Oscillations in energy metabolism

Organisation of mitochondrial metabolism is a quintessential example of a complex dissipative system which can display dynamic instabilities. Several findings have indicated that the conditions inducing instabilities are within the physiological range and that mild perturbations could elicit oscillations. Different mathematical models have been put forth in order to explain the genesis of oscillations in energy metabolism. One model considers mitochondria as an organised network of oscillators and indicates that communication between mitochondria involves mitochondrial reactive oxygen species (ROS) production acting as synchronisers of the energy status of the whole population of mitochondria. An alternative model proposes that extramitochondrial pH variations could lead to mitochondrial oscillations. Oscillatory phenomena in energy metabolism have also been investigated in vivo on the basis of ³¹P magnetic resonance spectroscopy (MRS) measurements of phosphocreatine post-exercise recovery in human and animal skeletal muscle. The corresponding results provide experimental evidences about the role exerted by cytosolic pH on oscillations. Finally a new simple non-linear mathematical model describing the overall chemical reaction of phosphocreatine recovery predicting oscillatory recovery pattern under certain experimental conditions is presented and discussed in the light of the experimental results reported so far.     

Modeling the synchronization of yeast respiratory oscillations

The budding yeast Saccharomyces cerevisiae exhibits autonomous oscillations when grown aerobically in continuous culture with ethanol as the primary carbon source. A single cell model that includes the sulfate assimilation and ethanol degradation pathways recently has been developed to study these respiratory oscillations. We utilize an extended version of this single cell model to construct large cell ensembles for investigation of a proposed synchronization mechanism involving hydrogen sulfide. Ensembles with as many as 10,000 cells are used to simulate population synchronization and to compute transient number distributions from asynchronous initial cell states. Random perturbations in intracellular kinetic parameters are introduced to study the synchronization of single cells with small variations in their unsynchronized oscillation periods. The cell population model is shown to be consistent with available experimental data and to provide insights into the regulatory mechanisms responsible for the synchronization of yeast metabolic oscillations.     

Calcium sensing receptor activation by a calcimimetic suggests a link between cooperativity and intracellular calcium oscillations

Activation of the calcium sensing receptor (CaR) by small increments in extracellular calcium (Ca(2+)(e)) induces intracellular calcium (Ca(2+)(i)) oscillations that are dependent on thapsigargin-sensitive intracellular calcium stores. Phenylalkylamines such as NPS R-568 are allosteric modulators (calcimimetics) that activate CaR by increasing the apparent affinity of the receptor for calcium. We determined, by fluorescence imaging with fura-2, whether the calcimimetic NPS R-568 could activate Ca(2+)(i) oscillations in HEK-293 cells expressing human CaR. NPS R-568 was more potent than Ca(2+)(e) at eliciting Ca(2+)(i) oscillations, particularly at low [Ca(2+)](e) (as low as 0.1 mm). The oscillation frequencies elicited by NPS R-568 varied over a 2-fold range from peak to peak intervals of 60-70 to 30-45 s, depending upon the concentrations of both Ca(2+)(e) and NPS R-568. Finally, NPS R-568 induced sustained (>15 min after drug removal) Ca(2+)(i) oscillations, suggesting slow release of the drug from its binding site. We exploited the potency of NPS R-568 for eliciting Ca(2+)(i) oscillations for structural studies. Truncation of the CaR carboxyl terminus from 1077 to 886 amino acids had no effect on the ability of Ca(2+) or NPS R-568 to induce Ca(2+)(i) oscillations, but further truncation (to 868 amino acids) eliminated both highly cooperative Ca(2+)-dependent activation and regular Ca(2+)(i) oscillations. Alanine scanning within the amino acid sequence from Arg(873) to His(879) reveals a linkage between the cooperativity for Ca(2+)-dependent activation and establishment and maintenance of intracellular Ca(2+) oscillations. The amino acid residues critical to both functions of CaR may contribute to interactions with either G proteins or between CaR monomers within the functional dimer.     

