Regimes are defined in Table 3. Introducing each new element of our model in turn to examine this same parameter space, we first include our deterministic variation of the frequency and analyse for intermittent synchronization, as well as permanent, but otherwise maintain the Lancaster et al.

The results are in Figure 4B , and the main regimes described in Table 3. This results in the splitting of the red region in the Lancaster et al. The dark blue region, where only glycolysis and OXPHOS are synchronized, is also made significantly larger, and there are spots of intermittently synchronized regimes that appear only briefly throughout the parameter space.

The next step is to introduce unweighted networks of glycolysis and OXPHOS oscillators. The result is in Figure 4C. This introduces a new regime, where only the networks are internally synchronized, and converts the dark green regime, where there is no synchronization, into the even further increased dark blue regime.

Once again, intermittent regimes are spotted briefly throughout the parameter space. The final step in constructing our full model, is to weight the glycolysis and OXPHOS networks according to Equations 3 and 4.

Figure 4D shows the results of this final simulation. This splits the new regime observed in the previous simulation into the purple, green and cyan regimes: the purple representing the same permanent synchronization within each network, the green a new intermittent synchronization of the OXPHOS network, and the cyan a new intermittent synchronization of the glycolysis network.

The weighting reduces the size of the dark blue region, giving more space to the blue and light blue, and as in the previous simulations produces small regimes of intermittent synchronization. In Amemiya et al. This model adopted an approach more similar to the mainstream discussed in the previous section.

We therefore offer a comparison between this model and the one we have presented here, to help illuminate further the differences between our approach and ones more characteristic of the cellular modeling mainstream, applied in the context of this experiment.

The Amemiya et al. The former is modeled as the first step, converting glucose and ATP into intermediaries, while the second is the last reaction, converting these intermediaries into ATP and pools of NADH and other products. The model focuses on the masses of the metabolites required for these reactions, from their entry into the cell to their consumption in the metabolic process.

This technique consists of seven autonomous linear differential equations and twenty two parameters to model the glycolysis metabolic branch only, which contrasts to the four non-autonomous non-linear oscillator equations of Equation 7 and the thirteen parameters of Table 2 to model both the glycolysis and OXPHOS branches.

In addition to a measure of coherence within a network, the order parameter may also be considered the amplitude of the network's mean field.

We can therefore consider it both an indication of the amplitude of our system, and the degree to which the glycolysis and OXPHOS networks are operating effectively. We introduce a modified Kuramoto order parameter s , where.

which takes into account both networks. This parameter can be compared to the time series of NADH fluorescence from a single cell in the Amemiya et al. We provide this comparison in Figure 6 , and this can be further compared to an equivalent output of the model in Figure 2 of Amemiya et al.

The modulation frequency of the glycolysis oscillations was extracted from group coherence analysis of the Amemiya et al. data, which found that for both cell groups close to and far from one another there was significantly coherent oscillations in the range 0.

This analysis is presented in Figure 5. The other frequencies were selected to maintain the same ratio with the extracted glycolysis modulation as discussed in Lancaster et al. Over the next This results in a trending decrease in the networks' amplitude and the emergence of oscillations.

After For the final s of the simulation F GO and F MO have reached 0 as the cells begin to die, their oscillations continue to diminish, and their NADH production dries up. Figure 5. Surrogate tested coherence between groups of cells examined in Amemiya et al. Red coloring indicates groups of cells far from one another, —1, μ m distance between their average positions, and blue close to one another, —μ m distance between their average positions.

The dimensions of the culture were 1, by 1, μ m. The solid colored lines are the median coherence of each pair of groups, and the shaded regions the range from the minimum to maximum coherence.

Figure 6. A Simulation of the HeLa experiment using a modified order parameter. B The time series of NADH fluorescence in a single cell in the Amemiya et al.

While the curve presented in Figure 6A depends on the initial phases of each oscillator, which are randomized, and therefore will not be identical from simulation to simulation, its oscillator features and overall trend are indicative of the parameters in Table 4.

And while this simulation is not an identical reflection of the experiment in every feature, it is an indication of the capacity of our model to reproduce the oscillating nature of biological processes, and the ease with which it can be adapted to a plethora of different cells and circumstances.

