Elucidating yeast glycolytic dynamics at steady state growth and glucose pulses through kinetic metabolic modeling

Microbial cell factories face changing environments during industrial fermentations. Kinetic metabolic models enable the simulation of the dynamic metabolic response to these perturbations, but their development is challenging due to model complexity and experimental data requirements. An example of this is the well-established microbial cell factory Saccharomyces cerevisiae, for which no consensus kinetic model of central metabolism has been developed and implemented in industry. Here, we aim to bring the academic and industrial communities closer to this consensus model. We developed a physiology informed kinetic model of yeast glycolysis connected to central carbon metabolism by including the effect of anabolic reactions precursors, mitochondria and the trehalose cycle. To parametrize such a large model, a parameter estimation pipeline was developed, consisting of a divide and conquer approach, supplemented with regularization and global optimization. Additionally, we show how this first mechanistic description of a growing yeast cell captures experimental dynamics at different growth rates and under a strong glucose perturbation, is robust to parametric uncertainty and explains the contribution of the different pathways in the network. Such a comprehensive model could not have been developed without using steady state and glucose perturbation data sets. The resulting metabolic reconstruction and parameter estimation pipeline can be applied in the future to study other industrially-relevant scenarios. We show this by generating a hybrid CFD-metabolic model to explore intracellular glycolytic dynamics for the first time. The model suggests that all intracellular metabolites oscillate within a physiological range, except carbon storage metabolism, which is sensitive to the extracellular environment.

Kinetic Modeling of Saccharomyces cerevisiae Central Carbon Metabolism: Achievements, Limitations, and Opportunities

Central carbon metabolism comprises the metabolic pathways in the cell that process nutrients into energy, building blocks and byproducts. To unravel the regulation of this network upon glucose perturbation, several metabolic models have been developed for the microorganism Saccharomyces cerevisiae. These dynamic representations have focused on glycolysis and answered multiple research questions, but no commonly applicable model has been presented. This review systematically evaluates the literature to describe the current advances, limitations, and opportunities. Different kinetic models have unraveled key kinetic glycolytic mechanisms. Nevertheless, some uncertainties regarding model topology and parameter values still limit the application to specific cases. Progressive improvements in experimental measurement technologies as well as advances in computational tools create new opportunities to further extend the model scale. Notably, models need to be made more complex to consider the multiple layers of glycolytic regulation and external physiological variables regulating the bioprocess, opening new possibilities for extrapolation and validation. Finally, the onset of new data representative of individual cells will cause these models to evolve from depicting an average cell in an industrial fermenter, to characterizing the heterogeneity of the population, opening new and unseen possibilities for industrial fermentation improvement.

Dietary nitrate does not reduce oxygen cost of exercise or improve muscle mitochondrial function in patients with mitochondrial myopathy

Muscle weakness and exercise intolerance negatively affect the quality of life of patients with mitochondrial myopathy. Short-term dietary nitrate supplementation has been shown to improve exercise performance and reduce oxygen cost of exercise in healthy humans and trained athletes. We investigated whether 1 wk of dietary inorganic nitrate supplementation decreases the oxygen cost of exercise and improves mitochondrial function in patients with mitochondrial myopathy. Ten patients with mitochondrial myopathy (40 ± 5 yr, maximal whole body oxygen uptake = 21.2 ± 3.2 ml·min−1·kg body wt−1, maximal work load = 122 ± 26 W) received 8.5 mg·kg body wt−1·day−1 inorganic nitrate (~7 mmol) for 8 days. Whole body oxygen consumption at 50% of the maximal work load, in vivo skeletal muscle oxidative capacity (evaluated from postexercise phosphocreatine recovery using 31P-magnetic resonance spectroscopy), and ex vivo mitochondrial oxidative capacity in permeabilized skinned muscle fibers (measured with high-resolution respirometry) were determined before and after nitrate supplementation. Despite a sixfold increase in plasma nitrate levels, nitrate supplementation did not affect whole body oxygen cost during submaximal exercise. Additionally, no beneficial effects of nitrate were found on in vivo or ex vivo muscle mitochondrial oxidative capacity. This is the first time that the therapeutic potential of dietary nitrate for patients with mitochondrial myopathy was evaluated. We conclude that 1 wk of dietary nitrate supplementation does not reduce oxygen cost of exercise or improve mitochondrial function in the group of patients tested.