Equality of average and steady-state levels in some nonlinear models of biological oscillations

Nonlinear oscillatory systems, playing a major role in biology, do not exhibit harmonic oscillations. Therefore, one might assume that the average value of any of their oscillating variables is unequal to the steady-state value. For a number of mathematical models of calcium oscillations (e.g. the Somogyi–Stucki model and several models developed by Goldbeter and co-workers), the average value of the cytosolic calcium concentration (not, however, of the concentration in the intracellular store) does equal its value at the corresponding unstable steady state at the same parameter values. The average value for parameter values in the unstable region is even equal to the level at the stable steady state for other parameter values, which allow stability. This holds for all parameters except those involved in the net flux across the cell membrane. We compare these properties with a similar property of the Higgins–Selkov model of glycolytic oscillations and two-dimensional Lotka–Volterra equations. Here, we show that this equality property is critically dependent on the following conditions: There must exist a net flux across the model boundaries that is linearly dependent on the concentration variable for which the equality property holds plus an additive constant, while being independent of all others. A number of models satisfy these conditions or can be transformed such that they do so. We discuss our results in view of the question which advantages oscillations may have in biology. For example, the implications of the findings for the decoding of calcium oscillations are outlined. Moreover, we elucidate interrelations with metabolic control analysis. This paper is dedicated to the memory of the late Reinhart Heinrich, who was the academic teacher of S.S. and, to a great extent, also of M.M.     

Crystal structure of the C-terminal clock-oscillator domain of the cyanobacterial KaiA protein

KaiA, KaiB and KaiC constitute the circadian clock machinery in cyanobacteria, and KaiA activates kaiBC expression whereas KaiC represses it. Here we show that KaiA is composed of three functional domains, the N-terminal amplitude-amplifier domain, the central period-adjuster domain and the C-terminal clock-oscillator domain. The C-terminal domain is responsible for dimer formation, binding to KaiC, enhancing KaiC phosphorylation and generating the circadian oscillations. The X-ray crystal structure at a resolution of 1.8 A of the C-terminal clock-oscillator domain of KaiA from the thermophilic cyanobacterium Thermosynechococcus elongatus BP-1 shows that residue His270, located at the center of a KaiA dimer concavity, is essential to KaiA function. KaiA binding to KaiC probably occurs via the concave surface. On the basis of the structure, we predict the structural roles of the residues that affect circadian oscillations.     

Response to temporal parameter fluctuations in biochemical networks

Metabolic response coefficients describe how variables in metabolic systems, like steady state concentrations, respond to small changes of kinetic parameters. To extend this concept to temporal parameter fluctuations, we define spectral response coefficients that relate Fourier components of concentrations and fluxes to Fourier components of the underlying parameters. It is also straightforward to generalize other concepts from metabolic control theory, such as control coefficients with their summation and connectivity theorems. The first-order response coefficients describe forced oscillations caused by small harmonic oscillations of single parameters: they depend on the driving frequency and comprise the phases and amplitudes of the concentrations and fluxes. Close to a Hopf bifurcation, resonance can occur: as an example, we study the spectral densities of concentration fluctuations arising from the stochastic nature of chemical reactions. Second-order response coefficients describe how perturbations of different frequencies interact by mode coupling, yielding higher harmonics in the metabolic response. The temporal response to small parameter fluctuations can be computed by Fourier synthesis. For a model of glycolysis, this approximation remains fairly accurate even for large relative fluctuations of the parameters.     

Calcium-dependent regulation of glucose homeostasis in the liver

A major role of the liver is to integrate multiple signals to maintain normal blood glucose levels. The balance between glucose storage and mobilization is primarily regulated by the counteracting effects of insulin and glucagon. However, numerous signals converge in the liver to ensure energy demand matches the physiological status of the organism. Many circulating hormones regulate glycogenolysis, gluconeogenesis and mitochondrial metabolism by calcium-dependent signaling mechanisms that manifest as cytosolic Ca²⁺ oscillations. Stimulus-strength is encoded in the Ca²⁺ oscillation frequency, and also by the range of intercellular Ca²⁺ wave propagation in the intact liver. In this article, we describe how Ca²⁺ oscillations and waves can regulate glucose output and oxidative metabolism in the intact liver; how multiple stimuli are decoded though Ca²⁺ signaling at the organ level, and the implications of Ca²⁺ signal dysregulation in diseases such as metabolic syndrome and non-alcoholic fatty liver disease.     

