samples is 3-4 s. Compared to conventional approaches, in which the perturbation is carried out in the fermentor, the BioScope offers a number of advantages. (1) A large number of different perturbation experiments can be carried out on the same day, because the physiological state of the fermentor is not perturbed. (2) In vivo kinetics during fed-batch experiments and in large-scale reactors can be investigated. (3) All metabolites of interest can be measured using samples obtained in a single experiment, because the volume of the samples is unlimited. (4) The amount of perturbing agent spent is minimal, because only a small volume of broth is perturbed. (5) The system is completely automated. Several system properties, including plug-flow characteristics, mixing, oxygen and carbon dioxide transfer rates, the quenching time, and the reproducibility have been explored, with satisfactory results. Responses of several glycolytic intermediates in Saccharomyces cerevisiae to a glucose pulse, measured using a conventional approach are compared to results obtained with the BioScope. The agreement between the results demonstrates that the BioScope is indeed a promising device for studying in vivo kinetics.     

Catching prompt metabolite dynamics in Escherichia coli with the BioScope at oxygen rich conditions

The design and application of a BioScope, a mini plug-flow reactor for carrying out pulse response experiments, specifically designed for Escherichia coli is presented. Main differences with the previous design are an increased volume-specific membrane surface for oxygen transfer and significantly decreased sampling intervals. The characteristics of the new device (pressure drop, residence time distribution, plug-flow behavior and O₂ mass transfer) were determined and evaluated. Subsequently, 2.8 mM glucose perturbation experiments on glucose-limited aerobic E. coli chemostat cultures were carried out directly in the chemostat as well as in the BioScope (for two time frames: 8 and 40 s). It was ensured that fully aerobic conditions were maintained during the perturbation experiments. To avoid metabolite leakage during quenching, metabolite quantification (glycolytic and TCA-cycle intermediates and nucleotides) was carried out with a differential method, whereby the amounts measured in the filtrate were subtracted from the amounts measured in total broth. The dynamic metabolite profiles obtained from the BioScope perturbations were very comparable with the profiles obtained from the chemostat perturbation. This agreement demonstrates that the BioScope is a promising device for studying in vivo kinetics in E. coli that shows much faster response (<10 s) in comparison with eukaryotes.     

Determination of in vivo oxygen uptake and carbon dioxide evolution rates from off-gas measurements under highly dynamic conditions

In vivo kinetics of Saccharomyces cerevisiae are studied, in a time window of 150 s, by analyzing the response of O(2) and CO(2) in the fermentor off-gas after perturbation of chemostat cultures by metabolite pulses. Here, a new mathematical method is presented for the estimation of the in vivo oxygen uptake rate (OUR) and carbon dioxide evolution rate (CER) directly from the off-gas data in such perturbation experiments. The mathematical construction allows effective elimination of delay and distortion in the off-gas measurement signal under highly dynamic conditions. A black box model for the fermentor off-gas system is first obtained by system identification, followed by the construction of an optimal linear filter, based on the identified off-gas model. The method is applied to glucose and ethanol pulses performed on chemostat cultures of S. cerevisiae. The estimated OUR is shown to be consistent with the independent dissolved oxygen measurement. The estimated in vivo OUR and CER provide valuable insights into the complex dynamic behavior of yeast and are essential for the establishment and validation of in vivo kinetic models of primary metabolism.     

Inhibitory effect of carbon dioxide on the fed-batch culture of Ralstonia eutropha: evaluation by CO2 pulse injection and autogenous CO2 methods

