Mechanical and Electrical Oscillations in Cardiac Muscle of the Turtle

During contractures of the turtle ventricle rapid changes in length induce sinusoidal oscillations under isotonic conditions. They are due to delayed responses to stretching and release, which can be demonstrated also under isometric conditions. Oscillations of two distinct frequencies are produced under different conditions and are distinguished as high- and low-frequency oscillations. In depolarized muscles the frequency is such that the duration of one cycle is about the same as that of a normal twitch, while in high-Ca solutions the duration can be the same as in high-K solutions or about six times lower. As reported previously, twitches are followed by weak mechanical and electrical oscillations. Their frequency agrees with the high-frequency oscillations. The same effects can also be induced by stretching and release. It is suggested that the phenomena observed are due to feedback mechanisms which originate in the contractile mechanism. The high-frequency oscillations are similar to those observed previously in other muscles, particularly insect fibrillar muscle, and are not due to changes in Ca concentration. The other mechanisms involve the membrane and possibly the intracellular Ca stores.     

The rhythm of yeast

Although yeast are unicellular and comparatively simple organisms, they have a sense of time which is not related to reproduction cycles. The glycolytic pathway exhibits oscillatory behaviour, i.e. the metabolite concentrations oscillate around phosphofructokinase. The frequency of these oscillations is about 1 min when using intact cells. Also a yeast cell extract can oscillate, though with a lower frequency. With intact cells the macroscopic oscillations can only be observed when most of the cells oscillate in concert. Transient oscillations can be observed upon simultaneous induction; sustained oscillations require an active synchronisation mechanism. Such an active synchronisation mechanism, which involves acetaldehyde as a signalling compound, operates under certain conditions. How common these oscillations are in the absence of a synchronisation mechanism is an open question. Under aerobic conditions an oscillatory metabolism can also be observed, but with a much lower frequency than the glycolytic oscillations. The frequency is between one and several hours. These oscillations are partly related to the reproductive cycle, i.e. the budding index also oscillates; however, under some conditions they are unrelated to the reproductive cycle, i.e. the budding index is constant. These oscillations also have an active synchronisation mechanism, which involves hydrogen sulfide as a synchronising agent. Oscillations with a frequency of days can be observed with yeast colonies on plates. Here the oscillations have a synchronisation mechanism which uses ammonia as a synchronising agent.     

Self-Excitation of Low-Frequency Oscillations in the Plasma Ring Formed by an ECR Discharge in a Narrow Coaxial Cavity

The conditions for the excitation of low-frequency oscillations in a plasma ring formed by an ECR discharge in a narrow coaxial cavity filled with argon were studied experimentally. The domain of the discharge parameters where these oscillations are stable is determined. It is supposed that the oscillations recorded are excited due to the appearance of an electrostatic wave propagating in the azimuthal direction.     

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.     

Stochastic models for circadian rhythms: effect of molecular noise on periodic and chaotic behaviour

Circadian rhythms are endogenous oscillations that occur with a period close to 24 h in nearly all living organisms. These rhythms originate from the negative autoregulation of gene expression. Deterministic models based on such genetic regulatory processes account for the occurrence of circadian rhythms in constant environmental conditions (e.g., constant darkness), for entrainment of these rhythms by light-dark cycles, and for their phase-shifting by light pulses. When the numbers of protein and mRNA molecules involved in the oscillations are small, as may occur in cellular conditions, it becomes necessary to resort to stochastic simulations to assess the influence of molecular noise on circadian oscillations. We address the effect of molecular noise by considering the stochastic version of a deterministic model previously proposed for circadian oscillations of the PER and TIM proteins and their mRNAs in Drosophila. The model is based on repression of the per and tim genes by a complex between the PER and TIM proteins. Numerical simulations of the stochastic version of the model are performed by means of the Gillespie method. The predictions of the stochastic approach compare well with those of the deterministic model with respect both to sustained oscillations of the limit cycle type and to the influence of the proximity from a bifurcation point beyond which the system evolves to stable steady state. Stochastic simulations indicate that robust circadian oscillations can emerge at the cellular level even when the maximum numbers of mRNA and protein molecules involved in the oscillations are of the order of only a few tens or hundreds. The stochastic model also reproduces the evolution to a strange attractor in conditions where the deterministic PER-TIM model admits chaotic behaviour. The difference between periodic oscillations of the limit cycle type and aperiodic oscillations (i.e. chaos) persists in the presence of molecular noise, as shown by means of Poincaré sections. The progressive obliteration of periodicity observed as the number of molecules decreases can thus be distinguished from the aperiodicity originating from chaotic dynamics. As long as the numbers of molecules involved in the oscillations remain sufficiently large (of the order of a few tens or hundreds, or more), stochastic models therefore provide good agreement with the predictions of the deterministic model for circadian rhythms.     