Muscle Metabolic Responses During Dynamic In-Magnet Exercise Testing: A Pilot Study in Children with an Idiopathic Inflammatory Myopathy

RATIONALE AND OBJECTIVES

The clinical utility of supine in-magnet bicycling in combination with phosphorus magnetic resonance spectroscopy ((31)P MRS) to evaluate quadriceps muscle metabolism was examined in four children with juvenile dermatomyositis (JDM) in remission and healthy age- and gender-matched controls.

MATERIALS AND METHODS

Two identical maximal supine bicycling tests were performed using a magnetic resonance-compatible ergometer. During the first test, cardiopulmonary performance was established in the exercise laboratory. During the second test, quadriceps energy balance and acid/base balance during incremental exercise and phosphocreatine recovery were determined using (31)P MRS.

RESULTS

During the first test, no significant differences were found between patients with JDM and their healthy peers regarding cardiopulmonary performance. The outcomes of the first test indicate that both groups attained maximal performance. During the second test, quadriceps phosphocreatine and pH time courses were similar in all but one patient experiencing idiopathic postexercise pain. This patient demonstrated faster phosphocreatine depletion and acidification during exercise, yet postexercise mitochondrial adenosine triphosphate synthesis rate measured by phosphocreatine recovery kinetics was approximately twofold faster than control (time constant 23 seconds vs 43 ± 7 seconds, respectively).

CONCLUSIONS

These results highlight the utility of in-magnet cycle ergometry in combination with (31)P MRS to assess and monitor muscle energetic patterns in pediatric patients with inflammatory myopathies.

31P MR spectroscopy and computational modeling identify a direct relation between Pi content of an alkaline compartment in resting muscle and phosphocreatine resynthesis kinetics in active muscle in humans

The assessment of mitochondrial properties in skeletal muscle is important in clinical research, for instance in the study of diabetes. The gold standard to measure mitochondrial capacity non-invasively is the phosphocreatine (PCr) recovery rate after exercise, measured by (31)P Magnetic Resonance spectroscopy ((31)P MRS). Here, we sought to expand the evidence base for an alternative method to assess mitochondrial properties which uses (31)P MRS measurement of the Pi content of an alkaline compartment attributed to mitochondria (Pi2; as opposed to cytosolic Pi (Pi1)) in resting muscle at high magnetic field. Specifically, the PCr recovery rate in human quadriceps muscle was compared with the signal intensity of the Pi2 peak in subjects with varying mitochondrial content of the quadriceps muscle as a result of athletic training, and the results were entered into a mechanistic computational model of mitochondrial metabolism in muscle to test if the empirical relation between Pi2/Pi1 ratio and the PCr recovery was consistent with theory. Localized (31)P spectra were obtained at 7T from resting vastus lateralis muscle to measure the intensity of the Pi2 peak. In the endurance trained athletes a Pi2/Pi1 ratio of 0.07 ± 0.01 was found, compared to a significantly lower (p<0.05) Pi2/Pi1 ratio of 0.03 ± 0.01 in the normally active group. Next, PCr recovery kinetics after in magnet bicycle exercise were measured at 1.5T. For the endurance trained athletes, a time constant τPCr 12 ± 3 s was found, compared to 24 ± 5s in normally active subjects. Without any parameter optimization the computational model prediction matched the experimental data well (r(2) of 0.75). Taken together, these results suggest that the Pi2 resonance in resting human skeletal muscle observed at 7T provides a quantitative MR-based functional measure of mitochondrial density.

Combined in vivo and in silico investigations of activation of glycolysis in contracting skeletal muscle

The hypothesis was tested that the variation of in vivo glycolytic flux with contraction frequency in skeletal muscle can be qualitatively and quantitatively explained by calcium-calmodulin activation of phosphofructokinase (PFK-1). Ischemic rat tibialis anterior muscle was electrically stimulated at frequencies between 0 and 80 Hz to covary the ATP turnover rate and calcium concentration in the tissue. Estimates of in vivo glycolytic rates and cellular free energetic states were derived from dynamic changes in intramuscular pH and phosphocreatine content, respectively, determined by phosphorus magnetic resonance spectroscopy ((31)P-MRS). Computational modeling was applied to relate these empirical observations to understanding of the biochemistry of muscle glycolysis. Hereto, the kinetic model of PFK activity in a previously reported mathematical model of the glycolytic pathway (Vinnakota KC, Rusk J, Palmer L, Shankland E, Kushmerick MJ. J Physiol 588: 1961-1983, 2010) was adapted to contain a calcium-calmodulin binding sensitivity. The two main results were introduction of regulation of PFK-1 activity by binding of a calcium-calmodulin complex in combination with activation by increased concentrations of AMP and ADP was essential to qualitatively and quantitatively explain the experimental observations. Secondly, the model predicted that shutdown of glycolytic ATP production flux in muscle postexercise may lag behind deactivation of PFK-1 (timescales: 5-10 s vs. 100-200 ms, respectively) as a result of accumulation of glycolytic intermediates downstream of PFK during contractions.