In order to see the effect of CO(2) inhibition resulting from the use of pure oxygen, we carried out a comparative fed-batch culture study of polyhydroxybutyric acid (PHB) production by Ralstonia eutropha using air and pure oxygen in 5-L, 30-L, and 300-L fermentors. The final PHB concentrations obtained with pure O(2) were 138.7 g/L in the 5-L fermentor and 131.3 g/L in the 30-L fermentor, which increased 2.9 and 6.2 times, respectively, as compared to those obtained with air. In the 300-L fermentor, the fed-batch culture with air yielded only 8.4 g/L PHB. However, the maximal CO(2) concentrations in the 5-L fermentor increased significantly from 4.1% (air) to 15.0% (pure O(2)), while it was only 1.6% in the 30-L fermentor with air, but reached 14.2% in the case of pure O(2). We used two different experimental methods for evaluating CO(2) inhibition: CO(2) pulse injection and autogenous CO(2) methods. A 10 or 22% (v/v) CO(2) pulse with a duration of 3 or 6 h was introduced in a pure-oxygen culture of R. eutropha to investigate how CO(2) affects the synthesis of biomass and PHB. CO(2) inhibited the cell growth and PHB synthesis significantly. The inhibitory effect became stronger with the increase of the CO(2) concentration and pulse duration. The new proposed autogenous CO(2) method makes it possible to place microbial cells under different CO(2) level environments by varying the gas flow rate. Introduction of O(2) gas at a low flow rate of 0.42 vvm resulted in an increase of CO(2) concentration to 30.2% in the exit gas. The final PHB of 97.2 g/L was obtained, which corresponded to 70% of the PHB production at 1.0 vvm O(2) flow rate. This new method measures the inhibitory effect of CO(2) produced autogenously by cells through the entire fermentation process and can avoid the overestimation of CO(2) inhibition without introducing artificial CO(2) into the fermentor.     

Generating short-term kinetic responses of primary metabolism of Penicillium chrysogenum through glucose perturbation in the bioscope mini reactor

A first study of the in vivo kinetic properties of primary metabolism of Penicillium chrysogenum is presented. Dynamic metabolite data have been generated by rapidly increasing the extracellular glucose concentration of cells cultivated under well-defined conditions in an aerobic glucose-limited chemostat followed by measurement of the fast dynamic response of the primary metabolite levels (glucose pulse experiment). These experiments were carried out directly in the chemostat as well as in a mini plug flow reactor (BioScope) outside the chemostat. The results of the glucose pulse experiments carried out in the chemostat and the Bioscope were highly similar. During the 90 s time window of the pulse experiment, the glucose consumption rate increased to a value twice as high as in the steady state, a much lower increase than observed for the fermenting yeast Saccharomyces cerevisiae under similar conditions. Although the observed metabolite patterns in P. chrysogenum were comparable to S. cerevisiae large differences in the magnitude of the dynamic behavior were observed between both organisms. During the pulse experiment the level of glycolytic and TCA cycle intermediates, and adenine nucleotides changed between two- and five-fold. Furthermore, a highly similar five-fold increase in the cytocolic NADH/NAD ratio could be calculated from two independent equilibrium assumptions (fructose 1,6 bis-phosphate to the pool of 2 and 3PG and oxaloacetate to fumarate with glutamate transaminase). It was also found that the C4 pool (aspartate, fumarate, and malate) became much more reduced due to this increase in NADH/NAD ratio. Equilibrium conditions were confirmed to exist in the hexose-P pool, the glycolysis between F16bP and 2+3PG and in the C4 pool of the TCA cycle (fumarate, malate, oxaloacetate and aspartate).     

Analysis of a continuous, aerobic, fixed-film bioreactor. I. Steady-state behavior

The analysis of a continuous, aerobic, fixed-film bioreactor is performed by simulating the behavior of penicillin production in a three-phase fluidized bed. Rigorous mathematical models are developed for a fluidized-bed fermentor in which bioparticles are fluidized by the liquid medium and air. The steady-state performance of the fluidized-bed reactor is appraised in terms of penicillin productivity and outlet concentration by considering the two extremes in contacting patterns, complete back-mix and plug flow, in the absence of a growing biofilm. The results show that the complete back-mix contacting pattern is preferred over that of plug flow due to the nature of the penicillin kinetic relationships. It is also shown that for the dual-nutrient (glucose and oxygen) penicillin reaction system the optimum biofilm thickness does not equal the penetration depth of a limiting nutrient, but depends upon the total reactor configuration.     

Influence of CO2 and low concentrations of O2 on fermentative metabolism of the rumen ciliate Dasytricha ruminantium