The conversion of established metabolic models, such as that of Lancaster et al. The step from Figures 4B,C for example overhauls the parameter space, introducing entirely new regimes and destroying once-firm fixtures of the non-network model.

It is clear from all of these results that networks result in an even greater area of the parameter space featuring synchronization, with the only regime of total desynchronization disappearing once networks are introduced, and the networks themselves never being desynchronized. This aligns well with the imperative of such biological processes to remain robust against significant external perturbations, and the expectation that these parameter values do not represent catastrophic departure from the healthy state of the system.

More significant perturbations of the coupling parameters, to both higher values and the entire elimination of more coupling modes, are likely required to completely desynchronize the networks, which would represent even further departures from the healthy parameter states of the cell.

In healthy human cells, ATP is produced primarily through OXPHOS, with support from glycolysis. In our model, this may be represented by synchronization between the networks, and between the OXPHOS network and its oxygen driving Lancaster et al.

Internal synchronization of both networks is also required to characterize a healthy condition: disregulation within the metabolic processes is a key indicator of a malfunctioning cell.

This state is represented in the bottom right of each graph in Figure 4 , but is significantly diminished in area with the addition of deterministic frequency modulation from Figure Figures 4A,B.

A cancerous state, may be indicated by an opposite state: a mode switch to the dominance of glycolysis, known as the Warburg effect, is reflected by synchronization between the networks and between glycolysis and glucose, but not OXPHOS and oxygen Lancaster et al.

Due to the decreased relevance of OXPHOS to the metabolic process in cancer, it may be represented by either ordered or disordered OXPHOS networks. This regime is found in the top left of each of Figure 4 , similarly decreasing in area between Figures 4A,B as with the bottom right regime.

Network models also offer greater potential for oscillator systems: while reducing oscillating differential equations to just their phase provides a much simpler system that still contains the key dynamics, only at the mesoscopic level of networks of many oscillators can the system amplitude be rebuilt.

Further work on this model could therefore provide not just an order parameter of the network indicative of its activity, but an amplitude of its production. The turn to deterministic non-autonomous frequencies and finite time synchronization analysis similarly promises a significant change to the dynamics of metabolic models.

However, with the introduction of this non-autonomicity comes greater challenges for numerical simulations: the numerical integration of non-linear oscillating differential equations is an already delicate task, and the addition of another dimension of time sensitivity requires alternative methods.

Further work with more sensitive numerical integration algorithms and more sophisticated methods for identifying intermittent synchronization would be likely to find a far greater role of the phenomenon in the model's parameter spaces, and further clarify exactly which dynamic we can expect to find at each parameter combination.

Non-autonomous oscillations pose a particular challenge to numerical integration schemes due to their two highly distinct frequency modes. Schemes designed to adapt to this situation may be able to provide greater clarity on our model, with which we may be able to further identify parameters leading to pathological states and more complex dynamics within the model.

The measured data analyzed in this paper were originally collected and presented by Amemiya et al. They are available at doi: The MatLab codes used for numerical modeling and analyses of the numerical and measured data can be found at doi: JRA proposed the inclusion of weighted networks, designed and ran the numerical simulations of the model, performed thorough investigation of the model behavior including the intermittent synchronization analysis, and drafted the manuscript.

AS conceived the study, and proposed to incorporate networks instead of individual oscillators used in the earlier version of the model.

She oversaw the development of the work, provided regular guidance at every stage, and advised about the structure and the content of the manuscript. All authors edited the manuscript and approved the submitted version.

This work was funded by the EU's Horizon research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

We would like to thank Maxime Lucas, Yevhen Suprunenko, Julian Newman, Gemma Lancaster, Peter Kloeden, Sam McCormack, Juliane Bjerkan, Lars F. Olsen, Takashi Amemiya, Kenichi Shibata and Lawrence Sheppard for useful discussions of this work.

Additionally we thank Takashi Amemiya, Kenichi Shibata, Yoshihiro Itoh, Kiminori Itoh, Masatoshi Watanabe and Tomohiko Yamaguchi for sharing their experimental data with us, and Lawrence Sheppard for sharing his group coherence algorithm.