Oscillatory behavior of Saccharomyces cerevisiae in continuous culture: I. Effects of pH and nitrogen levels

The appearance of sustained oscillations in bioreactor variables (biomass and nutrient concentrations) in continuous cultures of Saccharomyces cerevisiae indicates the complex nature of microbial systems, the inadequacy of current growth kinetic models, and the difficulties which may arise in bioprocess control and optimization. In this study we investigate continuous bioreactor behavior over a range of operating conditions (dilution rate, feed glucose concentration, feed ammonium concentration, dissolved oxygen, and pH) to determine the process requirements which lead to oscillatory behavior. We present new results which indicate that high feed ammonium concentrations may eliminate oscillations and that under oscillatory conditions ammonium levels are generally low and oscillatory as well. The effects of pH are complex and oscillations were only observed at pH values 5.5 and 6.5; no oscillations were observed at a pH of 4.5. Under our nominal operating conditions (feed glucose concentration 10 g/L, dilution rate 0.145 h(-1), feed ammonium concentration 0.0303M, dissolved oxygen level 50%, pH 5.5, and T = 30 degrees C) we found two possible final bioreactor states depending on the transient used to reach the nominal operating conditions. One of the states was oscillatory and characteristic of oxidative metabolism and the other was nonoscillatory and fermentative.     

Kinetic, dynamic, and pathway studies of glycerol metabolism by Klebsiella pneumoniae in anaerobic continuous culture: IV. Enzymes and fluxes of pyruvate metabolism

The activities of pyruvate kinase (PK), pyruvate: formate-lyase (PFL), pyruvate dehydrogenase (PDH), and citrate synthase (CS) involved in the anaerobic glycerol conversion by Klebsiella pneumoniae were studied in continuous culture under conditions of steady states and sustained oscillations. Both the in vitro and in vivo activities of PK, PFL, and PDH are strongly affected by the substrate concentration and its uptake rate, as is the in vitro activity of CS. The flux from phosphoenolpyruvate to pyruvate is found to be mainly regulated on a genetic level by the synthesis rate of PK, particularly at low substrate concentration and low growth rate. In contrast, the conversion of pyruvate to acetyl-CoA is mainly regulated on a metabolic level by the in vivo activities of PFL and PDH. The ratio of in vitro to in vivo activities is in the range of 1 to 1.5 for PK, 5 to 17 for PFL and 5 to 80 for PDH under the experimental conditions. The regulation of in vivo activity and synthesis of these enzymes is sensitive to fluctuations of culture conditions, leading to oscillations of both the in vitro and in vivo activities. In particular, PFL is strongly affected during oscillations; its average in vitro activity is only about half of its corresponding steady-state value under similar environmental conditions. The average in vitro activities of PDH and PK under oscillations are close to their corresponding steady-state values. In contrast to all other enzymes measured for the glycerol metabolism by K. pneumoniae PFL and PDH are more effectively in vivo utilized under oscillations than under steady state, underlining the peculiar role of pyruvate metabolism in the dynamic responses of the culture.     

Breaking of nonlinear cylindrical plasma oscillations

Nonlinear axisymmetric cylindrical plasma oscillations are investigated analytically and numerically. It is shown that the breaking of strongly nonlinear oscillations is attributed to a singularity in the electron density and occurs several periods after the onset of an off-axis density maximum. For weakly nonlinear conditions, an analytic dependence of the breaking time of the oscillations on their amplitude is obtained based on the effect of intersection of electron trajectories and is shown to agree with numerical results.     

