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

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.     

Full-scale model of glycolysis in Saccharomyces cerevisiae.

We present a powerful, general method of fitting a model of a biochemical pathway to experimental substrate concentrations and dynamical properties measured at a stationary state, when the mechanism is largely known but kinetic parameters are lacking. Rate constants and maximum velocities are calculated from the experimental data by simple algebra without integration of kinetic equations. Using this direct approach, we fit a comprehensive model of glycolysis and glycolytic oscillations in intact yeast cells to data measured on a suspension of living cells of Saccharomyces cerevisiae near a Hopf bifurcation, and to a large set of stationary concentrations and other data estimated from comparable batch experiments. The resulting model agrees with almost all experimentally known stationary concentrations and metabolic fluxes, with the frequency of oscillation and with the majority of other experimentally known kinetic and dynamical variables. The functional forms of the rate equations have not been optimized.     

Calcium and glycolysis mediate multiple bursting modes in pancreatic islets

Pancreatic islets of Langerhans produce bursts of electrical activity when exposed to stimulatory glucose levels. These bursts often have a regular repeating pattern, with a period of 10-60 s. In some cases, however, the bursts are episodic, clustered into bursts of bursts, which we call compound bursting. Consistent with this are recordings of free Ca2+ concentration, oxygen consumption, mitochondrial membrane potential, and intraislet glucose levels that exhibit very slow oscillations, with faster oscillations superimposed. We describe a new mathematical model of the pancreatic beta-cell that can account for these multimodal patterns. The model includes the feedback of cytosolic Ca2+ onto ion channels that can account for bursting, and a metabolic subsystem that is capable of producing slow oscillations driven by oscillations in glycolysis. This slow rhythm is responsible for the slow mode of compound bursting in the model. We also show that it is possible for glycolytic oscillations alone to drive a very slow form of bursting, which we call "glycolytic bursting." Finally, the model predicts that there is bistability between stationary and oscillatory glycolysis for a range of parameter values. We provide experimental support for this model prediction. Overall, the model can account for a diversity of islet behaviors described in the literature over the past 20 years.     

Sustained oscillations in glycolysis: an experimental and theoretical study of chaotic and complex periodic behavior and of quenching of simple oscillations

We report sustained oscillations in glycolysis conducted in an open system (a continuous-flow, stirred tank reactor; CSTR) with inflow of yeast extract as well as glucose. Depending on the operating conditions, we observe simple or complex periodic oscillations or chaos. We report the response of the system to instantaneous additions of small amounts of several substrates as functions of the amount added and the phase of the addition. We simulate oscillations and perturbations by a kinetic model based on the mechanism of glycolysis in a CSTR. We find that the response to particular perturbations forms an efficient tool for elucidating the mechanism of biochemical oscillations.     

How yeast cells synchronize their glycolytic oscillations: a perturbation analytic treatment

Of all the lifeforms that obtain their energy from glycolysis, yeast cells are among the most basic. Under certain conditions the concentrations of the glycolytic intermediates in yeast cells can oscillate. Individual yeast cells in a suspension can synchronize their oscillations to get in phase with each other. Although the glycolytic oscillations originate in the upper part of the glycolytic chain, the signaling agent in this synchronization appears to be acetaldehyde, a membrane-permeating metabolite at the bottom of the anaerobic part of the glycolytic chain. Here we address the issue of how a metabolite remote from the pacemaking origin of the oscillation may nevertheless control the synchronization. We present a quantitative model for glycolytic oscillations and their synchronization in terms of chemical kinetics. We show that, in essence, the common acetaldehyde concentration can be modeled as a small perturbation on the "pacemaker" whose effect on the period of the oscillations of cells in the same suspension is indeed such that a synchronization develops.     

Analysis of the dynamics of relaxation type oscillation in glycolysis of yeast extracts.

In yeasts, the glycolysis may display oscillations of its metabolites while it is converting glucose. The dynamics of the oscillations has been investigated in cytoplasmic extracts of yeast under relaxation type conditions by determining the time course of some of the glycolytic metabolites. The compounds of the nucleotide pool have been identified as fast variables and the glucose derivatives as slow variables of the relaxation type. The period of oscillation has been subdivided into four phases which represent prominent parts of the limit cycle in the phase plane of a slow versus a fast variable. From the reaction processes in these phases, a dynamical picture of the mechanisms of oscillations is suggested. Accordingly, the oscillation results from an alternating activity of the fructose bisphosphate and the polysaccharide synthesis, both of which are coupled to glycolysis via the nucleotide pool. The processes in the phases are analyzed by calculating the rates of the reaction steps in the biochemical pathway.     