The effects of ruminal concentrations of CO2 and O2 on glucose-stimulated and endogenous fermentation of the rumen isotrichid ciliate Dasytricha ruminantium were investigated. Principal metabolic products were lactic, butyric and acetic acids, H2 and CO2. Traces of propionic acid were also detected; formic acid present in the incubation supernatants was found to be a fermentation product of the bacteria closely associated with this rumen ciliate. 13C NMR spectroscopy revealed alanine as a minor product of glucose fermentation by D. ruminantium. Glucose uptake and metabolite formation rates were influenced by the headspace gas composition during the protozoal incubations. The uptake of exogenously supplied D-glucose was most rapid in the presence of O2 concentrations typical of those detected in situ (i.e. 1-3 microM). A typical ruminal gas composition (high CO2, low O2) led to increased butyrate and acetate formation compared to results obtained using O2-free N2. At a partial pressure of 66 kPa CO2 in N2, increased cytosolic flux to butyrate was observed. At low O2 concentrations (1-3 microM dissolved in the protozoal suspension) in the absence of CO2, increased acetate and CO2 formation were observed and D. ruminantium utilized lactate in the absence of extracellular glucose. The presence of both O2 and CO2 in the incubation headspaces resulted in partial inhibition of H2 production by D. ruminantium. Results suggest that at the O2 and CO2 concentrations that prevail in situ, the contribution made by D. ruminantium to the formation of ruminal volatile fatty acids is greater than previously reported, as earlier measurements were made under anaerobic conditions.     

Energetic and metabolic transient response of Saccharomyces cerevisiae to benzoic acid

Saccharomyces cerevisiae is known to be able to adapt to the presence of the commonly used food preservative benzoic acid with a large energy expenditure. Some mechanisms for the adaptation process have been suggested, but its quantitative energetic and metabolic aspects have rarely been discussed. This study discusses use of the stimulus response approach to quantitatively study the energetic and metabolic aspects of the transient adaptation of S. cerevisiae to a shift in benzoic acid concentration, from 0 to 0.8 mM. The information obtained also serves as the basis for further utilization of benzoic acid as a tool for targeted perturbation of the energy system, which is important in studying the kinetics and regulation of central carbon metabolism in S. cerevisiae. Using this experimental set-up, we found significant fast-transient (< 3000 s) increases in O(2) consumption and CO(2) production rates, of approximately 50%, which reflect a high energy requirement for the adaptation process. We also found that with a longer exposure time to benzoic acid, S. cerevisiae decreases the cell membrane permeability for this weak acid by a factor of 10 and decreases the cell size to approximately 80% of the initial value. The intracellular metabolite profile in the new steady-state indicates increases in the glycolytic and tricarboxylic acid cycle fluxes, which are in agreement with the observed increases in specific glucose and O(2) uptake rates.     

5-3H]glucose overestimates glycolytic flux in isolated working rat heart: role of the pentose phosphate pathway

We set out to study the pentose phosphate pathway (PPP) in isolated rat hearts perfused with [5-3H]glucose and [1-14C]glucose or [6-14C]glucose (crossover study with 1- then 6- or 6- then 1-14C-labeled glucose). To model a physiological state, hearts were perfused under working conditions with Krebs-Henseleit buffer containing 5 mM glucose, 40 microU/ml insulin, 0.5 mM lactate, 0.05 mM pyruvate, and 0.4 mM oleate/3% albumin. The steady-state C1/C6 ratio (i.e., the ratio from [1-14C]glucose to [6-14C]glucose) of metabolites released by the heart, an index of oxidative PPP, was not different from 1 (1.06 +/- 0.19 for 14CO2, and 1.00 +/- 0.01 for [14C]lactate + [14C]pyruvate, mean +/- SE, n = 8). Hearts exhibited contractile, metabolic, and 14C-isotopic steady state for glucose oxidation (14CO2 production). Net glycolytic flux (net release of lactate + pyruvate) and efflux of [14C]lactate + [14C]pyruvate were the same and also exhibited steady state. In contrast, flux based on 3H2O production from [5-3H]glucose increased progressively, reaching 260% of the other measures of glycolysis after 30 min. The 3H/14C ratio of glycogen (relative to extracellular glucose) and sugar phosphates (representing the glycogen precursor pool of hexose phosphates) was not different from each other and was <1 (0.36 +/- 0.01 and 0.43 +/- 0.05 respectively, n = 8, P < 0.05 vs. 1). We conclude that both transaldolase and the L-type PPP permit hexose detritiation in the absence of net glycolytic flux by allowing interconversion of glycolytic hexose and triose phosphates. Thus apparent glycolytic flux obtained by 3H2O production from [5-3H]glucose overestimates the true glycolytic flux in rat heart.     