UNDAMPED OSCILLATIONS OF PYRIDINE NUCLEOTIDE AND OXYGEN TENSION IN CHEMOSTAT CULTURES OF KLEBSIELLA AEROGENES

Klebsiella aerogenes was grown in chemostat culture with the pH controlled to ±0.01 and temperature to ±0.1°C. The oxygen tension of the culture was regulated by changing the partial pressure of oxygen in the gas phase and recorded by means of an oxygen electrode. Reduced pyridine nucleotide was monitored continuously in the culture by means of direct fluorimetry. On applying an anaerobic shock to the culture, damped oscillations in pyridine nucleotide fluorescence were obtained. Further anaerobic shocks decreased the damping and eventually gave rise to undamped oscillations of a 2–3 min period which continued for several days. These oscillations were paralleled by oscillations of the same frequency in respiration rate. The amplitude of the oscillations in the respiration rate was equivalent to only 1% of the total steady-state respiration, whereas that of pyridine nucleotide oscillations was equivalent to 10% of the total aerobic/anaerobic fluorescence response. The oscillations ceased on interrupting the glucose feed but restarted on adding excess glucose to the culture. Addition of succinate also restarted the oscillations so that they appear not to be of glycolytic origin. The frequency of oscillations varied with growth rate and conditions. Oscillations of much lower frequency were obtained under limited-oxygen and anaerobic conditions than under fully aerobic conditions. Under glucose-limited conditions, fluctuations were found in adenosine triphosphate (ATP) content which were in phase with the pyridine nucleotide oscillations, but under nitrogen-limited growth conditions no such fluctuations in ATP were observed. The primary oscillating pathway could not be identified but the mechanism would appear to be quite different from that involved in oscillations observed in yeast cells. The synchronization of oscillations and observations of negative damping could be explained by a syntalysis effect.     

Peripheral chemoreceptors in respiratory oscillations

The hypothesis that instability of cardiorespiratory control may depend on the response and sensitivity of carotid body chemoreceptors to arterial blood gases was studied in anesthetized cats under three different experimental conditions. 1) Following administration of the peripheral dopamine receptor blocker [domperidone (0.6-0.8 mg X kg-1, iv)], carotid chemoreceptor activity and its sensitivity to CO2 during hypoxia increased, leading to cardiorespiratory oscillations at low arterial PO2 in four of eight cats. Inhalation of 100% O2 promptly decreased chemoreceptor activity and eliminated the oscillations. Inhalation of CO2 stimulated the chemoreceptor activity and ventilation but did not eliminate the oscillations. Bilateral section of carotid sinus nerves abolished the cardiorespiratory oscillations. The implication is that the dopaminergic system in the carotid body keeps chemoreceptor responses to blood gas stimuli suppressed and hence cardiorespiratory oscillations damped. 2) Hypotension and circulatory delay induced by the partial occlusion of venous return led to cardiorespiratory oscillations at low but not at high arterial PO2. 3) A few cats developed cardiorespiratory oscillations without any particular experimental intervention. These oscillations were independent of arterial PO2 and chemoreceptor activity. Thus it is reasonable to conclude that the peripheral chemoreflex can play a critical role in developing cardiorespiratory oscillations in certain instances.     

