Kinetic modelling of glycolytic oscillations.

Glycolytic oscillations have been studied for well over 60 years, but aspects of their function, and mechanisms of regulation and synchronisation remain unclear. Glycolysis is amenable to mechanistic mathematical modelling, as its components have been well characterised, and the system can be studied at many organisational levels: in vitro reconstituted enzymes, cell free extracts, individual cells, and cell populations. In recent years, the emergence of individual cell analysis has opened new ways of studying this intriguing system.

Is distance from equilibrium a good indicator for a reaction's flux control?

By analysing a large set of models obtained from the JWS Online and Biomodels databases, we tested to what extent the disequilibrium ratio can be used as an estimator for the flux control of a reaction, a discussion point that was already raised by Kacser and Burns, and Heinrich and Rapoport in their seminal MCA manuscripts. Whereas no functional relation was observed, the disequilibrium ratio can be used as an estimator for the maximal flux control of a reaction step. We extended the original analysis of the relationship by incorporating the overall pathway disequilibrium ratio in the expression, which made it possible to make explicit expressions for flux control coefficients.

A detailed kinetic model of glycolysis in Plasmodium falciparum-infected red blood cells for antimalarial drug target identification.

Upon infection by the malaria parasite Plasmodium falciparum, the glycolytic rate of a red blood cell increases up to 100-fold, possibly contributing to lactic acidosis and hypoglycemia in patients with severe malaria. This dramatic increase in glucose uptake and metabolism was correctly predicted by a newly constructed detailed enzyme kinetic model of glucose metabolism in the trophozoite-infected red blood cell. Subsequently, we expanded the model to simulate an infected red blood cell culture, including the different asexual blood-stage forms of the malaria parasite. The model simulations were in good agreement with experimental data, for which the measured parasitic volume was an important parameter. Upon further analysis of the model, we identified glucose transport as a drug target that would specifically affect infected red blood cells, which was confirmed experimentally with inhibitor titrations. This model can be a first step in constructing a whole-body model for glucose metabolism in malaria patients to evaluate the contribution of the parasite's metabolism to the disease state.

Inhibitor titrations reveal low control of glyceraldehyde 3-phosphate dehydrogenase and high control of hexokinase on glycolytic flux in an aggressive triple-negative breast cancer cell line.

The glycolytic flux, and in particular lactate production, is strongly increased in cancer cells compared to normal cells, a characteristic often referred to as aerobic glycolysis or the Warburg effect. This makes the glycolytic pathway a potential drug target, in particular if the flux control distribution in the pathway has shifted due to the metabolic reprogramming in cancer cells. The flux response of a drug is dependent on both the sensitivity of the target to the drug and the flux control of the target, and both these characteristics can be exploited to obtain selectivity for cancer cells. Traditionally drug development programs have focused on selective sensitivity of the drug, not necessarily focussing on the flux control of the target. We determined the flux control of two steps that have been suggested to have high control in cancer cells, using two inhibitors, iodoacetic acid and 3-bromopyruvate, and measured a flux control of the glyceraldehyde 3-phosphate dehydrogenase close to zero, while the hexokinase holds 50% of all flux control in glycolysis in an invasive cancer cell line MDA-mb-231.

Uncovering the effects of heterogeneity and parameter sensitivity on within-host dynamics of disease: malaria as a case study.

BACKGROUND: The fidelity and reliability of disease model predictions depend on accurate and precise descriptions of processes and determination of parameters. Various models exist to describe within-host dynamics during malaria infection but there is a shortage of clinical data that can be used to quantitatively validate them and establish confidence in their predictions. In addition, model parameters often contain a degree of uncertainty and show variations between individuals, potentially undermining the reliability of model predictions. In this study models were reproduced and analysed by means of robustness, uncertainty, local sensitivity and local sensitivity robustness analysis to establish confidence in their predictions. RESULTS: Components of the immune system are responsible for the most uncertainty in model outputs, while disease associated variables showed the greatest sensitivity for these components. All models showed a comparable degree of robustness but displayed different ranges in their predictions. In these different ranges, sensitivities were well-preserved in three of the four models. CONCLUSION: Analyses of the effects of parameter variations in models can provide a comparative tool for the evaluation of model predictions. In addition, it can assist in uncovering model weak points and, in the case of disease models, be used to identify possible points for therapeutic intervention.

Computational modelling of the Δ4 and Δ5 adrenal steroidogenic pathways provides insight into hypocortisolism.