Dynamic in vivo metabolome response of Saccharomyces cerevisiae to a stepwise perturbation of the ATP requirement for benzoate export

Although much information is available on in vitro role of ATP in regulation, the in vivo kinetics of reactions in which ATP plays a role are only partly known. In order to study such reactions, it is therefore necessary to study the role of ATP in vivo. This study presents an in vivo, targeted perturbation of the ATP flux in aerobic glucose-limited chemostat cultures of Saccharomyces cerevisiae, which was accomplished by transiently (20 min) changing the extracellular undissociated benzoic acid concentration via the pH of the culture. The performed pH shifts resulted in, within about 20 s, a 40% decrease (pH upshift) or a 23% increase (pH downshift) of the calculated ATP consumption rate while the specific glucose uptake rate did not change because of the glucose-limited condition. The pH upshift resulted in a strong decrease in the glycolytic and TCA cycle fluxes; carbon and energy balances indicated an increased flux toward storage carbohydrates. As expected, the pH downshift leads to the opposite effects. Overall, consistent responses were observed in the metabolic fluxes, the off gas concentrations of O(2) and CO(2) and intracellular metabolite concentrations, except for the concentrations of adenosine nucleotides which unexpectedly only showed minor dynamics. This demonstrates that our knowledge of the regulation of the ATP level, the storage metabolism, and central carbon metabolism of yeast is still incomplete. The new dynamic metabolite datasets obtained in this study will prove of great value in developing kinetic models.     

A highly efficient method for liquid and solid cultivation of the anaerobic hyperthermophilic eubacterium Thermotoga maritima

An efficient and economical medium--Thermotoga maritima basal medium (TMB)--was designed for the cultivation of T. maritima under either liquid or solid conditions. When the broth was flushed with N2 or CO2 throughout cell growth in a 10-L fermentor (pH controlled to 6.5), the maximum cell density (OD600) on TMB containing 1% glucose rose to 2.0 or higher (1.63 x 10(9) cells mL(-1)). Sheath-less cells observed by electron microscopy were captured during growth in the fermentor. Using a two-layer plating method, isolated single-well colonies were consistently obtained within 24 h on the TMB in modified tissue culture flasks. The minimal inhibitory chloramphenicol concentrations for T. maritima on TMB agar were 5 microg mL(-1) after 24 h and 48 h, and 25 microg mL(-1) at 72 h.     

Glucose uptake rates of single E. coli cells grown in glucose-limited chemostat cultures

To evaluate the extent to which single-cell glucose uptake rates determine the overall specific growth rate of a culture, dilute chemostat cultures of Escherichia coli BL21 were grown in defined medium under glucose limitation. The glucose uptake dynamics of the cell population was examined at the single-cell level using the fluorescent glucose analog, 2-NBDG. Between dilution rates of 0.12 h(-1) and 0.40 h(-1), mean cellular protein content and steady-state, extracellular glucose concentrations increased with increasing dilution rate. However, the distribution of 2-NBDG uptake rates in the population remained constant over the range of dilution rates studied. This indicates that the growth of cells in continuous culture is not limited by the maximum rate of uptake of glucose but by the availability of glucose for transport. The work represents an example of how quantitative flow cytometry can be applied to gain detailed insight into microbial growth physiology.     

Characterization of an experimental miniature bioreactor for cellular perturbation studies

A mini bioreactor (3.0 mL volume) has been developed and shown to be a versatile tool for rapidly screening and quantifying the response of organisms on environmental perturbations. The mini bioreactor is essentially a plug flow device transformed into a well-mixed reactor by a recycle flow of the broth. The gas and liquid phases are separated by a silicone membrane. Dynamic mass transfer experiments were performed to determine the mass transfer capacities for oxygen and carbon dioxide. The mass transfer coefficients for oxygen and carbon dioxide were found to be 1.55 +/- 0.17 x 10(-5) m/s and 4.52 +/- 0.60 x 10(-6) m/s, respectively. Cultivation experiments with the 3.0 mL bioreactor show that (i) it can maintain biomass in the same physiological state as the 4.0 L lab scale bioreactor, (ii) reproducible perturbation experiments such as changing substrate uptake rate can be readily performed and the physiological response monitored quantitatively in terms of the O2 and CO2 uptake and production rates.     