Computational modeling of mitochondrial energy transduction

Mitochondria are the power plant of the heart, burning fat and sugars to supply the muscle with the adenosine triphosphate (ATP) free energy that drives contraction and relaxation during each heart beat. This function was first captured in a mathematical model in 1967. Today, interest in such a model has been rekindled by ongoing in silico integrative physiology efforts such as the Cardiac Physiome project. Here, the status of the field of computational modeling of mitochondrial ATP synthetic function is reviewed.

Prediction of muscle energy states at low metabolic rates requires feedback control of mitochondrial respiratory chain activity by inorganic phosphate

The regulation of the 100-fold dynamic range of mitochondrial ATP synthesis flux in skeletal muscle was investigated. Hypotheses of key control mechanisms were included in a biophysical model of oxidative phosphorylation and tested against metabolite dynamics recorded by (31)P nuclear magnetic resonance spectroscopy ((31)P MRS). Simulations of the initial model featuring only ADP and Pi feedback control of flux failed in reproducing the experimentally sampled relation between myoplasmic free energy of ATP hydrolysis (ΔG(p) = ΔG(p)(o')+RT ln ([ADP][Pi]/[ATP]) and the rate of mitochondrial ATP synthesis at low fluxes (<0.2 mM/s). Model analyses including Monte Carlo simulation approaches and metabolic control analysis (MCA) showed that this problem could not be amended by model re-parameterization, but instead required reformulation of ADP and Pi feedback control or introduction of additional control mechanisms (feed forward activation), specifically at respiratory Complex III. Both hypotheses were implemented and tested against time course data of phosphocreatine (PCr), Pi and ATP dynamics during post-exercise recovery and validation data obtained by (31)P MRS of sedentary subjects and track athletes. The results rejected the hypothesis of regulation by feed forward activation. Instead, it was concluded that feedback control of respiratory chain complexes by inorganic phosphate is essential to explain the regulation of mitochondrial ATP synthesis flux in skeletal muscle throughout its full dynamic range.

Unchanged muscle fiber conduction velocity relates to mild acidosis during exhaustive bicycling

Muscle fiber conduction velocity (MFCV) has often been shown to decrease during standardized fatiguing isometric contractions. However, several studies have indicated that the MFCV may remain constant during fatiguing dynamic exercise. It was investigated if these observations can be related to the absence of a large decrease in pH and if MFCV can be considered as a good indicator of acidosis, also during dynamic bicycle exercise. High-density surface electromyography (HDsEMG) was combined with read-outs of muscle energetics recorded by in vivo ³¹P magnetic resonance spectroscopy (MRS). Measurements were performed during serial exhausting bouts of bicycle exercise at three different workloads. The HDsEMG recordings revealed a small and incoherent variation of MFCV during all high-intensity exercise bouts. ³¹P MRS spectra revealed a moderate decrease in pH at the end of exercise (~0.3 units down to 6.8) and a rapid ancillary drop to pH 6.5 during recovery 30 s post-exercise. This additional degree of acidification caused a significant decrease in MFCV during cycling immediately after the rest period. From the data a significant correlation between MFCV and [H⁺] ([H⁺] = 10^−pH) was calculated (p < 0.001, Pearson’s R = −0.87). Our results confirmed the previous observations of MFCV remaining constant during fatiguing dynamic exercise. A constant MFCV is in line with a low degree of acidification, considering the presence of a correlation between pH and MFCV after further increasing acidification.