Dynamics of chemostat in which one microbial population grows on multiple complementary nutrients

The equations of a chemostat in which one microbial population grows on multiple rate-limiting nutrients are formulated. The dynamics of a chemostat involving growth on complementary nutrients is studied through stability analysis of the system of equations. Some conditions are derived that relate the dynamic behavior of the chemostat to its operating conditions and can be applied to any model for the specific growth rate of the population. It is shown that, if maintenance of the population is neglected, the system exhibits no sustained or damped oscillations. If maintenance of the population is considered, damped oscillations are observed for some operating conditions.     

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.     

Long-term facilitation of spontaneous calcium oscillations in astrocytes with endogenous adenosine in hippocampal slice cultures

It is well established that astrocytes release gliotransmitters and moderate neuronal activity in the central nervous system via intracellular Ca(2+) dynamics. Astrocytic Ca(2+) oscillations are one type of spontaneous Ca(2+) mobilization that occurs in astrocytes. However, the modulation of spontaneous astrocytic Ca(2+) oscillations, especially in pathophysiological conditions, is not yet fully understood. Here, we demonstrate that activation of adenosine receptors induces a long-lasting increase in the frequency of astrocytic Ca(2+) oscillations in rat hippocampal slice cultures. The long-term facilitation of the frequency of Ca(2+) oscillations was mediated by endogenous adenosine generated via breakdown of extracellular ATP by ecto-ATPase. We also demonstrate that local tissue injury with ultraviolet irradiation can cause this long-term facilitation of Ca(2+) oscillations via endogenous adenosine. Our data suggest that endogenous adenosine is one of the modulators of spontaneous astrocytic Ca(2+) oscillations in the rat hippocampus, and may play a significant role in altered Ca(2+) dynamics in astrocytes observed during pathophysiological conditions.     

Structure and kinetic behavior of linear multicompartment systems

The general kinetic behavior of a multicompartment system is shown to depend upon certain general structural features, including its connectivity, whether it is open, and whether it contains cyclic pathways. Structural influences are clarified by putting the system matrix in a certain form. For systems not strongly connected, a distinction is drawn between partially and completely open systems. Necessary and sufficient conditions are given for non-singularity of the system matrix and for asymptotic stability of the system. Sufficient conditions are given for non-overshooting and monotonic transitions. A system is demonstrated whose solution may contain a prolonged series of damped oscillations; but the oscillations are very slow and small; and it seems unlikely that oscillations could be detected experimentally in any biological system. This work was supported by U.S. Public Health Service Research Grant NS 08710 from the National Institute of Neurological Diseases and Stroke.     

Contribution to the study of periodic chronic myelogenous leukemia

The period (in the order of 40 to 80 days) in periodic chronic myelogenous leukemia (PCML) oscillations is quite long compared with the duration of the cell cycle of the hematopoietic stem cells from which the oscillations are presumed to originate (in the order of one or two days). Our objective is to understand the origin of these long-period oscillations using a G0 model for stem cell dynamics. We determine the local stability conditions and show under what conditions the Hopf bifurcation may occur. We interpret the role of each parameter in the loss of stability, and then examine a simpler model to try to deduce possible changes at the stem-cell level that might be responsible for the characteristics PCML.     

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.     

The Effect of Loss of Immunity on Noise-Induced Sustained Oscillations in Epidemics

The effect of loss of immunity on sustained population oscillations about an endemic equilibrium is studied via a multiple scales analysis of a SIRS model. The analysis captures the key elements supporting the nearly regular oscillations of the infected and susceptible populations, namely, the interaction of the deterministic and stochastic dynamics together with the separation of time scales of the damping and the period of these oscillations. The derivation of a nonlinear stochastic amplitude equation describing the envelope of the oscillations yields two criteria providing explicit parameter ranges where they can be observed. These conditions are similar to those found for other applications in the context of coherence resonance, in which noise drives nearly regular oscillations in a system that is quiescent without noise. In this context the criteria indicate how loss of immunity and other factors can lead to a significant increase in the parameter range for prevalence of the sustained oscillations, without any external driving forces. Comparison of the power spectral densities of the full model and the approximation confirms that the multiple scales analysis captures nonlinear features of the oscillations.     