Optimization of culture conditions in CO2 fixation for succinic acid production using Actinobacillus succinogenes

The culture conditions in CO(2) fixation by Actinobacillus succinogenes for succinic acid production were investigated by a model of available CO(2) in a 3-l fermentor. The results from the model analysis showed that the available CO(2) for succinic acid production in the fermentation broth is the sum of HCO(3) (-), CO(3) (2-), and CO(2) influenced by external culture conditions such as medium components, CO(2) partial pressures, and temperature. The optimized conditions for CO(2) supply in a 3-l fermentor were determined as follows: CO(2) partial pressure and stirring speed were maintained at 0.1 MPa and 200 r min(-1), respectively, with a pH of 6.8 and a temperature of 37°C; 0.15 mol l(-1) NaHCO(3) was added. Under the optimized conditions, a CO(2) fixation rate of 0.57 g l(-1) h(-1) was obtained, and a succinic acid concentration of 51.6 g l(-1) with a yield of 75.8% was reached. These results suggest that optimized conditions of CO(2) supply are effective in high succinic acid production and thus have potential applications in succinic acid production and CO(2) fixation.     

Direct effects of CO on cerebral energy metabolism in bloodless rats

Cerebrocortical b-cytochromes have been found to be sensitive to reduction in the presence of CO and O2 in vivo. CO-mediated cytochrome b reduction responses in "bloodless" rats were correlated in this study with changes in concentrations of high energy and glycolytic intermediates measured in cortex after rapid brain freezing. Cytochrome redox state and metabolite concentrations also were compared with cerebral blood flow (CBF) and cerebral metabolic rate for O2 (CMRo2) measured before and after CO administration. No definite biochemical evidence of energy limitation was found in parietal cortex after the fluorocarbon-for-blood exchange; however, CO had direct effects on brain metabolite concentrations. Fifteen-minute CO exposures at inspired CO/O2 of 0.003-0.06 increased cerebrocortical phosphocreatine and ADP and decreased creatine concentration. CO exposure produced no significant changes in either ATP concentration or CMRo2, although CBF increased slightly. These findings may be interpreted to indicate that CO binding to cytochrome aa3 at low CO/O2 in vivo increases extramitochondrial pH relative to that within the mitochondrial matrix. In the process, cytochrome b reduction levels increase, possibly signaling an increased efficiency of oxidative phosphorylation relative to O2 uptake by unblocked respiratory chains.     

Metabolome dynamic responses of Saccharomyces cerevisiae to simultaneous rapid perturbations in external electron acceptor and electron donor

Rapid perturbation experiments are highly relevant to elaborate the in vivo kinetics for mathematical models of metabolism, which are needed for selecting gene targets for metabolic engineering. Perturbations were applied to chemostat-cultivated biomass (D=0.05 h(-1), aerobic glucose/ethanol-limited) using the BioScope of Saccharomyces cerevisiae CEN. PK 113-7D over time span of 90 and 180 s. The availability of the external electron acceptor oxygen was decreased from fully aerobic to anaerobic conditions. It was observed that the changes in metabolome response under these conditions were limited to the pyruvate node. Acetaldehyde supply was used as an extra external electron acceptor during glucose perturbation under fully aerobic conditions. This had a strong effect on the metabolome dynamics and resulted in a significantly higher initial glycolytic flux. Dynamic response of the adenine nucleotides indicated that their behavior is not dictated by the glycolytic flux but is much more coupled to the cytosolic NADH/NAD(+) ratio through the equilibrium pool of fructose 1,6-bisphosphate and 2/3-phosphoglycerate. Also, the electron donor availability (glucose) was decreased. This did not result in significant changes in the concentrations of the glycolytic and tricarboxylic acid cycle metabolites, whereas the adenine nucleotides, especially ADP and AMP, showed the opposite response to that observed in a glucose pulse experiment. Surprisingly, trehalose was not mobilized in the time frame of 180 s.     

Distributed parameter model of an airlift fermentor

A distributed parameter model for an airlift fermentor is presented. A riser represents the airlift fermentor, with plug flow in both gas and liquid phases, a well-mixed section that acts as gas separator, and a downcomer with plug flow. The set of equations proposed makes possible both the understanding and design of the system. Macroscopic balances shows a behavior that is very close to conventional continuous stirred tank fermentor from the viewpoint of biomass production. In addition, the model predicts concentration profiles of biomass, substrate and oxygen in the liquid, and oxygen in the gas phase. This allows estimation of optimal gas flow rate for sufficient oxygen transfer with minimum energy input.     