Similar mitochondrial activation kinetics in wild-type and creatine kinase-deficient fast-twitch muscle indicate significant Pi control of respiration

Past simulations of oxidative ATP metabolism in skeletal muscle have predicted that elimination of the creatine kinase (CK) reaction should result in dramatically faster oxygen consumption dynamics during transitions in ATP turnover rate. This hypothesis was investigated. Oxygen consumption of fast-twitch (FT) muscle isolated from wild-type (WT) and transgenic mice deficient in the myoplasmic (M) and mitochondrial (Mi) CK isoforms (MiM CK(-/-)) were measured at 20°C at rest and during electrical stimulation. MiM CK(-/-) muscle oxygen consumption activation kinetics during a step change in contraction rate were 30% faster than WT (time constant 53 ± 3 vs. 69 ± 4 s, respectively; mean ± SE, n = 8 and 6, respectively). MiM CK(-/-) muscle oxygen consumption deactivation kinetics were 380% faster than WT (time constant 74 ± 4 s vs. 264 ± 4 s, respectively). Next, the experiments were simulated using a computational model of the oxidative ATP metabolic network in FT muscle featuring ADP and Pi feedback control of mitochondrial respiration (J. A. L. Jeneson, J. P. Schmitz, N. A. van den Broek, N. A. van Riel, P. A. Hilbers, K. Nicolay, J. J. Prompers. Am J Physiol Endocrinol Metab 297: E774-E784, 2009) that was reparameterized for 20°C. Elimination of Pi control via clamping of the mitochondrial Pi concentration at 10 mM reproduced past simulation results of dramatically faster kinetics in CK(-/-) muscle, while inclusion of Pi control qualitatively explained the experimental observations. On this basis, it was concluded that previous studies of the CK-deficient FT muscle phenotype underestimated the contribution of Pi to mitochondrial respiratory control.

Silencing of glycolysis in muscle: experimental observation and numerical analysis

The longstanding problem of rapid inactivation of the glycolytic pathway in skeletal muscle after contraction was investigated using (31)P NMR spectroscopy and computational modelling. Accumulation of phosphorylated glycolytic intermediates (hexose monophosphates) during cyclic contraction and subsequent turnover during metabolic recovery was measured in vivo in human quadriceps muscle using dynamic (31)P NMR spectroscopy. The concentration of hexose monophosphates in muscle peaked 40 s into metabolic recovery from maximal contractile work at 6.9 +/- 1.3 mm (mean +/- s.d.; n = 8) and subsequently declined at a rate of 0.009 +/- 0.001 mm s(1). It was next tested whether the current knowledge of the kinetic controls in the glycolytic pathway in muscle integrated in the Lambeth and Kushmerick computational model of skeletal muscle glycolysis explained the experimental data. It was found that the model underestimated the magnitude of deactivation of the glycolytic pathway in resting muscle, resulting in depletion of glycolytic intermediates and substrate for oxidative ATP synthesis. Numerical analysis of the model identified phosphofructokinase and pyruvate kinase as the kinetic control sites involved in deactivation of the glycolytic pathway. Ancillary 100-fold inhibition of both phosphofructokinase and pyruvate kinase was found necessary to predict glycolytic intermediate and ADP concentrations correctly in resting human muscle. Incorporation of this information into the model resulted in highly improved agreement between predicted and measured in vivo dynamics of hexose monophosphates in muscle following contraction. We concluded that silencing of the glycolytic pathway in muscle following contraction is most likely to be mediated by phosphofructokinase and pyruvate kinase inactivation on a time scale of seconds and minutes, respectively, and is necessary to prevent depletion of vital cellular substrates.

Magnitude and control of mitochondrial sensitivity to ADP

The transduction function for ADP stimulation of mitochondrial ATP synthesis in skeletal muscle was reconstructed in vivo and in silico to investigate the magnitude and origin of mitochondrial sensitivity to cytoplasmic ADP concentration changes. Dynamic in vivo measurements of human leg muscle phosphocreatine (PCr) content during metabolic recovery from contractions were performed by (31)P-NMR spectroscopy. The cytoplasmic ADP concentration ([ADP]) and rate of oxidative ATP synthesis (Jp) at each time point were calculated from creatine kinase equilibrium and the derivative of a monoexponential fit to the PCr recovery data, respectively. Reconstructed [ADP]-Jp relations for individual muscles containing more than 100 data points were kinetically characterized by nonlinear curve fitting yielding an apparent kinetic order and ADP affinity of 1.9 +/- 0.2 and 0.022 +/- 0.003 mM, respectively (means +/- SD; n = 6). Next, in silico [ADP]-Jp relations for skeletal muscle were generated using a computational model of muscle oxidative ATP metabolism whereby model parameters corresponding to mitochondrial enzymes were randomly changed by 50-150% to determine control of mitochondrial ADP sensitivity. The multiparametric sensitivity analysis showed that mitochondrial ADP ultrasensitivity is an emergent property of the integrated mitochondrial enzyme network controlled primarily by kinetic properties of the adenine nucleotide translocator.