This study demonstrates the application of a mathematical steroidogenic model, constructed with individual in vitro enzyme characterisations, to simulate in vivo steroidogenesis in a diseased state. This modelling approach was applied to the South African Angora goat, that suffers from hypocortisolism caused by altered adrenal function. These animals are extremely vulnerable to cold stress, leading to substantial monetary loss in the mohair industry. The Angora goat has increased CYP17A1 17,20-lyase enzyme activity in comparison with hardy livestock species. Determining the effect of this altered adrenal function on adrenal steroidogenesis during a cold stress response is difficult. We developed a model describing adrenal steroidogenesis under control conditions, and under altered steroidogenic conditions where the animal suffers from hypocortisolism. The model is parameterised with experimental data from in vitro enzyme characterisations of a hardy control species. The increased 17,20-lyase activity of the Angora goat CYP17A1 enzyme was subsequently incorporated into the model and the response to physiological stress is simulated under both control and altered adrenal steroidogenic conditions.

Intercellular communication induces glycolytic synchronization waves between individually oscillating cells.

Many organs have internal structures with spatially differentiated and sometimes temporally synchronized groups of cells. The mechanisms leading to such differentiation and coordination are not well understood. Here we design a diffusion-limited microfluidic system to mimic a multicellular organ structure with peripheral blood flow and test whether a group of individually oscillating yeast cells could form subpopulations of spatially differentiated and temporally synchronized cells. Upon substrate addition, the dynamic response at single-cell level shows glycolytic oscillations, leading to wave fronts traveling through the monolayered population and to synchronized communities at well-defined positions in the cell chamber. A detailed mechanistic model with the architectural structure of the flow chamber incorporated successfully predicts the spatial-temporal experimental data, and allows for a molecular understanding of the observed phenomena. The intricate interplay of intracellular biochemical reaction networks leading to the oscillations, combined with intercellular communication via metabolic intermediates and fluid dynamics of the reaction chamber, is responsible for the generation of the subpopulations of synchronized cells. This mechanism, as analyzed from the model simulations, is experimentally tested using different concentrations of cyanide stress solutions. The results are reproducible and stable, despite cellular heterogeneity, and the spontaneous community development is reminiscent of a zoned cell differentiation often observed in multicellular organs.

Studying Glycolytic Oscillations in Individual Yeast Cells by Combining Fluorescence Microscopy with Microfluidics and Optical Tweezers.

In this unit, we provide a clear exposition of the methodology employed to study dynamic responses in individual cells, using microfluidics for controlling and adjusting the cell environment, optical tweezers for precise cell positioning, and fluorescence microscopy for detecting intracellular responses. This unit focuses on the induction and study of glycolytic oscillations in single yeast cells, but the methodology can easily be adjusted to examine other biological questions and cell types. We present a step-by-step guide for fabrication of the microfluidic device, for alignment of the optical tweezers, for cell preparation, and for time-lapse imaging of glycolytic oscillations in single cells, including a discussion of common pitfalls. A user who follows the protocols should be able to detect clear metabolite time traces over the course of up to an hour that are indicative of dynamics on the second scale in individual cells during fast and reversible environmental adjustments. © 2018 by John Wiley & Sons, Inc.

Phosphofructokinase controls the acetaldehyde-induced phase shift in isolated yeast glycolytic oscillators.

The response of oscillatory systems to external perturbations is crucial for emergent properties such as synchronisation and phase locking and can be quantified in a phase response curve (PRC). In individual, oscillating yeast cells, we characterised experimentally the phase response of glycolytic oscillations for external acetaldehyde pulses and followed the transduction of the perturbation through the system. Subsequently, we analysed the control of the relevant system components in a detailed mechanistic model. The observed responses are interpreted in terms of the functional coupling and regulation in the reaction network. We find that our model quantitatively predicts the phase-dependent phase shift observed in the experimental data. The phase shift is in agreement with an adaptation leading to synchronisation with an external signal. Our model analysis establishes that phosphofructokinase plays a key role in the phase shift dynamics as shown in the PRC and adaptation time to external perturbations. Specific mechanism-based interventions, made possible through such analyses of detailed models, can improve upon standard trial and error methods, e.g. melatonin supplementation to overcome jet-lag, which are error-prone, specifically, since the effects are phase dependent and dose dependent. The models by Gustavsson and Goldbeter discussed in the text can be obtained from the JWS Online simulation database: (https://jjj.bio.vu.nl/models/gustavsson5 and https://jjj.bio.vu.nl/models/goldbeter1).