Integrated sampling procedure for metabolome analysis

Metabolome analysis, the analysis of large sets of intracellular metabolites, has become an important systems analysis method in biotechnological and pharmaceutical research. In metabolic engineering, the integration of metabolome data with fluxome and proteome data into large-scale mathematical models promises to foster rational strategies for strain and cell line improvement. However, the development of reproducible sampling procedures for quantitative analysis of intracellular metabolite concentrations represents a major challenge, accomplishing (i) fast transfer of sample, (ii) efficient quenching of metabolism, (iii) quantitative metabolite extraction, and (iv) optimum sample conditioning for subsequent quantitative analysis. In addressing these requirements, we propose an integrated sampling procedure. Simultaneous quenching and quantitative extraction of intracellular metabolites were realized by short-time exposure of cells to temperatures < or =95 degrees C, where intracellular metabolites are released quantitatively. Based on these findings, we combined principles of heat transfer with knowledge on physiology, for example, turnover rates of energy metabolites, to develop an optimized sampling procedure based on a coiled single tube heat exchanger. As a result, this sampling procedure enables reliable and reproducible measurements through (i) the integration of three unit operations into a one unit operation, (ii) the avoidance of any alteration of the sample due to chemical reagents in quenching and extraction, and (iii) automation. A sampling frequency of 5 s(-)(1) and an overall individual sample processing time faster than 30 s allow observing responses of intracellular metabolite concentrations to extracellular stimuli on a subsecond time scale. Recovery and reliability of the unit operations were analyzed. Impact of sample conditioning on subsequent IC-MS analysis of metabolites was examined as well. The integrated sampling procedure was validated through consistent results from steady-state metabolite analysis of Escherichia coli cultivated in a chemostat at D = 0.1 h(-)(1).     

Influence of body CO2 stores on ventilatory dynamics during exercise

Pulmonary CO2 flow (the product of cardiac output and mixed venous CO2 content) is purported to be an important determinant of ventilatory dynamics in moderate exercise. Depletion of body CO2 stores prior to exercise should thus slow these dynamics. We investigated, therefore, the effects of reducing the CO2 stores by controlled volitional hyperventilation on cardiorespiratory and gas exchange response dynamics to 100 W cycling in six healthy adults. The control responses of ventilation (VE), CO2 output (VCO2), O2 uptake (VO2), and heart rate were comprised of an abrupt increase at exercise onset, followed by a slower rise to the new steady state (t1/2 = 48, 43, 31, and 33 s, respectively). Following volitional hyperventilation (9 min, PETCO2 = 25 Torr), the steady-state exercise responses were unchanged. However, VE and VCO2 dynamics were slowed considerably (t1/2 = 76, 71 s) as PETCO2 rose to achieve the control exercise value. VO2 dynamics were slowed only slightly (t1/2 = 39 s), and heart rate dynamics were unaffected. We conclude that pulmonary CO2 flow provides a significant stimulus to the dynamics of the exercise hyperpnea in man.     

Quantitative analysis of flux along the gluconeogenic, glycolytic and pentose phosphate pathways under reducing conditions in hepatocytes isolated from fed rats.

Hepatocytes were isolated from the livers of fed rats and incubated with a mixture of glucose (10 mM), ribose (1 mM), mannose (4 mM), glycerol (3 mM), acetate (1.25 mM), and ethanol (5 mM) with one substrate labelled with 14C in any given incubation. Incorporation of label into CO2, glucose, glycogen, lipid glycerol and fatty acids, acetate and C-1 of glucose was measured at 20 and 40 min after the start of the incubation. The data (about 48 measurements for each interval) were used in conjunction with a single-compartment model of the reactions of the gluconeogenic, glycolytic and pentose phosphate pathways and a simplified model of the relevant mitochondrial reactions. An improved method of computer analysis of the equations describing the flow of label through each carbon atom of each metabolite under steady-state conditions was used to compute values for the 34 independent flux parameters in this model. A good fit to the data was obtained, thereby permitting good estimates of most of the fluxes in the pathways under consideration. The data show that: net flux above the level of the triose phosphates is gluconeogenic; label in the hexose phosphates is fully equilibrated by the second 20 min interval; the triose phosphate isomerase step does not equilibrate label between the triose phosphates; substrate cycles are operating at the glucose-glucose 6-phosphate, fructose 6-phosphate-fructose 1,6-bisphosphate and phosphoenolpyruvate-pyruvate-oxaloacetate cycles; and, although net flux through the enzymes catalysing the non-oxidative steps of the pentose phosphate pathway is small, bidirectional fluxes are large.