Dynamic Interaction of Spindles and Gamma Activity during Cortical Slow Oscillations and Its Modulation by Subcortical Afferents

Slow oscillations are a hallmark of slow wave sleep. They provide a temporal framework for a variety of phasic events to occur and interact during sleep, including the expression of high-frequency oscillations and the discharge of neurons across the entire brain. Evidence shows that the emergence of distinct high-frequency oscillations during slow oscillations facilitates the communication among brain regions whose activity was correlated during the preceding waking period. While the frequencies of oscillations involved in such interactions have been identified, their dynamics and the correlations between them require further investigation. Here we analyzed the structure and dynamics of these signals in anesthetized rats. We show that spindles and gamma oscillations coexist but have distinct temporal dynamics across the slow oscillation cycle. Furthermore, we observed that spindles and gamma are functionally coupled to the slow oscillations and between each other. Following the activation of ascending pathways from the brainstem by means of a carbachol injection in the pedunculopontine nucleus, we were able to modify the gain in the gamma oscillations that are independent of the spindles while the spindle amplitude was reduced. Furthermore, carbachol produced a decoupling of the gamma oscillations that are dependent on the spindles but with no effect on their amplitude. None of the changes in the high-frequency oscillations affected the onset or shape of the slow oscillations, suggesting that slow oscillations occur independently of the phasic events that coexist with them. Our results provide novel insights into the regulation, dynamics and homeostasis of cortical slow oscillations.     

Evidence that three histidine residues of a base non-specific and adenylic acid preferential ribonuclease from Rhizopus niveus are involved in the catalytic function.

In order to study the structure-function relationship of an RNase T2 family enzyme, RNase Rh, from Rhizopus niveus, we investigated the roles of three histidine residues by means of site-specific mutagenesis. One of the three histidine residues of RNase RNAP Rh produced in Saccharomyces cerevisiae by recombinant DNA technology was substituted to a phenylalanine or alanine residue. A Phe or Ala mutant enzyme at His46 or His109 showed less than 0.03%, but a mutant enzyme at His104 showed 0.54% of the enzymatic activity of the wild-type enzyme with RNA as a substrate. Similar results were obtained, when ApU was used as a substrate. The binding constant of a Phe mutant enzyme at His46 or His109 towards 2'-AMP decreased twofold, but that at His104 decreased more markedly. Therefore, we assumed that these three histidine residues are components of the active site of RNase Rh, that His104 contributes to some extent to the binding and less to the catalysis, and that the other two histidine residues and one carboxyl group not yet identified are probably involved in the catalysis. We assigned the C-2 proton resonances of His46, His104, and His109 by comparison of the 1H-NMR spectra of the three mutant enzymes containing Phe in place of His with that of the native enzyme, and also determined the individual pKa values for His46 and His104 to be 6.70 and 5.94. His109 was not titrated in a regular way, but the apparent pKa value was estimated to be around 6.3. The fact that addition of 2'-AMP caused a greater effect on the chemical shift of His104 in the 1NMR spectra as compared with those of the other histidine residues, may support the idea described above on the role of His104.     

TGF-β but not BMP signaling induces prechondrogenic condensation through ATP oscillations during chondrogenesis

Although both TGF-β and BMP signaling enhance expression of adhesion molecules during chondrogenesis, TGF-β but not BMP signaling can initiate condensation of uncondensed mesenchymal cells. However, it remains unclear what causes the differential effects between TGF-β and BMP signaling on prechondrogenic condensation. Our previous report demonstrated that ATP oscillations play a critical role in prechondrogenic condensation. Thus, the current study examined whether ATP oscillations are associated with the differential actions of TGF-β and BMP signaling on prechondrogenic condensation. The result revealed that while both TGF-β1 and BMP2 stimulated chondrogenic differentiation, TGF-β1 but not BMP2 induced prechondrogenic condensation. It was also found that TGF-β1 but not BMP2 induced ATP oscillations and inhibition of TGF-β but not BMP signaling prevented insulin-induced ATP oscillations. Moreover, blockage of ATP oscillations inhibited TGF-β1-induced prechondrogenic condensation. In addition, TGF-β1-driven ATP oscillations and prechondrogenic condensation depended on Ca(2+) influx via voltage-dependent calcium channels. This study suggests that Ca(2+)-driven ATP oscillations mediate TGF-β-induced the initiation step of prechondrogenic condensation and determine the differential effects between TGF-β and BMP signaling on chondrogenesis.     

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.     