Sustained simultaneous glycolytic and insulin oscillations in beta-cells

Chemical oscillation in glycolysis induced by glucose is an universal feature in all living cells. In beta-cells this is accompanied by sustained oscillations of concentration of insulin, which helps to keep the blood glucose level within optimum limits. Experiments in this regard had shown that the glycolytic and insulin oscillations are almost consistently in phase and their time periods are very close to each other at both high and low initial concentration of glucose. Experiments have also demonstrated the dynamical transition between the states of glycolytic oscillations indicating a saturation behaviour of glucose transporters at a higher glucose flow rate. We propose a phenomenological model to understand these simultaneous oscillations and how glycolysis provides a mechanism for pulsatory insulin secretion in the light of these basic experimental issues.     

Citrate oscillates in liver and pancreatic beta cell mitochondria and in INS-1 insulinoma cells

Oscillations in citric acid cycle intermediates have never been previously reported in any type of cell. Here we show that adding pyruvate to isolated mitochondria from liver, pancreatic islets, and INS-1 insulinoma cells or adding glucose to intact INS-1 cells causes sustained oscillations in citrate levels. Other citric acid cycle intermediates measured either did not oscillate or possibly oscillated with a low amplitude. In INS-1 mitochondria citrate oscillations are in phase with NAD(P) oscillations, and in intact INS-1 cells citrate oscillations parallel oscillations in ATP, suggesting that these processes are co-regulated. Oscillations have been extensively studied in the pancreatic beta cell where oscillations in glycolysis, NAD(P)/NAD(P)H and ATP/ADP ratios, plasma membrane electrical activity, calcium levels, and insulin secretion have been well documented. Because the mitochondrion is the major site of ATP synthesis and NADH oxidation and the only site of citrate synthesis, mitochondria need to be synchronized for these factors to oscillate. In suspensions of mitochondria from various organs, most of the citrate is exported from the mitochondria. In addition, citrate inhibits its own synthesis. We propose that this enables citrate itself to act as one of the cellular messengers that synchronizes mitochondria. Furthermore, because citrate is a potent inhibitor of the glycolytic enzyme phosphofructokinase, the pacemaker of glycolytic oscillations, citrate may act as a metabolic link between mitochondria and glycolysis. Citrate oscillations may coordinate oscillations in mitochondrial energy production and anaplerosis with glycolytic oscillations, which in the beta cell are known to parallel oscillations in insulin secretion.     

Linked oscillations of free Ca2+ and the ATP/ADP ratio in permeabilized RINm5F insulinoma cells supplemented with a glycolyzing cell-free muscle extract

We show in the accompanying paper that the steady-state level of free Ca2+ maintained by the organelles of permeabilized RINm5F insulinoma cells varies inversely with the ATP/ADP ratio when this ratio is set by addition of creatine phosphokinase and fixed ratios of creatine to creatine phosphate. We, therefore, asked whether acute cyclic alterations in the cytosolic ATP/ADP ratio in the range known to modulate O2 consumption might be involved in regulating the physiological activity of Ca2+ -ATPases and the cytosolic free Ca2+ level. To explore this hypothesis we combined two experimental systems: 1) permeabilized RINm5F insulinoma cells that can maintain a low medium Ca2+ concentration and 2) a cell-free extract of rat skeletal muscle that spontaneously exhibits oscillatory behavior of glycolysis and linked oscillations in the ATP/ADP ratio, when provided with glucose. The free Ca2+ level maintained by the permeabilized cells oscillated in phase with the glycolytic oscillations and correlated closely with the ATP/ADP ratio but not with glucose 6-phosphate, fructose 6-phosphate, orthophosphate, or pH. When glucokinase replaced hexokinase as the glucose phosphorylating enzyme, Ca2+ oscillations were induced by increasing the glucose concentration from 2 to 8 mM. The results demonstrate a link between metabolite changes and free Ca2+ levels in a reconstituted physiological system. They support a model in which oscillations in glycolysis and the ATP/ADP ratio may cause oscillations in cytosolic free Ca2+, beta-cell electrical activity, and insulin release.     

Sustained glycolytic oscillations in individual isolated yeast cells

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.     

Metabolic pathways reconstruction by frequency and amplitude response to forced glycolytic oscillations in yeast

The hypothesis that frequency and amplitude response can be used in a complicated metabolic pathway kinetics model for optimal parameter estimation, as speculated by its successful prior usage for a mechanical oscillator and a heterogeneous chemical system, is tested here. Given the complexity of the glycolysis model of yeast chosen, this question is limited to three kinetics parameters of the 87 in the in vitro model developed in the literature. The direct application of the approach, used with the uninformed selection of operating conditions for the oscillation of external glucose concentration, led to miring the data assimilation process in local minima. Application of linear systems theory, however, identified two natural resonant frequencies that, when excited by external forced oscillations of the same frequency, result in the expression of many harmonics in the Fourier spectra, that is, information-rich experiments. A single such information-rich experiment at one of the resonant frequencies was sufficient to break away from the local minima to find the optimum kinetics parameter estimates. The resonant frequencies themselves represent oscillation modes in glycolysis akin to those previously observed. Furthermore, operation of the bioreactor with large amplitude oscillations of glucose feed (25%) leads to enhanced ethanol average yield by 1.6% at the resonant frequency.     