The JWS online simulation database.

SUMMARY: JWS Online is a web-based platform for construction, simulation and exchange of models in standard formats. We have extended the platform with a database for curated simulation experiments that can be accessed directly via a URL, allowing one-click reproduction of published results. Users can modify the simulation experiments and export them in standard formats. The Simulation database thus lowers the bar on exploring computational models, helps users create valid simulation descriptions and improves the reproducibility of published simulation experiments. AVAILABILITY AND IMPLEMENTATION: The Simulation Database is available on line at https://jjj.bio.vu.nl/models/experiments/ . CONTACT: jls@sun.ac.za .

FAIRDOMHub: a repository and collaboration environment for sharing systems biology research.

The FAIRDOMHub is a repository for publishing FAIR (Findable, Accessible, Interoperable and Reusable) Data, Operating procedures and Models (https://fairdomhub.org/) for the Systems Biology community. It is a web-accessible repository for storing and sharing systems biology research assets. It enables researchers to organize, share and publish data, models and protocols, interlink them in the context of the systems biology investigations that produced them, and to interrogate them via API interfaces. By using the FAIRDOMHub, researchers can achieve more effective exchange with geographically distributed collaborators during projects, ensure results are sustained and preserved and generate reproducible publications that adhere to the FAIR guiding principles of data stewardship.

Targeting glycolysis in the malaria parasite Plasmodium falciparum.

UNLABELLED: Glycolysis is the main pathway for ATP production in the malaria parasite Plasmodium falciparum and essential for its survival. Following a sensitivity analysis of a detailed kinetic model for glycolysis in the parasite, the glucose transport reaction was identified as the step whose activity needed to be inhibited to the least extent to result in a 50% reduction in glycolytic flux. In a subsequent inhibitor titration with cytochalasin B, we confirmed the model analysis experimentally and measured a flux control coefficient of 0.3 for the glucose transporter. In addition to the glucose transporter, the glucokinase and phosphofructokinase had high flux control coefficients, while for the ATPase a small negative flux control coefficient was predicted. In a broader comparative analysis of glycolytic models, we identified a weakness in the P. falciparum pathway design with respect to stability towards perturbations in the ATP demand. DATABASE: The mathematical model described here has been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.bio.vu.nl/database/vanniekerk1. The SEEK-study including the experimental data set is available at DOI 10.15490/seek.1. INVESTIGATION: 56 (http://dx.doi.org/10.15490/seek.1. INVESTIGATION: 56).

Quantitative analysis of drug effects at the whole-body level: a case study for glucose metabolism in malaria patients.

We propose a hierarchical modelling approach to construct models for disease states at the whole-body level. Such models can simulate effects of drug-induced inhibition of reaction steps on the whole-body physiology. We illustrate the approach for glucose metabolism in malaria patients, by merging two detailed kinetic models for glucose metabolism in the parasite Plasmodium falciparum and the human red blood cell with a coarse-grained model for whole-body glucose metabolism. In addition we use a genome-scale metabolic model for the parasite to predict amino acid production profiles by the malaria parasite that can be used as a complex biomarker.

Construction and validation of a detailed kinetic model of glycolysis in Plasmodium falciparum.

UNLABELLED: The enzymes in the Embden-Meyerhof-Parnas pathway of Plasmodium falciparum trophozoites were kinetically characterized and their integrated activities analyzed in a mathematical model. For validation of the model, we compared model predictions for steady-state fluxes and metabolite concentrations of the hexose phosphates with experimental values for intact parasites. The model, which is completely based on kinetic parameters that were measured for the individual enzymes, gives an accurate prediction of the steady-state fluxes and intermediate concentrations. This is the first detailed kinetic model for glucose metabolism in P. falciparum, one of the most prolific malaria-causing protozoa, and the high predictive power of the model makes it a strong tool for future drug target identification studies. The modelling workflow is transparent and reproducible, and completely documented in the SEEK platform, where all experimental data and model files are available for download. DATABASE: The mathematical models described in the present study have been submitted to the JWS Online Cellular Systems Modelling Database (http://jjj.bio.vu.nl/database/penkler). The investigation and complete experimental data set is available on SEEK (10.15490/seek.1. INVESTIGATION: 56).

Allosteric regulation of phosphofructokinase controls the emergence of glycolytic oscillations in isolated yeast cells.