Numerical simulations were conducted using the High End Computing facility at Lancaster University. Akter, K. Diabetes mellitus and Alzheimer's disease: shared pathology and treatment? doi: PubMed Abstract CrossRef Full Text Google Scholar. Amemiya, T. Modeling studies of heterogeneities in glycolytic oscillations in hela cervical cancer cells.

Chaos Primordial oscillations in life: Direct observation of glycolytic oscillations in individual hela cervical cancer cells. CrossRef Full Text Google Scholar. Bandrivskyy, A. Wavelet phase coherence analysis: application to skin temperature and blood flow. Battle, C. Broken detailed balance at mesoscopic scales in active biological systems.

Science , — Bechtel, W. Complex Biological Mechanisms: Cyclic, Oscillatory, and Autonomous. Betz, A. Phase relationship of glycolytic intermediates in yeast cells with oscillatory metabolic control. Bosco, D. Possible implications of insulin resistance and glucose metabolism in Alzheimer's disease pathogenesis.

Carballido-Landeira, J. Nonlinear Dynamics in Biological Systems. New York, NY: Springer International Publishing. Catterall, W. The Hodgkin-Huxley heritage: from channels to circuits. Chaudhry, R. Biochemistry, Glycolysis. Treasure Island, FL: StatPearls Publishing.

Google Scholar. Cortassa, S. Computational modeling of mitochondrial function from a systems biology perspective. Mitochondrial Bioenerget.

Methods Mol. Ganitkevich, V. Glycolytic oscillations in single ischemic cardiomyocytes at near anoxia. Jafri, M. Modeling the mechanism of metabolic oscillations in ischemic cardiac myocytes. Jung, S. Kembro, J.

Mitochondrial chaotic dynamics: redox-energetic behavior at the edge of stability. Kennedy, R. Metabolic oscillations in beta-cells. Diabetes 51, S—S Kloeden, P. Nonautonomous Dynamical Systems. New York, NY: AMS Mathematical Surveys and Monographs. Kohnhorst, C.

Identification of a multienzyme complex for glucose metabolism in living cells. Kuramoto, Y. Chemical Oscillations, Waves, and Turbulence. Berlin: Springer-Verlag. Kurz, F. Spatio-temporal oscillations of individual mitochondria in cardiac myocytes reveal modulation of synchronized mitochondrial clusters.

Wavelet analysis reveals heterogeneous time-dependent oscillations of individual mitochondria. Heart Circ. Such effects could be associated with toxic effects of these molecules. NMR or near-infrared spectroscopy are non invasive techniques for monitoring energetic metabolism in vivo.

Clinical applications are developed for analysing brain, muscle or cardiac function in physiological and pathological conditions.

Abstract Cellular homeostasis requires permanent energy production and consumption. Publication types English Abstract Review. Enzymes bind temporarily to one or more of the reactants — the substrate s — of the reaction they catalyze.

In doing so, they lower the amount of activation energy needed and thus speed up the reaction. It is the major energy currency of the cell, providing the energy for most of the energy-consuming activities of the cell. It is one of the monomers used in the synthesis of RNA and, after conversion to deoxyATP dATP , DNA.

It regulates many biochemical pathways. NAD participates in many redox reactions in cells, including those in glycolysis and most of those in the citric acid cycle of cellular respiration.

NADP is the reducing agent produced by the light reactions of photosynthesis and is consumed in the Calvin cycle of photosynthesis and used in many other anabolic reactions. In eukaryotes, it occurs in the cytosol, where it converts a molecule of glucose into 2 molecules of pyruvic acid.

When isolated chloroplasts are illuminated, the medium in which they are suspended becomes alkaline — as we would predict if protons were being removed from the medium and pumped into the thylakoids where they reduce the pH to about 4.

Glutamine Cat. Glutamate Cat. Branched-Chain Amino Acids BCAA Cat. Triglyceride Cat. Glycerol Cat. Cholesterol Cat.