Temperature dependency and temperature compensation in a model of yeast glycolytic oscillations

Temperature sensitivities and conditions for temperature compensation have been investigated in a model for yeast glycolytic oscillations. The model can quantitatively simulate the experimental observation that the period length of glycolytic oscillations decreases with increasing temperature. Temperature compensation is studied by using control coefficients describing the effect of rate constants on oscillatory frequencies. Temperature compensation of the oscillatory period is observed when the positive contributions to the sum of products between control coefficients and activation energies balance the corresponding sum of the negative contributions. The calculations suggest that by changing the activation energies for one or several of the processes, i.e. by mutations, it could be possible to obtain temperature compensation in the yeast glycolytic oscillator.     

Glycolysis Is Governed by Growth Regime and Simple Enzyme Regulation in Adherent MDCK Cells

Due to its vital importance in the supply of cellular pathways with energy and precursors, glycolysis has been studied for several decades regarding its capacity and regulation. For a systems-level understanding of the Madin-Darby canine kidney (MDCK) cell metabolism, we couple a segregated cell growth model published earlier with a structured model of glycolysis, which is based on relatively simple kinetics for enzymatic reactions of glycolysis, to explain the pathway dynamics under various cultivation conditions. The structured model takes into account in vitro enzyme activities, and links glycolysis with pentose phosphate pathway and glycogenesis. Using a single parameterization, metabolite pool dynamics during cell cultivation, glucose limitation and glucose pulse experiments can be consistently reproduced by considering the cultivation history of the cells. Growth phase-dependent glucose uptake together with cell-specific volume changes generate high intracellular metabolite pools and flux rates to satisfy the cellular demand during growth. Under glucose limitation, the coordinated control of glycolytic enzymes re-adjusts the glycolytic flux to prevent the depletion of glycolytic intermediates. Finally, the model''s predictive power supports the design of more efficient bioprocesses.     

Carbohydrates induce mono-ubiquitination of H2B in yeast

Histone modifications have emerged to be a major regulatory mechanism for gene expression (1-4). However, it is not clear how histone modifications are physiologically regulated. Here, we show that mono-ubiquitinated H2B at lysine 123 (uH2B) in the yeast (Saccharomyces cerevisiae) is present in exponential phase and absent in stationary phase. A wide array of carbohydrates or sugars, including glucose, fructose, mannose, and sucrose, are capable of inducing uH2B in stationary phase yeast. In contrast, non-metabolic glucose analogs are defective in inducing uH2B. Furthermore, uH2B induction is inhibited by iodoacetate, an inhibitor of glyceraldehyde-3-phosphate dehydrogenase in glycolysis. Moreover, uH2B induction is markedly impaired in yeast mutants, in which glycolytic genes are deleted. These data indicate that glycolysis is required for the carbohydrate-induced mono-ubiquitination of H2B at lysine 123. Therefore, our study reveals a novel paradigm of metabolic regulation of histone modifications.     

Transduction of intracellular and intercellular dynamics in yeast glycolytic oscillations

Under certain well-defined conditions, a population of yeast cells exhibits glycolytic oscillations that synchronize through intercellular acetaldehyde. This implies that the dynamic phenomenon of the oscillation propagates within and between cells. We here develop a method to establish by which route dynamics propagate through a biological reaction network. Application of the method to yeast demonstrates how the oscillations and the synchronization signal can be transduced. That transduction is not so much through the backbone of glycolysis, as via the Gibbs energy and redox coenzyme couples (ATP/ADP, and NADH/NAD), and via both intra- and intercellular acetaldehyde.     