The modelling of the glycolytic oscillations in the potential of the oxidative-reductive status of the brain tissue in waking and anesthetized rats]

It was found that chemical hypoxia created by intraperitoneal injection of potassium cyanide (5-7 mg/kg) induced in both waking and anaesthetized (pentobarbital, 40 mg/kg) albino rats a significant decrease in the brain redox state potential (E) monitored with platinum electrodes. This decrease could be accompanied by a generation in some brain points of local chains of gradually damped quasisinusoidal E oscillations. Such oscillations were more expressed in waking than in anaesthetized animals. The frequency range of these oscillations was 4-7 cycles/min. This is the range of overlapping frequency ranges characteristic for the high level of vigilance (5-20 cycles/min) and slow-wave sleep and drowsiness (1.5-6 cycles/min). The amplitude of the observed oscillations was close to the maximal amplitude of the brain E oscillations characteristic for the high level of vigilance (up to several mV). The obtained evidence favors our suggestion that behavior-related E oscillations are formed by the oscillations in the redox balance of glycolysis. The similarity of the normal physiological oscillations and those simulated by us under abnormal conditions suggest a certain common mechanism of their generation.     

In-phase and antiphase self-oscillations in a model of two electrically coupled pacemakers

The dynamic behavior of a model of two electrically coupled oscillatory neurons was studied while the external polarizing current was varied. It was found that the system with weak coupling can demonstrate one of five stable oscillatory modes: (1) in-phase oscillations with zero phase shift; (2) antiphase oscillations with halfperiod phase shift; (3) oscillations with any fixed phase shift depending on the value of the external polarizing current; (4) both in-phase and antiphase oscillations for the same current value, where the oscillation type depends on the initial conditions; (5) both in-phase and quasiperiodic oscillations for the same current value. All of these modes were robust, and they persisted despite small variations of the oscillator parameters. We assume that similar regimes, for example antiphase oscillations, can be detected in neurophysiological experiments. Possible applications to central pattern generator models are discussed.     

Stomatal oscillations in orange trees under natural climatic conditions

BACKGROUND AND AIMS: Stomatal oscillations have been reported in many plant species, but they are usually induced by sudden step changes in the environment when plants are grown under constant conditions. This study shows that in navel orange trees (Citrus sinensis) pronounced stomatal oscillations occur and persist under natural climatic conditions. METHODS: Oscillations in stomatal conductance were measured, and related to simultaneous measurements of leaf water potential, and flow rate of sap in the stems of young, potted plants. Cycling was also observed in soil-grown, mature orchard trees, as indicated by sap flow in stem and branches. KEY RESULTS: Oscillations in stomatal conductance were caused by the rapid propagation and synchronization of changes in xylem water potential throughout the tree, without rapid changes in atmospheric conditions. CONCLUSIONS: The results show marked stomatal oscillations persisting under natural climatic conditions and underscore the need to discover why this phenomenon is so pronounced in orange trees.     

Dynamics of Predator‐Prey Interactions in Continuous Cultures

This paper studies the behavior of a general unstructured kinetic model for continuous bioreactors involving interactions between predator, prey and a limiting substrate. The analysis carried out in this paper shows how closed analytical conditions for arbitrary growth rates can be derived that describe the conditions for the existence of the interacting species in an oscillatory behavior. It is also demonstrated how practical diagrams in terms of operating and kinetic parameters can be constructed that classify the different behavior predicted by the model. Applications of these general results to a number of experimentally validated models have revealed that the saturation model always predicts hard oscillations for a certain range of dilution rates, for any values of model parameters. Bifurcation diagrams in the operating parameter space permitted the delineation of regions of hard oscillations, regions of static coexistence, regions of predator washout and regions of total washout. The analysis of the double saturation model has proven its ability to predict two Hopf points. Hard oscillations are therefore expected within the dilution rates corresponding to the two Hopf points. Practical diagrams were also constructed to delineate the boundaries separating hard oscillations from static coexistence and washout conditions.