Cholesterol Ester Cat. BHB Ketone Body Cat. ATP Cat. ROS Cat. GSH Cat. Malate Cat. Pyruvate Cat. NAD P H Cat. Dehydrogenase Cat. Metabolite Cat. Glycolysis is the metabolic pathway that breaks down glucose, yielding pyruvate and energy in the form of ATP and NADH.

Glucose is the primary fuel for all tissue types, and therefore glycolysis is used by all cells for energy production. In aerobic environments, pyruvate from glycolysis proceeds to the TCA cycle.

When oxygen is limited, pyruvate is subsequently converted into lactate which is secreted. Glycolysis is induced upon T-cell activation. Human peripheral blood T-cells in culture were activated with antibodies to CD3 and CD28 immobilized on magnetic beads.

The observed metabolic signature, with decreased glucose and increased lactate in the media, correlates to increased glycolytic activity in the T-cells.

RLU, relative luminescence units. Glutaminolysis is the metabolic pathway that breaks down glutamine into glutamate and subsequently, into TCA cycle metabolites. Glutamine is an abundant free amino acid in blood, and glutaminolysis can be elevated in cancer to support elevated biosynthesis and tumor growth.

Elevated glutamine metabolism in cancer cells; as cells grow they continuously consume glutamine and secrete glutamate. SKOV-3 ovarian carcinoma cells were cultured for 48 hours. The red line represents the luminescence values of the medium controls in RLU, relative luminescence units.

Lipogenesis is the metabolic pathway that converts carbohydrate precursors into triglycerides, which are long-term energy storage molecules. Lipogenesis occurs primarily in adipocytes.

Values were plotted as concentration of triglyceride per microtissue MT. The data were generously provided by InSphero, AG, Zurich, Switzerland. Lipolysis is the metabolic pathway that breaks down triglycerides into fatty acids and glycerol.

This pathway is used to release stored energy during fasting or prolonged exercise. Lipolysis occurs primarily in adipocytes. Insulin-mediated inhibition of glycerol release in adipocytes.

Adipocytes differentiated from 3T3-L1 MBX cells were treated with combinations of isoproterenol 25nM and insulin nM. After 90 minutes of treatment, a sample of the media was removed from each well. Each condition was tested in triplicate, and the error bars represent standard deviation. Glycerol release from adipocytes is a proxy for lipolysis.

Here, isoproterenol-stimulated lipolysis was inhibited twofold by insulin. Insulin is the hormone responsible for controlling energy storage after meals. Insulin acts by binding to receptors on cells to trigger glucose uptake, glycogen synthesis for short-term energy storage, and triglyceride synthesis for long-term energy storage.

Diabetes mellitus results when insulin action does not occur properly either the body does not produce enough insulin, or the body does not respond to insulin. Inhibition of the Monocarboxylate Transporter 1 MCT1 Promotes 3T3-L1 Adipocyte Proliferation and Enhances Insulin Sensitivity.

Bailey, et al. International Journal of Molecular Sciences. Using Promega assays, the authors measure glucose uptake and triglyceride content of 3T3-L1 cells following insulin stimulation.

By analyzing multiple metabolites in parallel from your samples, you can get a comprehensive understanding of which metabolic pathways are most active in your model system.

Work from Garofano, et al. published in Nature Cancer characterizes glioblastoma subtypes. Using single cell RNA-seq, four unique tumor subtypes were determined based on cellular metabolic and developmental features.

Then, six different Promega metabolite assays were used to empirically validate the active metabolic pathways in patient-derived cell models for each subgroup including glucose uptake, glycolysis, glutaminolysis, lipid metabolism and oxidative stress.

Metabolic profiling was also used to test the efficacy of drugs for tumor subtypes. Hear from a scientist who helped develop our metabolite detection assays. Sign up to watch on-demand. Article: Choose the Right Bioluminescent NAD Detection Assay for Your Application.

Promega scientists wrote this article help you decide. Researchers often run these assays in parallel with their cellular metabolism assay. Read this article to get the details. We use these cookies to ensure our site functions securely and properly; they are necessary for our services to function and cannot be switched off in our systems.

They are usually only set in response to actions made by you which amount to a request for services, such as logging in, using a shopping cart or filling in forms. You can set your browser to block or alert you about these cookies, but some parts of our services will not work without them.