Connexin 43 hemichannels contribute to cytoplasmic Ca2+ oscillations by providing a bimodal Ca2+-dependent Ca2+ entry pathway

Many cellular functions are driven by changes in the intracellular Ca(2+) concentration ([Ca(2+)](i)) that are highly organized in time and space. Ca(2+) oscillations are particularly important in this respect and are based on positive and negative [Ca(2+)](i) feedback on inositol 1,4,5-trisphosphate receptors (InsP(3)Rs). Connexin hemichannels are Ca(2+)-permeable plasma membrane channels that are also controlled by [Ca(2+)](i). We aimed to investigate how hemichannels may contribute to Ca(2+) oscillations. Madin-Darby canine kidney cells expressing connexin-32 (Cx32) and Cx43 were exposed to bradykinin (BK) or ATP to induce Ca(2+) oscillations. BK-induced oscillations were rapidly (minutes) and reversibly inhibited by the connexin-mimetic peptides (32)Gap27/(43)Gap26, whereas ATP-induced oscillations were unaffected. Furthermore, these peptides inhibited the BK-triggered release of calcein, a hemichannel-permeable dye. BK-induced oscillations, but not those induced by ATP, were dependent on extracellular Ca(2+). Alleviating the negative feedback of [Ca(2+)](i) on InsP(3)Rs using cytochrome c inhibited BK- and ATP-induced oscillations. Cx32 and Cx43 hemichannels are activated by <500 nm [Ca(2+)](i) but inhibited by higher concentrations and CT9 peptide (last 9 amino acids of the Cx43 C terminus) removes this high [Ca(2+)](i) inhibition. Unlike interfering with the bell-shaped dependence of InsP(3)Rs to [Ca(2+)](i), CT9 peptide prevented BK-induced oscillations but not those triggered by ATP. Collectively, these data indicate that connexin hemichannels contribute to BK-induced oscillations by allowing Ca(2+) entry during the rising phase of the Ca(2+) spikes and by providing an OFF mechanism during the falling phase of the spikes. Hemichannels were not sufficient to ignite oscillations by themselves; however, their contribution was crucial as hemichannel inhibition stopped the oscillations.     

Effects of synergistic signaling by phytochrome A and cryptochrome1 on circadian clock-regulated catalase expression.

Persistent oscillation in constant conditions is a defining characteristic of circadian rhythms. However, in plants transferred into extended dark conditions, circadian rhythms in mRNA abundance commonly damp in amplitude over two or three cycles to a steady state level of relatively constant, low mRNA abundance. In Arabidopsis, catalase CAT3 mRNA oscillations damp rapidly in extended dark conditions, but unlike catalase CAT2 and the chlorophyll a/b binding protein gene CAB, in which the circadian oscillations damp to low steady state mRNA abundance, CAT3 mRNA oscillations damp to high steady state levels of mRNA abundance. Mutational disruption of either phytochrome- or cryptochrome-mediated light perception prevents damping of the oscillations in CAT3 mRNA abundance and reveals strong circadian oscillations that persist for multiple cycles in extended dark conditions. Damping of CAT3 mRNA oscillations specifically requires phytochrome A but not phytochrome B and also requires the cryptochrome1 blue light receptor. Therefore, we conclude that synergistic signaling mediated through both phytochrome A and cryptochrome1 is required for damping of circadian CAT3 mRNA oscillations in extended dark conditions.     

Integration,coincidence detection and resonance in networks of spiking neurons expressing Gamma oscillations and asynchronous states

