A theoretical treatment of damped oscillations in the transient state kinetics of single-enzyme reactions

An extension of the available kinetic theory for reactions in the transient state is presented which establishes that single-enzyme reactions may exhibit damped oscillations under the conditions of standard kinetic experiments performed by stopped-flow techniques. Such oscillations may occur for reasonable magnitudes of rate constants in the enzymic reaction mechanism and at physiological concentrations of enzyme and substrate. In the simplest reaction systems, the oscillations will be strongly damped and lead to progress curves resembling those of a reaction governed by standard exponential transients; statistical regression methods may then have to be applied for their detection and characterization. The observation that single-enzyme reactions may exhibit oscillatory behaviour points to a previously unrecognized possible source of the damped oscillations observed in metabolic systems such as the pathways of glycolysis or photosynthesis.     

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.     

Dihydroxyacetone-induced oscillations in cytoplasmic free Ca2+ and the ATP/ADP ratio in pancreatic beta-cells at substimulatory glucose

Glucose stimulation of pancreatic beta-cells causes oscillatory influx of Ca2+, leading to pulsatile insulin secretion. We have proposed that this is due to oscillations of glycolysis and the ATP/ADP ratio, which modulate the activity of ATP-sensitive K+ channels. We show here that dihydroxyacetone, a secretagogue that feeds into glycolysis below the putative oscillator phosphofructokinase, could cause a single initial peak in cytoplasmic free Ca2+ ([Ca2+]i) but did not by itself cause repeated oscillations in [Ca2+]i in mouse pancreatic beta-cells. However, in the presence of a substimulatory concentration of glucose (4 mm), dihydroxyacetone induced [Ca2+]i oscillations. Furthermore, these oscillations correlated with oscillations in the ATP/ADP ratio, as seen previously with glucose stimulation. Insulin secretion in response to dihydroxyacetone was transient in the absence of glucose but was considerably enhanced and somewhat prolonged in the presence of a substimulatory concentration of glucose, in accordance with the enhanced [Ca2+]i response. These results are consistent with the hypothesized role of phosphofructokinase as the generator of the oscillations. Dihydroxyacetone may affect phosphofructokinase by raising the free concentration of fructose 1,6-bisphosphate to a critical level at which it activates the enzyme autocatalytically, thereby inducing the pulses of phosphofructokinase activity that cause the metabolic oscillations.     

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.     

Thermodynamic and kinetic studies of a stoichiometric model of energetic metabolism under starvation conditions

Abstract A stoichiometric model of anaerobic glycolysis is presented and the influence on its dynamics by the ATP-consuming membrane transport processes and substrate input rate are studied. The model is represented by a system of four ODE (ordinary differential equations), mass conservation equations and functions of state variables, such as thermodynamic efficiency. A low substrate input rate provokes damped oscillations while a high enrgy load determines sustained oscillations in all the metabolites and in thermodynamic efficiency. Due to the lack of linearity between fluxes and forces in the oscillatory region it may be stated that oscillations appear when the system is kinetically controlled.     

Oscillatory enzyme reactions and Michaelis–Menten kinetics

Oscillations occur in a number of enzymatic systems as a result of feedback regulation. How Michaelis–Menten kinetics influences oscillatory behavior in enzyme systems is investigated in models for oscillations in the activity of phosphofructokinase (PFK) in glycolysis and of cyclin-dependent kinases in the cell cycle. The model for the PFK reaction is based on a product-activated allosteric enzyme reaction coupled to enzymatic degradation of the reaction product. The Michaelian nature of the product decay term markedly influences the period, amplitude and waveform of the oscillations. Likewise, a model for oscillations of Cdc2 kinase in embryonic cell cycles based on Michaelis–Menten phosphorylation–dephosphorylation kinetics shows that the occurrence and amplitude of the oscillations strongly depend on the ultrasensitivity of the enzymatic cascade that controls the activity of the cyclin-dependent kinase.     