Like the other cookies we use, strictly necessary cookies may be either first-party cookies or third - party cookies. We use these cookies to remember your settings and preferences. For example, we may use these cookies to remember your language preferences. We use these cookies to collect information about how you interact with our services and to help us measure and improve them.

Although energy storage is inherently beneficial, exceeding the capacity for cells to store TGs has led to metabolic diseases such as obesity, diabetes, and fatty liver disease. We study how cells store metabolic energy as TGs in organelles called lipid droplets LDs. Specifically, we study the molecular basis for how cells synthesize TGs, how cells form LDs, how proteins target to LDs, and how TGs are utilized to meet energetic demands.

Our laboratory studies these fundamental questions using a wide range of cutting-edge interdisciplinary approaches, including biophysical, biochemical, and cell biological methods.

We also investigate the physiological importance of these lipid storage mechanisms in various cellular and animal models, including models of metabolic diseases or cancer. Identification of two pathways mediating protein targeting from ER to lipid droplets. Nat Cell Biol.

In this paper, for the sake of simplicity, we have selected phase oscillators and restricted the discussion to phase-phase interactions. Nevertheless, in observations of real life systems the chronotaxicity can be identified from phase dynamics alone, even when amplitude dynamics is complex 37 , thus making our model verifiable by experimental observations.

Moreover, by identifying the characteristics of chronotaxicity we have shown that one in principle can detect a transition to a carcinogenic state of cellular functioning, provided metabolic oscillations are present in both states of the cell.

The described inverse approach methods found evidence of chronotaxicity in this case, as expected from the numerical simulations of the model.

Cellular metabolism may be affected by many more processes and interactions than those considered here. The simplicity of the model could easily facilitate the inclusion of further couplings, for example the consideration of calcium dynamics or genetic factors in energy production.

Calcium has been shown to directly influence mitochondrial dynamics via many pathways 50 , 51 , while genetic mutations can have a direct effect on mitochondrial function These effects could be included in the model as influences to couplings, extra oscillators, or adaptations of the external drivers.

Results presented in this paper set up bases for experimental verification of the hypothesis that chronotaxicity can be used to identify transitions between metabolic states in a cell, for example the metabolic switch observed in cancer cells. We have demonstrated evidence of chronotaxicity in real metabolic oscillations, which led to a new way of studying metabolic processes inside a cell.

The model provides a framework within which the existing understanding of biochemical reactions involved in metabolic processes along with new observations based on recently introduced functional imaging methods 2 , 3 , 4 , 5 can be unified in a single picture.

Furthermore, focusing on the transitions between metabolic states could facilitate the development of new therapeutic strategies. As a real life example of driven metabolic oscillations we use glycolytic oscillations in individual isolated yeast cells recorded by Gustavsson et al.

The brief description of the experiments setup is presented below, for more details see the original work by Gustavsson and co-authors The class of chronotaxic systems identifies oscillatory dynamical systems with dynamics ordered in time chronos — time, taxis — order Such ordering is typical for driven oscillators, where the drive system determines the dynamics of a response system.

Chronotaxic systems can sustain their dynamics even with continuous external perturbations. Introduced for low-dimensional and high-dimensional dynamical systems 34 , 35 , 36 , chronotaxic systems have been shown to be useful in studies of living systems, one example being the application to the cardiorespiratory system In addition to living and open systems, which are in continuous contact with the external environment, chronotaxic systems are nonautonomous dynamical systems 29 , i.

their dynamics explicitly depends on time, as shown in the equation,. Alternatively, chronotaxic systems can be described by drive and response systems, as follows. The main defining feature of chronotaxic systems is a time-dependent steady state of point attractor x A t see Fig.

The trajectory x A t can be viewed as a uniformly hyperbolic trajectory 53 which is linearly attracting in such a way that the distance between a neighboring trajectory and x A t can only contract in an unperturbed chronotaxic system.

For more details and for relations between chronotaxic and other dynamical systems see ref. A simple example is given by unidirectionally coupled phase oscillators with phase φ X driven by a phase φ P as shown in the equation,. where and ω 0 is the natural frequency of the observed oscillator, is coupling strength and ω is the frequency of the driving oscillator.