Control of glycolytic dynamics by hexose transport in Saccharomyces cerevisiae

It is becoming accepted that steady-state fluxes are not necessarily controlled by single rate-limiting steps. This leaves open the issue whether cellular dynamics are controlled by single pacemaker enzymes, as has often been proposed. This paper shows that yeast sugar transport has substantial but not complete control of the frequency of glycolytic oscillations. Addition of maltose, a competitive inhibitor of glucose transport, reduced both average glucose consumption flux and frequency of glycolytic oscillations. Assuming a single kinetic component and a symmetrical carrier, a frequency control coefficient of between 0.4 and 0.6 and an average-flux control coefficient of between 0.6 and 0.9 were calculated for hexose transport activity. In a second approach, mannose was used as the carbon and free-energy source, and the dependencies on the extracellular mannose concentration of the transport activity, of the frequency of oscillations, and of the average flux were compared. In this case the frequency control coefficient and the average-flux control coefficient of hexose transport activity amounted to 0.7 and 0.9, respectively. From these results, we conclude that 1) transport is highly important for the dynamics of glycolysis, 2) most but not all control resides in glucose transport, and 3) there should at least be one step other than transport with substantial control.     

Substrate effects on oscillations in metabolism, calcium and secretion in single mouse islets of Langerhans

Glucose induces complex patterns of oscillations in intracellular Ca2+ concentration ([Ca2+]i), metabolism and secretion in islets of Langerhans including "slow" and "fast" pulses with period of 2-5 min and 10-20 s respectively. In an effort to elucidate the origin of slow oscillations, individual mouse islets were exposed to different fuels including glyceraldehyde, pyruvate, methyl pyruvate and alpha-ketoisocaproate (KIC), all of which bypass key steps of glycolytic metabolism, while monitoring [Ca2+]i, oxygen consumption and secretion. Glyceraldehyde gave rise to slow oscillations only when substimulatory glucose was also added to the media. Glucosamine, an inhibitor of glucokinase, blocked these slow oscillations. KIC, pyruvate, and methyl pyruvate did not give rise to slow oscillations alone or with glucose present. The addition of glucose to islets bathed in nutrient-rich cell culture media accelerated metabolism and initiated slow oscillations while glyceraldehyde did not. It is concluded that glucose has a special role in accelerating metabolism and generating slow oscillations in isolated islets of Langerhans from mice. Combined with previous observations of Ca2+ dependency for all oscillations in islets, we propose that interactions between Ca2+ influx and glycolysis are responsible for the slow oscillations. In contrast, fast oscillations can occur independent of glycolytic flux.     

Phosphofructo-2-kinase/fructose-2,6-bisphosphatase modulates oscillations of pancreatic islet metabolism

Pulses of insulin from pancreatic beta-cells help maintain blood glucose in a narrow range, although the source of these pulses is unclear. It has been proposed that a positive feedback circuit exists within the glycolytic pathway, the autocatalytic activation of phosphofructokinase-1 (PFK1), which endows pancreatic beta-cells with the ability to generate oscillations in metabolism. Flux through PFK1 is controlled by the bifunctional enzyme PFK2/FBPase2 (6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase) in two ways: via (1) production/degradation of fructose-2,6-bisphosphate (Fru2,6-BP), a potent allosteric activator of PFK1, as well as (2) direct activation of glucokinase due to a protein-protein interaction. In this study, we used a combination of live-cell imaging and mathematical modeling to examine the effects of inducibly-expressed PFK2/FBPase2 mutants on glucose-induced Ca(2+) pulsatility in mouse islets. Irrespective of the ability to bind glucokinase, mutants of PFK2/FBPase2 that increased the kinase:phosphatase ratio reduced the period and amplitude of Ca(2+) oscillations. Mutants which reduced the kinase:phosphatase ratio had the opposite effect. These results indicate that the main effect of the bifunctional enzyme on islet pulsatility is due to Fru2,6-BP alteration of the threshold for autocatalytic activation of PFK1 by Fru1,6-BP. Using computational models based on PFK1-generated islet oscillations, we then illustrated how moderate elevation of Fru-2,6-BP can increase the frequency of glycolytic oscillations while reducing their amplitude, with sufficiently high activation resulting in termination of slow oscillations. The concordance we observed between PFK2/FBPase2-induced modulation of islet oscillations and the models of PFK1-driven oscillations furthermore suggests that metabolic oscillations, like those found in yeast and skeletal muscle, are shaped early in glycolysis.     

Oscillations in Yeast Observed Electrically

It has previously been demonstrated that oscillations occur in actively growing yeast cultures. These oscillations occur because yeast cells synchronize their glycolytic pathway following a saturation period. Periodic changes in the levels of intermediate metabolites in glycolysis as well as changes in pH ofthe media have been measured, that demonstrate this phenomenon. Here we observe that the conductivity of the media also changes periodically when yeast cells are cultured under similar conditions. As conductivity is easily measured, this provides a simple, more quantitative method to study these changes than those currently used. An electrical biosensor referred to as ECIS (electrical cell surface impedance sensing) was used to study the small conductivity changes (in the order of 0.1%). No significant differences in the observed periods were found in the two yeast strains or the commercially purchased yeast extract studied.