Glycolytic oscillations in isolated rabbit ventricular myocytes

Previous studies have shown that glycolysis can oscillate periodically, driven by feedback loops in regulation of key glycolytic enzymes by free ADP and other metabolites. Here we show both theoretically and experimentally in cardiac myocytes that when the capacity of oxidative phosphorylation and the creatine kinase system to buffer the cellular ATP/ADP ratio is suppressed, glycolysis can cause large scale periodic oscillations in cellular ATP levels (0.02-0.067 Hz), monitored from glibenclamide-sensitive changes in action potential duration or intracellular free Mg2+. Action potential duration oscillations originate primarily from glycolysis, since they 1) occur in the presence of cyanide or rotenone, 2) are suppressed by iodoacetate, 3) are accompanied by at most very small mitochondrial membrane potential oscillations, and 4) exhibit an anti-phase relationship to NADH fluorescence. By uncoupling energy supply-demand balance, glycolytic oscillations may promote injury and electrophysiological heterogeneity during acute metabolic stresses, such as acute myocardial ischemia in which both oxidative phosphorylation and creatine kinase activity are inhibited.     

Stimulus-Induced Oscillations in Guard Cell Cytosolic Free Calcium

Ca2+ is implicated as a second messenger in the response of stomata to a range of stimuli. However, the mechanism by which stimulus-induced increases in guard cell cytosolic free Ca2+ ([Ca2+]i) are transduced into different physiological responses remains to be explained. Oscillations in [Ca2+]i may provide one way in which this can occur. We used photometric and imaging techniques to examine this hypothesis in guard cells of Commelina communis. External Ca2+ ([Ca2+]e), which causes an increase in [Ca2+]i, was used as a closing stimulus. The total increase in [Ca2+]i was directly related to the concentration of [Ca2+]e, both of which correlated closely with the degree of stomatal closure. Increases were oscillatory in nature, with the pattern of the oscillations dependent on the concentration of [Ca2+]e. At 0.1 mM, [Ca2+]e induced symmetrical oscillations. In contrast, 1.0 mM [Ca2+]e induced asymmetric oscillations. Oscillations were stimulus dependent and modulated by changing [Ca2+]e. Experiments using Ca2+ channel blockers and Mn2+-quenching studies suggested a role for Ca2+ influx during the oscillatory behavior without excluding the possible involvement of Ca2+ release from intracellular stores. These data suggest a mechanism for encoding the information required to distinguish between a number of different Ca2+-mobilizing stimuli in guard cells, using stimulus-specific patterns of oscillations in [Ca2+]i.     

Dynamic aspects of insulin action: synchronization of oscillatory glycolysis in isolated perifused rat fat cells by insulin and hydrogen peroxide

Glucose oxidation to CO2 was investigated in isolated perifused rat epididymal fat cells. Insulin stimulated rates of oxidation up to 30-fold. Multiple pulses of insulin or prolonged perifusion with the hormone led to a time-dependent desensitization of the cells. The action of insulin could be mimicked by H2O2. Reversal of H2O2 effects was associated with a damped oscillation of large initial amplitude. Initiation of perifusion with insulin induced rates of glucose oxidation that oscillated around a mean elevated rate with an amplitude of about +/- 4% of the mean, significantly larger than the measurement error. Basal rates did not show clear oscillations. The oscillations after insulin had a statistically significant period of around 14 min. The results were the same with C1- or C6-labeled glucose and occurred in the presence of both 0.275 and 5.5 mM glucose in the perifusion medium. The oscillations were interpreted as the result of insulin- or H2O2-induced synchronization of oscillatory glycolysis by individual fat cells. The similarity of the observed oscillatory period with the period of oscillatory insulin secretion by pancreatic beta cells suggests that oscillatory glycolysis may constitute the internal pacemaker for the latter process.     

Intra- and inter-islet synchronization of metabolically driven insulin secretion

Insulin secretion from pancreatic beta-cells is pulsatile with a period of 5-10 min and is believed to be responsible for plasma insulin oscillations with similar frequency. To observe an overall oscillatory insulin profile it is necessary that the insulin secretion from individual beta-cells is synchronized within islets, and that the population of islets is also synchronized. We have recently developed a model in which pulsatile insulin secretion is produced as a result of calcium-driven electrical oscillations in combination with oscillations in glycolysis. We use this model to investigate possible mechanisms for intra-islet and inter-islet synchronization. We show that electrical coupling is sufficient to synchronize both electrical bursting activity and metabolic oscillations. We also demonstrate that islets can synchronize by mutually entraining each other by their effects on a simple model "liver," which responds to the level of insulin secretion by adjusting the blood glucose concentration in an appropriate way. Since all islets are exposed to the blood, the distributed islet-liver system can synchronize the individual islet insulin oscillations. Thus, we demonstrate how intra-islet and inter-islet synchronization of insulin oscillations may be achieved.     