The time-dependent point attractor will exist if the condition of chronotaxicity 35 is fulfilled, i. if and if the coupling strength ε t does not change its sign.

Taking into account that the dynamical system x is chronotaxic due to the influence from the driver p , chronotaxicity will change when the external influence from p changes.

This makes chronotaxicity a perfect candidate for investigation in the study of metabolic oscillators under changing driving influences. One of main advantages of chronotaxicity is that it can be identified experimentally from a single time series, whereas otherwise the identification of drive-response relationship would require measurements of the driver as well as the response system.

To identify chronotaxicity in a time series, a method named phase fluctuation analysis PFA was recently developed where Ψ s , t is the mother wavelet which is time-shifted according to t and scaled according to the parameter s.

The oscillation can then be traced in W T s , t. The instantaneous frequency of the oscillation at each time point can be estimated using either the synchrosqueezed wavelet transform 55 or a ridge-extraction method The phase is then calculated by integrating over the instantaneous frequency in time.

The estimation of angular velocity can be found by smoothing over the frequency extracted from the wavelet transform. In this approach, perturbations are assumed to be due to an uncorrelated Gaussian process.

In chronotaxic systems, perturbations decay due to the influence of the point attractor and the divergence from the attractor is similar to the original Gaussian process In contrast, in non-chronotaxic systems, where the phase of oscillation is neutrally stable, the perturbations are integrated over, resulting in a random walk i.

Brownian noise. To distinguish these two cases, detrended fluctuation analysis DFA 57 is performed on the phase fluctuations extracted from the time series.

The DFA technique explores the fractal self-similarity of fluctuations at different timescales in Δφ. The scaling of fluctuations is determined by the self-similarity parameter α.

To estimate α the time series is integrated in time and divided into sections of length n. The local trend is removed for each section by subtracting a fitted polynomial, usually a first order fit 57 , The root mean square fluctuation F n for the scale equal to n is then defined by the following equation,.

where Y n t is the integrated and detrended time series of length N. The self-similarity parameter is given by the gradient of the line of the plot of log F n against log n. The self-similarity parameter α for Δφ for uncorrelated Gaussian noise as expected in chronotaxic systems gives a value of 0.

In Fig. Supplementary Fig. S5 shows how this method may be applied for an example ATP signal obtained from the model. In order to reliably test for chronotaxicity, it should be noted that the time series should be sufficiently long, i. contain at least 30 cycles of oscillation may vary depending on the characteristics of the data , be evenly sampled and have a sampling frequency which is high enough to capture the dynamics at the frequency of interest How to cite this article : Lancaster, G.

et al. Modelling chronotaxicity of cellular energy metabolism to facilitate the identification of altered metabolic states. Törnroth-Horsefield, S. Opening and closing the metabolite gate. Article ADS CAS PubMed PubMed Central Google Scholar. Azarias, G. Selective ion changes during spontaneous mitochondrial transients in intact astrocytes.

PloS One 6, e, doi: Article CAS ADS PubMed PubMed Central Google Scholar. Merrins, M. Direct measurements of oscillatory glycolysis in pancreatic islet β-cells using novel fluorescence resonance energy transfer FRET biosensors for pyruvate kinase M2 activity. Article CAS PubMed PubMed Central Google Scholar.

Furuya, K. Real-time luminescence imaging of cellular ATP release. Methods 66, — Article CAS PubMed Google Scholar. Rieger, B. Lateral pH gradient between OXPHOS complex IV and F0F1 ATP-synthase in folded mitochondrial membranes.

Article CAS ADS PubMed Google Scholar. Ralph, S. Aspects Med. Cloonan, S. Mitochondria: commanders of innate immunity and disease? Wallace, D. Mitochondria and cancer. Cancer 12, — Seyfried, T. Cancer as a metabolic disease. Article CAS Google Scholar.

Kroemer, G. Cancer Cell 13, — Vander Heiden, M. Understanding the Warburg effect: the metabolic requirements of cell proliferation. Science , — Fulda, S. Targeting mitochondria for cancer therapy. Drug Discovery 9, — Aon, M.