UNLABELLED: Oscillations are widely distributed in nature and synchronization of oscillators has been described at the cellular level (e.g. heart cells) and at the population level (e.g. fireflies). Yeast glycolysis is the best known oscillatory system, although it has been studied almost exclusively at the population level (i.e. limited to observations of average behaviour in synchronized cultures). We studied individual yeast cells that were positioned with optical tweezers in a microfluidic chamber to determine the precise conditions for autonomous glycolytic oscillations. Hopf bifurcation points were determined experimentally in individual cells as a function of glucose and cyanide concentrations. The experiments were analyzed in a detailed mathematical model and could be interpreted in terms of an oscillatory manifold in a three-dimensional state-space; crossing the boundaries of the manifold coincides with the onset of oscillations and positioning along the longitudinal axis of the volume sets the period. The oscillatory manifold could be approximated by allosteric control values of phosphofructokinase for ATP and AMP. DATABASE: The mathematical models described here have been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.mib.ac.uk/webMathematica/UItester.jsp?modelName=gustavsson5. [Database section added 14 May 2014 after original online publication].

Heterogeneity of glycolytic oscillatory behaviour in individual yeast cells.

There are many examples of oscillations in biological systems and one of the most investigated is glycolytic oscillations in yeast. These oscillations have been studied since the 1950s in dense, synchronized populations and in cell-free extracts, but it has for long been unknown whether a high cell density is a requirement for oscillations to be induced, or if individual cells can oscillate also in isolation without synchronization. Here we present an experimental method and a detailed kinetic model for studying glycolytic oscillations in individual, isolated yeast cells and compare them to previously reported studies of single-cell oscillations. The importance of single-cell studies of this phenomenon and relevant future research questions are also discussed.

From steady-state to synchronized yeast glycolytic oscillations II: model validation.

UNLABELLED: In an accompanying paper [du Preez et al., (2012) FEBS J279, 2810-2822], we adapt an existing kinetic model for steady-state yeast glycolysis to simulate limit-cycle oscillations. Here we validate the model by testing its capacity to simulate a wide range of experiments on dynamics of yeast glycolysis. In addition to its description of the oscillations of glycolytic intermediates in intact cells and the rapid synchronization observed when mixing out-of-phase oscillatory cell populations (see accompanying paper), the model was able to predict the Hopf bifurcation diagram with glucose as the bifurcation parameter (and one of the bifurcation points with cyanide as the bifurcation parameter), the glucose- and acetaldehyde-driven forced oscillations, glucose and acetaldehyde quenching, and cell-free extract oscillations (including complex oscillations and mixed-mode oscillations). Thus, the model was compliant, at least qualitatively, with the majority of available experimental data for glycolytic oscillations in yeast. To our knowledge, this is the first time that a model for yeast glycolysis has been tested against such a wide variety of independent data sets. DATABASE: The mathematical models described here have been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem.sun.ac.za/database/dupreez/index.html.

From steady-state to synchronized yeast glycolytic oscillations I: model construction.

UNLABELLED: An existing detailed kinetic model for the steady-state behavior of yeast glycolysis was tested for its ability to simulate dynamic behavior. Using a small subset of experimental data, the original model was adapted by adjusting its parameter values in three optimization steps. Only small adaptations to the original model were required for realistic simulation of experimental data for limit-cycle oscillations. The greatest changes were required for parameter values for the phosphofructokinase reaction. The importance of ATP for the oscillatory mechanism and NAD(H) for inter-and intra-cellular communications and synchronization was evident in the optimization steps and simulation experiments. In an accompanying paper [du Preez F et al. (2012) FEBS J279, 2823-2836], we validate the model for a wide variety of experiments on oscillatory yeast cells. The results are important for re-use of detailed kinetic models in modular modeling approaches and for approaches such as that used in the Silicon Cell initiative. DATABASE: The mathematical models described here have been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem.sun.ac.za/database/dupreez/index.html.

Sustained glycolytic oscillations in individual isolated yeast cells.

UNLABELLED: Yeast glycolytic oscillations have been studied since the 1950s in cell-free extracts and intact cells. For intact cells, sustained oscillations have so far only been observed at the population level, i.e. for synchronized cultures at high biomass concentrations. Using optical tweezers to position yeast cells in a microfluidic chamber, we were able to observe sustained oscillations in individual isolated cells. Using a detailed kinetic model for the cellular reactions, we simulated the heterogeneity in the response of the individual cells, assuming small differences in a single internal parameter. This is the first time that sustained limit-cycle oscillations have been demonstrated in isolated yeast cells. DATABASE: The mathematical model described here has been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem.sun.ac.za/database/gustavsson/index.html free of charge.