Calcium oscillations: phenomena, mechanisms and significance

Many hormones that mobilise intracellular calcium via inositol 1,4,5 trisphosphate induce oscillations in cytoplasmic free Ca. Two basic oscillatory patterns occur: quasi-sinusoidal oscillations and repetitive free Ca transients. The mechanisms responsible for generating these oscillations are not clear; calcium-induced calcium release, interplay between two intracellular calcium pools and repetitive generation of InsP3 are discussed. The significance of different oscillatory patterns induced by different agonists in the same cell is emphasised, and mechanisms by which the oscillators may retain-receptor specific information are proposed, such as negative feedback onto receptors or G-proteins by protein kinase C. Reasons why cells generate free Ca oscillations and possible consequences such as oscillations in downstream pathways are explored. The possibility that pathological conditions such as aluminium toxicity are exerted through distortion of oscillatory free Ca signalling is raised.     

Glucose‐dependent Insulin Modulation of Oscillatory Lipolysis in Perifused Rat Adipocytes

Objective: We showed glucose‐dependent lipolytic oscillations in adipocytes that are modulated by free fatty acids (FFAs). We hypothesized that the oscillations are driven by oscillatory glucose metabolism that leads to oscillatory formation of α‐glycerophosphate (α‐GP), oscillatory removal of long‐chain coenzyme A (LC‐CoA) by α‐GP to form triglycerides, and oscillatory relief of LC‐CoA inhibition of triglyceride lipases. This study examined the effect of insulin on this hypothesis. Research Methods and Procedures: Samples were collected every minute from perifused rat adipocytes during the basal state followed by insulin (±glucose) or isoproterenol (±insulin; n = 4 each). Results: Insulin caused a significant increase in glycerol release (18%), with a concomitant significant decrease in FFA release (38%). Without glucose, insulin had no effect on glycerol release while still decreasing FFA release (35%). Insulin (5 μU/mL) attenuated the response of lipolysis to isoproterenol (～3‐fold increase with isoproterenol vs. 2‐fold increase with insulin + isoproterenol). However, 1 mU/mL insulin amplified the lipolytic response (～5‐fold increase in glycerol release with insulin + isoproterenol), with a concomitant increase in FFA reesterification (no increase in FFA release compared with isoproterenol alone). Discussion: We interpret these results to be due to insulin's ability to increase glucose uptake and conversion to α‐GP, thus removing LC‐CoA inhibition of triglyceride lipases. While the physiological importance of lipolytic oscillations remains to be determined, we hypothesize that such an oscillation may play an important role in the delivery of FFAs to the liver, β cells, and other tissues.     

The blue-light reaction in plasmodia of Physarum polycephalum is coupled to respiration

The influence of inhibitors of energy metabolism (2-deoxy-D-glucose, monoiodoacetate, KCN) as well as various substrates for respiration (sodium acetate, glycine, glutamine, α-ketoglutarate, pyruvate) were investigated with respect to the effect of blue light (450 nm) on contractile behaviour of plasmodial strands of Physarum polycephalum. When the energy metabolism is not experimentally modified, blue light induces a prolongation of the period of the contraction-relaxation cycle. This effect appears within 2–3 min and seems to represent the primary reaction of this organism to blue light. Inhibition of respiration by KCN completely abolished this response to blue-light irradiation. In contrast, an impediment of glycolysis enhanced the effect. This indicates that the reaction to blue light is related to respiration, i.e., to the function of mitochondria. Among different substrates for respiration only α-ketoglutarate combined with pyruvate and applied in the presence of inhibitors of glycolysis showed an enhancement of the photoresponse, i.e., a prolongation of the period and an increase of the amplitude of the force oscillations. This indicates that the pyruvate and α-ketoglutarate-dehydrogenase complexes functioning in mitochondrial respiration are involved in the primary blue-light reaction of plasmodia of Physarum polycephalum.     

Spatio-temporal dynamics of glycolysis in cell layers. A mathematical model

Glycolytic oscillations occur in many cell types and have been intensively studied in yeast. Recent experimental and theoretical research has been focussed on the oscillatory dynamics and the synchronisation mechanism in stirred yeast cell suspensions. Here we are interested in the spatio-temporal organisation of glycolysis in cell layers. To this end we study a grid of a few thousand compartments each containing a cell. The intracellular dynamics is described by a core model of glycolysis. The compartments can exchange metabolites via diffusion. The conditions for oscillatory dynamics in a single compartment are investigated by bifurcation analysis. The spatio-temporal behaviour of the cell layer is studied by simulations. The model predicts the propagation of repetitive wave fronts induced by a substrate gradient. The formation of these waves crucially depends on the diffusive exchange of the reaction product between cells. Depending on the kinetic parameters complex spatio-temporal behaviour such as periodic termination of waves can arise. In these cases the cellular oscillation characteristics depend on the location of the cell in the array.     