Synchronized whole cell oscillations in mitochondrial metabolism triggered by a local release of reactive oxygen species in cardiac myocytes. Kurz, F. Wavelet analysis reveals heterogeneous time-dependent oscillations of individual mitochondria.

Heart Circ. O'Rourke, B. Oscillations of membrane current and excitability driven by metabolic oscillations in heart cells. Goldbeter, A.

Computational approaches to cellular rhythms. Nature , — Cortassa, S. A mitochondrial oscillator dependent on reactive oxygen species. Tu, B. Metabolic cycles as an underlying basis of biological oscillations.

Cell Biol. Mitochondrial oscillations in physiology and pathophysiology. Article CAS MathSciNet PubMed PubMed Central Google Scholar. Olsen, L. Ganitkevich, V. Glycolytic oscillations in single ischemic cardiomyocytes at near anoxia.

Spatio-temporal oscillations of individual mitochondria in cardiac myocytes reveal modulation of synchronized mitochondrial clusters. PNAS , — Chandra, F. Glycolytic oscillations and limits on robust efficiency. Article CAS ADS MathSciNet PubMed MATH Google Scholar. Spiller, D. Measurement of single-cell dynamics.

Kiviet, D. Stochasticity of metabolism and growth at the single-cell level. Higgins, J. A chemical mechanism for oscillation of glycolytic intermediates in yeast cells. PNAS 51, — Pedersen, M. Single and cell population respiratory oscillations in yeast: A 2—photon scanning laser microscopy study.

FEBS Lett. Kloeden, P. Nonautonomous Dynamical Systems American Mathematical Soc, Clemson, P. Discerning non-autonomous dynamics. Article ADS MathSciNet Google Scholar.

Warburg, O. Metabolism of tumours. CAS Google Scholar. Koppenol, W. Cancer 11, — Bertram, R. Interaction of glycolysis and mitochondrial respiration in metabolic oscillations of pancreatic islets.

Suprunenko, Y. Chronotaxic systems: a new class of self-sustained nonautonomous oscillators. Chronotaxic systems with separable amplitude and phase dynamics.

E 89, , doi: Article CAS ADS Google Scholar. Generalized chronotaxic systems: time-dependent oscillatory dynamics stable under continuous perturbation. E 90, , doi: Inverse approach to chronotaxic systems for single-variable time series.

Gustavsson, A. Sustained glycolytic oscillations in individual isolated yeast cells. FEBS J. Diaz-Ruiz, R. Tumor cell energy metabolism and its common features with yeast metabolism. Acta , — CAS PubMed Google Scholar. Entrainment of heterogeneous glycolytic oscillations in single cells.

Lancaster, G. Detecting chronotaxic systems from single-variable time series with separable amplitude and phase. Entropy 17, — Article ADS Google Scholar. Natter, K. Yeast and cancer cells—common principles in lipid metabolism.

Tornheim, K. The purine nucleotide cycle: Interactions with oscillations of glycolytic pathway in muscle extracts. Modulation by citrate of glycolytic oscillations in skeletal muscle extracts. Reijenga, K.

Control of glycolytic dynamics by hexose transport in Saccharomyces cerevisiae. Training of yeast cell dynamics. Boiteux, A. Control of oscillating glycolysis of yeast by stochastic, periodic and steady source of substrate: a model and experimental study.

Özalp, V. Time-resolved measurements of intracellular ATP in the yeast Saccharomyces cerevisiae using a new type of nanobiosensor. Thoke, H. Tight coupling of metabolic oscillations and intracellular water dynamics in Saccharomyces cerevisiae. PLOS One 10, e, doi: Glancy, B. Effect of calcium on the oxidative phosphorylation cascade in skeletal muscle mitochondria.

Biochemistry 52, — Brandon, M. Mitochondrial mutations in cancer. Oncogene 25, — Bishnani, Z. Safety criteria for aperiodically forced systems. Article MathSciNet MATH Google Scholar. Kaiser, G. A Friendly Guide to Wavelets Birkhäuser, Boston,