Gamma oscillations are widely seen in the awake and sleeping cerebral cortex, but the exact role of these oscillations is still debated. Here, we used biophysical models to examine how Gamma oscillations may participate to the processing of afferent stimuli. We constructed conductance-based network models of Gamma oscillations, based on different cell types found in cerebral cortex. The models were adjusted to extracellular unit recordings in humans, where Gamma oscillations always coexist with the asynchronous firing mode. We considered three different mechanisms to generate Gamma, first a mechanism based on the interaction between pyramidal neurons and interneurons (PING), second a mechanism in which Gamma is generated by interneuron networks (ING) and third, a mechanism which relies on Gamma oscillations generated by pacemaker chattering neurons (CHING). We find that all three mechanisms generate features consistent with human recordings, but that the ING mechanism is most consistent with the firing rate change inside Gamma bursts seen in the human data. We next evaluated the responsiveness and resonant properties of these networks, contrasting Gamma oscillations with the asynchronous mode. We find that for both slowly-varying stimuli and precisely-timed stimuli, the responsiveness is generally lower during Gamma compared to asynchronous states, while resonant properties are similar around the Gamma band. We could not find conditions where Gamma oscillations were more responsive. We therefore predict that asynchronous states provide the highest responsiveness to external stimuli, while Gamma oscillations tend to overall diminish responsiveness.     

Internal noise-driven circadian oscillator in Drosophila

An internal noise-driven oscillator was studied in a two-variable Drosophila model, where both positive feedback and negative feedback are crucial to the circadian oscillations. It is shown that internal noise could sustain reliable oscillations for the parameter which produces a stable steady state in the deterministic system. The noise-sustained oscillations are interpreted by using phase plane analysis. The period of such oscillations fluctuates slightly around the period of deterministic oscillations and the coherence of oscillations becomes the best at an optimal internal noise intensity, indicating the occurrence of intrinsic coherence resonance. In addition, in the oscillatory region, the coherence of noisy circadian oscillations is suppressed by the internal noise, but the period is hardly affected, demonstrating the robustness of the Drosophila model for circadian rhythms to the intrinsic noise.     

Effects of caffeine, tetracaine, and ryanodine on calcium-dependent oscillations in sheep cardiac Purkinje fibers

Membrane current and tension were measured in voltage-clamped sheep cardiac Purkinje fibers. Elevating the intracellular calcium concentration ([Ca2+]i) results in oscillations of membrane current and tension both at rest and during stimulation. During stimulation, an oscillatory transient inward current and an after contraction follow repolarization. We have examined the effects on the oscillations of changing the extracellular calcium concentration ([Ca2+]o) and of adding various drugs. In agreement with previous work, high concentrations of drugs that affect the sarcoplasmic reticulum, namely caffeine (10-20 mM), tetracaine (1 mM), and ryanodine (10 microM), abolish the oscillations. However, at lower concentrations, these three drugs have different effects on the oscillations. Caffeine (1-2 mM) decreases the oscillation amplitude but increases the frequency. Tetracaine (100-500 microM) has little effect on the magnitude of the oscillations but decreases their frequency. Ryanodine, at all concentrations used (0.1-10 microM), eventually abolishes the oscillations but, in doing so, decreases the magnitude, leaving the frequency unaffected. When [Ca2+]o was changed in order to vary [Ca2+]i, both the frequency and the magnitude of the oscillations always changed in the same direction. This suggests that these three drugs have effects in addition to just changing [Ca2+]i.     

Site-directed mutagenesis of the hole-forming toxin aerolysin: studies on the roles of histidines in receptor binding and oligomerization of the monomer

The six histidines of the channel-forming protein aerolysin have been replaced one at a time with asparagine by site-directed mutagenesis, and each of the modified proteins has been purified. Three proteins had the same hemolytic activity as native toxin, but the others, those changed at His107, His132, or His332, were less able to disrupt both human and rat erythrocytes. The largest reduction in activity, more than 100-fold, was observed with the His132 mutant protein. Studies with radioiodinated samples showed that it had approximately the same affinity as native aerolysin for the rat erythrocyte receptor. However, once bound to either rat or human erythrocytes, it was much less able to carry out the next essential step in hole formation, aggregation to form a stable oligomer. Aggregation was also reduced by replacing His107, but the contrast with native aerolysin and the effect on hemolytic activity were less pronounced. The protein modified at His332 behaved in a different way from those substituted at positions 107 and 132. Its affinity for the rat erythrocyte receptor was considerably lower than the affinity of the wild-type protein, but when bound it appeared to aggregate normally. The results suggest that His132 and perhaps His107 are involved in the aggregation of aerolysin whereas His332 may be at or near the receptor binding site.