Synchronized ATP oscillations have a critical role in prechondrogenic condensation during chondrogenesis

The skeletal elements of embryonic limb are prefigured by prechondrogenic condensation in which secreted molecules such as adhesion molecules and extracellular matrix have crucial roles. However, how the secreted molecules are controlled to organize the condensation remains unclear. In this study, we examined metabolic regulation of secretion in prechondrogenic condensation, using bioluminescent monitoring systems. We here report on ATP oscillations in the early step of chondrogenesis. The ATP oscillations depended on both glycolysis and mitochondrial respiration, and their synchronization among cells were achieved via gap junctions. In addition, the ATP oscillations were driven by Ca²⁺ oscillations and led to oscillatory secretion in chondrogenesis. Blockade of the ATP oscillations prevented cellular condensation. Furthermore, the degree of cellular condensation increased with the frequency of ATP oscillations. We conclude that ATP oscillations have a critical role in prechondrogenic condensation by inducing oscillatory secretion.     

Control of glycolytic oscillations by temperature

External control of oscillatory glycolysis in yeast extract has been performed by application of either homogeneous temperature oscillations or stationary, spatial temperature gradients. Entrainment of the glycolytic oscillations by the 1/2- and 1/3-harmonic, as well as the fundamental input frequency, could be observed. From the phase response curve to a single temperature pulse, a distinct sensitivity of NADH-oxidizing processes, compared with NAD-reducing processes, is visible. Determination of glycolytic intermediates shows that the feedback-regulated phosphofructokinase as well as the glyceraldehyde-3-phosphate dehydrogenase are the most temperature-sensitive steps of glycolysis. We also find strong concentration changes in ATP and AMP at varying temperatures and, accordingly, in the energy charge. Construction of a feedback loop for spatial control of temperature by means of a Peltier element allowed us to apply a temperature gradient to the yeast extract. With this setup it is possible to initiate traveling waves and to control the wave velocity.     

Oscillations in glycolysis: multifactorial quantitative analysis in muscle extract

A multifactorial quantitative analysis of oscillations in glycolysis was conducted in the postmicrosomal supernatant of rat muscle homogenates incubated in the presence of yeast hexokinase. Oscillations in adenine nucleotides, D-fructose 1,6-bisphosphate, triose phosphates, L-glycerol 3-phosphate, ³HOH generation from D-[5-³H]glucose, NADH and L-lactate production were documented. The occurrence of such oscillations were found to depend mainly on the balance between the consumption of ATP associated with the phosphorylation of D-glucose, as catalyzed by both yeast and muscle hexokinase, and the net production of ATP resulting from the further catabolism of D-fructose 6-phosphate, as initiated by activation of phosphofructokinase. The oscillatory pattern was suppressed in the presence of D-fructose 2,6-bisphosphate. It is proposed that the quantitative information gathered in this study may set the scene for further studies in extracts of cells other than myocytes, e. g. hepatocytes and pancreatic islet cells, in which no oscillation of glycolysis was so far observed.     

Changes in the rabbit brain cortex redox potential accompaning episodes of ECoG-arousal during slow-wave sleep

Local cortex E variations are well expressive indices of rate and peculiarities of energy metabolism. The brain E is determined by the ratio of processes occurring in two energy compartments in glycolysis, in whish glucose is split without oxygen utilization and in oxidative metabolism. In the present investigation, the brain cortex E changes were recorded with implanted platinum electrodes during slow wave sleep. Under such conditions, the E lowering detects acceleration in glycolytic compartment, whereas the E local rising shows acceleration in oxidative metabolism in the tissue surrounding the electrode. Earlier in rats, we have found that E significantly lowered in metabolic active cortical sites during episodes of SWS, and supposed that acceleration of glycolysis increased. Slow oscillations (a 20-40-sec prolongation of the amplitude up to several dozens millivolts) appeared at the same time. We considered these E slow oscillations to reflect changes in the rate in compartment of glycolysis. In this research, we have found the E slow oscillations to be created by regular episodes of ECoG-arousal which were accompanied by E decreases, i. e. by acceleration in glycolysis. We think the data presented show existence of functional system supporting a low level of arousal. As in any complex system with feed back connections, this system works in oscillatory regime.